tag:blogger.com,1999:blog-18662596082025142892024-02-20T11:09:34.863-08:00Ecologist At WorkLearning to ID plants and other random thoughts and ideas, mostly related to ecologyAnonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.comBlogger28125tag:blogger.com,1999:blog-1866259608202514289.post-42530304579459440802016-06-14T19:40:00.001-07:002016-06-14T19:40:55.936-07:00Fothergilla gardenii - Dwarf fothergillaThis is one of several plantings that went along with the construction of the Environmental Center here at Pace - Pleasantville. In fact, this picture is of a shrub just outside the door to my building.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxlNceUDT8xzXqM8JDbvXZfSN2rf0gF_1_nVkUtAK1Mvp0cb2JR_tguU9IfgtedjU4h_gy6Bq2zbmoeirjQtJ-R1ZKCkhih5C4aVjYCGhHI-3BCFZkDaV8ACgtSZSSgGzi9uUAFIM2bC8/s1600/20160608_120657.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxlNceUDT8xzXqM8JDbvXZfSN2rf0gF_1_nVkUtAK1Mvp0cb2JR_tguU9IfgtedjU4h_gy6Bq2zbmoeirjQtJ-R1ZKCkhih5C4aVjYCGhHI-3BCFZkDaV8ACgtSZSSgGzi9uUAFIM2bC8/s640/20160608_120657.jpg" width="360" /></a></div>
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When I first saw it, I thought it might be some sort of alder, based on the leaf shape. I looked through all the books I had available to me, but didn't find anything convincing. So I asked our local naturalist and he said "<i>Forthergilla</i>". From there, I went to the internet - first stop, Wikipedia. The genus <i>Forthergilla</i> has the common name Witch Alder. According to the <a href="https://en.wikipedia.org/wiki/Fothergilla" target="_blank">Wikipedia entry</a>, there are only two or three species in the genus. The family is <a href="https://en.wikipedia.org/wiki/Hamamelidaceae" target="_blank">Hamamelidaceae</a>, the witch-hazel family. So while alder is in the common name, this species isn't in the same family as the genus <i>Alnus </i>(Betulacea - the birches). It made me pretty happy that at least I wasn't the only person to think of this resemblance.<br />
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So why couldn't I find this plant in any of my books? Well, most all of my guides are northeast based. And my favorite website for identification, GoBotany, is also northeast based. According to information from the Missouri Botanical Garden <a href="http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=a430" target="_blank">entry</a> for <i>F. gardenii</i>, this species is native to the southeast US. This makes me wonder if I should start expanding my collection of guides.Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-73269964348791799592016-05-27T06:15:00.002-07:002016-05-27T06:15:24.639-07:00Linden viburnum - Viburnum dilatatumI went for a nice walk with my cousin in Rockefeller State Park Preserve yesterday evening. He identified a number of the plants there for me. This one is of particular interest, because it is a non-native reported as becoming more widespread in natural areas.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSUgqV5dUqGgsjkvbrqs96NyRY0s8H_m9y0Tpn0ISfjHMCqv1uNI31G4mYE-pXkOdppozz64HWjD7QmNvlRnsG_H4i4s8-dPhuXmD1IDiH1J_iiFUhYA6puoOxnaGLqraOO73Y2DQJWQw/s1600/20160526_182327.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSUgqV5dUqGgsjkvbrqs96NyRY0s8H_m9y0Tpn0ISfjHMCqv1uNI31G4mYE-pXkOdppozz64HWjD7QmNvlRnsG_H4i4s8-dPhuXmD1IDiH1J_iiFUhYA6puoOxnaGLqraOO73Y2DQJWQw/s640/20160526_182327.jpg" width="360" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><i>Viburnum dilatatum</i></td></tr>
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Honestly, I don't think it would have stood out to me as anything out-of-the-ordinary. Very little is known about the potential ecological impacts of its spread, but it is assumed that it can crowd out natives, particularly along forest edges. It is native to east Asia and commonly cultivated/planted in gardens throughout the mid-Atlantic USA.<br />
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Some distinguish characteristics:<br />
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<ul>
<li>Gleason and Cronquist note that it lacks stipules and it's leaves are hairy on both sides. I don't recall noticing this in the field, but I also wasn't looking carefully. (I tried to zoom in to the pic, but no luck.)</li>
<li>The fruits are apparently quite showy. I'll keep my eye out for this in the future.</li>
<li>The <a href="http://www.hort.uconn.edu/plants/index.php" target="_blank">UCONN Plant Database</a> also had a good <a href="http://www.hort.uconn.edu/plants/detail.php?pid=525" target="_blank">entry for this species</a>, which pointed out features like pubescents on both surfaces of the leaves, but more densely so near veins, and the presence of bright orange lenticels. </li>
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I'll keep an eye out for these features next time I'm botanizing in the park! Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-80572573961967598552016-04-30T12:05:00.004-07:002016-04-30T12:06:08.550-07:00NemesiaI like spending time in botanic gardens. For the purposes of becoming better at plant identification, it's nice to be able to look at a plant and have a label nearby that tells me 'the answer'. However, in most gardens, many of the labeled specimens are exotics or hybrids. Nevertheless, looking at the plants and studying their characteristics, then connecting them to the genera listed, still seems like a good way for me to learn more.<br />
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Two weeks ago we made our first trip of the season to our local botanic garden, <a href="https://www.oldwestburygardens.org/" target="_blank">Old Westbury Gardens</a>. Being so close, we became members here last year, and find that it's a great place to bring our daughter for a few hours of running around outside. These little plants caught my eye, and I was pleasantly surprised to see that they're native to South Africa. Well, to be clear, as someone who studies invasion biology, I didn't think that was so great, but as someone who's spent sometime studying the flora of the Cape Region of South Africa, seeing these guys made me feel a bit nostalgic.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQNGSWhJ_I3lxh2asQn5vqF7JS0YGyhGSQqXgemmzTLqYXy-WywqW6xQYQs7raT_rGVG4v6RPiDDHkDHrR0mUVJYdIoYudDjRD8p-D2b3EEEKHesQoOlz6sY5MC6L69oIf4ZE80TW5UR8/s1600/20160416_112226.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQNGSWhJ_I3lxh2asQn5vqF7JS0YGyhGSQqXgemmzTLqYXy-WywqW6xQYQs7raT_rGVG4v6RPiDDHkDHrR0mUVJYdIoYudDjRD8p-D2b3EEEKHesQoOlz6sY5MC6L69oIf4ZE80TW5UR8/s640/20160416_112226.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><i>Nemisia</i> hybrid</td></tr>
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Their were a number of different varieties, all equally pretty I think.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwKNS3T02jVo1YDA8M4R1fm2EYKmDMZrEBCDVPp4-AKxM8bGwqgpAALGNPAXXTC_ZJQq0BLPRdSL5Q-9Nrv38kEI0s0lIg2hgfpRhxv55h4C3Wcm9MK93tsDP-pgDAOSrp3aD4BOo_u3Q/s1600/20160416_112916.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwKNS3T02jVo1YDA8M4R1fm2EYKmDMZrEBCDVPp4-AKxM8bGwqgpAALGNPAXXTC_ZJQq0BLPRdSL5Q-9Nrv38kEI0s0lIg2hgfpRhxv55h4C3Wcm9MK93tsDP-pgDAOSrp3aD4BOo_u3Q/s640/20160416_112916.jpg" width="360" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><i>Nemesia fruiticans</i></td></tr>
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This last one was particularly stunning.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ8SEybJoV6F1NzHcry3lVv1QsZo3OWLUyLs_7hG29xuqmKoV1iUEGVho9JYbhyuMGs_QMdWG0dbkHWIl2ynV0H4Dy-yAXAY8QoNyp5BI8GQ3Z5ndv6PrUweq7CqwvMfoWLQU-MxArMHc/s1600/20160416_113932.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ8SEybJoV6F1NzHcry3lVv1QsZo3OWLUyLs_7hG29xuqmKoV1iUEGVho9JYbhyuMGs_QMdWG0dbkHWIl2ynV0H4Dy-yAXAY8QoNyp5BI8GQ3Z5ndv6PrUweq7CqwvMfoWLQU-MxArMHc/s640/20160416_113932.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><i>Nemesia </i>hybrid</td></tr>
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While writing this post, I looked up <i>Nemesia</i> in the book <i><a href="http://www.amazon.com/Field-Guide-Fynbos-John-Manning/dp/1770072659" target="_blank">Field Guide to Fynbos</a>. </i>I was happy to see the genus in there, but not surprised that <i><a href="http://www.plantzafrica.com/plantnop/nemesiafrut.htm" target="_blank">N. fruiticans</a></i> (they only one of these three with a species name) was not listed. This field guide is not exhaustive. But the generic description sounds pretty right - leaves opposite, variously toothed, flowers solitary, combinations of white, yellow, orange, pink, or blue, calyx 5-lobed, corolla 5 lobed and strongly 2-lipped. There are about 60 different species of these little guys, about 25 in the fynbos. </div>
Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-82689148973812727392016-03-24T06:49:00.000-07:002016-03-24T06:49:07.267-07:00Magnolia 'Elizabeth'Spring is definitely coming in the NY metro area. This past Sunday I spent a few hours walking around the <a href="http://nysparks.com/historic-sites/24/details.aspx" target="_blank">Planting Field Arboretum</a> with my daughter. It was a great day, just a bit cool (around 50F), and oddly, a few hours before we would get an inch of snow. We saw many plants blooming, but the one I want to talk about in this post is the Magnolia tree we saw.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinmm7h7QbaM7yExZHWbCm-DhB0Uk3YOPHc-xRuNQ1vZtbbuO2BA9eY6CdUZ86OHJ4a5F0ugH5PeJEIq8UStytv_nBoQ6Z5u73-34fAYj14UtdYXDmb8S_faZ2iy0FV0xT5DzT_JiPvJnw/s1600/20160320_162739.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinmm7h7QbaM7yExZHWbCm-DhB0Uk3YOPHc-xRuNQ1vZtbbuO2BA9eY6CdUZ86OHJ4a5F0ugH5PeJEIq8UStytv_nBoQ6Z5u73-34fAYj14UtdYXDmb8S_faZ2iy0FV0xT5DzT_JiPvJnw/s640/20160320_162739.jpg" width="360" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><div style="font-size: medium; text-align: start;">
I love the site of flowering trees in the early Spring!</div>
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To be honest, I'm still not 100% certain this is a Magnolia, and I haven't been able to get it to species. The first place I looked was the <a href="http://www.syracuseuniversitypress.syr.edu/fall-2003-catalog/trees-ny.html" target="_blank">Trees of New York: Native and Naturalized</a> by Donald Leopold. But the <i>Magnolia</i> species described in there didn't quite fit what I was seeing. In particular, the bud on this tree is fairly big and hairy, which didn't match the buds described in this book.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkHs73uIFnRk6urSRBygnCmuQs_WN5Nq-qguPlYD9dWqed-X6O1Xh0vLlfUKl4aKSdQ_nM30p6yjtxxgycGISKQlOTyiicSxiGQclZLrZe7aeD4iYSOPTX0EkAIRSQ57hcLodiLfmqKnc/s1600/20160320_162856.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkHs73uIFnRk6urSRBygnCmuQs_WN5Nq-qguPlYD9dWqed-X6O1Xh0vLlfUKl4aKSdQ_nM30p6yjtxxgycGISKQlOTyiicSxiGQclZLrZe7aeD4iYSOPTX0EkAIRSQ57hcLodiLfmqKnc/s640/20160320_162856.jpg" width="360" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Bud, not so focused. And bark of relatively young twig.</td></tr>
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I tried looking through a few of my other books, but eventually went to the internet and started Google searching terms like "fuzzy flower bud early spring" and what not. Ultimately, the images and descriptions I found that best fit my observations were for <a href="http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=d133" target="_blank"><i>Magnolia</i> 'Elizabeth'</a>. This is a cross between <i>M. acuminata</i> (Cucumber tree) and <i>M. denudata</i> (Yulan magnolia), so a native and a exotic, respectively. It was neat to read on the Missouri Botanical Garden site that this variety is patented by the Brooklyn Botanical Garden. All things considered, it makes a lot of sense that this tree would be planted at an estate along the north shore of Long Island.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4Mq8vmu0RG8OKso38Lj_T6c_LDuoK7TuR_YDQWTdMo0hM07ADeIBexgHZgVi1COXzbBrSp5kjLW9fnZOz9fEnAHV9ReC1TNf-HoJpVclKUv2RvQNbTsC2e8-fHGkwGcN0w7z_pNZkAv0/s1600/20160320_162802.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4Mq8vmu0RG8OKso38Lj_T6c_LDuoK7TuR_YDQWTdMo0hM07ADeIBexgHZgVi1COXzbBrSp5kjLW9fnZOz9fEnAHV9ReC1TNf-HoJpVclKUv2RvQNbTsC2e8-fHGkwGcN0w7z_pNZkAv0/s640/20160320_162802.jpg" width="360" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">My daughter, enjoying the early spring day outside, while dad takes pictures of plants.</td></tr>
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<br />Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-16214647577575135892015-12-02T06:36:00.001-08:002015-12-02T06:37:32.196-08:00Japanese barberry - Berberis thunbergii<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEo0RWqB7DIDUtiwUrTxHXwby2Pd7W_IGuTSTsnQtsrdg4-EBM4RTIQPCXjfcwgh1udUlekiArHNv0Mcs_vgA2nJibxXnyr4z8652vBh7P67RrdHCL2m8fUoJn_s6j49KuI5tNRYNSN9w/s1600/20151127_140048.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEo0RWqB7DIDUtiwUrTxHXwby2Pd7W_IGuTSTsnQtsrdg4-EBM4RTIQPCXjfcwgh1udUlekiArHNv0Mcs_vgA2nJibxXnyr4z8652vBh7P67RrdHCL2m8fUoJn_s6j49KuI5tNRYNSN9w/s400/20151127_140048.jpg" width="225" /></a></div>
My wife, daughter, and I went for a nice walk the Friday after Thanks Giving at <a href="http://parks.ny.gov/parks/133/details.aspx" target="_blank">Fahnestock State Park</a>. Along the way I noticed a fairly large infestation of Japanese barberry. This is a plant that I'm fairly confident in my ability to identify in the field, but I wanted to use this opportunity to learn more about its characteristics.<br />
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I usually ID this based on the red fruits, straight spines/ thorns, and the surrounding environment and plant community. However, in the past, I've not bothered thinking about the difference between Common barberry (<i>Berberis vulgaris</i>), which is native to Europe, and Japanese barberry (<i>B. thunbergii</i>). One of the key differences is that Common barberry has sharply toothed leaf margins, while Japanese barberry has 'entire leaf margins' (no teeth). It's late Autumn in NY. Looking at this picture, it's clear that leaf characteristics are not going to help me.<br />
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Another trait difference is that Common barberry as 3-pronged spines. I didn't recall seeing this in the field. When I zoom into this picture, it becomes pretty blurry, but I'm pretty sure that each of the spines is by itself. So I'm going with Japanese barberry as my ID.<br />
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Both Japanese and Common barberry are in the <a href="https://en.wikipedia.org/wiki/Berberidaceae" target="_blank">Berberidaceae family</a> (i.e., the barberry family). There's some nice information on this family both in the above referenced Wikipeadia page and in <a href="http://www.efloras.org/florataxon.aspx?flora_id=1&taxon_id=10100" target="_blank">eFlora</a>. Seems to be a fairly species rich family (ca. 650 species), but relatively few here in northeast North America (based on <a href="http://newenglandwild.org/store/books-from-the-society/flora-novae-angliae" target="_blank">Flora Novea Angliae</a>).<br />
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Sources used:<br />
previous knowledge<br />
<a href="http://newenglandwild.org/store/books-from-the-society/flora-novae-angliae" target="_blank">Flora Novea Angliae</a><br />
<a href="http://www.na.fs.fed.us/fhp/invasive_plants/weeds/common-barberry.pdf" target="_blank">USFS Weed of the Week information sheet (Common barberry)</a>Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com1tag:blogger.com,1999:blog-1866259608202514289.post-32078761114949341742015-11-25T07:19:00.000-08:002015-11-25T07:19:00.045-08:00American crab apple - Malus coronaria<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0g_Y-Meciu-50Glxe1zIJUDns4H5LOj-i4bTgXfZL56cSKmIVpBfu502z2Z8Sai2gc6XUrSEOaFASPZr7wVWUc6pstCUJYwO52QmdYOHP4y0RpFMwLZURXKRWvheS0PEs9upMzohrZpE/s1600/20151124_091113.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0g_Y-Meciu-50Glxe1zIJUDns4H5LOj-i4bTgXfZL56cSKmIVpBfu502z2Z8Sai2gc6XUrSEOaFASPZr7wVWUc6pstCUJYwO52QmdYOHP4y0RpFMwLZURXKRWvheS0PEs9upMzohrZpE/s640/20151124_091113.jpg" width="640" /></a></div>
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There are a lot of plants in my own backyard that I'd like to work on IDing here. This is the first. American crab apple or wild crab apple or sweet crab apple ... let's just go with <i>Malus coronaria</i>. This tree caught my eye because the fruit have turned a beautiful yellow / gold color this fall (and presumably every fall). I'm not fully convinced it's <i>M. coronaria</i> though. From what I saw, it lacks the thorn-like structures at the end of the twigs. That might be just based on the branch I pulled off the tree, or it might be some sort of cultivar. Or perhaps I just got it wrong.<br />
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Sources used:<br />
GoBotany<br />
Trees of New York State Native and Naturalized<br />
Trees of Eastern North America (Princeton Guides)Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-57657854338064680802015-11-24T09:42:00.000-08:002015-11-24T09:42:04.801-08:00Changing the focus of this blogI started this long neglected blog to write down ideas I had as worked my way through getting my PhD in Ecology and Evolution. I've since gotten said degree, finished my postdoc, and started as an assistant professor at Pace University in New York. I've also started a <a href="http://mlammens.github.io/" target="_blank">different blog</a> (of sorts) using Github pages. <div>
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So where does that leave this site? I had thought of continuing to neglect it for a while, until I finally just closed it all together. But today, I had another idea. You see, while I fancy myself a plant ecologist, I'm not especially good at knowing the names of many plants. I've wanted to get better at this for a long time, and perhaps some day I will. So I'm going to use this space to post pictures of plants I try to ID. </div>
Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-15597036433321253642014-08-04T13:52:00.001-07:002014-08-04T13:52:18.636-07:00Did I say local field work? Going international!One of my earliest posts here was about why I enjoyed <a href="http://ecologistatwork.blogspot.com/2012/07/pros-and-cons-of-local-field-work.html" target="_blank">local field work</a> (and some of the pitfalls of it too). Well, I'm writing this post from Calvinia, South Africa, a location that is definitely not local for me. I am here as part of my postdoc work, collecting data on plant functional traits in one of the most diverse floras in the world with a group of about eight people. As the postdoc on this project I had to do quite a bit of leg work before getting here related to examining existing data from the region, putting together species lists, helping to determine optimal sampling locations, etc. Fortunately, because the research team I'm with has carried out several similar studies in various parts of South Africa, most of the challenging logistics were worked out by others with much more experience. To that end, all I really need to do is learn how to drive a standard, on the left side of the road. But putting together a species observation list and sampling location plan was definitely a new experience for me. When I started a few months ago, I had imagined that I would have to have things planned out roughly to the day, as our time is limited and the area we are covering is vast. I quickly learned that what we're after is more of a sketch of a plan. What that means is that most every night I'll sit down with the botanist in our team and help him decide on the best spots to sample the next day. And our species list is getting updated daily - checking off what we've observed, dropping some species, adding others. Really, the key is to be flexible. However, this flexibility requires preparation. It's best if I can load up the vegetation survey data a colleague collected several years ago in a matter of minutes, and the hours of examining these data before hand has definitely helped me to navigate it on the fly.<br />
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Planning considerations aside, scientifically the most important part of this trip is for me to just get out into these incredible plant communities and to experience the field and lab work involved in our project. I've been spending the past year organizing, cleaning, and analyzing data collected in previous years without fully understanding what the system looks like. I've read a lot about it, but have never seen it with my own eyes. Now I can better understand some of the ambiguities in our datasets. For example, I've now held a specimen in my hand and had the thought "what the heck is the leaf on this thing?" This experience is absolutely invaluable for me while I'm wrapping up some of the analyses I've started, and moving forward with new ones. I'm hoping to have a few posts on some of my insights (or causes of confusion!) during the rest of this trip.<br />
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On a personal level, this trip is also my longest international trip, and I gave a lot of thought into packing, and trying to be minimal about what I brought (even if I did most of my packing the day before I left). I didn't want to bring anything I wouldn't use (except my small first aid kit. I'm ok carrying that around without using it). So far it's working out well. I promise more biologically relevant pictures in the future, but for now, here's a pic of what I thought I would need for multiple weeks of field work. (Note - Nessy, the green monster, didn't come. The shoes are my wife's (though I'm told they are comfortable). And yes, one of my carry-on items did end up being the Leaf Area Meter. I'll try to sucker one of the other group members into dragging it home!)<br />
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<br />Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-59926322813449057852014-07-14T06:48:00.000-07:002014-07-14T06:48:58.689-07:00Reflection<span style="font-family: Arial; font-size: 14px;">Today, a bit of a story ...</span><br />
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<tr><td class="tr-caption" style="text-align: center;">Kinsman Pond from ledges of North Kinsman</td></tr>
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<span style="font-family: Arial; font-size: 14px;">I stood near the edge of the clearing with the two scientists, straining my ears to hear the call of a Bicknell’s Thrush. They played the recording, and we listened. As I recall, it was a relatively cool summer evening, though it was often cool in the evening at Kinsman Pond campsite. It was 2002. I had just finished my third year of college, and I was working as a backcountry campsite caretaker for the <a href="http://www.outdoors.org/lodging/campsites/campsites-profile.cfm" target="_blank">Appalachian Mountain Club</a>. I had been dreaming of having this job for at least two years at that point, and a few cold, rainy days aside, I was enjoying every moment of it. It was a stark contrast from the previous summer, when I worked </span><span style="font-family: Arial; font-size: 14px;">at Brookhaven National Labs</span><span style="font-family: Arial; font-size: 14px;"> as a research assistant for one of my professors. That too was a great experience and important for my development as a scientist. But living in the woods, spending my days doing trail work, sleeping in a canvas tent, dealing with black flies ... that was the life!</span><br />
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<span style="font-family: Arial;"><span style="font-size: 14px;">On this particular evening, two scientists from the <a href="http://www.vinsweb.org/" target="_blank">Vermont Institute of Natural Science</a> came to my site, and were planning to spend the night so they could survey for Bicknell's Thrush both that evening and very early the next morning. We chatted for a while, and they told me that they were using known locations of this bird, along with environmental information from those locations, to build a model to predict where it might be observed. I had no knowledge of species distribution modeling, and honestly, probably only a vague notion of what a "species niche" was. What I did know was that I </span></span><span style="font-family: Arial; font-size: 14px;">as a physics major, I knew what the word model meant. I knew that any such model would likely be constructed using some computer programming language. I naively thought you would probably code that up in C or C++, because hey, isn't that what most scientists were using? But most importantly, I thought "I could probably learn to do that". </span><br />
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<span style="font-family: Arial;"><span style="font-size: 14px;">I've told this story many times over the last 7+ years, in part as a way of explaining to people how I went from physics to ecology. To be honest, the path from physics to ecology was not direct. I finished my degree, spent two more years working as a caretaker, and then spent two years working in a neuroscience research group. But this experience stuck with me, and eventually I got to "build ecological models". I was reflecting on this again recently and I finally went and looked to see if any publications resulted from this field work these scientists had been doing. Here's what I found:</span></span><br />
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<span style="font-family: Arial;"><span style="font-size: 14px;">Lambert et al. 2005. A practical model of Bicknell's Thrush distribution in the northeaster United States. The Wilson Bulletin 117(1): 1-12.</span></span><br />
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<span style="font-family: Arial;"><span style="font-size: 14px;">And here was the line I was looking for - "</span><span style="font-size: 14px;">during 2000–2002 ... we recorded the presence or presumed absence of Bicknell’s Thrush on 130 mountains first sampled by Atwood et al. (1996) (New York: n = 30, Vermont: n = 56, New Hampshire: n = 26, Maine: n = 18)." I'm assuming that one of the 26 New Hampshire locations was Kinsman Pond.</span></span><br />
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<span style="font-family: Arial;"><span style="font-size: 14px;">Perhaps the best part of finding this paper is that since that meeting in 2002, I have acquired the knowledge necessary to understand what these researchers were working on. The species distribution model that they constructed is pretty uncommon compared to today's methods. It appears to be a mixture of quantile regression, which is reminiscent of some of the first distribution models used (e.g., Bioclim), and basic pattern observation. The model options for presence-absence data are quite numerous now, and it would be interesting to see how different the distribution predictions are using more modern techniques. </span></span><br />
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<span style="font-family: Arial;"><span style="font-size: 14px;">It's nice to look back on this story and think "yeah, I did learn how to do that."</span></span>Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-47351414609871733142014-07-10T07:51:00.001-07:002014-07-10T07:51:32.768-07:00Stratified random sampling in R using dplyr<html xmlns="http://www.w3.org/1999/xhtml">
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<title>A recent Gist I wrote</title>
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xaXpygKB5dWVlFrb5mQOydwB7i0J6ubFjh7npdh1XXdKUdEAmoj3W5Db4m4QE1LVCapO1XgH2D%2FkB08JF83SNM9ZhZf5I9%2B7Rz8J%2FI3IIfrMb5LHcjByu%2BUvGUKxQ%2FkcaLYdZ40f8JWOkw%2BA4iEBtlYSmddP1HFw%2FdKtShd1YQrncW61ZeqsIAcmYleEIEKAhx1ry8ND6aFh%2F8V9VHtiPdBPGObFcRVTzQgcz40RO7WEpW0ba3k2z3i6zBvlL9xO4ka%2F1EVnLTSa%2Buo%2BmkNzrwWDyPcz4lWOAxAp2%2BTrKORXoPGvm6d5aKpzt50u4573rAOfhP1CUXfpbjl36l4XWpysmXBCr6PbGqqsTnSRvReJFj4Xl9rvYfHFko%2FqPrb9YYEpV1CsKxTiSrXhisap%2F%2BC%2B6uu%2F8CZVz1iWlY7fGdnKxd2eM7WS2lcof2ANfjrBHRsoomvoE%2BuiF%2FpXpsCFnJYVZIVk7UsM85PYeLXYofPYf9H42YsMdtUq%2FMTd79Ho4bf2S7Gq9PVRxDC6lKG1VpVBV9cvFXGr6oVycSFZ%2FauXWquCnKooTpFvcfy0YiWVX%2BI%2FD8UOPXvp%2BE5%2Bom3JHt0IXP6MxS5U%2FAqovYd3l62%2BltAxkkq6q7T7LR3xT%2Bcz8gICtekEZU28Hq3d9JkEXhcfclufMmmZusgqh%2B5ww%2B7k3Vwcd9XbHh1JbiELt3Fu67QYbvmRs%2FCg5by%2Fr3TnRlZXhu7ijl5o6qlZ%2BrQrpkGp3PTVTZFKpwyqWabnH%2Fce5T6T%2Ba%2BNhiV5b7vOiQWG1XNvGNzngqewJWX%2BO7%2BPupIVbDas6n8HPju1ZMXmrvkcJ%2FhQ1Ya89RaqlV9P%2Bu0DacBdfrcx5rlPXMqW5%2B%2FVv8cfLHuP4t%2F6ZgDdhPFR8DGRmRoMk6R6Yc9MgU65TdN%2BKH32y1gyJruJn9x3%2BQ4%2B1zUvkZZYoyqq52HfJR1T3OUca8Ss9VrVhgoR1nngEaUXl%2BEwnEj%2B5Lg7fIsNx%2FsEWwXdT%2BI%2FD8UOO75zqXdKad2WS2XFS9L3XHH%2FH3m9r4nePnO%2F7Ys%2Fk6qErLYy0lJ6agZeeN%2FwwccYGT1QoEPwJqvCIveWiGhaw0jqw4olppFhqa8b%2FC%2BdTSMfJ8SlX%2Fp%2B918A8%2Bor5fxP%2FNTuvM3TtoeHe%2FThlVC9NKslFVNwNc6blq86mEHcyuYlSiOqOvmLPKAkLhPzbxCP6j62%2B9f0qwwjHOiiWI80kKVVktH0mD79lpNHuEPZ9yx6Q3iKpAKUiIS%2BdKK4ZmEpg0z1gZ%2FjhD12TDPydq2A6DMfTF%2FCCSlRZO0fLXPJsLM9o5%2FJ%2BS1UU8jHffrIaAVo2H93qXRX3g%2FV5fZeaqtAxwpeeqH3Trtr4z%2Boo5qyzjqus%2FuvixZ5JszVn3T9bAuDz2jM54qngC1XyGupJhFtiO%2BapVZZeFqvBG9bLT64cJ8zEW2juBk3sMRUbTMA9ggQX%2FxuNExVKRpvwrklXWFA5ZaUTl2d%2FRNOseP4pZYB18QoGHvnMyyNx5aXCbSf9x47s%2BV9Vv%2FQ2nBFacueFU%2BfxH298aemcj%2BAollosRz0QwI9ygM56qmBNbdKZpA5nYorobKAtV1yzEXc4xMjWQ2Xzu%2BE7FzK0BZnfYN3ezIOaa7cYL%2BL91Kw6%2BwooX2cJdqES1Yl3fwkumIJzZeGJX6gvVmzcdfOOV0JL6h1jjlZuVAa78e1Xd1scYiWP5mRhHlc9%2F9PFYhwhrwqz%2BfBOLKP8AaClJVcxhKRb%2FbHAgM5D5bBD67tR1UFX8XUSS8JcpqS8QN340V4kWuHQHNRnlvBhKfbH7Vr8H6fkKWPUwq6eGeuYgy1ZNqcPGOz6%2BR9SZ1V7of6CvfPi4Z0Y6zuSjamFa6bv2XhUpNzRDI2ruGXdyLNC1U%2FVs9fxHH4912DsxkOnMds9tPgd%2FPNEpvw99qvKrPL3r8FZaC3Vl26BE558ratV5h5brrxqrSjZWe2oL%2FbGSS62BPrSGWgP31eFR1ZYP7%2F23Jv5tWjqelgG%2BMe9VoU1C5X6i5fIfCh7GYRjtwIM65C%2FhnJc6S%2F9XnldPHdKgJoWtn6q6WQa0qq4yZuwG%2BY%2FxN2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYseVnpcgqGjNm7EYTNd1MEGK0kaUITo7BMiNUZj1D6RBgIRmWfxAO%2FFpHr1Vl6qOHh2WCxTJWwxWpzzycMW1rU6TJ5QMexTRpz5cqLpp7Tvw4WJlhBGp%2BBo7p79qA4m5Bmngs%2F5fXJWZFOsN86VmYRFb3agsKnuuswqLabGc2wig6q2t%2BjKX3TfZN4tc1P6Y0CV1XT7c%2Buvjor4tXpcgXo5daH5QVaUf8fJhRy0f8ShZltOdLW1lj1bW5cG1qRVxmL77HjjgmvE9R%2FzPNIBmL4pz2%2FS4zGXS56nQyJ70tVuA43%2FnhhXCDWLVTsHLHWSNKIav78VHwuOp%2FIIMipCx1YtdARq2zGvoUS986vnXcXu35aXmpqlsfXTwuQ3eviwCdg68rVx9cjSm%2F72K8qp0Ka69yLaEXBOWD7i5NogZ0pBfagNRNqJFxxsqEFfWPwLL%2B09uwHqe3jaYjJJ1eWCSe0SKcjaeJvbvxVmCVVIo0mRsZbeHSfvd3JVC1cDG3mnyFKyZVeNRZBYmKOKvFKsJysjg6o%2BzmrAAX9OBrN1HQg9KAVKq66wPik8r6uPCT1iQBH4jbAtCO9c7Gmb8KgVM%2BfqdTH%2Fyu9bWEasxz4a06Nd5xLnewJl9aLgT0WD2Vqon8Ot6IYncG62CUwRrSIF%2FgCGtkgnsnosow2zrYZMcO3HPU%2FiPwqxhxq40cvmkhMjI00%2FaV%2FG5xiVySOYQtkapLVRdU5HNTVb3sG3VWD28VlUA7vFWus3rbPl76oT28l06y2%2FaVj6ru%2BnC8vD4Cb%2FWFUMG%2FT4XH2hcKkKBASfsT6vpA4Buj1ydHk5BqNakbb68qVa4%2BFe7kXqsqkWWbd4sS5D7Nq8qnh9fhq6ASUbCGlDUMzYSvyueGPCTnI541tkrS2bvxqGrS9jZl7inw218N%2Fe75%2B2RdsdMygrCWQjrAh6pe8igqsjo4SsrB0VkV1VPprIau8tLvS92Xk%2BgMXVU0X8ZyaqQIe9z14TWS14fjYceRL%2B1585dWnQL%2FP5PsR790%2F%2BRHvwQRrA%2FU9YliQHhQVZ%2FkNwJPM6d8qumNqgkP%2F0mw8lE1zh7dUfyzR3fECSoZKDuzd6IZZrcwKtdQ8FVVjzwQWaTGlIj%2F8bZ2hrK8%2FmKhznTC9jV7MiHrLH2pir3s0qaWj5Q6KQe3zmoyT2uZzqoVE5InEAzWijBJLnFcKMQlb2pRH8sWpuLEltWH42E86rbr1I2LlGV43EFndIv7J6NbZDvXuNsHHvmrqvpgcshjZLvsG56mlmoIoIpQuUZV3SSUF1VlSr1JNtlU%2FLPJJlp9qqruehS%2F3vUolXr3DHZmdah6zyC%2Fm3sGfdu%2F353R5d2ebHiTzlX1GloX7%2Bisiscu11nlsp9izM7nFX8lu4aOEJeoD253wLdAkNfHqb%2B4Uzne1nzFunMl2j7LFl%2F1byOn%2FJ452FykRVV%2B%2FwUv3dqB93QSKHKdW71RtRSqWnUDmQP7T287sJ%2FL6B3bIU1yVbtd284wVNPqYwVwRMWR1T8ALqz12mMbzupQde2xzeesGEaAsoCZ%2B7I7D5y8HqqKTF%2B5qaqrs4r5U97TYn24Ui%2BMSl%2FL5w4rGd%2FUaKUyJBf1YbWjaZALrVXVx6m%2FuFM5Pr%2BN0IR9NxOqNnLKB6m1enX53u354H7lm700rf1vxKgKMUqcrYAU0Qq1jF6xzJjjwH6jGB6jaR4AQ964gTXA%2FzUUPFDv2r6dcu8vxEe%2BHv9Z62vgq7WUlzWibUsKgIsTMuWnqp7OqjUswt%2FeP%2FExJx8CD9Nqw5NRlPrAcBdU67668PbGCiq8837RST9I1ded8qspOrT6urVcqfn5%2B%2Bj4So%2BqOjPn0bQXVUcVbylY8MQuzMOLvLHqKgJ%2Faotc974YP33f44mOxUd%2BQXtZI8ZXERIvM6rq6ay2vyHKvOOP%2BD3f70P2ZwTFdQkq1P71dV%2F18N6uK6tRZeuDNcJ3rzr4ys9V6Ybqy0upij9VnFeLGzFqXMfGUzUvHTyrAXo3UF7W8PeqPBMsU6QUvxVqiFVVOPzcEKrq6Kx2LIoyh1%2FG74dfFt%2F7adrru4qu7qseXp%2BqpdYHE1IDGTUeXnak9k5sPkfXuV36Z4X%2B9Xf2vHMO%2BW4LelR1Tz2KPy8Pk9Pb%2FXrGsmM%2B2v4Gzp8YYrYjN9a7Y2eS5mu%2F%2Ft6bVJ1VlwJqkPepKi1UPRVd3fro43V1fa%2BjPt2o2k7QrQ3Z%2BA4dnVsNXeKUBzolL1%2BbDK7rU%2Fd6XTZELtRtroeDrMTsRDdVxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjBeb6o%2By0Pt5KEzRo61BQha4rq6dBmzsnnUdfrlhLodptTKuFmDVJLn0sd0ZGdafebSRTli2lRY0tO8OVCkMzSS0VYAfPQuvfUp3VeDG%2BiNKTVLFK3ZU7aM6KnDijC0TqWfiqSo2CGxdvO7TnwP7e2RBZwpo1jB9Nss3n5Eu3rMmwTX%2BdtTuaqr4lULqUjgBkOUvuaJT4gG7ntEQYW3qvxWdWaOgsrn8SpSdDAxm6CnAhXk3WKLNXSzKqWKU%2BVVGCxCXi9rBegxCbcDgJy73WXiOQzpbYhBUUKy5Al9TxZ%2BpD6nolyZQaBC1QcgsKloK4S79Y%2F4gKvIWCpm7TwRa3Pr271z2L1ZTe0ajwxWVTFnZSl9cVo5JMl3qq8r3WNSU5VVFTIKKhAlyMV5HVq9nKS9X2J9xomXApF8O0Ckq3lHKYaKHfDZ7unU0wykYMos4oZh1fpFI18QcvyS8vpwJH7%2BQrGPOqi%2FX%2Bo7EOtngJHDEi6L%2F%2Bs6hlU%2FD6CzWFkAqt1jpU9fZmf77wPSuKNxTJURXJp6cCXIyXk7WyVEWioaCnc%2FzgvKzvcsbf3lmuczj6G5UcJoZr7ez5%2B7b%2FraojcFPVijWdBE3gs1SqYquqRNyKW05noTVR0lxzxxrtADVQQkBb8QA4yaiRVjGqFKqipK%2BsJvamNFdzeR5bmse%2BCp930lWAvfEyslaWqrbu7DcFwcI3lIBq78TU0NTQ3olkXn5ZZrftQ6mrX4LAaDthLszH6iaGTa4KaZ0gHqcWFMJVlqq6Gha6AapXcHpzA2A%2B9y%2FWIqTUJ0%2FySZ324drbsueLHBt5BYmKm4AEFqw6G89CemT1w%2FuTtfJUjRf0n3HCo%2B%2BdPdC5iq1iBzqFgrAi%2FL26%2BW2rL74B0S0vUNwd91fBRFHzx7TNkOL%2FNcnu%2Fh83n6q6Ghb6qhf6AW3lAmD0F0j9pR0lQZ3a81a10iHJSLzUm9e%2FpRIXtfdACCJRo7YAeuPFHN6LfOvfklTWB7%2F%2BLe%2BzKk9V%2FV66%2B9KmNvy6qa37EiHI7otDd4QCa9F8aKImBUhkNY5MRVngeRKRjifZxqM3n6olvSrTPEMnQK1sAIyEG5liIXcATLtXVxooBCX40ttDEN%2FmjzQUr4MXg4Hm%2B6O5M1y7%2BhSTD4SzpPvQeOGt9Pq3vM8qjaq9s6e3UUa80qgahTzx6W2nt4UfjhK6g9DfgxxnP9%2BJzB7D%2B6ikuB8SXrEPKUSKfYZ731WOqtaYHXyNUQitm8%2FVPUMnQK18AIwZdXcATLvXglGwRa89kT%2F%2BeCvWeKUNIr7b%2Fpdn%2Fd3kUxHVC%2B9P1NKoauvk14gNLtTBZnFqW%2F3om1ngo8BHzaT9Q8Ps4eeEk20%2BB3vo%2FD0prRSwxlqvJdmdv6dQCbuMB%2FoqR9Xm3F3rB8CVyAAvlwC4OANMFwHUzQB3gbokPzh%2F%2FPFNuSlcxK%2BrEeSjELUYLyOqN1WHZmQ3Jza0EBtcEGgx7wp2AkmSGGaURUlymJjHPZB%2FvTH4d%2FbcXPJXS9YenlZaBcRIEBNL%2FJxn%2FlqJg82hnSQGbaTkeLeLydIgJQWcyw1%2F3Rlgan3UVHVUHIGB9lFKWq%2FoKkg%2BKlHdeGtMRlS%2FEMAf7955hpNV1RTFfwKhLYYpkcO0DmK%2BrmlBqNnzfHFgwb9GrQUbJ8GfH9QrCZjh5zReUbZ5C7R4i85IKZIe7iPEdF6tlT9AXV4ZYEHVUupTiqpxGahqZ55COsVyPGjMhsoZUhVuEYUC1cp61BaU31DOpsspEafyWxUrlW4L6tJN2VgB%2Fkghh6a0uX8w5o3nSQ%2F3gYmUcgacyw2v73NLz6HVpxRV41Iy8MtUCVj9ZwDGtNqzRf0TY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8ZujsFqucCyqMe0eRbGjEmI2nhR%2FHG6FDdmTYPuyzRFFsxGn7Euw%2FqXMzQ8LucGaZThkjub4WXQkmmasrIxYyU5%2Bbrm7ksJ6coR7obNoDIUgX%2FNSo1DlOxuxtV32QT8D%2FgMRcKk%2BWOQRvmKgrSGoRNgjuA1djarJcu%2FXfgzuKpUq%2Fx57MRgjX6dmqhhorKyW1sW20ofqz5LDw%2F327dsPDLvLTS%2FWYrnS%2BJoZ1GwrvZM08R4nFand95Qtux%2B0ckDH00N9c6mvpCPkbgwbCAzmsaF1mHFiklUiBnIgGh3SqwTbbyorOjBqK2ZFHhJTaTVuaW4fJ2rVTd4y4ZTvbN%2BMp0C35UdP4prB1cxaw%2Bl%2FL0TQzNd2eM7Wa2VblPeAZe60pFBF%2B0fZbpYyll6%2BDgsJ4J4iTwNEms3SxV4kZ2D3sJd1vkks6V4viSOdhYF67RnmFQjd%2FuTO2%2FwH8n98sJACwjIeqFfVtDa923hbnyiHUjWte%2FLaB3l2FpnLV5UQW6rry2HDCmD4JavQB40nVsq1Dl4S%2BPFxovn1sGysmoFPsUaISwHAaxWdMs6Zfmw1A%2BXwnESbjglb2gUssrpU4QoMuhcUYfLXulhaWfp4fEa7bhGl7gzgLN2s1RVRBlWuGySUcjqhaesV6Vj3e0ZJZJV4OWqZY5xqTSf0p3Cui%2FtvlW%2BEA2lJIZf5p9RFSHC5LQ%2BvLX4EcnVdNd86SDXLMibAkc8FnTfQ%2FelwVvUeFRYbWZ87AO3PKnET9qhr01U2QJ8KHc6zNzjX1jaFQik0%2F5qN3ewtLN08bzlEyC7CkFY382mqnDZJIkaXnhaq1Kx7vakkdXB62qseJTuFObWYPAzFD0R4l6xD%2FEcf2xssSvLl2W7H1HiG9k4HGc4VguHkSv%2BOU3L7wHrL6OqwAeejwCWb%2BgxNHNunWIUmwyhHut0WNncjRfbc4r9yfzXdkXAbCtAXIySZbgcLOUst2PRruI8pyiGwmn1SFZZqnKXpVHDC08VN6Nh3e1JqZE%2BUSVk1SNqVdWGs3w7DEiv2FtiyMLB7rnOrMcjysrG4aEZHKvzAixX6XM3TlQZMQR%2B3dTpbRAmx7uyeycgXK2W45%2B%2BtwuSYu1CS0oSvm845SW3IQ%2BYhYAklapRl5uoz2o6qYcvplJYKSRTeaoW3rN%2FDOSNp%2BsQUrCFRFVnX0T7g%2Bi7psZKz1zR%2FeoStapq306uqNaWU1U7frc%2FtvdPibxomHNz%2FRdk4fXGo32TDjbOKFQNPBbN1V%2BeNMnv3BJiNfj11BbWIKNeTguq9vhOjCU4UWVqRrw3dG%2FnpO5NedvTqepgKWedW6eHL6bS0MzH99x8qrrvwT8G8sbTqUrB5uV13Eenuv3jTO%2FlnZWOF94vfz2jQ1TcoGhkymlmSLrU%2BGPHnoH55tniRzT2jCy87vjz4fWOsmCSRNWew3sneP2jykdfcC81%2BOKJQG0gK9ckalbUSKi8ijPVYQ8ihZAqxakcLOUsoftIv0rSta8PyLiFVF5ReaqibyZJw4kXnkpVGlZ3Vx%2Bn%2FcNM52VNuPh%2BA4%2Fx1zN0oqK9kxCPHLK7QanjNvTO2sFyzN13yaTKNpyNstW%2F7b8g0PKdXDBIwEwlTKoaWDXqkmOoocbnk0CgSEjDgwRai7p8Tlbcyys3V02rwx57%2FK2mqB4XY2ln6eKF4Cq8zuqkyLhVmqrcN2nDiReeGqvQsXqKiPpk9SAqzAw%2FFa9ndOTHWPWR7Tju9cydT6mwWM0I7rA67%2FRdMvzJjV3ZcF6wuCsr8sc%2BwfgTuEGU6NtW2ptF7Xvi5uELkwK0REIuyCaoHi%2FF0s7Sw%2BM1Np%2BDqUHjcnhZI9yVFvd54Sn0o2NLURR0yKrzsqbgfq0AzvC2%2F63q9YzHxSEg7Jk7tkN9HsqD7p0YyHRme%2BY2n4MkTqf8HFZzagv%2BuQF3dXCYWil6xYH9fPotlHcP7Gcrbh7eTVZqxi8fZCtVj72wlLMEyn7Nr8Tb6sUdsmmNl%2FM6X2l4mqMLd7XqaHGfg3I%2Bqemngy3NeKvrvKwput%2Fdt9p50MZSBD0hIOyW08gdBsOsOgX4DopKL2zMFMpJa4fUDsNWQLlu5d0VNxfvNDc14%2Bc4q1r12AtL0UrmKP6cVXiaevGNMXedKV7qoFyf1KOeBvZ6yKrzsqaoY4IGqKkyZszYjeh2qiuHNmbMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmLEym65O7%2FcNb59Dlp1cnvWvuA8FoEYxnda02A2oVVr3SlbMmlyuNM3p9MYZTaf3%2B4YXZ3EZMXp7JrOdWZ36VAp%2FoyzwEUhYfkStC3XBXMGdZ%2FT3fXj%2BPr0rWbHAAuhkTt7Mrobvb5ETbA24WrRYK0al01sani9qw%2F8rU34yL2pW7vK5OPNKG7tyXq3b7%2Bges9SJXQMZSn1Kxe%2BdoOkq2488o%2B0yGtSwJqNK3aPrpWoUBU%2B19k1A4tGvBCMw4BPgpU%2FfW4n6U4nK97ewh4ZY00JeBg11evllhR6QXKfXwbudXYXvnf1kE67f%2FGQTLrClly%2BEoNR4WEUKomYndtHrT7tftKaTHYtIiiR76CUQO5VrGOd0jzfegd9tvIPFkXzy%2BgidZHthoQbeirVeo9QfhcebFqLajkWnhjUcyoum0UJyXVe3%2Bqw9qF%2B5mtHDU0G8E7uGZij4MAggIB6F2W8eVdc1xxdxfwssH%2BsfX1zXbP8CdXqdy6p1eh28%2B5Dju7K49g7Xb%2BKaPRxZaeX3zn58D6eICg8SMCusPVaM1fK19pTyhQCoSpfYqguz3S%2ByBpvejQ%2B91HpN1tBc9xh6QxTlTMP%2FscNbVfUROhd8awUqXjgitpBcV9maXA0uqO9YVGpYgTULzlNrvUYZi3VcHZQx54MgrZ6XcSeO9m2%2FEsSjL%2FEHUb%2BdlFXYlaMqq0HJvUROWteuP1%2BoGlsUI4wNy400%2Fjq9Dl4canzCFRY1nUwQykf5rYEMEnx8AKmtwsO4wkJXezZbdVFGqb%2B4A7UuMYq0JHFGyA7tObTHAodJSGcpXPeY1Q7N4J41sOofPkPDfyPHw3X2WAHcWqHpJBGfIyo8yAYZHgPfkKtzUsl2uTFUagQ%2BSri6bRgRPiqnq%2BPGI4miKK7pCsnpW0amaMRz16n1NfUc1SpqUcq8liaahugm1%2F0mUOqI47vniptMrtNbGt5RlOGqMSr81BCrhyCvmjukGp%2B0FY9YfdNJlc6wwFsFUYQ%2F3nEQqFG9Wg1I6B7z%2B%2BT33ZmV1Qfx1p5WtopFc0KSBLxD1Fo5vulKVEu2ywurogaX23R1gZ2KGXChq8u3uuoLL6lP7%2ByxHbQsLmuhEFVkiXODT0hNZx0RND0tKe8r2L%2Fo%2FZNoMsF%2FuU6vg3f3L3J8V9ZRbj23DkdJVfkBO5OYJ6oSjweEaiys1Bl28O5m8cez%2Fs8G7Zlwv2WPrKj6JBP14LrHVgxHVBxZ8XNCWh%2FET4cxcOdqOgT8mJuocvyxHY4ibqlUVVNDZ5ycGnILx3Zlp4akQezbmLEYmcKYRugSQyvVliOLW0qWuPJUZf0ndjkt1DMHCUTubajTu9R1%2FXV6Hbz7kOMTtpg%2Fzt0wu5UglG%2FL%2F%2FcJotLq4w5o1XgR8Kt1iVn10AwmkxC37qcdi7tflDU01z1mtdDAMDeH%2F2vXnFXVB%2FAwh7ddEEQ61PjmguSHHM9qsWR30C8XHiue2lCooUdVVvPkU47nPPmUXDKoHXWmu2F0tGMa1V4IelncUrLEhW1D1CvU0je0Arz%2BvCOL4wYsfPqBOr3FaRaZTq%2BDd%2Fe6KnwUXnPg3G3lfJRYPu6WktCqj1793TGBXJcYI4HB0825lAkmmKSPJad7LDLAuFWIqj6ID92OLghjMAGPNYF62COqCm%2FrZ4X2TuCj108rqalRyuyTrRCS7yCCrhCVA6IG8xHFLM7My5fFLSVLXPm00u5bU19g%2FXmKqyub%2BmL3rblfOYrrNJ3e0vAio1Wp8iuH586OYXCSfbJJrbjo6B5b800sQqqPLt5OdBHxnODHd6oFSJcE2wRqlOa8rIUH%2FKxFiQy675z6EoWeTNLNEt%2BADDBEWCipa4%2Fatae2uJQLhU5vF1Wn93uGF2dxdXoKUuged2vVp1J4JxDWdRpa4Fua8x7Z3jMnn6V63Xl5srjXkyWuPFWFjmhOW7mm6K71dHq%2Ff3gx4yBjl2P9q%2FVdRgvdr9VCqCJdAWFbSha3mKz6RNW9W2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzVgaDZXN7TCsYM1ZICw1dWVC6QQmPPvtzn72m%2F6DGlfrg%2FDNqWUZc2dpzuOL3PW0xqhwm1PqMVtkZlcJBHsm8P2tcK13GNnkOD%2B%2FvvpO%2BHbsxisPqZ3TdT0lXFzf2Ye9sfDEIq%2BytySDoqfXOxj4kXWUMnTfI2tidv1evSQi8FGU%2F3qbRAUwjleD%2FPh18x%2F%2B98wrtj9KtsQi0Dl3a0gpwsU01Ta0CVY1kSfqyoDYx7f3UoPtlHse8f1m9R%2FDw%2Fu67aO1PoG6H1DPn1a1SOl4QFddrXydZdXVxI%2Bzh53D1IwoQ4kq%2Fh5%2BLqB0y1nilmfHrbD7X%2F09qqq4F2cz1D9hjWZ2y6aaDrJ0hldqhK%2FBzWi%2F87eze1wtEkX3P4TKeoAZBHINZDW2ZlK4AiHASrmMPI8Y8J3i7z1NLeJafYOWmKldbLGV8kY824rdC%2F0gp47aka2qVyNlwmbtEvlUoMnF6eIeoOenV0skqdHFhmS8s6hEKDBIdWlu%2Frwkwzz797NOop9acFxXzf4yBhXhOKWbvxIP7w0Bx1aiHzdH%2BRlXVnb%2BXdxwYKLcXuGE7y4scE%2FAPPtJ8VIYXY3wC1HcHMqDG9xK1ZWlUXSrmIV9clVcFBBkPR3sKjw2n6F2BrF7Q2wWdBd2F38laNczU7bh0fJGPNs5vWUjIzsjr339h6b0Ov6zb%2Fv5PQL897auEuMQLbXleYWvkvxO6uPFF%2FC6%2BqNLFdfSL7nrgrgccXSPZpbmgaFd2%2FCjr7jrULJUd4zYeyfVBk%2BvfiUrnwo3vRmGcFuLeXAsI4oJ3qfhX1%2FSmZXg%2BdqE85%2Bs%2FfP2HttQmaV8WvnGGeusMz%2FCUyV0LZbJSX8Q3CKkRfCYgYxoqj2sV1oA0ZtTxyCxKIKtVl%2FjcGV%2FEaJP4XDEWQaSE7u7oGvmVv%2Fm1pfe6dVy3%2FS2JTFzPnF7n6n4S1FC5aHLDySp0cWEwr4NmVOriOg%2FfTVX5xTsWcdQ%2BtWV0i3W5TdnPWcPWQRE%2BhhiOgOGr%2FikuFCz5oDvJpu9DAtpiHXfbakUHKfjUV7DivsUfzw2FxkbTq0D%2BczSNomUUojZe5LVROW9JfTTIeDz7k9Uu1UI%2FopZC1cLfq%2BsjiJokkRXlSHjsBi54OSyVzGEhrlIIVOhwZxRkNbr%2FiaX3%2BnhCt%2F1lio6P%2FAKyLkw3A0ClKu%2BeChVBc2R1dHQDjwUeU%2BviVlVh4IsHUlV8lo9JCXgYR7YH34MkVK78w%2Bv98a2frJvCG%2BudFSNfnPlJRvdNwoz2X1j1QGb1b%2FfZwlGwSUTN%2Bn9Jsr5JP3z3JY6%2F96Uk23Icf%2BqPFwmlnrkZe5yfifTMRdTbTsS43Bt33pXzsnEYHXHpP9UD7eniRJ3YvX2tfQdvlS9g06OqQ1SxaQmdrPE8Uf1Se1x5WcfpxweK7xRGwZryURVKa2j7yvuc7a9eP1VzOtlFh%2F18HV3c1vxWA%2FIAFSlafEjdanNX9uHnAguRfOlIJ3981O5vkYL78j1kfIPfvGoggyPi%2BVTn%2Fw7aJZ9P4cgJVwj64SGgTiMex3fMMVtpf7xIKL3wU1a9%2Bdzmc6z6hZ%2FaWz3UyYiKgakY4zefs%2BeVMf8HyLO%2Bhf9UXUEgR9Tmj5vssv0zwJWlqkNUGNe7%2BWxSvd2VQ1Y5Uf0cXFYj3Jug8E4H3tOPavzLhzG1L%2B5zjmwAolKVz8kLJV5zMZOujm5V1WrGD6So%2BCy9eH3%2FhWaXtH9X9nxKdUvYGHf%2Bnq1wlO390OdTvbNtLPA8nII3Fg881gaP3%2F8KiIcEyLuv%2FxCdhdVbB8NSPCaUgKJw%2FQf3P7gf7wbJJ9vvLLDQmQWJ745czTsO7O%2FMBhbKNapiSCTkM8cjuBFRkzQDXOy44hn4X4HvpwcZ1z7IL6d5d%2BNPug2nckQNOakf7wSXF1lVRF3q4JgJzonD%2BqSiQHPK5ehd2cG%2FKydVYUx92%2FsMaIOacsxVsRXd3%2BcnN7o6urpzVXxrGylI%2BoBAp%2FThiPFo306%2BcR2eI3%2Fom8%2B1wTiM73mty63gWLLHz8WxI%2Fa2E3f92Qq0MSGV7Z2JxhdSJzfi52bIdePXkxu7sjCK%2Bb6%2F3XAWpCFXiLrDllcrTm3ZcLZco6qgmi2HaW9EJM8Ao%2BPyZ%2FrZoMuFJZ0l77zDkPhtyu1WgF2UzLGcmXLhdyqyylrefb%2F5eZsrE0y7Ck6%2B5G%2FndalqBdp9znh0h%2FSVk6KDKWxTn%2B90dXH1qNp4sfvS6W2gTgd5S8xVqgWgT25EYoNoZn3ra7w%2BzjYa3g%2BddcBmVO8l%2FpD4w8B7h%2FYUpiA88ZCuuAeS%2BtsObWoDvKRGzR9jwm1VvhvDr6vsCKH5Y9%2FyO7B3FYrtOJ6CQGRHuUZVQbX8Jo%2BpgiDJ5xrq0cs9bvBx1TVdaVC8iAj5fad6Duo6uWvivLaR3S28xMqTuwnOmmwqJ1Wbj3rjYXirV4W11A5G1mRaurh6VO2%2BBE5Sk3Mrkogjq%2Fn4HiB3A87AemdpOrewTUIHhMBx%2BL%2BedI36TdAN%2FGwjkKhe1idHmd%2BjjCpe2nTbe42c2NU9p3JF%2FbnqUpO6bp0OUfkkYWRKbMQwMiWfrlTail6KhNTdATzTfmenP9ZP82YqVdde88Y%2F%2FJw6rL1OooqelK4rm2%2B2W%2BBQvlXSc5J851GTu1InXedW8xotTClIDZ1Lv%2BSQng1tWcvVbrVcsb80fVmp61bTRL0LzmjJzfhS8Km66jtnogXVLan7JxCFM2HXoeZNqAxErWijfQcftDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxoz9%2F2u4KsiaNO1gTOYkgWLZCarynNZV6uyy6zRcFwRkdJzX1iee%2F64%2BhRBIyIR81S6W3CtZKy%2BHR53neZrO8zLFT0NXdhn%2BH9PyuTN2Gx0sqydraWHlz8rYyAyt9KVXs7%2BJjBQLTzbfr0X0PUh2BQokTLBsuXhJvoED6LqNFxsvhph9BYoOXl3o2vjRBNN4jJlcMxzU6Azmya41r%2BcgsAakBv9R0VQdJkfnOUHUeV6O%2BLav%2Bv9p5JV9T9zzWzXescZ3caU0LHMMSkrX1kkubXlF1F7rEyWIzRaWJ1YI8UJ%2BvWSB16%2BJzg594yoW%2Fmr3rSqHCX6ZyHUDwY9U5a5rhvWhGVxmhkvQrMwqtq5ZXZvA853ZX3YnSRLZ1suo5rrhFOt%2F9umRqTbSWAaaCJdv%2F%2Bcnn2omdQbN7Mmnbv9nGAX66FQFXZ1v7QXyhNqM%2FsY5lA6rqfNcKr53VkjTlr98EMwJxT6M%2FjryNUUQRvgnSgQNv4nLHP3JnWDutsQDqSHr8kGmr5jYw%2BquIMkKxNnnZX7Ax187qszwETXn17HPiqka%2B4zguOmVi21fJv5P97%2FGGatWadrF3es8FX0iq%2BmdjbrwsGhXOdZYsTb20EsYH1DGow1HhS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2Fy8vL6%2Bvqfn5%2Ft7e339%2Ff29vbo6Ojz8%2FP6%2Bvr19fX19fWmpqbLy8v6%2Bvr4%2BPjT09Pr6%2Bv6%2Bvrr6%2Buqqqrz8%2FPt7e2ioqLPz8%2Fa2trW1taioqLr6%2Bvi4uL5%2BflVVVXNzc3%2F%2F%2F%2FW1tbj4%2BPh4eHq6ur8%2FPz%2F%2F%2F%2F29vb7%2B%2Fvz8%2FP09PTMzMz%2F%2F%2F%2F%2F%2F%2F%2F5%2Bfn19fX%2F%2F%2F%2Fy8vL9%2Ff0AAADZ2dn8%2FPz7%2B%2Fv8%2FPzp6em%2Fv7%2F7%2B%2Fvq6urp6en%2B%2Fv7%2F%2F%2F%2F4ck%2FmAAAA8nRSTlMAGgDUzwIP8SMQ759fCgUvqfDGFeIYA78fbxNTt98%2FhsV%2FBhdD4Q1rRI%2Bvwo3ATxJTD18IoKWasozTETbQ4D40IX5hC6dAMR7RXydvEsRuotKLkZCATYahkzOxQlFqmbZwJiUhFWy1wyJYcXI7gB2XIEFbgjxgiWFtfTSFMy8wSYgEqFBDTSE2KCpnSyZZUaZHRFAsDuWBYJJ7AVZQpC0Z6njBKWjdN4dlMV30iN8bV7%2BzJJeHMRiDYsR6U9yVYxdP2c1dj8CKFZZVFjtaaTxOI9cMKQk4NnBW4PKUOmiNI%2FkwWoQYUdQOSk6GvkUURFSM3n71h14AAB4tSURBVHhe7J2HfyPHmaa%2FYicCDTQCQRAkQWgABpMcDSkOw3CGM5o8Gk2QRjlZOVjBsizbcs5pndb22r7d23ybc7zbdDnnnHPO%2Bd6%2F4FjdIGu6vmp280CtbF%2B%2Fkkn%2Fnip%2BaPSDDqA%2BFOm7J3ncIoDi0NAQkY3d2IaJSws2NNZZnCouduhAsrgf7o4BYy59O4fvn3ROJQKoREkBGKqYytAJCCEQWh220I81TPFIozLaNiCMH4PJr47WIooL1C1isUUsFSwpkMqPAMARDUIFjLcYpj5tGbmqw%2BP6bhz49jZwbZ9S9k8Kd20QQLDdzFbdIz%2FJJ0OFyJFaI6mOcZ6HGOzAGxdi0tN8JL063CmJwi9FviX34m4FUrlxl0PgaBgIbrXJJfVp08yTrbq2tt99bINtCj9p%2F2TiZMMigCzYGa0WxwBgrEjxCBUici56obyLjsF%2B%2Fez8KGLwUdxVJuq9HZcpljX16lgjlaeg8hTpmUVNqubcUjzNKnBbGIBbJS6pT8nMo5ilAms3kxsAbElvsP0DqP2Ttt9KsEYIoBELpWxWDyHMocSDdUiCYMYDvJmAl5sUE%2BcDgiaiLMd6FrTJUmskFaTyEah8JPZsiru8WGL8ouLpx2rfqshkVQix%2Bz%2FOoyRIte64GalXsb5%2FJFX7J4UfxsVI3EUcMyrVrbqAtbVVB1x96q39f4Yo0goYpBJ6EmhWa31nx3WrUmskFaTyJah8iVSofNrqY2umHOeNsyIQ457ksUTnlP0dq4NfVyuLrpTKLlHy0sUp1UASq%2F2Txr2ASAiiwJvNYrVzBLjUbJ4BjlS0qbdE%2F%2FStUgAExAMyWG2jI2EFDd3qujNsWcPOesxquY6d1OOSmiMbId4YCTT%2BBEq0xDjRKACM8mO1HwF2mYm%2BDnRdrRRht5hUmRPHAeD4CdL3jwBEBQ3OheC84VE%2FXi2L1Q9fB14kOgFc%2F%2BzeVgmgJKuVTnzsPSh2iFoncY82uVrw14aH1%2FxCNVbszO4heYa0vDPk30uc%2F%2BOxv2LgBAAGdjSM8R548OvqoxHiUl0bYWyX7R8h1P5J22%2BHUIlAxXSl5FYDeZS67hHgTO%2F%2F2aoPbWy12r9JqFVifFsqsLYGbGtlJyq%2BV2TuBRrA3WTgs%2FAY70S30519XFebg19X3520%2BbakctBO2j%2BZ%2BNt23qsdwduyWCWnjjB1h%2FZvdWkqhPxKVhi3gMamh2Ilhn304xeIaTVJpVlsTp9FLRt3F9DPgvtmX1czbf4FSeXghcT9k4WXLYxtg8oYrLJRKZNTC7XWa7R%2Fq1RDCDfq7RltpDwixPTcjIdii1R87MYnptUktdKYn6Pz89ZSJj6l6k8NcA%2Bc9bqavvmF6jbdHqwW0vYP5%2Fq9dLGo7qVTrY5OXKnXr0yM7m3V%2BFzIAs4S0crEckCmBDOedY1UCmI3%2BtN0LjUucan0yDOycjD8PZk4VJDCB3%2B%2FqmmtSqlc68g2dUYKlLJ%2FUrgzMl73Gu3xESfFqorzwO0OsXiI4kmrCe%2FSRoQ4T3slOK2ea0qa001Tgci0E2TiQkVk5tHooO9XnYJDWcP3TzovT4xOL5dJixDqXz29gHhGRZTRIRogzT2l5mk6b8F%2BG5KhtyB5%2Fj%2B2mie3mie3mlvNk1vNk1vNk1vNk1vNrZbouy65VR8%2BsST3UJbGpopjJYZdoNsFXGOptDrpfAn9LGWvU5xaLJFvmr9Ycu3kzstYuiHrUuaUFsfGFg%2FyQOFa%2BHaCIAeHMNTnPgA%2FwSrnrg3UPPD%2B1R8AHnwQ%2BIEUq7xONv4w%2Brk7ex2vBhRhng9ks%2BoyGAXU6XYrROTzXnTg4PrRW3EAIQQI8tueVn3I%2BGarnNuoz4%2BOztdZ%2F%2Bpl4KWXgMspVnmdbHwWIgxm91XHA7JxiJ1A64jHvJg0WS0CmBqzWf3NLSG2NmGTnopCOm8l8RZKpNsDSbG0l1UfUXyjVcZLqE8EoGCirj1cC%2F20Eq3yOgjrML6wwHgLFoWxUGHzicx1iB4CQJy7Iee7S4biAw4QUM9k1XhodzE%2B1yRqzo2zk3YXkPZaZODoEJl48avVU5pVQQjFJltVUgHfZJX9N%2FDDuJ3Cerdr%2FasvA5icBPByolVeB6yO5B2go%2FOXdzpJLuAVVseuGOv0%2F2M%2Bce6EnO0uIRO3elPbciars9UyhSlXZ%2FkJvoVSCS3OaeNRCTi%2F59j7UGFc0J7XVSWVad2hpv5VEO9fPQXgwx8GcMr4CRybTHWg6ijungJOuRo%2Fhp%2BgMD%2BBw4Y6Xb3OrOSG1BTPdKxCJZNVfJn6%2BbKhTnMcGG9yTv%2B5Zrb6CQT4LLtQEAkBIRKtFgR2IgpZrDa8aEzvX60AQBAAQIVi6bdzEa9jA7aso3FnGph2NA58ncJ8HTBsz5%2FQ69QkD1OM9TmNju7yYsqxmtFqI46fo36eg8HSzwM%2Fb7L3fR6RkYPwfTdzQVBtOklWuT1ulfevCiH0%2FtV7sZt7zd1ovM5F4KKqozgBpHMA6BB1AIDNb0yuGOvIVPAk8YT1BztW3fq5rXMb9fZjcexEEwEHpjPw%2BLjxDPwH2xHgvIIPMy5EBqtCiBSr6f2rswAaQjQAzCbsFVYn2NwMVB3FCWD1AeC9RO8FADb%2FmZ6az7fzcf15%2BWr7BzhWnYnV5irr1gPtWCX9swSbQHOrXN5qck61ByTgfPY9DzUC%2Fs6GICfsbVXCFKtp%2FatL%2FY9pHQKAJUOZyUnwOnNzYR3GhWAcKmDzHbU9GfpsvfcpPsh11ZhNZXVTG5qbt6hJ8l%2FOT%2FeITPyjX6l9kG8mqe0cwGp6%2F%2BrdAHCd6Lr%2BewKopNbh3Gx1kDoET%2FHBrqvGzCmrc6QlGFFA480k3jxdZpsJEoCgeE8lhfdQQ2JocjKj1fT%2B1RoAvJ%2Fo%2FQBQS7fK63CeZjW9TsOrM14dHW%2Br%2Ban6vF3qZbJKyurBpGnQQpicNDY0E4aAXnQC73%2BNh3XZsv5V1ow6RzQnv4%2FyMjJZ6nDO64jMdaZHJxgvUHnZND%2Bh%2FuguHdXmU0KEUF8PPpES0esZG5pJDAkxdDPOk%2FdC5Mmt5smt5smt5smt5lbz5Fbz5Fbz5Fbz5FZzq%2BYGw13usyHXNjcHKKrHZwuvpKWLinmDsECGlAwdND5R2vIg39VWq0atfV5Y14fs2ryIktVqjbUepmUW9zI2CUyes9AlnvJZtEfiaAEL%2B7OabBqJQ619rSnT4jwKiCHaRaD08MdFvVDnWhVXWpm9jFYrEf5AwoYQz1INNQZ7QG91GJfJkH%2BGBzSyghWyJoUAhJi0SIXRAaw292W1eSBWE4uI3YAIGAOYVsWl1sGsvhLhY3FahN6SqXLs0xZKxud5QurmeQee0xGIRnrRD%2FVGFE6iJKIQj0gdYsjI1RCzKhErnWrVj3Hy0Y3OwCDaqx2Ya92%2FVeBYhK8DbLplAbcC7MT2vh%2FEMZPVyhraZAjgMGRe9S2RQiWJg519D%2BoMnPi4e1n1oReZJXLHKtJqNUFrNaZ1EKuzIswstzp%2B6dK44Vm%2B3Ah%2BCmiZ9%2FsDxFNBnX6%2FrTYVHuwMvJBmdcFs1YdmtYp7yLVRdEFUSNBaiGsdwKqKxq0vAF%2BwuNVTn%2B68buH7uQqxdRYnXWL5XXxtYKtChfHEgcHPwKEeSixPJO3BZHVdt1oQc64NwEZM3zqpxPn6%2Bpth9fiLwIvHmdUOwswaVDTPb%2BB%2BYnkYP3dwx2rmu6XWQZyBhdgogHj5XYTChhCm%2BoWqZtXttn4EYW7Wpy%2Beqbi%2FXshk1dqy9mMVH9ja%2BgCY1YcsIcQW0DGp%2BGkcJpYbeGlfVktAaXCrzYM5A6%2FQ3lZpJWE7C9UYr0wBP4kwSh%2BTKrmSmsWqNdwctrhV0Q%2B3ipMnway6eF7usjYe4lZbpRpeIBbge%2FZlVZnI0nyXOjD4PTCHu8hk26tvh6gQ5ypKH5MacSWVW63G9VnDTriYLnNRhEyLdWSaWzLX8AU5%2Fkn98zpXwW6X1Mj%2F0NkCFhKOym0emVgYbKXag74HNtchGGyPTmyH2VbZ1adLVbykpGpW41xKJalV34qd30KwjkxjS2YX4WLXFfY%2BFmEakz3SYpt%2BH7lSXWFHJVud%2BvfXanNAqzxpj1vQpSpeLmQ7VUmpUivrTw9EmDJlyty25SD6oVHD404zqTQiMaOF3R%2FS%2BIboZ6Mw4PrDB3UGFpRchxTkSX3cwePQd0ZW2P8ZNHkvRJ7cap7cap7cam41T241T241T241T241t%2Bq2aOAs0rdVcquuXawYFrpdTF6%2Fl6eDJUqOu0SDxvdpH8mtus8eR9HUnQ3ftK4vANslPSdxisOlKcjZ8uc6jI9Ryzy%2FWKEuq%2BUn9KOHW5VA%2BVASn%2BrQAcR2wy%2FJvAWwoYjyuD4vFDnwTdi33ZhV1z55ybJYx0B9sw2UDOvrRqK0dAHcZ16C2xp2T1ywntO4d3aCcJXPH696M4EPm0s1aQWkISRQPpTEgcUWGQKAkLknBtIRlFbGm6yUokyeHDJyGLT6QKRVTcPJS8P6Wq%2F1ibnlNg4b1tcFwHR3jOunn8KmEGLkhG3fMeJofPR8yQcWXX1%2BuTAa%2BMAFTWpBAKLAtALSEBIoH0riAIrdwa1KEVA2OAfMQyZ5csjM14llHX2tahqOX2PLSr0%2F6kkwrK9r6ts%2BFcKaq1eZix7h%2BAnG%2B4uZr%2Bl8oUK%2B3p3hLiJURVhkjyANgQzUOJTEIWN3BrUqRSgbBs5KKcrlySHOE1tXIq1qGl8V1MPh0KJlWF%2FX0AVYQjuk9xuvb7CGTzB%2BP6w6UL1D4wsoLrLttrEbW7cRjpGR8iFXcaMl3x3UKmxlw8BZKUWZPF6IS%2BVauVSVNjDWHQMu8PWBI6u1%2BEFc%2FaTBNQE7Um3Gf3RrZMIbLzgaf6cHKTV%2Bgr%2BgrF4w2iAj5UNrGmeWpga2GmXNzHkpjbKXsc22v5HUutIAsDbEpao8gCg%2FxtcHJsn19XV%2F7kGE4VafkvVtMF5oEp0ul3QezHhSKvTXYfSpJ%2FY6BSylSKd86A7FjZaqzwxsNXqEOxI4K2WmI2InI3z7fTLGDx93KHxLY5ZKvQ3IbDYN6wMDgLa%2Brnf5i16C1Y%2BMb9cHGJdp%2BpwHMxsFAkjTGg3qUgkYlo7MlA85ihssWZMFZ1Cr1rA6TgycWzVTFcP2%2B4lSh50hoqfkWxopleddFoD6nGl9YAD6%2BrptrB2SuE6xNNClubLjdtFgfDtmHqworrRG72x0qQSEokzUOJTEw7daI71B75akTyXVwFkpTrlVrjVZ6hDRZZy8ZJZKzkUPjTNkWh%2FYsJL%2BxzzIeLfH8Z3YyZ0D8eS2ZSAUlUD5UBIH2qfPD%2F7ORvpUUg2clTJTocK33%2FzOpi91iFqwfvCaQ%2BYEM43H1FjKerzN01UPqJ4O4nj1XAMyjXOrA%2FHktmUgFJVE%2BZBELueNyeVmQk8mZW7dJ2nI5VIljwaZP0Z5uFZzU34kdYiubY2cdygpwbRylLoeb7MwKkSB7ZjVaSEzvToYT25bFkK1IXPKh0LkcD7dowNIVNkx8ugLO%2FY4TddqbsqPpA6R06TvvORxEnDeCzFo8l6IPLnVPLnVPLnV3Gqe3Gqe3Gqe3Gqe3Gpu1dzf%2B5Zx1ShxcPUHT2uqktR9uN%2F4ST9UWThIq65taI95S7gaAsyddTWPzc%2FCB85JnHT3ZdVuUULel2C1UsTCYK8at0XAUMsNrdqm9pi9uQd4%2B5kPq569Prk%2BgOISkaEPeXS%2BDns%2FfJzXJ2oplMnGAoC1fVlV28%2FkGVX529x750BW5YcvgEox7EYrAYAQrL835ICJW09Xq09b5vkNGPi5kYl5jbPHVVmrjQMfqpWI9SE%2FQvTIRB0lnQdEgZlXarw%2BLRVBaTZ4o3opu9XOVQALCVK9%2BaqxkjcTDGT12RqKQBG1Z4eIDgMAEevvlVyGc2%2FYKRScYc8033pmHIxbq1crgZWxPrm4qwyc%2F1CN9D7kCnwfldtxTOPRRxc4j3biuOLqyKOEmGy0apCptTJa7RYRxnTc3yvlFYxWpdRBrDZnPIQvjuYQUQ0QgkgIredTchnOo5PRGufWZH3Y%2BVmPceDUZ12Ac1ld5zt%2FBF1G60MOqkA1CLxZjdPVlo01zkOpM%2BU4b9kpa5oxGyf7%2FGQ2qz5UCyrLyoaSp1V6KKVtKfvirkNEDWCH1khlL74u8Trnl3oTTqXIOXBnbw0mTgSdQ6bXg4zeh7wePrZX0%2FjVsF%2BS8UhqoPEppFhlNkaEAKA3cJJtvi3oYCfWY4a73BUu1Q%2Bri8JBWj0UjbP%2BXsllOPfCRtc7PJ3L%2B8RKMXsd8%2BOKKzgngMmqJ4TWh1xBtSq%2FHtL4j1uyC4vxUiRV449ZKVa5DfNBecmDjHcpjh9FYyM81VSHg5S7XHZXPJBVMe9J2JgXQ0Rvi8ZZf2%2FIARO3Xd93bc5hd4rmOkIYuSASOienWisBf7J2F%2Bl9yMF8oTAfHNHrHHGGq8MOMY5Qqs6D4SqApHUDlY1Uq803IPNGM46xOb3S60F9JIHd5Wa7K%2B5vjcj8B%2Bdbxei9SbE1FPb3yrD%2B3r14ESgmzR%2BUE93xaQC1u8q8D1neA4%2FxOmO%2FUHAqBo67AmKcnMK4B0qIspFqlVY3AGysanRzTgJrppx2l8vvige7W7pmeTPAjGddG%2Br394L19751nJzCFeDpsrEPucjmZ%2BdK%2BIxFhjAbKVZpxYK1osO56MGDlLtcdlc8sFVn%2BHQABKdl735Cf%2B9bwtUQwOBB1g%2BGiYfZSLVKFxuXyBwn5S6X3RUPbpWcJgkx1JS9%2Bwn9vW8lZ82xB1%2BfiU4ZEOYNCqablDXqLlfXGuz1M3kvRJ7vZKt5cqu51Ty51Ty51Ty51Ty51Ty51dxqntyqe5W%2BrZP3A3dhd4g6NrpkSqc7BibV%2FgjtM4twDXRsjIyxYXMI9dUcn7Lk1VdfVd%2FexFSAA18nOXs%2F8GGrhoUF1KzDxOyVbAAvMKv34RNkSGdxbGyxY%2Bb%2F%2Bs84xFKCefnoFoCUngEebT3LoppfjM265ZZb1Lc3Ma94IgbcItsUxlPWSWZWk%2Fty8fyMBXgzzzN5lSkAaH%2BNDdTwx2jM1aC7iDCLrpE%2F0XLZ86kBNZd4mvuwiv5f%2FAwt2sb5yGrV9d3kA8b3GfUN9Yus0YdvTzrn6ySbrZYAWEJYAEqs6tGjkDG8iBrjj8Mj1oh1N71g8xZ6dTLg%2FHvvk1w75Ot13JexOUCoMNvFViQVFzJYnZubU9%2F44svmAyb6ptNCFWHM%2FVvvT9p%2BkdFqtE4y36DIqi%2BtHo6a%2FGp6X64AgNtuAwBBsawB3tnpf6e%2F6Ih%2BE8DCC9p1%2BAjaaABAFUdM%2FE%2F9Zcm1C8%2FHPw5UiMUF4GY8VoWY96zXZfuIQLWQwSoA9S198WX3BqRAH8AN7TBadAv8L36%2Fhp28lO1YbTDbKuaO1cgq%2FKFIJ1yXrwGrrLLzrHX661PsRbfUbQKsTBfWu%2FHRNoAfs9Dl%2FI87KxZ7HWwCm8o1270Zr6vB6T8ddRkqqZmtmhdf5qsJTmktOoVJQCw7hl3%2F09jJV7JZ%2FWAJKsUUq%2FrfgG4AwFNP8fV%2Bj27nttvkV%2F1Qsi4egcwXY%2FzyjxKssFqLVB7Edae%2B9gBQb17Hgzfz49v8d%2FAXiUKuUkLjV4FfbaBkasYDipUYhdj9h7T8QhHe2%2F820TrtzyqX2kjSyhYX7QHmXf%2Bz6KfRzGS1UT4FlXtSra6ryevJ%2Fbp0224ols96zxchU9c3bwrX7wSA10llro7umXcA9TNd1Odi3Jf8E%2BTHOLk1fMZpt53PoObqUtsA2kpryrFakVJPFivqHjijVSa1Ol2VWolpZVKJkqwGHqI8SZmsfrADFXzRZJWvnyyDaoH166afgXuHEMY7wzfvhVUA6N2Mz1i4f0KIiadgndH4kY9b6HU1fh%2FaPXr8ceq1tcWwi965ZQDL57xilmM1%2BszJb9b023sPO9Hu9uqA36n4QDum7gLkbipUgQvEtTKpBCTcqI6KMN4ns1ktPwqVapNb5Vqj62q1wPqB0626dv%2Fm52mHLeiOBypyRHvqbUwtLEyhPezEeRXAn22hGuMdeB%2BLtvpjHjqx%2BqdXZfXK6ul20rHK%2B2%2FDjxTFhIwKwLoiZEbJ2Nb%2BOFvnVH3TtUYbzy35ScveVvCJbFZbUMGXs7yzKURWC0OsHzjdqn18a1rMzwvWDP2xBsZ7D7GVyclZnnzyHe94cnLZ0Xhh8vfwR1%2FU1s4%2BiSj880rLTYrelzeXsxyr0lpAFIyyNd1hXuS6XEeYepmvc6q%2B6c%2BBVYLSKqVyTc9ls3ofVKxeyjrJrBeC9c2mWD0%2B3CQKAmJpPrNVJlisDlFveWJiuUfE%2BGv4B804ryCWCsXSmBfzjf3%2Fbiku1Y2k8pzZ8ABv4wwNFBGlwF4HTYFtDuFks1qDyvNp6yRzq6pvlm%2Fe6ip7uzTs7NFlTGKkTNmzIgKNBCIWbXg6oGA6bclrngJbG9gYZ2VUiNEVh96sCCmdwYQnMCpUmJtC4YB7IRz67kneC5Ent5ont5ont5ont5pbzZNbzZNbzZNbzZNbXZhaiIPcagtRii5ljQsYJy%2B4rnn3dlGkNzH4KFomHIbz0liR9T8fKF%2BcmlqUnMcdA7qUKXt0xNqAbZgeWu3%2FwFfRz4%2BQKa2rLUOTAYoV0%2FK0tg1qceFu7SzMi58i4Ul2i6a9VUzYIWiimdnqm7%2Fu8amv3XPna5LzHEFjck6C9P7kvZrRhICBhVZFNPYw%2BnmYWNzSGH7lGjR6yrhW47OwJbfxLOm53%2FspZhX4w8AFcXTDcJh1pn7jDRAL3viNqY7RK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<h1 class="title">
Stratified random sampling with dplr</h1>
<h4 class="author">
<em>Matthew E. Aiello-Lammens</em></h4>
<h4 class="date">
<em>July 10, 2014</em></h4>
</div>
<div class="section level4" id="setup">
<h4>
Setup</h4>
Let’s say I have a number of sample units for which I have observed some characteristic(s) at two time-points. In my specific case, I have species abundance data for 120 plots in 1992 and 2011. Using these data, I calculated the species turn-over between the two time points for each plot. I then shuffled the 2011 plots, leading to random pairing of plots between the two time points, and recalculated the turn-over.<br />
There are many cases in which we may want to do something similar to this, and many non-parametric randomization methods use a similar setup. The particular problem I faced is that the plots were stratified into broad vegetation types, Fynbos, Thicket, and Grassland. When shuffling the 2011 plots, I wanted to shuffle plots <em>only within</em> their vegetation type. I thought up of a number of complicated ways to write a function to do this, and even started coding one up. Then I thought about how I could use <code>dplyr</code> to carry out stratified random sampling. Here’s an example of how it works.<br />
</div>
<div class="section level4" id="make-a-data-set">
<h4>
Make a data set</h4>
Here is a sample data set including 20 plots (p1, …, p20), randomly assigned into one of three categories. I’ve printed out the data set, since it’s small.<br />
<pre class="r"><code>## Load dplyr
require( dplyr )</code></pre>
<pre><code>## Loading required package: dplyr
##
## Attaching package: 'dplyr'
##
## The following objects are masked from 'package:stats':
##
## filter, lag
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union</code></pre>
<pre class="r"><code>## Make data.frame
df <- data.frame( plot = paste( "p", 1:20, sep = "" ),
category = sample( x = letters[1:3], size = 20, replace = TRUE ),
stringsAsFactors = FALSE )
## Print data.frame, arranged by category
print( arrange( df, category ) )</code></pre>
<pre><code>## plot category
## 1 p3 a
## 2 p8 a
## 3 p12 a
## 4 p1 b
## 5 p2 b
## 6 p4 b
## 7 p5 b
## 8 p9 b
## 9 p15 b
## 10 p17 b
## 11 p19 b
## 12 p20 b
## 13 p6 c
## 14 p7 c
## 15 p10 c
## 16 p11 c
## 17 p13 c
## 18 p14 c
## 19 p16 c
## 20 p18 c</code></pre>
</div>
<div class="section level4" id="simple-shuffle">
<h4>
Simple shuffle</h4>
Shuffling plots, disregarding their category classification, is easy - just use <code>sample</code>. Below I’ve printed out the shuffled paired-plots.<br />
<pre class="r"><code>## Shuffle plots
plots_shuffled <- sample( df$plot )
## Print plots and plots_shuffled together
print( cbind( df$plot, plots_shuffled ) )</code></pre>
<pre><code>## plots_shuffled
## [1,] "p1" "p5"
## [2,] "p2" "p13"
## [3,] "p3" "p16"
## [4,] "p4" "p14"
## [5,] "p5" "p1"
## [6,] "p6" "p3"
## [7,] "p7" "p20"
## [8,] "p8" "p2"
## [9,] "p9" "p11"
## [10,] "p10" "p19"
## [11,] "p11" "p10"
## [12,] "p12" "p17"
## [13,] "p13" "p9"
## [14,] "p14" "p7"
## [15,] "p15" "p6"
## [16,] "p16" "p8"
## [17,] "p17" "p15"
## [18,] "p18" "p4"
## [19,] "p19" "p12"
## [20,] "p20" "p18"</code></pre>
</div>
<div class="section level4" id="stratified-random-sampling-shuffling">
<h4>
Stratified random sampling (shuffling)</h4>
But what if we want to account for the category classification? Here’s how I used <code>dplyr</code> to perform stratified random sampling.<br />
<pre class="r"><code>## Use dplyr group_by and mutate to randomly sample within category
df <-
group_by( df, category ) %.%
mutate( strat_rsamp = sample( plot ) )
print( arrange( df, category ) )</code></pre>
<pre><code>## Source: local data frame [20 x 3]
## Groups: category
##
## plot category strat_rsamp
## 1 p3 a p12
## 2 p8 a p3
## 3 p12 a p8
## 4 p1 b p5
## 5 p2 b p20
## 6 p4 b p9
## 7 p5 b p15
## 8 p9 b p17
## 9 p15 b p1
## 10 p17 b p2
## 11 p19 b p4
## 12 p20 b p19
## 13 p6 c p11
## 14 p7 c p14
## 15 p10 c p7
## 16 p11 c p10
## 17 p13 c p16
## 18 p14 c p18
## 19 p16 c p13
## 20 p18 c p6</code></pre>
We could also return just a vector of the shuffled samples, without the data.frame. Convenient, but not very pretty code-wise<br />
<pre class="r"><code>( group_by( df, category ) %.%
mutate( strat_rsamp = sample( plot ) ) )$strat_rsamp</code></pre>
<pre><code>## [1] "p5" "p20" "p8" "p9" "p15" "p16" "p11" "p3" "p19" "p18" "p14"
## [12] "p12" "p13" "p10" "p4" "p6" "p1" "p7" "p17" "p2"</code></pre>
</div>
<div class="section level4" id="conclusion">
<h4>
Conclusion</h4>
There you have it - stratified random sampling. There may be an even easier way to do this (perhaps I missed a function or didn’t dive into <code>sample</code> enough?), but this seems pretty easy to me. Thanks <code>dplyr</code>!<br />
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Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com1tag:blogger.com,1999:blog-1866259608202514289.post-79723763672885520842014-06-21T14:22:00.003-07:002014-06-21T14:22:35.029-07:00Difficulties of opportunistic field dataIt seems that every time I work with field data, both data I collected and data I have been given to analyze, I come across a few common problems. There are usually transcription errors to deal with, which can be easy to handle when I have access to the original data sheets. There are outliers to detect, some sleuthing to be done to determine if "this tree really is 40 meters tall? or 4 meters tall?" And other similar problems, mostly due to little mistakes made here and there. But a problem I've been thinking about recently is how to deal with opportunistic field data.<br />
<br />
Since, as far as I know, I just made this term up, let me describe what I mean. Opportunistic data are data collected piecemeal while collecting the data you have planned to collect. Or, they are data that "add information" but are not consistently collected at every site you visit. For example, when I ran my first transects to collect size and reproductive trait data for Glossy buckthorn I noticed that many plants appeared to have been browsed. Based on my reading prior to my field work, I was confident that buckthorn wasn't browsed by the native fauna, so I wasn't planning on collecting this type of information. However, I thought "hey, I should make a record when a plant looks like it's been chewed on". But I didn't make it uniform, I didn't add it to the data sheet as another column (the data sheets were already printed out and didn't have space for an extra column!). I just committed to commenting on it in the "Notes" column. At some point I also started noting whether a plant was damaged or not, also in the "Notes" column. By the time I got to transcribing the data into CSV files, I really couldn't distinguish damage, from browsing, from failure to make a note of either. I was left with data for some plants, and not really knowing if plants that weren't noted were free from damage/ browsing, or unobserved for damage/browsing.<br />
<br />
Perhaps the biggest problem I had is that if I started recording a piece of information in the way I described above, I wasn't really as dedicated to it as I was to the data I originally set out to collect. As another example, I have photos of some of my seedling plots, but not the ones that I thought, "oh, there aren't that many here. I'll note the number and that will be fine". This might seem like an action taken out of laziness, but really I think data collection involves constant triage. "I need to measure X number of plants. This extra information is not as important as achieving that goal." In the end, I collected plenty of incomplete data during my field work, mostly as observations jotted down as notes, which never saw any type of formal analysis. However, these notes were important to return to when I was thinking about my system while sitting in my office. "Oh that's right, there was a breakout of oat crown rust in some of those areas that seemed to affect fruit counts on some of my plants. Disease may play a role in the population dynamics of this system." Now I'm working with data sets collected by others, that include similar incomplete pieces of information. As someone new to the system, I'm gaining insight from some of this information, but it's hard not to look at some of it and think "if we only had quantitative measures of soil depth for the full data set, we'd be able to say so much more!"<br />
<br />
I'm sure I'll continue to collect opportunistic data in the future. If I didn't I wouldn't really be doing my job of observing patterns in nature. Also, I'd like to delve deeper into analysis methods that can be used with these data. Based on conversations I've had with colleagues in the past, I know that we need not simply shelve data because it's not consistent. But ultimately, I do hope that the next time I'm in the field collecting and something interesting comes up, I'll think, "I should take care in collecting that information, I'm going to want that information!"Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-17433319105641740992014-04-10T04:45:00.001-07:002014-04-10T04:45:38.245-07:00Completing my PhD (whilst working as a Post Doc)Just over a week ago I defended my PhD. Almost 10 months ago I started my Post Doc. This shuffling of the order in which one "should" progress is not uncommon. I know at least a few other people who started their post doc, then went back to their PhD institution to defend. About four weeks ago, as I was finishing up my dissertation to send it off to my committee, I would say that I wasn't sure it was a good idea to take a post doc before you finish. The past 10 months have certainly been challenging. Going into it, I figured that I could probably work between 60 and 80 hours a week. After all, there are so many hours in the day. Start my post doc work at 7 AM, finish up around 4 PM, that still leaves me 6 to 7 hours of work time before I need to go to sleep. I quickly realized that was pretty naive. Perhaps some can work that hard for extended periods of time, but likely not many (as this post at Dynamic Ecology suggests <a href="http://bit.ly/1kD6KzG">http://bit.ly/1kD6KzG</a>). This meant that it took me longer to complete my dissertation than I initially anticipated. But now, looking through the rose tinted glasses that come with a successful defense, it's easy to think, "oh yes, this was definitely a good idea". So, I thought I might list a few pros and cons, based on my experience.<br />
<br />
Pros:<br />
* My post doc is in a lab I had been following for some time, focusing on research that is incredibly interesting to me, with excellent colleagues - hard to beat that.<br />
* I work close enough to home, in a flexible enough environment, to partially solve the two body problem. (My wife has a faculty position at a medical school on Long Island. We don't want to live separately and I would never ask her to leave her position so I can take a three year temporary position.)<br />
* I am going to get to go to the Cape Floristic Region of South Africa! How cool is that?<br />
* Working on my post doc gave me a wider view of the field of plant ecology, which helped me frame my PhD work as I was finishing up. In general, there was a great deal of reciprocal transfer of knowledge (in my own head) between my post doc project and my PhD work.<br />
<br />
Cons:<br />
* No free time, or almost none. I turned down a lot of invitations from family and friends over the past ten months, and always felt guilty when I didn't.<br />
* As I said above, the time to completion for my PhD was extended. This was perhaps the greatest challenge.<br />
* Hours wise, I'm pretty confident that I was fulfilling my post doc obligations, but I wasn't as efficient or as productive as I wanted to be. In part I think this was because my intellectual energy was split,<br />
* I did not publish my chapters as I completed them, leaving me with three unpublished dissertation chapters (but perhaps it will be nice to have manuscripts almost ready to submit over the next year.)<br />
<br />
Where to now? I'm excited to devote most of my energy to my post doc work (I have to reserve some to wrap up side projects that I let languish), and I'm optimistic about what I can accomplish in the next year and a half. I wouldn't be in this position if I had waited until I was finished to take a post doc. With that said, I have every intention on giving my future students a realistic portrayal of what this decision can feel like. And given the number of finishing PhD students who start their post docs early, I assume they too will do what they think is best for them at that time, just like I did.Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com1tag:blogger.com,1999:blog-1866259608202514289.post-10835307382824976252013-09-17T13:29:00.000-07:002013-09-17T13:29:50.530-07:00Examining whether the order of scaling and log-transformation matters<!-- saved from url=(0014)about:internet -->
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The following question has come up as I continue to explore datasets
related to my current PostDoc work.
<em>Given a dateset that requires log-transformation in order
to fit a normal distribution, does it matter if I log-transform
then scale the data versus scale then log-transform?</em><br />
First, let's get some data that could be considered as needing
log-transformation
to meet the assumptions of normality. I downloaded the dataset
of plant specific leaf area (SLA) from Reich 1999, as used and cited in
Logan 2012, from the websit associated with Logan 2012
<a href="http://users.monash.edu.au/~murray/BDAR/">here</a>.<br />
<pre><code class="r">## Require packages
require(ggplot2)
</code></pre>
<pre><code>## Loading required package: ggplot2
</code></pre>
<pre><code class="r">require(reshape2)
</code></pre>
<pre><code>## Loading required package: reshape2
</code></pre>
<pre><code class="r">
## Read in the data
LeafArea <- read.csv("~/Google Drive/Professional/Short-R-Examples/reich.csv")
## Quick peek at the data
head(LeafArea)
</code></pre>
<pre><code>## LOCATION FUNCTION LEAFAREA
## 1 Newmex Shrub 105.0
## 2 Newmex Tree 124.0
## 3 Newmex Tree 83.8
## 4 Newmex Shrub 39.7
## 5 Newmex Shrub 51.2
## 6 Newmex Shrub 66.0
</code></pre>
<pre><code class="r">
## Make a histogram of the LeafArea
qplot(LEAFAREA, data = LeafArea, geom = "histogram", binwidth = 10)
</code></pre>
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" /> <br />
<pre><code class="r">
## Now look at this same data, log10 transformed
qplot(log10(LEAFAREA), data = LeafArea, geom = "histogram")
</code></pre>
<pre><code>## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust
## this.
</code></pre>
<pre><code>## Warning: position_stack requires constant width: output may be incorrect
</code></pre>
<img alt="plot of chunk unnamed-chunk-1" 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" /> <br />
Ok, now lets see how things look when I scale, then log10 tranform,
versus log10 transform, then scale.<br />
<pre><code class="r">## First scale the log transform
LeafArea$ScaleLog <- log10(scale(LeafArea$LEAFAREA))
</code></pre>
<pre><code>## Warning: NaNs produced
</code></pre>
<pre><code class="r">
## Next Lof then scale
LeafArea$LogScale <- scale(log10(LeafArea$LEAFAREA))
## Now plot these two
LeafArea_m <- melt(data = LeafArea, id.vars = c(1:3))
p <- ggplot(LeafArea_m, aes(x = value, colour = variable)) + geom_density()
p
</code></pre>
<pre><code>## Warning: Removed 33 rows containing non-finite values (stat_density).
</code></pre>
<pre><code>## Warning: Removed 1 rows containing non-finite values (stat_density).
</code></pre>
<img alt="plot of chunk unnamed-chunk-2" 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" /> <br />
Defnitely different in the density plots. What about histograms?<br />
<pre><code class="r">h <- ggplot(LeafArea_m, aes(x = value, fill = variable)) + geom_histogram(position = "identity",
alpha = 0.4)
h
</code></pre>
<pre><code>## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust
## this.
</code></pre>
<img alt="plot of chunk unnamed-chunk-3" 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IBPUGfSFAQQQAABBKwAAd5KMEcAAQQQQCBBAgT4BHUmTUEAAQQQQMAKEOCtBHMEEEAAAQQSJECAT1Bn0hQEEEAAAQSsAAHeSjBHAAEEEEAgQQIE+AR1Jk1BAAEEEEDAChDgrQRzBBBAAAEEEiRAgE9QZ9IUBBBAAAEErAAB3kowRwABBBBAIEECBPgEdSZNQQABBBBAwAoQ4K0EcwQQQAABBBIkQIBPUGfSFAQQQAABBKwAAd5KMEcAAQQQQCBBAgT4BHUmTUEAAQQQQMAKEOCtBHMEEEAAAQQSJECAT1Bn0hQEEEAAAQSsAAHeSjBHAAEEEEAgQQIE+AR1Jk1BAAEEEEDAChDgrQRzBBBAAAEEEiRAgE9QZ9IUBBBAAAEErAAB3kowRwABBBBAIEECBPgEdSZNQQABBBBAwAoQ4K0EcwQQQAABBBIkQIBPUGfSFAQQQAABBKwAAd5KMEcAAQQQQCBBAgT4BHUmTUEAAQQQQMAKEOCtBHMEEEAAAQQSJECAT1Bn0hQEEEAAAQSsAAHeSjBHAAEEEEAgQQIE+AR1Jk1BAAEEEEDAChDgrQRzBBBAAAEEEiRAgE9QZ9IUBBBAAAEErAAB3kowRwABBBBAIEECBPgEdSZNQQABBBBAwAoQ4K0EcwQQQAABBBIkUOxbW1q0aJFSpeLiYmm8LiVBhha03KKioqyVnY02a3tLSkqy0mYtu6CgIEO92Xy2ZWVlUldX13yiEFvVMN1k2xqk3DiPBa2blh1nnunaardn828539pcWFgopaWlsR7Xth+Z546AdwG+oqIiRU/fiBqvS0mQoQX949A3hWyUna0219TUSFVVlfM2q/PfNm8xZafrznEdy9Mlqd/+xPoN9a+betFpR6UM3/m5ora2tqkkoderYbpJP9BocA9SbpzHoJap/+LMM11b7fZsHddabr79LetxVVlZmdF+1mOYyW8BLtH73T/UDgEEEEAAgUgCBPhIbOyEAAIIIICA3wIEeL/7h9ohgAACCCAQSYAAH4mNnRBAAAEEEPBbgADvd/9QOwQQQAABBCIJEOAjsbETAggggAACfgsQ4P3uH2qHAAIIIIBAJAECfCQ2dkIAAQQQQMBvAQK83/1D7RBAAAEEEIgkQICPxMZOCCCAAAII+C1AgPe7f6gdAggggAACkQQI8JHY2AkBBBBAAAG/BQjwfvcPtUMAAQQQQCCSAAE+Ehs7IYAAAggg4LcAAd7v/qF2CCCAAAIIRBIgwEdiYycEEEAAAQT8FiDA+90/1A4BBBBAAIFIAgT4SGzshAACCCCAgN8CBHi/+4faIYAAAgggEEmAAB+JjZ0QQAABBBDwW4AA73f/UDsEEEAAAQQiCRDgI7GxEwIIIIAAAn4LEOD97h9qhwACCCCAQCQBAnwkNnZCAAEEEEDAbwECvN/9Q+0QQAABBBCIJECAj8TGTggggAACCPgtQID3u3+oHQIIIIAAApEECPCR2NgJAQQQQAABvwUI8H73D7VDAAEEEEAgkgABPhIbOyGAAAIIIOC3AAHe7/6hdggggAACCEQSIMBHYmMnBBBAAAEE/BYgwPvdP9QOAQQQQACBSAIE+Ehs7IQAAggggIDfAgR4v/uH2iGAAAIIIBBJgAAfiY2dEEAAAQQQ8FuAAO93/1A7BBBAAAEEIgkQ4COxsRMCCCCAAAJ+CxDg/e4faocAAggggEAkAQJ8JDZ2QgABBBBAwG8BArzf/UPtEEAAAQQQiCRAgI/Exk4IIIAAAgj4LUCA97t/qB0CCCCAAAKRBAjwkdjYCQEEEEAAAb8FCPB+9w+1QwABBBBAIJIAAT4SGzshgAACCCDgtwAB3u/+oXYIIIAAAghEEiDAR2JjJwQQQAABBPwWIMD73T/UDgEEEEAAgUgCBPhIbOyEAAIIIICA3wIEeL/7h9ohgAACCCAQSYAAH4mNnRBAAAEEEPBbgADvd/9QOwQQQAABBCIJEOAjsbETAggggAACfgs4CfAffvihPPzww35LUDsEEEAAAQQSJJDxAP/dd9/JU089JVu2bEkQG01BAAEEEEDAb4HiTFdv5syZMnLkSFm8ePEuRX399ddSVVWVsr60tDRlubi4WBqvS0mQoYWioiIpLCzMStnZarO2NxtlFxQUGGstO90U5lgIkp+Wp3nW1tamKzrw9iDlqnVdXZ1pd7qMw7Q5XV4lJSWi3nHmma5Muz0bx5aWrX/L+dZmbW+mvbUMJr8F0r+jfo/6v/7669KjRw/Zc889d5vLrFmzZM2aNfXbjj76aBk2bFj9sr7Qg0jfCF1P+gacrTeFbLVZ3wj1TaFNmzZpuWteeTltmjAJWlQHC7BdBvQPnG3bHZWB0nbq1ClQuoe+WhkoXdu2bQOlC5qoS5cuQZOmTafHlvZznHmmLfQ/CbJ1XOvfsk5lZWX/qYm7WbbarH3cvn37jL53VldXu4OkpEgCGQvwemn+6aeflhEjRsiSJUtk3bp1ot/F77vvvvUVveiii+pf6wtNs3Jl6ptoixYtpKKiIiWdi4V27dqJnu1onVxP2Wpz165dZdu2beZfujaXbdiQLkng7fomuKOkTGpqatLu0/j4aG6HDQHqqMF99erVgc7gg+TXXH0abtM3YP3gGuTKwcoYT5Q0yGmbV61a1bA6Tl5n67ju0KGD+bAeZ/8FBctWm7t37y6bNm2S7du3B61q6HR6DPfs2TP0fuzgTiBjAV47f8yYMaYl+klPl7NxWdAdJSUhgAACCCDgj0DGAryeKRxyyCGmpd9++618/PHH0rt3b39aTk0QQAABBBBIsEDG76JXO730e8EFFySYkaYhgAACCCDgl4CTAO9Xk6kNAggggAACyRcgwCe/j2khAggggEAeChDg87DTaTICCCCQqwInnHCC/PnPf26y+kceeaTcd999Kdt1oDW9B+yf//xnyvqkL2TsJrukw9E+BBBAAIH4BfTno/rT6JYtW6ZkvmPHDjOWwSWXXGLGV7EbKysrUwbK+uqrr8xPBPVnt/rrLZ3056ifffZZyk+u9dddQQalsuXk4pwz+FzsNeqMAAII5LDAMcccU3/j9Zw5c8ygPPq7/dtuu80MwqRjFxxxxBGiQf3888+XoUOHSnl5udx6660yZcoUmT17tmn9T3/6U5O+devW8utf/7pe5JlnnpF+/frJAQccIK+++mr9en2hY31MmDBBOnbsKHo14IMPPkjZnqQFAnySepO2IIAAAjkg8POf/1weeeQRMxDPX/7yFznppJNMkNdA/cILL4gGaA3My5cvNwNgffrpp+by+tlnny165q1n5/qB4KCDDhLddtVVV8mDDz6Y0vK3337bBPlbbrklZf3f/vY3WbBggeiZ/t577y133XVXyvYkLXCJPkm9SVsQQACBHBA45ZRT5Fe/+pVMmzZN5s6dK/Pnzze1Xrt2rZx55pmyxx57mOWtW7ea+eDBg+XAAw9MaZleXtezbx3eXM/4bVpNpGf/OuT2UUcdJb/97W9T9tMPEOvXr5fhw4ebS/a2rJRECVkgwCekI2kGAgggkCsCOhDaOeecI1dffbX06dNHDj/8cDMsuC7r2bsOtTtkyJD6sfR1yN/G03PPPSczZswwwVpvqlu6dGl9khdffFEuvvhi+fvf/y56013DST8svPzyy+YKgQ6nnuSJS/RJ7l3ahgACCHgqoN+t693t5513nqmhPiNh7Nixot+rT5482XznrjfGNTVp4NY74/v27SvPPvuseTKpfcaCPkukV69esmzZMvnNb36TksX48eOlW7duZgA23da5c+eU7Ula4Aw+Sb1JWxBAAIEcEdCb4Bo/KfSJJ54wl9obPtFSL9k3nN566636Rf2OXi/NN0z/ySefmO16J75eKdCHWenUsKx//OMf5sNF3E9+NAV59L9IZ/C7e8Kajje/u/UetZWqIIAAAgh4LtAwWAepalPp9bK+De67yyfpwV3bHCrA6yci/WdvTrDL+mhY/W2i3p3IhAACCCCAAALZFwgV4PU3gzr4wHvvvWfm+lr/6Seo1157TQ477LDst4gaIIAAAggggICE+g5e70zU3x/qbxEb/uawsLDQjCSEJwIIIIAAAukEKv/+khldLl265raXHX1Ms5fgm9s3X7aFCvD6fYb+9vDhhx/OFx/aiQACCCAQs4AOHauj1EWdNBaVRd05j/YLdYneuugIQzqAwIABA2Tfffet/6e/S2RCAAEEEEAAgewLhDqDt9U999xz5Re/+IW52a7hYP06YAETAggggAACCGRfIHSA198Sbt682Yz929xPELLfNGqAAAIIIIBA/gqEvkSvQf24444zYwjrY/qYEEAAAQQQQMA/gdABXpugwwtOnDhRdGjB/v371//jO3j/OpgaIYAAAkkX0NHrjj76aPN4WB1r/sknnwzV5Mcee0zuueeeJvfRp92tXr26ye2+bgh9iV4bok/nufbaa3dpE9/B70LCCgQQQACBDAtcfvnlcsUVV8jxxx8va9asMU+e02fO21Hu9I59Hba24aQnqnY0Ox3uVh8/ayf9Obj+/Nt+Da1j3Ou63U1VVVVSUlKSsml361ISOFqIFOCvvPJK+frrr3epoj5399hjj91lPSsQQAABBBDIlEB5ebm89NJLMmjQIOnZs6e8++67ZhC27du3y+mnn26Cs36lPH36dNGzfT1B7dq1q3z44YcyZ86clGrdeuut5klz+qFgwoQJcvLJJ6dstwsfffSReSiOfnBo37693H777eaxtRdeeKF5jr0+7Ob11183A8PZfVzPIwV4PYO337/rXEe200schxxyiOv6Ux4CCCCAQJ4L3HHHHXLzzTeLjraqN4Lrs+b1a+T777/fXLb//e9/L4sXLzbPj9cz9Yceekj23ntvueyyy8yz6IuKiozghg0bzJPpnn/+eTMQz8iRI5sM8FOnTpUpU6aYR93edttt8uijj8rAgQNl5cqV5sOGPgnvgAMOyGrPRArwP/zhD1MqPWLECPnqq69Mo0499dSUbSwggAACCCCQKQEN6HqSef3115t/n3/+uTlr1/vD9Gx9+PDhpmgbt+bPny8XXHCBuWSvAV0fN2sD/IIFC2TFihWi37nrpJfed3e1WrfNmzdPbrrpJn1phmnXDxh6Nn/wwQebdfvss4+5SmAWsvS/SDfZNa6rAitqw+8wGqdhGQEEEEAAgbgF9HtyHZvlgw8+MFnrpXEN2vbBaG+++aZZr8Fbz7ovvfRSc0PdU089Zc64G363PmzYMOnRo4foNn10rT5fRW8m392k25YsWWI2LVq0SPQeNB0ATgeC05iol//1KavZnCKdwev37N98842ptzZEHxOrn3TuvPPObLaFshFAAAEE8lBg2rRpMn78eGnXrp3o9+4afDXY6s1us2fPltNOO808N/7ee++VjRs3yi9/+Uvp2LGjWac30NkbxLt162buIxs7dqz53l7P/u0NdPrz8NLSUqM7adIk8/27vdlcT25nzpwpnTt3lnHjxsno0aOld+/eZjmb3REpwN94440p4wjrE+X222+/+sZns0GUjQACCCCQXwJ6+f3tt982P+HW58DboKyX3h944AFzNq/rdbrqqqvMhwBN03AkVit2zTXXSHV1tVm02+2Zuk1j53qmr49Lb9WqlVm1du1a6dKli8ydO9ecBL/zzjs2aVbmkQK83kynDwvQy/J6k51eDtGfFDAhgAACCCCQLQH7s7fG5dvgbtfrSWlzkw3szaWx22xw12U9g9enrs6YMUO2bdsmenNfNqdIAV5/HqA30/373/+W1q1bm087f/rTn8yNC9lsDGUjgAACCCCQTYG77747m8WnlB3ptPv888+XE0880VyCWL9+vbmbUH869/7776dkzgICCCCAAAK7COjP0nY+evx7/dslU1Y0Foh0Bq+BXH8naG84+NGPfmQGBFi4cKG5K7FxISwjgAACCCBgBR7/QV/7MvL8Z5H3zJ8dIwV4vaFu6dKlMnTo0HqpV155xfz8oH4FLxBAAAEEENiNgP40TUeKizrZIWSj7p8v+0UK8DoUn/5UTn9CoKMB6dl8hw4dZMyYMfniRjsRQAABBBDwWiDSd/B6g52O+3vooYeay/T6swP9cb/9aYLXLaZyCCCAAAII5IFApDP4zZs3m8EDbrjhBjPEnw77p5ftG16yzwM7mogAAggggIC3ApHO4PUueh25R38Lr5M+h/eMM84QvaOeCQEEEEAAAQSyLxApwOtTefTpPfaSvAb3s88+e5fH7mW/edQAAQQQQCDpAvpwmNWrV0dupj6URk9U9elvgwcPlieffDJUXvo01XvuuSfUPi4SRwrwbdq0qR9k31ZSB/LXcYCZEEAAAQQQcCmg48k3fGhMw7J1PPrGU+N1l19+uVxxxRWiQ8vqU+J0rPqtW7fW77a7O/63bNlSv13TNnzYmtZFn9OS7SnSd/C/+93v5JhjjpEhQ4ZIz5495eWXX5YBAwZwF322e5PyEUAAAQSMgI64OnnyZPMI1/bt28vtt99ufu2lvwJbvny56FPnXn/9dfOo2fLycnPj+KBBg0xMe/fdd0WHs9UH15x++unmw4MOyz59+nTzCFp9yEzXrl3NE+PmzJmTIn7rrbeam871Q8GECROafJ58yk4ZWoh0Bq+XQ9544w0566yzzJ30OsCNfuoJM35vhtpDtggggAACCJhHw06ZMsU8+lWf0f7oo4+KxqqVK1eaYH7dddfJF198YaT0K2e9Mn3CCSfI/vvvbx4Vqw+quf/++81l+2eeecaMK6+PpF2zZo089NBDMmvWLNEnzOnz5e2kz5d/9tlnzZPl9EE0d911l92UlXmkM3itab9+/cy/rNSaQhFAAAEEEGhGQE86b7rpJpNCHx978803m7N5DfY67bPPPuYsXC+lv/fee3L99debf/oQNT1r79+/vzlb1/FedNIn1umkAV1/OVZWViYa0PVha/phQCf9qnrFihWiJ8E66X1qX3/9tXTv3t0su/5fpDN415WkPAQQQAABBMIIaFC3j3ldtGiReea7PiNex2zRoP7hhx/Kt99+Kzoq3rnnnit6dq6TXrrXoF1RUWEGc3vzzTfNeg3eU6dONSO26g11eoY+cODAlO/+hw0bJj169DDbnnjiCfNc+k6dOpn9s/G/yGfw2agsZSKAAAIIILA7Ab1cbp+PMmnSJPP9u35XrpPeADdz5kzzONdx48bJ6NGjpXfv3mZZt0+bNk3Gjx9vbhTX7931w4F+GNCb8WbPni2nnXaauenu3nvvlY0bN5qb8Dp27GjW6Q1+ffr00WykW7duZpTXsWPHmsCvZ//212YmgeP/EeAdg1McAggggEC8AvZMvXGuepb93XffiX1m+9q1a6VLly4yd+5c8zRUvWteJ738/vbbb4veGa/PjrdBWS+9P/DAA+Zs3j5TXkdu1Q8BmmZ3951dc8015hHqmu/utut6VxMB3pU05SCAAAIIOBewwV0L7ty5s7z44osyY8YM2bZtm7lxrmGF2rZt23Cx/rUN7naF3mHf3JTtwG7rRoC3EswRQAABBBIvcPfddye+jbaB3GRnJZgjgAACCCCQIAHO4BPUmTQFAQQQyAWBwsJC8113LtQ1l+tIgM/l3qPuCCCAQA4KnN1r7xysde5VmUv0uddn1BgBBBBAAIG0AgT4tEQkQAABBBBAIPcECPC512fUGAEEEEAAgbQCBPi0RCRAAAEEEEAg9wS8u8lO765sOOk4wY3XNdyeqddabjbL9r3NmaifeqebwpQbNG3c6dK1QbfbtgYpO0iaIGVqGpuXnQfdL4502fx7ymbZ2bDW/sp0m+0xHMexQR6ZEfAuwDceAUj/OBqvi4Ni1tp1zWZTtr3CvBmOat2q2XSZ2JipNqerq/7Bzlq8KOXhCU3tc1qjD2JNpXu88P+fstTUdrteyy4oTB/gn9q4ye6Sdh70jfXJDRvNwyfSZRg0v3T56HbNq/DTT6Ru53/ppuKuXdIlCbxdh95U60z8TaWrRLaOay0339qs7dW+zkY/pzsO2O5OwLsAX1lZmdJ6/eNsvC4lQcSF6urqZvfUcYb1jyQTZTdb8M6NmWpzunJra2ulrrZOamtq0yWV6prm/WwGtUXpg/ZOaCkqDFhumn6z5YaZ19TUiLbd5WQeL6neO59qlW6K8xjUY1rLjDPPdPW327N1XGv/5tvfsvaxvsdlsp/NMWw7l7mXAqnXw72sIpVCAAEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcECPA50ElUEQEEEEAAgbACBPiwYqRHAAEEEEAgBwQI8DnQSVQRAQQQQACBsAIE+LBipEcAAQQQQCAHBAjwOdBJVBEBBBBAAIGwAgT4sGKkRwABBBBAIAcEijNZxy1btsjcuXNl48aNsueee8qoUaOkuDijRWayOeSNAAIIIIBAzghk9Ax+/vz50rdvX5k0aZIBeeutt3IGhooigAACCCCQywIZPZ0ePny4tGnTxviUlJSYM/mGWHPmzJFNmzbVrxo0aJD069evfllfFBUV1eeRsuF7LrSprGo2By23sLBQOnfu3Gy6TGzMVJvT1bW0tFS0n7T8dFObwrJ0Scz2stpAyaSgsECKa9MfjmX/OZ6C5RosVatWrYIljDFVQUGB1JXtNKyrS5trnMegHtPav3HmmbYB/0mQzeNaqxDkuA7alqDpstVm/Ttu166dtG7dOmhVQ6erqakJvQ87uBVI/476PerTvn17s/dHH30kS5culUsvvTQlt+7du5uD0K5s2bKl7Nixwy6auR6oVVXNB+OUHQIuVFdXN5tS34B1alyfZneKaWOYNj/2zbeBSj29W9e06TTA19bWSs3Of+mm6gBpNI8aSX+RSKkLagtN2enKleUfpk1iE9T94H/syybnZTuDrL5R1QUItE1mEmGDBlqp1XLT7zzjiy/TJ9qZIkgf61dk2s++H9eBGhwwkVrr33M+tVmPa33fzMR7Z0B2knkgkNEAr+17//335emnn5YLL7xQNIA3nIYOHdpwUdatWyf6vX3DqUWLFlJRUdFwVSyv0+Wpbwj66btxfWIpPE0mYdqcrh22qCDt0P7RYJfuw4/mWVET7ENXdVGJrULTc7Xe+SYc9xlBVYDjRs9w9I1fP9i4nPTYKqqqDvTBIkg7tO5B+ljf+LWfg6SN2yPMcR1n2Wqtf8/51GY9rrdv327+xWnZMC917dSpU8NVvPZMIKMBftmyZfLCCy/IxRdfLNm4DOqZNdVBAAEEEEDAmUBGA/zMmTPN2eDtt99uGjRkyBAZOXKks8ZREAIIIIAAAvkqkNEAP2XKlHx1pd0IIIAAAghkVSD9HVBZrR6FI4AAAggggEAUAQJ8FDX2QQABBBBAwHMBArznHUT1EEAAAQQQiCJAgI+ixj4IIIAAAgh4LkCA97yDqB4CCCCAAAJRBAjwUdTYBwEEEEAAAc8FCPCedxDVQwABBBBAIIoAAT6KGvsggAACCCDguQAB3vMOonoIIIAAAghEESDAR1FjHwQQQAABBDwXIMB73kFUDwEEEEAAgSgCBPgoauyDAAIIIICA5wIEeM87iOohgAACCCAQRYAAH0WNfRBAAAEEEPBcgADveQdRPQQQQAABBKIIEOCjqLEPAggggAACngsQ4D3vIKqHAAIIIIBAFAECfBQ19kEAAQQQQMBzAQK85x1E9RBAAAEEEIgiQICPosY+CCCAAAIIeC5AgPe8g6geAggggAACUQQI8FHU2AcBBBBAAAHPBQjwnncQ1UMAAQQQQCCKAAE+ihr7IIAAAggg4LkAAd7zDqJ6CCCAAAIIRBEgwEdRYx8EEEAAAQQ8FyDAe95BVA8BBBBAAIEoAgT4KGrsgwACCCCAgOcCBHjPO4jqIYAAAgggEEWAAB9FjX0QQAABBBDwXIAA73kHUT0EEEAAAQSiCBDgo6ixDwIIIIAAAp4LEOA97yCqhwACCCCAQBQBAnwUNfZBAAEEEEDAcwECvOcdRPUQQAABBBCIIkCAj6LGPggggAACCHguQID3vIOoHgIIIIAAAlEECPBR1NgHAQQQQAABzwUI8J53ENVDAAEEEEAgigABPooa+yCAAAIIIOC5AAHe8w6ieggggAACCEQRIMBHUWMfBBBAAAEEPBcgwHveQVQPAQQQQACBKAIE+Chq7IMAAggggIDnAgR4zzuI6iGAAAIIIBBFgAAfRY19EEAAAQQQ8FyAAO95B1E9BBBAAAEEoggQ4KOosQ8CCCCAAAKeCxDgPe8gqocAAggggEAUAQJ8FDX2QQABBBBAwHMBArznHUT1EEAAAQQQiCJAgI+ixj4IIIAAAgh4LkCA97yDqB4CCCCAAAJRBIqj7JTJfVq0aJGSfXFxsTRel5Ig4kJJSUmzexYWFor+y0TZzRa8c2OYNqdrhy0rSDuKiopMm3WebioJ+NGwqCB9XlpWQUGBBCk3Xb1StqfpY5tWvevq6uyik7m2t1Cdg5QbsB1B+liPFy07SNq4IcIc13GWreXmW5v1vau0tNT5cR1nv5HX9xfwLsBXVFSktErfiBqvS0kQdeHjj5rds660RGoLCqVi4MBm09mNZW+8bl82O3/kB32b3a4b9U24qqoqbTqT9vPPAqX73wD5tdu6TWpra6WmpiZtno+kTWETpM9r57uvFO18QwpSrs010DxNH2seNW1ai2z7LlCgreq1T6BigyQyH2Z2Ogf5YBH0WPjfVavTFq3HVutNm2Xjxo1p047rWJ42jSZ4Yv2GQOl+sucemflbTlO6vodogM/I+0gzZatLmL/lZrIKtUn7Tf+OKysrM9rm2D+Qh2oliYMIBDwPC5IVaRBAAAEEEEDAFwECvC89QT0QQAABBBCIUYAAHyMmWSGAAAIIIOCLAAHel56gHggggAACCMQoQICPEZOsEEAAAQQQ8EWAAO9LT1APBBBAAAEEYhQgwMeISVYIIIAAAgj4IkCA96UnqAcCCCCAAAIxChDgY8QkKwQQQAABBHwRIMD70hPUAwEEEEAAgRgFCPAxYpIVAggggAACvggQ4H3pCeqBAAIIIIBAjAIE+BgxyQoBBBBAAAFfBAjwvvQE9UAAAQQQQCBGAQJ8jJhkhQACCCCAgC8CBHhfeoJ6IIAAAgggEKMAAT5GTLJCAAEEEEDAFwECvC89QT0QQAABBBCIUYAAHyMmWSGAAAIIIOCLAAHel56gHggggAACCMQoQICPEZOsEEAAAQQQ8EWAAO9LT1APBBBAAAEEYhQgwMeISVYIIIAAAgj4IkCA96UnqAcCCCCAAAIxChDgY8QkKwQQQAABBHwRIMD70hPUAwEEEEAAgRgFCPAxYpIVAggggAACvggQ4H3pCeqBAAIIIIBAjAIE+BgxyQoBBBBAAAFfBAjwvvQE9UAAAQQQQCBGAQJ8jJhkhQACCCCAgC8CBHhfeoJ6IIAAAgggEKMAAT5GTLJCAAEEEEDAFwECvC89QT0QQAABBBCIUYAAHyMmWSGAAAIIIOCLAAHel56gHggggAACCMQoQICPEZOsEEAAAQQQ8EWAAO9LT1APBBBAAAEEYhQgwMeISVYIIIAAAgj4IkCA96UnqAcCCCCAAAIxChDgY8QkKwQQQAABBHwRIMD70hPUAwEEEEAAgRgFCPAxYpIVAggggAACvggQ4H3pCeqBAAIIIIBAjAIE+BgxyQoBBBBAAAFfBAjwvvQE9UAAAQQQQCBGAQJ8jJhkhQACCCCAgC8CBHhfeoJ6IIAAAgggEKMAAT5GTLJCAAEEEEDAFwECvC89QT0QQAABBBCIUYAAHyMmWSGAAAIIIOCLAAHel56gHggggAACCMQoQICPEZOsEEAAAQQQ8EWAAO9LT1APBBBAAAEEYhQojjGvXbKqrq6Wxx9/XL755hvp16+fjBo1apc0rEAAAQQQQACB+AUyegY/f/586d69u0yePNkE+WXLlsXfAnJEAAEEEEAAgV0EMnoG/8knn8iZZ54pRUVFMnjwYFm+fLn079+/vhI7duyQ2tra+uWamhopKCioX9YXutx4XUqCqAuNymkqm6Blx5kuVJtjbodxCJhnU2Zh19f3uONyU+oZoOygfZySbxMLJq8AZerucZZrqxMkzyBpwtRP8wuap61nXPNslG3LdN1mW54tPy7DxvnYchqvZ9kfgYwG+I0bN0qrVq1Ma3W+bdu2lJbfcsst5szerhwzZowce+yxdjGj84t79Yo3/4D5XRpvqSKDD4o3xz7/E29+5Na0wAH7N70th7ZcGvDYz3aT2rVr57QK2XZp0aJFRttbWVmZ0fzJ/PsLZDTAt2zZUvQsvaSkRPRgaNOmTUqNr732Wqmrq6tft2HDBvnss8/ql/WFHqQVFRUp61ws6JuB1nvdunUuikspI1tt7tq1q/kQ1viDWErlMrCgZwKlpaXmWMlA9s1m2WtncPryyy9TriQ1u0NMG/XY0qtXetXK5VRWViadOnWSVatWuSzWlJWt47pDhw7myoG+v7iestVm/Wp006ZNsn379ow1Wa/M9uzZM2P5k/H3F8jod/B77bVXfcBesWKF9OjRI6XG+sZeWFhY/y9lIwsIIIAAAgggEFkgo2fwI0aMkFmzZsnChQvN2fDo0aMjV5QdEUAAAQQQQCC4QEYDfHl5uUycONFcntdLsEwIIIAAAggg4EYgo5fobRMI7laCOQIIIIAAAm4EnAR4N02hFAQQQAABBBCwAgR4K8EcAQQQQACBBAkQ4BPUmTQFAQQQQAABK0CAtxLMEUAAAQQQSJAAAT5BnUlTEEAAAQQQsAIEeCvBHAEEEEAAgQQJEOAT1Jk0BQEEEEAAAStAgLcSzBFAAAEEEEiQAAE+QZ1JUxBAAAEEELACBHgrwRwBBBBAAIEECRDgE9SZNAUBBBBAAAErQIC3EswRQAABBBBIkAABPkGdSVMQQAABBBCwAgR4K8EcAQQQQACBBAkQ4BPUmTQFAQQQQAABK1BQt3OyC8z/K7BgwQL55ptv5PTTT//vyoS/uu++++Tggw+WwYMHJ7yl/23elVdeKdddd520bt36vysT/GrFihUye/ZsueyyyxLcytSmzZs3TyoqKmTMmDGpGxK8dOedd8pRRx0lAwcOTHAraVo6Ac7gmxCqrq4W/ZdPU2VlpdTU1ORTk80bf21tbd60Wft3x44dedNebaj+HVdVVeVVm/VvOZ+O67zq3BCNJcCHwCIpAggggAACuSJAgM+VnqKeCCCAAAIIhBDgO/gmsNauXWsu3+61115NpEje6s8++0zKy8ulffv2yWtcEy167733pH///lJcXNxEimSt3rZtm6xatUr69u2brIY105pvv/3WfPW0xx57NJMqWZs+/fRT6dKli7Rt2zZZDaM1oQQI8KG4SIwAAggggEBuCHCJPjf6iVoigAACCCAQSoAAH4qLxAgggAACCOSGQH588RixL5555hn54osvzHfSxx13nHTs2DFiTrmzm/6k6O6775YJEyZIq1atcqfiIWuq7Xz88cfNWAf9+vWTUaNGhcwhN5PnS//a3vnXv/4lb775phQVFcmPf/xj6dOnj92U2PncuXPN+5Z+/37aaadJWVlZYttKw5oX4Ay+CZ/3339fNm/eLJMmTZKDDjpInnvuuSZSJme13ox0xx13yOeffy5JH/9o/vz50r17d5k8ebIJ8suWLUtORzbRknzqXyXQGwpffvll82H1jDPOMAP8JP241uNY233hhRdK165d5dVXX23iaGB1PggQ4Jvo5d69e8tJJ51ktpaUlMimTZuaSJmc1fqBZvz48ZIPdxt/8sknMmTIEHNmpyP3LV++PDkd2URL8ql/laC0tFTOP/988wsJ/ZWE/g0nPcDrL0J09M3t27fLypUrpUOHDk0cDazOBwEu0TfRyy1btjRbNm7cKDNnzpSf/OQnTaRMzup8uHxpe0v71X4FoXM960n6lE/9q32pH8z1n34tMWPGDBk5cqQUFubHOc2sWbNMgNc2M+WvAAG+Qd//8Y9/NMN47r///jJu3DjR38Lr+Oynnnqq9OrVq0HKZLxcvXq13HvvvaYxo0ePNme0yWhZ+lboBzgdslUDgA7r2aZNm/Q7kSLnBLRvp02bJnqfxZFHHplz9Y9a4Z/97Gfy1VdfmftMLr300qjZsF+OCxDgG3SgPnjETno57/777xf9Q0nqYDd6KV4ftJKPk/apDuyz3377iT6ApUePHvnIkOg261js+gF26NChcuihhya6rbZxb7zxhmzdulWGDx9uvo7gg6uVyc85Ab6Jfteb6vQy7l//+leTonPnzjJx4sQmUrM61wRGjBghehlz4cKF5ixer2AwJUtg6dKlovdabNmyRV566SXTuEsuuaT+q5lktfb/W3PAAQfIAw88IDqSnT5g54QTTkhiM2lTQAFGsgsIRbJkCuglXL0ZiwmBJAlwXCepN6O3hQAf3Y49EUAAAQQQ8FYgP24p9ZafiiGAAAIIIJAZAQJ8ZlzJFQEjoHcw33DDDWgggAACzgUI8M7JKRABBBBAAIHMCxDgM29MCQkR0OE/H3vssfrWzJkzx4yUpiv0zuUBAwaY39PrCHlLliypT2df6Fjo+pM8Ox1++OFmWGBdXrBggRx44IFm5LGTTz7ZjMFg0zFHAAEEoggQ4KOosU9eCujvqXVENDvpTyj199UfffSRXHTRRfLwww/Ll19+KYcccohMmTLFJquff/zxx2ZQHbvCLq9Zs0ZOPPFEufzyy+WDDz4wDze68cYbbTLmCCCAQCQBAnwkNnbKRwEd3fCVV14xv6vWsb5feOEFOeWUU6Rbt26yePFi0THtdSjUgQMHio4SGHSaPXu2DBo0SMaMGSOtW7eWa6+9VvRJhkwIIIDA9xFgoJvvo8e+eSWgD+446qijRB/Hqb+dP+yww8wjhPUBJo8++qj5pw900THfdRS1oJMOKfruu+/Kvvvum7KLPiyEEfZSSFhAAIEQAgT4EFgkRUCftvfEE0+YJ5Tpa50efPBB80AiHRlPh77V7+avvvrqXbD0meQ6/r1ONTU1sn79evNaL/3rh4V58+aZZf3fqlWr8uKpfvUN5gUCCMQuwCX62EnJMMkC+l35a6+9Ji/vfM742LFjTVM1UPft29cEdz2bnz59uhkmtLGDXspftGiRWa1PKNShRHU65phjzCX+t956yyzrd/vHH398qKsAZkf+hwACCDQQ4Ay+AQYvEUgnoN+RH3HEEeZmubZt25rkZ555pnlmgd4Fr0FbH1Ck389/9913KdnpWf0555wjegPdwQcfbD4QaAJ9st0f/vAHk69ektflqVOnmmfVp2TAAgIIIBBCgKFqQ2CRFIHmBNatWyfl5eXNPnNcPwDo0740XeNJL9vrA446derUeBPLCCCAQGgBAnxoMnZAAAEEEEDAfwG+g/e/j6ghAggggAACoQUI8KHJ2AEBBBBAAAH/BQjw/vcRNUQAAQQQQCC0AAE+NBk7IIAAAggg4L8AAd7/PqKGCCCAAAIIhBYgwIcmYwcEEEAAAQT8FyDA+99H1BABBBBAAIHQAgT40GTsgAACCCCAgP8C/wfDBBKI4PSS+gAAAABJRU5ErkJggg==" /> <br />
<hr />
Let's try this one more time with simulate data.<br />
<pre><code class="r"># Generate some random data that needs a log transform
Sample_Data <- exp(rnorm(n = 500, mean = 0, sd = 1))
# Plot the data before transform
qplot(x = Sample_Data, geom = "histogram", binwidth = 1)
</code></pre>
<img alt="plot of chunk unnamed-chunk-4" 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" /> <br />
<pre><code class="r"># Plot the data after transform
qplot(x = log(Sample_Data), geom = "histogram")
</code></pre>
<pre><code>## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust
## this.
</code></pre>
<img alt="plot of chunk unnamed-chunk-4" 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" /> <br />
<pre><code class="r">
# Now compare Scaling then log transform vs Log transform then scaling
Sample_Data_Test <- data.frame(ScaleLog = log(scale(Sample_Data)), LogScale = scale(log(Sample_Data)))
</code></pre>
<pre><code>## Warning: NaNs produced
</code></pre>
<pre><code class="r">
h <- ggplot(melt(Sample_Data_Test), aes(x = value, fill = variable)) + geom_histogram(position = "identity",
alpha = 0.4)
</code></pre>
<pre><code>## Using as id variables
</code></pre>
<pre><code class="r">h
</code></pre>
<pre><code>## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust
## this.
</code></pre>
<img alt="plot of chunk unnamed-chunk-4" 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" /> <br />
I'm not sure what to make of this. It's clear that the order of
scaling and log transforming matters. However, I'm not sure which
order makes more sense. It certainly seems that Log then Scale
produces a nice centered distribution. Though the result seems a bit
leptokurtic.<br />
However, one observation that is very clear is that by scaling the
data first, I ended up with many values equal to 0, which when then
log transformed were assigned NA. This happened in both examples.
This definitely leads me to think that the order to do thins is
<strong>Log then Scale</strong>.<br />
</body>
</html>
Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-65449165397842109352013-09-13T14:40:00.000-07:002013-09-13T14:40:15.097-07:00Hungry, hungry ... something?I was out and about at various Long Island field sites this past Monday, collecting Glossy Buckthorn leaves for a colleague in Belgium, and I noticed something I've never seen before - rampant herbivory of Glossy Buckthorn. Here's an example of what it looks like.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQlco-TpiKnGNMf-pmX5_2KGzcl7m1VthEnNsOSXI2azbJw7MuBtWk0pFbYRdqJmCaKDhqdTvnWgmQqK8ULQUPxBUl80OKUxOvfoLIb3tsHrAYqU3heM1bo_y0RlBnYqmz-Eb7bnT5xFw/s1600/Buckthorn-Herbivory.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="265" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQlco-TpiKnGNMf-pmX5_2KGzcl7m1VthEnNsOSXI2azbJw7MuBtWk0pFbYRdqJmCaKDhqdTvnWgmQqK8ULQUPxBUl80OKUxOvfoLIb3tsHrAYqU3heM1bo_y0RlBnYqmz-Eb7bnT5xFw/s400/Buckthorn-Herbivory.jpg" width="400" /></a></div>
I've been visiting various field sites to examine Glossy Buckthorn for about five years now, and I've observed signs of herbivory here and there, but never to this extent. What's more, I was hard pressed to find <i>any</i> leaves that were not chewed on.<br />
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I sent an email to a friend at UNH who has studied buckthorn many years now, and asked him if he's seen anything like this. No, he hasn't, but he's heard of this type of herbivory on buckthorn from a colleague in the Kittery, Maine area. So based on this lead, the suspect is the larva of the moth <i>Magusa divaricata. </i>Sadly, these days I'm pretty busy finishing my PhD, doing my postdoc work, finishing up various projects, etc, so I don't think I'm going to be able to squeeze in more field time in the immediate future to seek out what's eating the buckthorn, but maybe I'll get lucky when I go out to collect data later this October (though I suspect the moths will be long gone by then). In any case, it's an interesting observation to stow away and come back to in the future.Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-74500779913110566542013-05-13T06:07:00.001-07:002013-05-13T06:07:41.030-07:00What Strunk and White has come to mean to me.Recently I was offered an excellent post doc position in the lab of Prof. John Silander at the University of Connecticut. This is big for me - it means my years as a grad student (6 so far) are coming to a close, I'll be working in a lab whose research I've been following for many years now, I'll continue to work in plant systems, I'll be applying and greatly expanding my analysis and programing skill set, and on a practical level, I can work in this lab and continue to live on Long Island, where my wife has a good job as an Assistant Professor at Hofstra Medical School. The logistics of my position are bit complicated, but all setup. Those are some of the good things. The challenge has been wrapping up my thesis. You would think that after 6 years my manuscripts would be mostly complete, but reflecting back on my experience, I have begun to realize how little time I spent on my thesis compared to all the other things I've done in grad school. Having not taken any biology since high school, I spent a lot of time taking classes. I also took a lot of classes focusing on math and statistics in ecology. I've done a lot of departmental service related things, which has led me to believe that receiving a Departmental Service Award is both a good and bad sign. And I've been involved in, and continue to be involved in, side projects. Add in TAing, peer reviews for journals, etc., etc., - you get my point. This all adds up to the last few months and next few weeks as being a crunch time for writing, and through this time I've been keeping my copy of William Strunk and E.B. White's <i>The Elements of Style</i> close at hand.<br />
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Why the <i>Elements of Style</i>? It is not the book that was used in my college writing class (that was <i>The Bedford Handbook</i>). It's not about scientific writing. For all I know, it may not even be what my writing friends would recommend. But it is highly recommended by many professors in my department, which is why I picked it up in the first place. Regardless of why I began using this book, it has become quite important to me as a writer. In particular, it has two meanings for me. One, contained within its short descriptions of the rules of writing is the promise that I can become a better writer. I read one of the 'Principles of composition' and think, 'Yeah, that does sound better. I can do that in my writing.' Or I can look at the one of the 'Elementary rules of usage', and then go back to my manuscript, search for instances in which I break a rule, and fix it. I can make my writing cleaner, clearer, and more concise. The second meaning is a bit more symbolic. I like to read a bit from this book before I start writing for the day. I don't necessarily set out to apply what I read, I just find that it puts me in a writing mood. So at the end of a long day of grading problem sets or writing R code, if I look at my copy of Strunk and White, and I know that I didn't crack it open that day, I know I probably didn't do any writing. Sure, this is followed by a pang of guilt, but it also comes with an increased motivation to get some text down the next day, which is ultimately going to get me through writing my PhD.<br />
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And that's what Strunk and White has come to mean to me.Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-54549196659756242842013-03-20T06:17:00.003-07:002013-03-20T06:18:21.633-07:00The Excitement of DataI am embarrassed to admit it, but I am just now getting around to analyzing the data I collected from the 2012 field season. I do tend to spend the winter months plugging away at computer based projects, and this year has been even busier than years past. I've been working on developing new tools for SDMs and finishing my demographic model sensitivity analysis project, as well as keeping up with my TA obligations and working on an addition to the climate change paper I've discussed previously here. But this post isn't meant to talk about being busy, it's to express my excitement about analyzing another seasons worth of Glossy Buckthorn data.<br />
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One data set I've collected that I'm particularly keen to look at is from a small buckthorn population in northern New Hampshire, on forest service land. In the fall of 2010 I marked approximately 150 individual plants at this site. Unexpectedly, during the late summer/ early fall of 2011, this site was mowed. I lost most of my tags, but about 45 remained connected to the cut plants. Glossy Buckthorn is somewhat notorios for its ability to re-sprout after damage - this is one characteristic that makes it hard to manage. Rather than abandon the site altogether, I decided I would measure the basal diameters (also called diameter at ankle height, or DAH) of the remaining tagged plants. Here is a preliminary plot of what these results look like, showing basal diameter in 2010 versus basal diameter in 2012.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivqlIambBcJeP_6QpIL3FVmiSk4sdJiB_QRNYlI_Nafc6Bhf8cjJgZ0jusczBNJS1JbYZquIPjufF8ZZvfX38SAn7oZNn3RCzdXFLnhSUyD2H9EqnL3Za7eupU-Cr26eUrzf0NfGE8hyU/s1600/WinnFalls-Prelim.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivqlIambBcJeP_6QpIL3FVmiSk4sdJiB_QRNYlI_Nafc6Bhf8cjJgZ0jusczBNJS1JbYZquIPjufF8ZZvfX38SAn7oZNn3RCzdXFLnhSUyD2H9EqnL3Za7eupU-Cr26eUrzf0NfGE8hyU/s1600/WinnFalls-Prelim.png" height="192" width="320" /></a></div>
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The x-axis is the DAH in 2010 and the y-axis is DAH in 2012. I can see that some plants are not recovering, however it looks like many have grown quite a bit. Also, all of the plants with a DAH > 0 represent some form of regrowth - either regrowth of the original tagged stem or growth of new sprouts. A tenacious plant, for sure. I wrote a bit more about this particular site in <a href="http://ecologistatwork.blogspot.com/2012/11/management-and-resilience.html" target="_blank">another post</a> as well.<br />
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Simple preliminary plots like this one have me looking forward to poking at my data and getting to my full analysis over the next few weeks.Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-48825505758872519752013-01-05T09:43:00.000-08:002013-01-05T09:43:34.266-08:00Seeing the Forest, or The Importance of WritingI'm now well into my 6th year of grad school, and partly because of that, I've been doing a lot more writing than in years past. I'm writing job applications, I'm writing manuscript drafts, I'm writing (occasionally) here on this blog. And I'll be honest, writing is not always as easy as programming or field work. In fact, it's almost never that easy. I haven't mentioned it much on the blog, but most of the research I do is actually quantitative and programatic in nature. I spend little time in the field compared to how much time I spend working on R code. That's not a complaint - just a fact. As the amount of writing I do increases, especially for job apps, it strikes me that this process is very important to help me focus on the bigger picture of my research goals. <div>
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If asked what type of research I do, I'll often say, "I develop quantitative methods to answer questions in conservation biology". Where do those questions come from? For the past five and half years, they have mostly come from sitting around with my colleagues, discussing some paper, and thinking, "Yeah, but what about this thing they don't talk about ..." or "That seems good, but what would you do to make it even better ...". Or from talking with other Ecologists and Evolutionary Biologists (particularly my committee members) about some pattern that just hasn't been explained that well. In a large part, that's how my research project on non-native species lag-phase dynamics has come about. Let me delve into my own thesis project a bit more - I took this question about lag-phase dynamics (i.e. what's going on during that lag-phase) and said, "ok, given some data, how might I go about understanding the processes going on during that time? I can build a model, simulate the most likely processes, and see if the simulation matches reality." (There you go folks, a description of my PhD in two sentences.) I decided on the "most likely processes", chose the types of models I would need for simulation, and got started. This is a good project management technique - everything got broken down into little pieces. Each piece was further subdivided. The subdivisions get translated into programming projects. The subdivision continues from there. So where I am now is at a point of wrapping up multiple projects, most of which involve finishing of pieces of code here and there. And it takes a conscious effort to step back and look at the project as a whole. (It doesn't help that the integration of each part of the project is the last step!) And that's where the writing comes in. I'm forced to step away from my coding for a bit, and describe the research I do. It's not writing code - it's posing questions relavent to conservation, then developing ways to answer those questions. And while I always know this, hours debugging an R script will pretty much clear my mind of everything not related to that script. So for now, I welcome that time dedicated to writing (like right now), and appreciate the focus it give me, so I'm not missing the forest for the trees.</div>
Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-26313228091134590432012-12-18T10:10:00.000-08:002012-12-18T10:10:19.063-08:00Reviewing the causes of extinction due to climate change<div dir="ltr">
This post is a few weeks late now, but I wanted to discuss a paper I co-lead with another student in my department, Abby Cahill, which recently became available online through the journal The Proceedings of the Royal Society B. We even got the cover photo for the print edition, which is pretty neat! You can access the abstract for the article <a href="http://rspb.royalsocietypublishing.org/content/early/2012/10/15/rspb.2012.1890.abstract" target="_blank">here</a>, and if you want a pdf, just drop me a line. </div>
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This article is the result of work a group of us students in E&E at Stony Brook did during, and following, a seminar lead by Prof. John Wiens. We set out to investigate how climate change has caused documented local extinctions. We employed systematic review methods, trying as best we could to create a replicable review study. This was the second systematic review that I participated in. The other review I worked on was with the Gurevitch Lab, in which we carried out <a href="http://onlinelibrary.wiley.com/doi/10.1002/ece3.431/full" target="_blank">a field synopsis and systematic review of invasive species research</a>. As authorship order would indicate, I played a much smaller part in that review than this one. However, working with the Gurevitch Lab members during the early development of their review, I gained an appreciation for the usefulness of these review techniques. With that said, after writing our climate change review, and a follow up we just sent off for review on the causes of range limits, I do wonder if there are any ways to make literature reviews even better (more on that later).<br />
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Back to our review - on some levels what we really wanted to know is if climate change will cause local population extinctions because organisms reach some physiological limit (e.g. it's just too hot) or by some other means (e.g. interruption of some biotic process). Though my thesis research involves an invasive plant, many of my research interests, and most of my side projects in the Akcakaya Lab, fall squarely in the climate change / conservation biology realm. So this question really resonated with me. Carrying out the review yielded two major results. One, for those studies that identify the proximate causes of climate change related extinction, there are many more cases in which disruption of biotic interactions is the cause. Second, very few studies actually identify a proximate cause of extinction. This second point actually surprised me, but discussing our findings with more established conservation biologists, few shared in my surprise. Considering this finding, we also tried to outline some ideas for how we may pursue conservation research to address this lack of knowledge. Hopefully this review will be helpful to young scientists looking for research ideas. <br />
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Beyond this particular review and these particular results, carrying out this review and writing the paper made me start thinking about just how literature reviews are carried out. At this point, I would say that I am a proponent of the systematic review approach (for background literature have a look at <a href="http://onlinelibrary.wiley.com/doi/10.1111/j.1523-1739.2006.00485.x/abstract" target="_blank">Pullin and Stewart's ConsBio article</a> or the Gurevitch Lab paper cited above - which is open-access). However, it is certainly not without its faults. For example, to my knowledge, the best way to carry out a repeatable literature search is to use a set of search terms in a database such as ISI's Web of Science. I've done searches in this particular database, and indeed, the results are replicable. However, there is a temporal bias in these databases, due to the fact that many articles published prior to the 1980s do not have digitally indexed titles or abstracts. Many of my professors have stressed the importance of not ignoring older literature, but how do we get this literature into reviews systematically? Also, there are many examples of these searches failing to find relavent literature. When this happens we face the question of whether to add literature that we know is relavent, thus making the search results less transparent, or leaving it out, which personally, leaves me with a funny feeling of failing to cover the full 'parameter space' of my potential data, if you will. I don't have any great ideas about how to address these issues. At the end of the day, I find some comfort in the idea that a thorough literature search may not return every relavent study ever published, but neither does a transect return information on every plant in a population (or even that transect, given observer error), and as with the transect data, if done correctly we can say we've thoroughly 'sampled' the population.<br />
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Another concern I have with systematic reviews is that they often entail extraction of some pieces of data from studies, to be further analyzed (e.g. the number of species examined or the documented causes of local extinction). This may seem pretty straight forward - the information I want has got to be in the paper, I mean, it was published! But in practice, data extraction can be quite difficult, especially when you are trying to extract from hundreds of papers with several people. We employed carefully crafted Google Forms, which despite our "carefulness" needed lots of editing once everyone started using them, and ultimately, lead to us going over our data set several times. An idea that I've been tossing around is to invite the original study authors to help in this process. Sure, this will not always be possible. Some authors will not have the time, some will not be able to be contacted, and of course, there's always the possibility that some will not be happy with the way you intend to include their study. I have no reason to believe this, but I have this funny feeling that someone is going to read our ProcB paper and say "I most certainly did identify the causes of extinction for this species!". To that I say, while the paper has been published, it doesn't mean the information shouldn't be updated. Perhaps a review should be an active process? A wiki of some sort? The review authors can set-up the structure, provide their assessment, and then the cited study authors can be invited to edit/add/remove information about their research - with some editorial control by the review authors I suppose. Sounds like a cool project to me. Also sounds like a lot of time and work. But perhaps another step forward for literature reviews?</div>
Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-84503590719111774542012-11-23T13:16:00.000-08:002012-12-18T10:12:07.366-08:00Management and Resilience The White Mountains of New Hampshire is the place that inspired me to study ecology. So when I was coming up with my PhD project I wanted at least some of my field work to be in this region. (As an aside, one of the bonuses of the PhD program at Stony Brook is that you can develop a project independent of your adviser's research program, so to some extent, you can choose where you want to work.) In fact, while I was developing my project, I contacted the Botanist for the White Mountain National Forest and asked him if there were any non-native plant species he thought were particularly concerning. Glossy buckthorn - that was his first answer. So as I've described a bit <a href="http://ecologistatwork.blogspot.com/2012/07/on-how-i-chose-my-samples-part-1.html" target="_blank">here</a>, in 2009 I set up my first transect about a 1/2 mile or so from the trailhead of the Winniweta Falls Trail.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoOYl2qNZxt5OUuhkRO_S3RK59EoyeIGVoM_feQHJBBiMH-8_IHBAXU8DM8eK5mjIohYAin6vipQ4kMedA00r40bV4uOj1aN0l7MmixzRGvRD7J5xkIMXF8O1VQBYyXHsjzzE12J9ayUA/s1600/DSCN1782.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoOYl2qNZxt5OUuhkRO_S3RK59EoyeIGVoM_feQHJBBiMH-8_IHBAXU8DM8eK5mjIohYAin6vipQ4kMedA00r40bV4uOj1aN0l7MmixzRGvRD7J5xkIMXF8O1VQBYyXHsjzzE12J9ayUA/s1600/DSCN1782.JPG" /></a></div>
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I'll leave a discussion of the physical characteristics of this site for another post. Today I want to share some of my observations from here, which I think demonstrate the tenacity of Glossy Buckthorn. In September of 2010, I marked 147 individual plants along three 30m transects in a field heavily infested with Glossy Buckthorn. This field was just one of several open fields in the area (along the Jackson Ski Touring trails, for those of you who are curious) that had a high density of buckthorn. I believe these areas are maintained as open fields to provide wildlife habitat for organisms such as moose.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHONPNvUBw4QLMF-t34Hz48U4aKFgrfsq85XIGYNe6zd1tuH1orqUkleMAWGVaqLtKII5igBobF9WFEWxT9TEVHeI5tULoTVemnm018BlsN4LlPgZIyaQEM3GnyzJLZrToRbbRAIDfEOE/s1600/DSCN0899.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHONPNvUBw4QLMF-t34Hz48U4aKFgrfsq85XIGYNe6zd1tuH1orqUkleMAWGVaqLtKII5igBobF9WFEWxT9TEVHeI5tULoTVemnm018BlsN4LlPgZIyaQEM3GnyzJLZrToRbbRAIDfEOE/s1600/DSCN0899.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Dense Glossy Buckthorn cover in an open field near Winniweta Falls Trailhead</td></tr>
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A little out of the field of view of the picture above, I set down one of my three 30m x 1m <a href="http://en.wikipedia.org/wiki/Belt_transect" target="_blank">belt transects</a>, which contained 115 buckthorn plants. As you can see below, many of these plants are taller than my 2m measuring pole.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsGaygBT-3YqKPVPWhLOohAc68GdoEAAHue01IDYKEC3k7YiNWaw8j_HQVeGhWpGJWnqS2sl1simotkbs1lKlyKtvSXwZziZTvb-ctFvIuf5Sq5sS8XSuBl1G9izWINvSnC5V2Tarn0m0/s1600/DSCN1021.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsGaygBT-3YqKPVPWhLOohAc68GdoEAAHue01IDYKEC3k7YiNWaw8j_HQVeGhWpGJWnqS2sl1simotkbs1lKlyKtvSXwZziZTvb-ctFvIuf5Sq5sS8XSuBl1G9izWINvSnC5V2Tarn0m0/s1600/DSCN1021.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Transect 3 - Many buckthorn platns taller than my measuring pole!</td></tr>
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I received permission from the Forest Service to sample at this location, I even have a letter on official USFS letter head, so I was pretty confident that my site would go undisturbed after setting up my transects and tagging the plants. Plus, this isn't a high traffic area for hikers. But between my 2010 visit and my 2011 visit there were to major storms, including Hurricane Irene, that flooded the area, so I was expecting some impacts. But I was pretty shocked when I showed up the Fall of 2011 to this!<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTVGmi7EpN53VqBVi-fPSZWufwZb4OA7vd8My1fwvBrLAjEQLrrRcWE_1jKGpTWE-5guVP_a9bXJgcKop2xCnyitjZ8lh75kjc1qnwrAyMDv7uYluaO3HYVUaF9Vv2-51690lB3hICOhU/s1600/DSCN1219.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTVGmi7EpN53VqBVi-fPSZWufwZb4OA7vd8My1fwvBrLAjEQLrrRcWE_1jKGpTWE-5guVP_a9bXJgcKop2xCnyitjZ8lh75kjc1qnwrAyMDv7uYluaO3HYVUaF9Vv2-51690lB3hICOhU/s1600/DSCN1219.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Winn Falls site after mowing</td></tr>
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And here's that transect that had all of those greater than 2m tall plants.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUh6Q5qaOnR3V097rCFV2h7OIcOIRZID3VK-DxHNbhdze25bv-pXFZ0lajYnaGwdtbZKPcB-7h6CXkZuBJpzQZmgvxN4wPGAAEw2WRBFaZKq07li7t-fe5HzUpLnpbflhuSanmV6qKAbI/s1600/DSCN1221.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUh6Q5qaOnR3V097rCFV2h7OIcOIRZID3VK-DxHNbhdze25bv-pXFZ0lajYnaGwdtbZKPcB-7h6CXkZuBJpzQZmgvxN4wPGAAEw2WRBFaZKq07li7t-fe5HzUpLnpbflhuSanmV6qKAbI/s1600/DSCN1221.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Transect 3 - after mowing</td></tr>
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As it turns out, there was some miscommunication and this locale was approved for a mowing. It would be foolish to harbor any bitterness about a destroyed site. After all, the forest service is just trying to manage this invasive plant and keep this wildlife opening, well, open. But I do have to wonder if the mower thought twice about running over orange flags, plants marked in a line with flagging tape, or plants clearly marked with shining little metal tags. <br />
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So, seeing this for what it was, I collected the tags I could find, measured the basal diameter of the plants who still had tags attached to them (hey, after all, that's a years worth of growth in basal diameter I could measure there, even if I couldn't say much about height), and left with the plan to come back in 2012 and see what happens. You see, buckthorn is notoriously tenacious - it re-sprouts quite readily. The most affective way to manage buckthorn is to cut it and immediately apply a weed killer (this is based on research reported in several papers, many from the Natural Areas Journal). I had a suspicion I would come back in a year and see plenty of re-growth. Of the 147 plants originally tagged, I was able to leave 44 and recover 45. That left 58 unaccounted for. Given how high the flood waters came from the two large storms that hit this area in 2011, I suspect that many of them are in the Ellis River or along its banks. This season I returned to Winn Falls and was tacken aback by the amount of re-growth.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4oV5ows56121dgDFRjfk5EpMURLqHCPKgfP8XGuymVKqkaL02blwkrnEKGk92om14bFU_2340ttfqxpw0Dzce4Sgh5yNJD3NiT3H32Q59OeOAIZFUQNTMJGII_dYxdvSYNcRuGi4QfJM/s1600/DSCN1784.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4oV5ows56121dgDFRjfk5EpMURLqHCPKgfP8XGuymVKqkaL02blwkrnEKGk92om14bFU_2340ttfqxpw0Dzce4Sgh5yNJD3NiT3H32Q59OeOAIZFUQNTMJGII_dYxdvSYNcRuGi4QfJM/s1600/DSCN1784.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Transect 3 - one year post mowing</td></tr>
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I haven't completely entered and analyzed these data, but taking a quick peak, about 5 of the 44 left were dead. Three more were missing. And it looks like on average there was about 40cm of re-growth. Also, many of them had multiple basal stems. I suspect returning next year I will find many of these with fruit on them. Ultimately, these data may not make into my population model. My sample size is very small (38 plants - lost 8 and gained 2 this year). But I think these data are still interesting. They make me wonder how affective a management strategy that involves cutting every couple of years can really be. Also, before the mowing, this field was a giant reservoir of Glossy Buckthorn seeds. I can't help but think about the role this reservoir might play in the spread of buckthorn into nearby logging sites or down river. Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-33512279649920953692012-11-05T19:11:00.001-08:002012-12-18T10:12:07.360-08:00After the storm<div><p dir=ltr>I'm lacking time to do a fuller post these days, which is sad because I have several ideas bouncing around my head. I'll try to make some time later this week. In the mean time, this is just a quick note to say that I'm very curious what, if any, the affect of Hurricane Sandy will be on my Long Island field plots. I finished this season's work in the UNH area about a week and a half ago, and was planning to visit Caleb Smith last week, but obviously that plan was changed. For now, Caleb Smith is closed to the public, so it may be some time before I can finish this year's work. I'll do a post once I collect this data. Everyone stay safe for now.</p>
</div>Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-30988994101950302602012-10-18T06:12:00.002-07:002012-12-18T10:12:07.359-08:00In the field with my wifeMy wife is so awesome that she insisted on using two of her floating holidays to help me out in the field in my southern New Hampshire sites this past September. It was great to have Gina in the field for multiple reasons. First, not to get too cheesy, but I really enjoy hanging out with her. Second, field work goes so much faster with another person. Third, it was interesting to get some new ideas about doing field work from someone who isn't as tied up in the project as myself.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilWZCWgfBkx4I9HFjyPSpcXxAVExkt8lOkdvZ59HRDtxe8BiNfTBkEiLYV4-kfkNdyrtprYM1mwCaRz39GFWBEBxcJyZfR7xB3x6jzdTDOf-g212DCJy5avIXe7LVcyoGb0r6sP698dgc/s1600/DSCN1725.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilWZCWgfBkx4I9HFjyPSpcXxAVExkt8lOkdvZ59HRDtxe8BiNfTBkEiLYV4-kfkNdyrtprYM1mwCaRz39GFWBEBxcJyZfR7xB3x6jzdTDOf-g212DCJy5avIXe7LVcyoGb0r6sP698dgc/s1600/DSCN1725.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Gina, ready to measure some plants!</td></tr>
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One of the best ideas Gina had for me was to draw a rough map for each of my quadrats, showing the general position of each tagged plant in the plot. At first, this seemed like an awful lot of work, but thinking about it a bit further, and failing to find a few of last seasons marked plants, made me reconsider. If you have ever tried to find tagged plants you know that sometimes it's very hard. A year's worth of debris has accumulated, often times hiding tags under a layer of compost. Some researchers employ tricks and tools such as using a metal detector. I have not gotten to this point - partly because I cant afford a metal detector. So, lacking a metal detector, I'll dig around in the duff for upwards of 30 minutes looking for a single tag. Here's what I imagine a quadrat map might look like.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbpdlzK2wivIm-FGd0Ofl4enCGxrJuMuB2-iV3aEwXlYD5ycwbIghu2Go77m5LVb9QW6cMQMTXUsLXNw3gWBDyU9Pm_O2odj7QVqEK2pf6O91H_Z8AQ0b5gC43z6_KOECm8PEMEOL4DaM/s1600/sample.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbpdlzK2wivIm-FGd0Ofl4enCGxrJuMuB2-iV3aEwXlYD5ycwbIghu2Go77m5LVb9QW6cMQMTXUsLXNw3gWBDyU9Pm_O2odj7QVqEK2pf6O91H_Z8AQ0b5gC43z6_KOECm8PEMEOL4DaM/s1600/sample.png" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">An example of a 'quadrat map'</td></tr>
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The numbers indicate the tag number for each plant. Clumps of plants with sequential tags might be listed together with a general shape of the clump. Distinguishing characteristics, such as the presence of a particularly large tree would be noted. Etcetera. I really like this idea, and I don't think it will take much time to sketch out such maps in the field when tagging plants. Next season, as I prepare to make some of my sites longer term monitoring plots (i.e. places to go back to <i>after</i> I finish my PhD) I think I'll start making these quadrat maps.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNFE8gtM55SfaginlMOdHpIlw-ed3gtWuw9JcTXWUAMjFmBH-782NBpFS53DZdvCZmXjFyz3U0VLS48cQqNSY0-PGSNmA4MIeHtvWeuDUj8dHCJjb9eWrfZ7UbfYUOqdyTT19ZtMFTXaY/s1600/DSCN1726.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNFE8gtM55SfaginlMOdHpIlw-ed3gtWuw9JcTXWUAMjFmBH-782NBpFS53DZdvCZmXjFyz3U0VLS48cQqNSY0-PGSNmA4MIeHtvWeuDUj8dHCJjb9eWrfZ7UbfYUOqdyTT19ZtMFTXaY/s1600/DSCN1726.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Happy field workers at the end of the day!</td></tr>
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<br />Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-11117112735994752682012-09-13T05:37:00.001-07:002012-12-18T10:12:25.269-08:00Field Site or Classroom?The answer to this post's title is - both!<br />
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This past week I lead a lab exercise I developed for the course I'm TAing this semester, Ecology Lab, out in one of my Glossy buckthorn field sites. The primary instructor, Professor Catherine Graham, was away on a conference, and rather than teach one of the old lab activities, I decided to get out into the field with my class of 19 students. I knew I wanted to do a lab that covered some general information on non-native species and going into this TA from the beginning, I thought it would be fun to incorporate my nearby field sites into the course somehow. So here was a great opportunity!<br />
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I wasn't interested in having my class 'do' my field work for me, so I had to come up with something that made sense to carryout in these plots. I realized that I could plan an activity that answered some question, or curiosity, of mine about these sites, but that I just haven't had the time to delve into myself. For example, looking around my field sites, I'm often curios about what species are in these plots, beyond simply characterizing them as oak-birch-beech upland forests. So this last Friday I had the students run belt transects in one of my plots and in a near-by section of woods that has only a small number of buckthorn plants present. <br />
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I haven't done to many analyses on the data yet, but looking at overall number of plants counted and relative frequencies and densities of individual plant species, a few things definitely stand out. The most obvious is that maple leaf viburnum is a very common species in the woods around Stony Brook University. Low-bush blueberry also seems to be pretty common, though more variable than the viburnum. Another is that there were fewer plants counted in the buckthorn plot. There are hundreds of explanations for this and almost no way our data will address which explanations are plausible, but as an observation, I thought it was interesting. As an assignment, I have my students doing a few analyses and making some interpretations and speculations about our observations - I'm really excited to see what they come up with!Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-62690421717996837382012-09-06T10:47:00.001-07:002012-12-18T10:12:07.363-08:00Niche models, the (sub)urban environment, and my uncle's backyardI use ecological niche models and species distribution models fairly extensively in my research - both my thesis work and side projects. For some time now my advisor has been involved in projects that link these types of models with population projection models, so when I was thinking about researching the patterns and processes of the invasion of Glossy buckthorn, it made sense to me that I would employ similar techniques. Additionally, I have only found a dozen or so unique presence records for Glossy buckthorn here on Long Island, so I thought it may be good do a SDM focused just on the island here. I haven't completed this part of my project, so don't get excited, I don't have any results to share with you yet. Anyhow, I've spent a fair bit of time gathering more occurrence locations from numerous public lands (parks and what not) in Nassau and Suffolk County, and had been thinking that carrying out an SDM would be pretty straight forward.<br />
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SIDE BAR: Looking for invasive species is a bit funny for me. When I go to a new location that I think is likely to have buckthorn, I'm giddy with anticipation. I'm excited when I find it and disappointed when I don't. Now, objectively speaking, if buckthorn is in fact having a strong negative effect on native ecosystems (most likely the case in my New Hampshire populations), then shouldn't I be happy when I don't find it? Yeah, it's complicated I guess...<br />
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Ok, back to modeling, and how spending time in the field has affected my thinking. One thing I tend to think about often when in the field is how Glossy buckthorn got to that particular spot? Where is the nearest, next-oldest, population? Glossy buckthorn seeds can be dispersed by any one of the many bird species that eat its fruit, but not too far. The fruit has a laxative effect (<a href="http://botanical.com/botanical/mgmh/b/buckth80.html" target="_blank">on humans too</a>), so birds don't hold it, or the seeds, for long. Because nearly all of my field sites are embedded in suburban areas, they all have at least some length of border shared with someones backyard. At my Long Island sites, I can see backyards from many of my plots. Initially I hadn't thought much of this, but while visiting my uncle and his family in New Jersey a while I back, I noticed that there in the unmaintained garden next to the patio there was a Glossy buckthorn tree. Me - "Uncle Joe, did you plant that tree?" Uncle Joe - "Oh no, that came with the house." So there you have it, people in the suburbs may be inclined to plant this tree in there backyard.<br />
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What are the implications of this on my models and how I use them? I'm not sure yet. On the one hand, it makes me think of possible uses of high-res remote sensing and how it may be used to determine what types of plants are growing in urban and suburban yards. This technology and its applications are improving rapidly, and we are getting to the point that identification of individual species from satellite imagery may be possible. (Yeah, that's crazy!) On the other hand, can I use the results of my distribution models to identify distances between populations if plants in your neighbors backyard are actually the source for my populations? I'm not sure, and will definitely be giving this more thought as the project progresses in the near future.Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-13167758225972583152012-08-29T09:05:00.002-07:002012-12-18T10:12:07.357-08:00On how I chose my samples - Part 2<div>
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So last I left off on the topic of <a href="http://ecologistatwork.blogspot.com/2012/07/on-how-i-chose-my-samples-part-1.html" target="_blank">choosing samples</a> I was discussing how I realized that I really needed to have a good look around me and think about what I was trying to accomplish in order to help me come up with a sampling scheme. And for the most part, that's just what I did. During my field visits in the Summer and Fall of 2009, and even somewhat during field visits in 2010, I spent several hours standing in patches of Glossy Buckthorn thinking about how best to select plants to tag and follow. Sometimes I would call my friend Adam (also studying plant ecology at the time) and bounce ideas off of him (or ask him to generate random numbers for me). Sometimes I would call my wife and complain about the dense blackberry bushes, multi-flora rose, ticks, etc - ya know, sometimes you just need to whine a bit.<br />
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Here are a few of the standout observations that helped me develop my sampling scheme:<br />
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<ul>
<li>Glossy buckthorn patches vary in density and I wanted to avoid over-representing plants in areas of high density or under-representing plants in areas of low density</li>
<li>For the purposes of my study I want to follow individuals, therefore areas that are bare of Glossy buckthorn are not good places to look for plants to follow (yeah - this one is obvious)</li>
<li>Glossy buckthorn grows in varying ecological conditions (under story, gaps, riparian zones, uplands, etc.) and my samples should come from as many of these conditions as is feasible</li>
<li>The ecological conditions mentioned above are generally clumped. That is, the ecological conditions I'm interested in usually make up their own patch (e.g. a large patch of understory or wetland)</li>
</ul>
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With these observations and thoughts in mind, I decide that the most important aspect of my sampling scheme should be that I select individual plants to follow across different plant densities and in different ecological conditions. So here's the final sampling scheme I chose:</div>
<div>
<ul>
<li>Ecological conditions - I selected a specific combination of ecological conditions (e.g. upland-understory forest) and using a GPS outlined the borders of a Glossy buckthorn infestation <b>within</b> the bounds of the borders of the ecological condition.</li>
<li>Individual plants - Once I had the border of an infestation, I selected 15 to 20 random points within these bounds where I set up 2x2m plots, or quadrats. Within these plots, I tagged and measured all Glossy buckthorn plants that were taller than 10cm. Plants smaller than 10cm were considered saplings, which were sampled differently.</li>
</ul>
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This type of sample scheme is essentially a stratified-random design, stratified across ecological condition and random within that condition. So far I think it has worked out pretty well.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjyBtVStdlOOxkgKPC1BqbTeHUThePR9d9GDrFTK3D-GmxzKAPH42hhMxivdKDIcqkWTrw-Niq96gdRCSr-3vGNVFFfbo1lbdxqWooFCRK5KjMVrHas6oFwMp6xjOBdNWjkdg8kVas90s/s1600/DSCN0999.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjyBtVStdlOOxkgKPC1BqbTeHUThePR9d9GDrFTK3D-GmxzKAPH42hhMxivdKDIcqkWTrw-Niq96gdRCSr-3vGNVFFfbo1lbdxqWooFCRK5KjMVrHas6oFwMp6xjOBdNWjkdg8kVas90s/s1600/DSCN0999.JPG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Random 2x2m plot in a large forest gap. Orange flags mark the corners of the quadrat.</td></tr>
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Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0tag:blogger.com,1999:blog-1866259608202514289.post-51072836564157210542012-08-15T12:02:00.003-07:002012-12-18T10:13:08.271-08:00Fieldwork, ESA, and MovingThe last few weeks have been filled with fieldwork in New Hampshire, travel to Portland, OR for the annual Ecological Society of America (ESA) meeting, and moving from our home out near Stony Brook to a new place in Nassau County (closer to NYC and to my wife's new job) - hence the lack of posts. Here's a brief post concerning my experiences at the recent ESA meeting.<br />
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While in Portland I participated in some audiocasts with a group of friends and colleagues, during which we discussed some conference highlights. At the end of each day (the meeting was four full days) we gathered and talked about one standout presentation we saw that day. Give a listen to these audiocasts if you're curious a) what ecologists think and say about each others presentations, b) if you're curious what I thought were a few standout talks, and c) if you want a bit more than an hours worth of entertainment. The audiocasts can be downloaded from my friend <a href="https://sites.google.com/site/gabrielyospinphd/" target="_blank">Gabe Yospin</a>'s website for our <a href="https://sites.google.com/site/gabrielyospinphd/blog/esa2012mondayaudiocast" target="_blank">Monday</a>, <a href="https://sites.google.com/site/gabrielyospinphd/blog/esa2012wednesdayaudiocast" target="_blank">Wednesday</a>, and (coming soon) Thursday sessions. Gabe also did solo sessions on Sunday and Tuesday that are worth listening to. <br />
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This was my first ESA meeting and I must say, I was impressed. ESA is a (relatively) large meeting, approximately 4,500 people this year. There are more than twenty concurrent sessions at a time! Which means during any session there was usually more than one talk I wanted to see. Also, the conference center was so large that if back-to-back sessions were on opposite ends of the center, it was almost impossible to see both talks in their entirety (had to leave one early and still showed up at the other late). But these problems aside, I was definitely impressed and inspired by the science reported at this meeting. Anonymoushttp://www.blogger.com/profile/07634756775386726298noreply@blogger.com0