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moose-migration-repeatability.html
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moose-migration-repeatability.html
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<title>Repeatability of Migration Routes in Moose</title>
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<h1 class="title toc-ignore">Repeatability of Migration Routes in Moose</h1>
<h4 class="author"><em>Fernando Campos</em></h4>
<h4 class="date"><em>2017-08-19</em></h4>
</div>
<br>
<hr>
<p><br></p>
<div id="study-objectives" class="section level1">
<h1>Study Objectives</h1>
<ol style="list-style-type: decimal">
<li><p>Make a descriptive statistical assessment of moose motion during migration.</p>
<ul>
<li><p>How does the orientation of daily movement steps change change over the annual cycle and in relation to the seasonal migrations?</p></li>
<li><p>How do step lengths change over the annual cycle and in relation to the seasonal migrations?</p></li>
</ul></li>
<li><p>Quantify repeatibility in the migration paths of moose, focusing on within-individual vs. between-individual variation.</p></li>
</ol>
<br>
<hr>
<p><br></p>
</div>
<div id="data-preparation" class="section level1">
<h1>Data Preparation</h1>
<div id="load-packages-and-helper-functions" class="section level2">
<h2>Load packages and helper functions</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Load packages</span>
<span class="kw">Sys.setenv</span>(<span class="dt">TZ =</span> <span class="st">'UTC'</span>)
list.of.packages <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"zoo"</span>, <span class="st">"plyr"</span>, <span class="st">"raster"</span>, <span class="st">"rgeos"</span>, <span class="st">"rgdal"</span>, <span class="st">"maptools"</span>,
<span class="st">"adehabitatLT"</span>, <span class="st">"readr"</span>, <span class="st">"RColorBrewer"</span>, <span class="st">"tidyr"</span>,
<span class="st">"lubridate"</span>, <span class="st">"dplyr"</span>, <span class="st">"ggplot2"</span>, <span class="st">"scales"</span>, <span class="st">"viridis"</span>,
<span class="st">"mclust"</span>, <span class="st">"adehabitatHR"</span>, <span class="st">"gridExtra"</span>, <span class="st">"stringr"</span>,
<span class="st">"nlme"</span>)
new.packages <-<span class="st"> </span>list.of.packages[<span class="op">!</span>(list.of.packages <span class="op">%in%</span><span class="st"> </span><span class="kw">installed.packages</span>()[,<span class="st">"Package"</span>])]
<span class="cf">if</span> (<span class="kw">length</span>(new.packages)) <span class="kw">install.packages</span>(<span class="kw">unlist</span>(new.packages))
<span class="kw">lapply</span>(list.of.packages, require, <span class="dt">character.only =</span> T)
<span class="kw">source</span>(<span class="st">"code/plotting-functions.R"</span>)
<span class="kw">setwd</span>(<span class="st">"~/Dropbox/MooseNavigation"</span>)
<span class="co"># If reloading workspace</span>
<span class="co"># Getting very large, so moved out of Dropbox</span>
<span class="kw">load</span>(<span class="st">"~/Documents/Projects/MooseNavigation/MooseNavigation.RData"</span>)</code></pre></div>
<p><br></p>
</div>
<div id="read-and-prepare-data" class="section level2">
<h2>Read and prepare data</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Load data and parse sex and date/time columns</span>
moose <-<span class="st"> </span><span class="kw">read_tsv</span>(<span class="st">"data/AA_AC by year.txt"</span>,
<span class="dt">col_types =</span> <span class="kw">cols</span>(<span class="dt">Sex =</span> readr<span class="op">::</span><span class="kw">col_factor</span>(<span class="dt">levels =</span> <span class="kw">c</span>(<span class="st">"F"</span>, <span class="st">"M"</span>)),
<span class="dt">GMT_date =</span> <span class="kw">col_datetime</span>(<span class="st">"%d/%m/%Y %H:%M:%S"</span>)))
<span class="co"># Ensure points sorted by animal and timestamp</span>
moose <-<span class="st"> </span>moose <span class="op">%>%</span>
<span class="st"> </span><span class="kw">arrange</span>(Object_ID, GMT_date)
moose<span class="op">$</span>year_animal <-<span class="st"> </span><span class="kw">paste</span>(moose<span class="op">$</span>Year, moose<span class="op">$</span>Object_ID, <span class="dt">sep =</span> <span class="st">"_"</span>)
<span class="co"># Convert to spatial points data frame</span>
coords <-<span class="st"> </span><span class="kw">as.data.frame</span>(<span class="kw">cbind</span>(moose<span class="op">$</span>Locale_E, moose<span class="op">$</span>Locale_N))
points <-<span class="st"> </span><span class="kw">SpatialPoints</span>(coords)
<span class="kw">proj4string</span>(points) <-<span class="st"> </span><span class="kw">CRS</span>(<span class="st">"+init=epsg:3021"</span>)
moose_spdf <-<span class="st"> </span><span class="kw">SpatialPointsDataFrame</span>(points, <span class="kw">data.frame</span>(<span class="kw">select</span>(moose, <span class="op">-</span><span class="kw">matches</span>(<span class="st">"Locale"</span>))))</code></pre></div>
<p><br></p>
</div>
<div id="convert-points-to-trajectories" class="section level2">
<h2>Convert points to trajectories</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Based on "moose-year" start date of Mar. 21</span>
<span class="co"># Re-assign points to the relevant moose year (each one starts on Mar. 21)</span>
<span class="co"># Create ltraj object of annual tracks</span>
moose_annual <-<span class="st"> </span><span class="kw">as.ltraj</span>(<span class="dt">xy =</span> <span class="kw">as.data.frame</span>(moose[, <span class="kw">c</span>(<span class="st">"Locale_E"</span>, <span class="st">"Locale_N"</span>)]),
<span class="dt">date =</span> moose<span class="op">$</span>GMT_date, <span class="dt">id =</span> moose<span class="op">$</span>yrMooseID,
<span class="dt">infolocs =</span> <span class="kw">as.data.frame</span>(moose[, <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">7</span><span class="op">:</span><span class="dv">15</span>)]))</code></pre></div>
<p><br></p>
</div>
<div id="cleanup" class="section level2">
<h2>Cleanup</h2>
<p>Here, we convert to a data frame to obtain movement metrics. We also round the relocation interval to the nearest day. This is useful later for filtering out long steps, e.g., when we want to visualize daily step lengths.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">mma <-<span class="st"> </span><span class="kw">tbl_df</span>(<span class="kw">ld</span>(moose_annual))
mma <-<span class="st"> </span>mma <span class="op">%>%</span>
<span class="st"> </span><span class="kw">group_by</span>(id) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">start_date =</span> <span class="kw">min</span>(date),
<span class="dt">dt_days =</span> <span class="kw">round_any</span>(dt, <span class="dv">86400</span>) <span class="op">/</span><span class="st"> </span><span class="dv">86400</span>,
<span class="dt">month_of =</span> <span class="kw">month</span>(date, <span class="dt">label =</span> <span class="ot">TRUE</span>),
<span class="dt">year_of =</span> <span class="kw">year</span>(date)) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">rename</span>(<span class="dt">nsd =</span> R2n)
<span class="co"># Create a "plot date" (all in the same year) for easy visualization</span>
mma<span class="op">$</span>plot_date <-<span class="st"> </span><span class="kw">ymd</span>(<span class="kw">paste</span>(<span class="st">"2000"</span>, <span class="kw">month</span>(mma<span class="op">$</span>start_date), <span class="kw">day</span>(mma<span class="op">$</span>start_date), <span class="dt">sep =</span> <span class="st">"-"</span>)) <span class="op">+</span><span class="st"> </span><span class="kw">days</span>(mma<span class="op">$</span>nDaysYr)</code></pre></div>
<p><br></p>
<!-- ## Clustering -->
<!-- This chunk applies several clusting algorigthms to the data and determines the optimal method and number of clusters based on BIC of each algorithm and N. The clustering is based on location and NSD for both summer and winter months for each animal. The idea is to find groups of individuals who show similar migration patterns. The trajectories of the different clusters are plotted at the bottom of the page. -->
<!-- ```{r clustering, message = FALSE, warning = FALSE} -->
<!-- ``` -->
<p><br></p>
<hr>
</div>
</div>
<div id="movement-metric-plots" class="section level1">
<h1>Movement metric plots</h1>
<p><br></p>
<div id="relative-turn-angle-plots" class="section level2">
<h2>Relative turn angle plots</h2>
<p>0 is same direction as previous step</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Plot circular histogram of relative turn angles for each animal</span>
<span class="kw">ggplot</span>(<span class="kw">filter</span>(mma, dt_days <span class="op">==</span><span class="st"> </span><span class="dv">1</span> <span class="op">&</span><span class="st"> </span><span class="op">!</span><span class="kw">is.na</span>(rel.angle)), <span class="kw">aes</span>(<span class="dt">x =</span> rel.angle)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_histogram</span>(<span class="dt">bins =</span> <span class="dv">24</span>, <span class="dt">color =</span> <span class="st">"black"</span>, <span class="dt">fill =</span> <span class="st">"gray50"</span>, <span class="dt">alpha =</span> <span class="fl">0.5</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_continuous</span>(<span class="dt">limits =</span> <span class="kw">c</span>(<span class="op">-</span>pi, pi),
<span class="dt">breaks =</span> <span class="kw">seq</span>(<span class="op">-</span>pi, pi <span class="op">-</span><span class="st"> </span>pi<span class="op">/</span><span class="dv">12</span>, <span class="dt">by =</span> pi<span class="op">/</span><span class="dv">6</span>),
<span class="dt">labels =</span> <span class="kw">c</span>(<span class="kw">seq</span>(<span class="dv">180</span>, <span class="dv">330</span>, <span class="dt">by =</span> <span class="dv">30</span>), <span class="kw">seq</span>(<span class="dv">0</span>, <span class="dv">150</span>, <span class="dt">by =</span> <span class="dv">30</span>))) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_polar</span>(<span class="dt">start =</span> <span class="op">-</span>pi) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Relative Turn Angle"</span>, <span class="dt">y =</span> <span class="st">"Count</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>()</code></pre></div>
<p><img src="figures/moose-migration-repeatability/rel_angle_plot_combined-1.png" width="1152" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">ggplot</span>(<span class="kw">filter</span>(mma, dt_days <span class="op">==</span><span class="st"> </span><span class="dv">1</span> <span class="op">&</span><span class="st"> </span><span class="op">!</span><span class="kw">is.na</span>(rel.angle)),
<span class="kw">aes</span>(<span class="dt">x =</span> rel.angle)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_histogram</span>(<span class="dt">bins =</span> <span class="dv">24</span>, <span class="dt">color =</span> <span class="st">"black"</span>, <span class="dt">fill =</span> <span class="st">"gray50"</span>, <span class="dt">alpha =</span> <span class="fl">0.5</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_continuous</span>(<span class="dt">limits =</span> <span class="kw">c</span>(<span class="op">-</span>pi, pi),
<span class="dt">breaks =</span> <span class="kw">seq</span>(<span class="op">-</span>pi, pi <span class="op">-</span><span class="st"> </span>pi<span class="op">/</span><span class="dv">12</span>, <span class="dt">by =</span> pi<span class="op">/</span><span class="dv">6</span>),
<span class="dt">labels =</span> <span class="kw">c</span>(<span class="kw">seq</span>(<span class="dv">180</span>, <span class="dv">330</span>, <span class="dt">by =</span> <span class="dv">30</span>), <span class="kw">seq</span>(<span class="dv">0</span>, <span class="dv">150</span>, <span class="dt">by =</span> <span class="dv">30</span>))) <span class="op">+</span>
<span class="st"> </span><span class="kw">facet_wrap</span>(<span class="op">~</span>month_of) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_polar</span>(<span class="dt">start =</span> <span class="op">-</span>pi) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Relative Turn Angle"</span>, <span class="dt">y =</span> <span class="st">"Count</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>()</code></pre></div>
<p><img src="figures/moose-migration-repeatability/rel_angle_plot_monthly-1.png" width="1152" /></p>
<p><br></p>
</div>
<div id="absolute-turn-angle-plots" class="section level2">
<h2>Absolute turn angle plots</h2>
<p>Up is North</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">ggplot</span>(<span class="kw">filter</span>(mma, dt_days <span class="op">==</span><span class="st"> </span><span class="dv">1</span> <span class="op">&</span><span class="st"> </span><span class="op">!</span><span class="kw">is.na</span>(abs.angle)), <span class="kw">aes</span>(<span class="dt">x =</span> abs.angle)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_histogram</span>(<span class="dt">bins =</span> <span class="dv">24</span>, <span class="dt">color =</span> <span class="st">"black"</span>, <span class="dt">fill =</span> <span class="st">"gray50"</span>, <span class="dt">alpha =</span> <span class="fl">0.5</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_continuous</span>(<span class="dt">limits =</span> <span class="kw">c</span>(<span class="op">-</span>pi, pi),
<span class="dt">breaks =</span> <span class="kw">seq</span>(<span class="op">-</span>pi, pi <span class="op">-</span><span class="st"> </span>pi<span class="op">/</span><span class="dv">4</span>, <span class="dt">by =</span> pi<span class="op">/</span><span class="dv">4</span>),
<span class="dt">minor_breaks =</span> <span class="kw">seq</span>(<span class="op">-</span>pi, pi <span class="op">-</span><span class="st"> </span>pi<span class="op">/</span><span class="dv">12</span>, <span class="dt">by =</span> pi<span class="op">/</span><span class="dv">12</span>),
<span class="dt">labels =</span> <span class="kw">c</span>(<span class="st">"N"</span>, <span class="st">"NE"</span>, <span class="st">"E"</span>, <span class="st">"SE"</span>, <span class="st">"S"</span>, <span class="st">"SW"</span>, <span class="st">"W"</span>, <span class="st">"NW"</span>)) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_polar</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Absolute Turn Angle"</span>, <span class="dt">y =</span> <span class="st">"Count</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>()</code></pre></div>
<p><img src="figures/moose-migration-repeatability/abs_angle_plot_combined-1.png" width="1152" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">ggplot</span>(<span class="kw">filter</span>(mma, dt_days <span class="op">==</span><span class="st"> </span><span class="dv">1</span> <span class="op">&</span><span class="st"> </span><span class="op">!</span><span class="kw">is.na</span>(abs.angle)),
<span class="kw">aes</span>(<span class="dt">x =</span> abs.angle)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_histogram</span>(<span class="dt">bins =</span> <span class="dv">24</span>, <span class="dt">color =</span> <span class="st">"black"</span>, <span class="dt">fill =</span> <span class="st">"gray50"</span>, <span class="dt">alpha =</span> <span class="fl">0.5</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_continuous</span>(<span class="dt">limits =</span> <span class="kw">c</span>(<span class="op">-</span>pi, pi),
<span class="dt">breaks =</span> <span class="kw">seq</span>(<span class="op">-</span>pi, pi <span class="op">-</span><span class="st"> </span>pi<span class="op">/</span><span class="dv">4</span>, <span class="dt">by =</span> pi<span class="op">/</span><span class="dv">4</span>),
<span class="dt">minor_breaks =</span> <span class="kw">seq</span>(<span class="op">-</span>pi, pi <span class="op">-</span><span class="st"> </span>pi<span class="op">/</span><span class="dv">12</span>, <span class="dt">by =</span> pi<span class="op">/</span><span class="dv">12</span>),
<span class="dt">labels =</span> <span class="kw">c</span>(<span class="st">"N"</span>, <span class="st">"NE"</span>, <span class="st">"E"</span>, <span class="st">"SE"</span>, <span class="st">"S"</span>, <span class="st">"SW"</span>, <span class="st">"W"</span>, <span class="st">"NW"</span>)) <span class="op">+</span>
<span class="st"> </span><span class="kw">facet_wrap</span>(<span class="op">~</span>month_of) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_polar</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Absolute Turn Angle"</span>, <span class="dt">y =</span> <span class="st">"Count</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>()</code></pre></div>
<p><img src="figures/moose-migration-repeatability/abs_angle_plot_monthly-1.png" width="1152" /></p>
<p><br></p>
</div>
<div id="step-length-distributions" class="section level2">
<h2>Step length distributions</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Plot histogram of step lengths for each animal</span>
<span class="kw">ggplot</span>(<span class="kw">filter</span>(mma, dt_days <span class="op">==</span><span class="st"> </span><span class="dv">1</span> <span class="op">&</span><span class="st"> </span><span class="op">!</span><span class="kw">is.na</span>(dist)),
<span class="kw">aes</span>(<span class="dt">x =</span> dist)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_histogram</span>(<span class="dt">bins =</span> <span class="dv">50</span>, <span class="dt">color =</span> <span class="st">"black"</span>, <span class="dt">fill =</span> <span class="st">"gray50"</span>, <span class="dt">alpha =</span> <span class="fl">0.5</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"Step Length (m)"</span>, <span class="dt">y =</span> <span class="st">"Count</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">facet_grid</span>(month_of <span class="op">~</span><span class="st"> </span>., <span class="dt">scales =</span> <span class="st">"free_y"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_sqrt</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_cartesian</span>(<span class="dt">xlim =</span> <span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">20000</span>))</code></pre></div>
<p><img src="figures/moose-migration-repeatability/step_length_plot-1.png" width="1152" /></p>
<p><br></p>
</div>
<div id="density-of-step-lengths" class="section level2">
<h2>Density of step lengths</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">mma<span class="op">$</span>plot_date <-<span class="st"> </span><span class="kw">as.POSIXct</span>(mma<span class="op">$</span>plot_date)
<span class="kw">ggplot</span>(<span class="kw">filter</span>(mma, dt_days <span class="op">==</span><span class="st"> </span><span class="dv">1</span> <span class="op">&</span><span class="st"> </span><span class="op">!</span><span class="kw">is.na</span>(dist)),
<span class="kw">aes</span>(<span class="dt">x =</span> plot_date, <span class="dt">y =</span> dist<span class="op">/</span><span class="dv">1000</span>)) <span class="op">+</span>
<span class="st"> </span><span class="kw">stat_density_2d</span>(<span class="dt">geom =</span> <span class="st">"raster"</span>, <span class="kw">aes</span>(<span class="dt">fill =</span> ..density..),
<span class="dt">contour =</span> <span class="ot">FALSE</span>, <span class="dt">n =</span> <span class="dv">200</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_fill_gradientn</span>(<span class="dt">colours =</span> <span class="kw">c</span>(<span class="st">"#FFFFFF"</span>, <span class="kw">rev</span>(<span class="kw">viridis</span>(<span class="dv">9</span>, <span class="dt">option =</span> <span class="st">"magma"</span>))),
<span class="dt">trans =</span> <span class="kw">sqrt_trans</span>(),
<span class="dt">name =</span> <span class="st">"Density"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Julian Day"</span>, <span class="dt">y =</span> <span class="st">"Step Length (km)</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_y_sqrt</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_datetime</span>(<span class="dt">date_breaks =</span> <span class="st">"1 month"</span>, <span class="dt">date_labels =</span> <span class="st">"%d-%b"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_cartesian</span>(<span class="dt">expand =</span> <span class="ot">FALSE</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme</span>(<span class="dt">panel.ontop =</span> <span class="ot">TRUE</span>,
<span class="dt">panel.background =</span> <span class="kw">element_rect</span>(<span class="dt">fill =</span> <span class="ot">NA</span>),
<span class="dt">panel.grid.minor =</span> <span class="kw">element_blank</span>())</code></pre></div>
<p><img src="figures/moose-migration-repeatability/step_density_plot-1.png" width="1152" /></p>
<p><br></p>
</div>
<div id="nsd-plot" class="section level2">
<h2>NSD plot</h2>
<p>Against day of year (as if all occurred in same year)</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">ggplot</span>(mma, <span class="kw">aes</span>(<span class="dt">x =</span> plot_date, <span class="dt">y =</span> <span class="kw">sqrt</span>(nsd<span class="op">/</span><span class="dv">1000000</span>))) <span class="op">+</span>
<span class="st"> </span><span class="kw">stat_density_2d</span>(<span class="dt">geom =</span> <span class="st">"raster"</span>, <span class="kw">aes</span>(<span class="dt">fill =</span> ..density..),
<span class="dt">contour =</span> <span class="ot">FALSE</span>, <span class="dt">n =</span> <span class="dv">200</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="kw">aes</span>(<span class="dt">group =</span> burst), <span class="dt">alpha =</span> <span class="fl">0.05</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_fill_gradientn</span>(<span class="dt">colours =</span> <span class="kw">c</span>(<span class="st">"#FFFFFF"</span>, <span class="kw">rev</span>(<span class="kw">viridis</span>(<span class="dv">20</span>, <span class="dt">option =</span> <span class="st">"magma"</span>))),
<span class="co"># trans = sqrt_trans(),</span>
<span class="dt">name =</span> <span class="st">"Density"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_datetime</span>(<span class="dt">date_labels =</span> <span class="st">"%b"</span>, <span class="dt">date_breaks =</span> <span class="st">"1 month"</span>,
<span class="dt">date_minor_breaks =</span> <span class="st">"1 month"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Date"</span>, <span class="dt">y =</span> <span class="st">"Net displacement (km)</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">expand_limits</span>(<span class="dt">y =</span> <span class="dv">0</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_cartesian</span>(<span class="dt">expand =</span> <span class="ot">FALSE</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme</span>(<span class="dt">panel.ontop =</span> <span class="ot">TRUE</span>,
<span class="dt">panel.background =</span> <span class="kw">element_rect</span>(<span class="dt">fill =</span> <span class="ot">NA</span>),
<span class="dt">panel.grid.minor =</span> <span class="kw">element_blank</span>())</code></pre></div>
<p><img src="figures/moose-migration-repeatability/nsd_density_plot-1.png" width="1152" /></p>
<p><br></p>
</div>
</div>
<div id="map" class="section level1">
<h1>Map</h1>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Maps of tracks</span>
<span class="co"># High-res map of Sweden (need to download once, then can reload from file)</span>
swe <-<span class="st"> </span>raster<span class="op">::</span><span class="kw">getData</span>(<span class="dt">name =</span> <span class="st">"GADM"</span>, <span class="dt">country =</span> <span class="st">"SWE"</span>, <span class="dt">path =</span> <span class="st">"data"</span>,
<span class="dt">download =</span> <span class="ot">FALSE</span>, <span class="dt">level =</span> <span class="dv">0</span>)
nor <-<span class="st"> </span>raster<span class="op">::</span><span class="kw">getData</span>(<span class="dt">name =</span> <span class="st">"GADM"</span>, <span class="dt">country =</span> <span class="st">"NOR"</span>, <span class="dt">path =</span> <span class="st">"data"</span>,
<span class="dt">download =</span> <span class="ot">FALSE</span>, <span class="dt">level =</span> <span class="dv">0</span>)
lan <-<span class="st"> </span>raster<span class="op">::</span><span class="kw">getData</span>(<span class="dt">name =</span> <span class="st">"GADM"</span>, <span class="dt">country =</span> <span class="st">"SWE"</span>, <span class="dt">path =</span> <span class="st">"data"</span>,
<span class="dt">download =</span> <span class="ot">FALSE</span>, <span class="dt">level =</span> <span class="dv">1</span>)
nor_lan <-<span class="st"> </span>raster<span class="op">::</span><span class="kw">getData</span>(<span class="dt">name =</span> <span class="st">"GADM"</span>, <span class="dt">country =</span> <span class="st">"NOR"</span>, <span class="dt">path =</span> <span class="st">"data"</span>,
<span class="dt">download =</span> <span class="ot">FALSE</span>, <span class="dt">level =</span> <span class="dv">1</span>)
vb <-<span class="st"> </span>lan[lan<span class="op">$</span>NAME_<span class="dv">1</span> <span class="op">==</span><span class="st"> "Västerbotten"</span>, ]
cities <-<span class="st"> </span><span class="kw">readShapePoints</span>(<span class="st">"~/Documents/Projects/MooseNavigation/ne_10m_populated_places/ne_10m_populated_places.shp"</span>,
<span class="dt">proj4string =</span> <span class="kw">CRS</span>(<span class="kw">proj4string</span>(swe)))
cities_swe <-<span class="st"> </span>cities[swe, ]
cities_nor <-<span class="st"> </span>cities[nor, ]
<span class="co"># Project to RT90</span>
swe <-<span class="st"> </span><span class="kw">spTransform</span>(swe, <span class="kw">CRS</span>(<span class="kw">proj4string</span>(points)))
nor <-<span class="st"> </span><span class="kw">spTransform</span>(nor, <span class="kw">CRS</span>(<span class="kw">proj4string</span>(points)))
lan <-<span class="st"> </span><span class="kw">spTransform</span>(lan, <span class="kw">CRS</span>(<span class="kw">proj4string</span>(points)))
nor_lan <-<span class="st"> </span><span class="kw">spTransform</span>(nor_lan, <span class="kw">CRS</span>(<span class="kw">proj4string</span>(points)))
vb <-<span class="st"> </span><span class="kw">spTransform</span>(vb, <span class="kw">CRS</span>(<span class="kw">proj4string</span>(points)))
cities_swe <-<span class="st"> </span><span class="kw">spTransform</span>(cities_swe, <span class="kw">CRS</span>(<span class="kw">proj4string</span>(points)))
cities_nor <-<span class="st"> </span><span class="kw">spTransform</span>(cities_nor, <span class="kw">CRS</span>(<span class="kw">proj4string</span>(points)))
<span class="co"># Convert to data frame for plotting</span>
swe_df <-<span class="st"> </span><span class="kw">fortify</span>(swe)
nor_df <-<span class="st"> </span><span class="kw">fortify</span>(nor)
lan_df <-<span class="st"> </span><span class="kw">fortify</span>(lan)
nor_lan_df <-<span class="st"> </span><span class="kw">fortify</span>(nor_lan)
cities_swe <-<span class="st"> </span><span class="kw">as.data.frame</span>(cities_swe)
cities_nor <-<span class="st"> </span><span class="kw">as.data.frame</span>(cities_nor)</code></pre></div>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Create map</span>
<span class="kw">ggplot</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_polygon</span>(<span class="dt">data =</span> swe_df, <span class="kw">aes</span>(<span class="dt">x =</span> long, <span class="dt">y =</span> lat, <span class="dt">group =</span> group),
<span class="dt">size =</span> <span class="fl">0.5</span>, <span class="dt">fill =</span> <span class="st">"gray95"</span>, <span class="dt">color =</span> <span class="ot">NA</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_polygon</span>(<span class="dt">data =</span> nor_df, <span class="kw">aes</span>(<span class="dt">x =</span> long, <span class="dt">y =</span> lat, <span class="dt">group =</span> group),
<span class="dt">size =</span> <span class="fl">0.5</span>, <span class="dt">fill =</span> <span class="st">"gray95"</span>, <span class="dt">color =</span> <span class="ot">NA</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="dt">data =</span> lan_df, <span class="kw">aes</span>(<span class="dt">x =</span> long, <span class="dt">y =</span> lat, <span class="dt">group =</span> group),
<span class="dt">size =</span> <span class="fl">0.1</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="dt">data =</span> nor_lan_df, <span class="kw">aes</span>(<span class="dt">x =</span> long, <span class="dt">y =</span> lat, <span class="dt">group =</span> group),
<span class="dt">size =</span> <span class="fl">0.1</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="dt">data =</span> swe_df, <span class="kw">aes</span>(<span class="dt">x =</span> long, <span class="dt">y =</span> lat, <span class="dt">group =</span> group),
<span class="dt">size =</span> <span class="fl">0.5</span>, <span class="dt">color =</span> <span class="st">"black"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="dt">data =</span> nor_df, <span class="kw">aes</span>(<span class="dt">x =</span> long, <span class="dt">y =</span> lat, <span class="dt">group =</span> group),
<span class="dt">size =</span> <span class="fl">0.5</span>, <span class="dt">color =</span> <span class="st">"black"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_point</span>(<span class="dt">data =</span> cities_swe, <span class="kw">aes</span>(<span class="dt">x =</span> coords.x1, <span class="dt">y =</span> coords.x2)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_label</span>(<span class="dt">data =</span> cities_swe, <span class="kw">aes</span>(<span class="dt">x =</span> coords.x1, <span class="dt">y =</span> coords.x2,
<span class="dt">label =</span> NAMEASCII), <span class="dt">nudge_y =</span> <span class="dv">8000</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_point</span>(<span class="dt">data =</span> cities_nor, <span class="kw">aes</span>(<span class="dt">x =</span> coords.x1, <span class="dt">y =</span> coords.x2)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_label</span>(<span class="dt">data =</span> cities_nor, <span class="kw">aes</span>(<span class="dt">x =</span> coords.x1, <span class="dt">y =</span> coords.x2,
<span class="dt">label =</span> NAMEASCII), <span class="dt">nudge_y =</span> <span class="dv">8000</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="dt">data =</span> mma, <span class="kw">aes</span>(<span class="dt">x =</span> x, <span class="dt">y =</span> y, <span class="dt">group =</span> burst),
<span class="dt">alpha =</span> <span class="fl">0.5</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_fixed</span>(<span class="dt">xlim =</span> <span class="kw">bbox</span>(moose_spdf)[<span class="dv">1</span>, ], <span class="dt">ylim =</span> <span class="kw">bbox</span>(moose_spdf)[<span class="dv">2</span>, ]) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_osa</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_colour_discrete</span>(<span class="dt">guide =</span> <span class="ot">FALSE</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Easting"</span>, <span class="dt">y =</span> <span class="st">"Northing</span><span class="ch">\n</span><span class="st">"</span>)</code></pre></div>
<p><img src="figures/moose-migration-repeatability/create_moose_map-1.png" width="1152" /></p>
<br>
<hr>
<p><br></p>
</div>
<div id="identification-of-migrants-overview" class="section level1">
<h1>Identification of Migrants: Overview</h1>
<p>The objective of this section is to identify individual migration events in the set of moose movement data using a semi-automated method based on the animal’s net squared displacement (NSD) over one annual cycle. Individual moose that show migratory behavior will have an NSD pattern that differs from resident, nomadic, or dispersing individuals. We also want to calculate various parameters for each migration event (spring and fall).</p>
<p><br></p>
<hr>
<p><br></p>
</div>
<div id="prepare-data" class="section level1">
<h1>Prepare data</h1>
<div id="smooth-nsd" class="section level2">
<h2>Smooth NSD</h2>
<p>We first apply a rolling mean function to get a smoothed NSD. This is modified slightly from Singh et al. 2016 in that I’m using a center-aligned rolling mean rather than a right-aligned rolling mean.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">mma<span class="op">$</span>plot_date <-<span class="st"> </span><span class="kw">as.POSIXct</span>(mma<span class="op">$</span>plot_date)
df <-<span class="st"> </span>mma
df<span class="op">$</span>NSDm <-<span class="st"> </span>df<span class="op">$</span>nsd <span class="op">/</span><span class="st"> </span><span class="dv">1000000</span>
<span class="co"># Now estimate MSD using 30 time steps)</span>
apply_rollmean <-<span class="st"> </span><span class="cf">function</span>(df) {
z <-<span class="st"> </span><span class="kw">zoo</span>(df<span class="op">$</span>NSDm, df<span class="op">$</span>nDaysYr)
<span class="co"># The rolling mean was right-aligned in Singh, Allen and Ericsson 2016</span>
df<span class="op">$</span>rollmean_r <-<span class="st"> </span><span class="kw">rollapply</span>(z, <span class="dt">width =</span> <span class="dv">30</span>, <span class="dt">align =</span> <span class="st">"right"</span>, <span class="dt">partial =</span> <span class="ot">TRUE</span>,
<span class="dt">FUN =</span> mean, <span class="dt">na.rm =</span> <span class="ot">TRUE</span>)
<span class="co"># Proceeding here with center-aligned rolling mean</span>
df<span class="op">$</span>rollmean_c <-<span class="st"> </span><span class="kw">rollapply</span>(z, <span class="dt">width =</span> <span class="dv">30</span>, <span class="dt">align =</span> <span class="st">"center"</span>, <span class="dt">partial =</span> <span class="ot">TRUE</span>,
<span class="dt">FUN =</span> mean, <span class="dt">na.rm =</span> <span class="ot">TRUE</span>)
<span class="kw">return</span>(df)
}
<span class="co"># Apply the rolling-mean functions</span>
df <-<span class="st"> </span>df <span class="op">%>%</span>
<span class="st"> </span><span class="kw">group_by</span>(id) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">do</span>(<span class="kw">apply_rollmean</span>(.)) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">rename</span>(<span class="dt">MSD =</span> rollmean_c,
<span class="dt">MSD_r =</span> rollmean_r,
<span class="dt">MooseYrID =</span> id)</code></pre></div>
<p><br></p>
<p>We can compare the two different rolling-mean methods for first 16 animals. This figure shows that the right-aligned rolling mean gives estimates for xmidA and xmidB that are shifted forward in time. The drawback of the center-aligned rolling mean is that it estimates an earlier start date for when the animal first leaves its seasonal range to embark on migration, but the model parameters do not depend on this and should be better estimated by the center-aligned rolling mean.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">temp <-<span class="st"> </span><span class="kw">filter</span>(df, MooseYrID <span class="op">%in%</span><span class="st"> </span><span class="kw">levels</span>(df<span class="op">$</span>MooseYrID)[<span class="dv">1</span><span class="op">:</span><span class="dv">16</span>])
temp <-<span class="st"> </span><span class="kw">gather</span>(temp, var, value, NSDm, MSD, MSD_r)
temp<span class="op">$</span>var <-<span class="st"> </span><span class="kw">factor</span>(temp<span class="op">$</span>var, <span class="dt">levels =</span> <span class="kw">c</span>(<span class="st">"NSDm"</span>, <span class="st">"MSD_r"</span>, <span class="st">"MSD"</span>))
<span class="kw">ggplot</span>(temp) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="kw">aes</span>(<span class="dt">x =</span> plot_date, <span class="dt">y =</span> <span class="kw">sqrt</span>(value), <span class="dt">color =</span> var),
<span class="dt">size =</span> <span class="fl">0.7</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Date"</span>, <span class="dt">y =</span> <span class="st">"Net displacement (km)</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">expand_limits</span>(<span class="dt">y =</span> <span class="dv">0</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">facet_wrap</span>(<span class="op">~</span>MooseYrID, <span class="dt">scales =</span> <span class="st">"free"</span>, <span class="dt">ncol =</span> <span class="dv">4</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_datetime</span>(<span class="dt">date_labels =</span> <span class="st">"%b"</span>, <span class="dt">date_breaks =</span> <span class="st">"1 month"</span>,
<span class="dt">date_minor_breaks =</span> <span class="st">"1 month"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_color_manual</span>(<span class="dt">values =</span> <span class="kw">c</span>(<span class="st">"gray80"</span>, <span class="st">"lightblue"</span>, <span class="st">"dodgerblue4"</span>),
<span class="dt">name =</span> <span class="st">""</span>,
<span class="dt">labels =</span> <span class="kw">c</span>(<span class="st">"Actual"</span>, <span class="st">"Right-aligned rolling mean"</span>,
<span class="st">"Center-aligned rolling mean"</span>)) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme</span>(<span class="dt">strip.background =</span> <span class="kw">element_blank</span>(),
<span class="dt">axis.text.x =</span> <span class="kw">element_text</span>(<span class="dt">angle =</span> <span class="dv">90</span>),
<span class="dt">panel.grid =</span> <span class="kw">element_blank</span>(),
<span class="dt">legend.key.width =</span> grid<span class="op">::</span><span class="kw">unit</span>(<span class="fl">0.5</span>, <span class="st">"cm"</span>)) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_cartesian</span>()</code></pre></div>
<p><img src="figures/moose-migration-repeatability/roll_mean_comparison-1.png" width="1152" /></p>
<p><br></p>
</div>
</div>
<div id="model-smoothed-nsd" class="section level1">
<h1>Model smoothed NSD</h1>
<div id="fit-models-to-smoothed-nsd" class="section level2">
<h2>Fit models to smoothed NSD</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Now we fit each of the models described in Bunnefeld et al. 2011 and Singh et al. 2012</span>
<span class="co"># Change starting values if no conv (=mean), such as a specific value, or median etc.</span>
<span class="co"># Providing a start improve model convergence, which can also be obtained by using parameters from previously estimated models</span>
<span class="co"># First a null model</span>
null.HRmod <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span>A,
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> A <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> A <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">groups =</span> <span class="op">~</span>MooseYrID,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">A =</span> <span class="kw">mean</span>(df<span class="op">$</span>MSD)))
<span class="co"># Sedentary HR model</span>
asym.HRmod <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span>Asym<span class="op">*</span>(<span class="dv">1</span> <span class="op">-</span><span class="st"> </span><span class="kw">exp</span>(lrc <span class="op">*</span><span class="st"> </span>nDaysYr)),
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> Asym <span class="op">+</span><span class="st"> </span>lrc <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> Asym <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">groups =</span> <span class="op">~</span>MooseYrID,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">Asym =</span> <span class="kw">summary</span>(null.HRmod)<span class="op">$</span>tTable[<span class="dv">1</span>],
<span class="dt">lrc =</span> <span class="op">-</span><span class="fl">0.002</span>))
<span class="co"># Dispersal model with distance (Asym) and timing (xmid) varying between individuals.</span>
ranef.Dispmod <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span>Asym <span class="op">/</span><span class="st"> </span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmid <span class="op">-</span><span class="st"> </span>nDaysYr) <span class="op">/</span><span class="st"> </span>scal)),
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> Asym <span class="op">+</span><span class="st"> </span>xmid <span class="op">+</span><span class="st"> </span>scal <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> Asym <span class="op">+</span><span class="st"> </span>xmid <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">groups =</span> <span class="op">~</span>MooseYrID,
<span class="dt">na.action =</span> na.exclude,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">Asym =</span> <span class="kw">summary</span>(asym.HRmod)<span class="op">$</span>tTable[<span class="dv">1</span>],
<span class="dt">xmid =</span> <span class="dv">30</span>, <span class="dt">scal =</span> <span class="dv">2</span>))
<span class="co"># Dispersal model with Distance, timing and duration (scal) varying between individuals.</span>
full.Dispmod <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span>Asym <span class="op">/</span><span class="st"> </span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmid <span class="op">-</span><span class="st"> </span>nDaysYr) <span class="op">/</span><span class="st"> </span>scal)),
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> Asym <span class="op">+</span><span class="st"> </span>xmid <span class="op">+</span><span class="st"> </span>scal <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> Asym <span class="op">+</span><span class="st"> </span>xmid <span class="op">+</span><span class="st"> </span>scal <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">groups =</span> <span class="op">~</span>MooseYrID,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">Asym =</span> <span class="kw">summary</span>(ranef.Dispmod)<span class="op">$</span>tTable[<span class="dv">1</span>],
<span class="dt">xmid =</span> <span class="kw">summary</span>(ranef.Dispmod)<span class="op">$</span>tTable[<span class="dv">2</span>],
<span class="dt">scal =</span> <span class="kw">summary</span>(ranef.Dispmod)<span class="op">$</span>tTable[<span class="dv">3</span>]),
<span class="dt">control =</span> <span class="kw">list</span>(<span class="dt">pnlsTol =</span> <span class="dv">10</span>))
<span class="co"># Simple Migration model with only distance varying between individuals</span>
asym.Migrmod <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span>asym<span class="op">/</span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmidA <span class="op">-</span><span class="st"> </span>nDaysYr) <span class="op">/</span><span class="st"> </span>scale1)) <span class="op">+</span>
<span class="st"> </span>(<span class="op">-</span>asym <span class="op">/</span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmidB <span class="op">-</span><span class="st"> </span>nDaysYr) <span class="op">/</span><span class="st"> </span>scale2))),
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> asym <span class="op">+</span><span class="st"> </span>xmidA <span class="op">+</span><span class="st"> </span>xmidB <span class="op">+</span><span class="st"> </span>scale1 <span class="op">+</span><span class="st"> </span>scale2 <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> asym <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">groups =</span> <span class="op">~</span>MooseYrID,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">asym =</span> <span class="dv">5515</span>,<span class="dt">xmidA =</span> <span class="dv">90</span>, <span class="dt">xmidB =</span> <span class="dv">242</span>,
<span class="dt">scale1 =</span> <span class="dv">4</span>, <span class="dt">scale2 =</span> <span class="dv">4</span>))
<span class="co"># More complex migration model with distance, timing of Migration 1 (xmidA) and timing of migration 2 (xmidB)</span>
ranef2.Migrmod <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span>asym<span class="op">/</span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmidA <span class="op">-</span><span class="st"> </span>nDaysYr) <span class="op">/</span><span class="st"> </span>scale1)) <span class="op">+</span>
<span class="st"> </span>(<span class="op">-</span>asym <span class="op">/</span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmidB <span class="op">-</span><span class="st"> </span>nDaysYr)<span class="op">/</span>scale2))),
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> asym <span class="op">+</span><span class="st"> </span>xmidA <span class="op">+</span><span class="st"> </span>xmidB <span class="op">+</span><span class="st"> </span>scale1 <span class="op">+</span><span class="st"> </span>scale2 <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> asym <span class="op">+</span><span class="st"> </span>xmidA <span class="op">+</span><span class="st"> </span>xmidB <span class="op">~</span><span class="st"> </span><span class="dv">1</span> <span class="op">|</span><span class="st"> </span>MooseYrID,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">asym =</span> <span class="dv">2200</span>, <span class="dt">xmidA =</span> <span class="dv">100</span>,
<span class="dt">xmidB =</span> <span class="dv">295</span>, <span class="dt">scale1 =</span> <span class="dv">10</span>, <span class="dt">scale2 =</span> <span class="dv">15</span>),
<span class="dt">control =</span> <span class="kw">list</span>(<span class="dt">tolerance =</span> <span class="fl">0.1</span>))
<span class="kw">summary</span>(ranef2.Migrmod)
<span class="co"># Complete migration model with all parameters varying between individuals. Normally this will struggle to converge in a dataset</span>
<span class="co"># that contain a mix of migrants and non-migrants, and is more important in later stages when estimating timing of movements for</span>
<span class="co"># migratory individuals only using the NSD rather than the MSD</span>
<span class="co"># I COULD NOT GET THIS ONE TO CONVERGE DESPITE A LOT OF TINKERING, SO COMMENTED OUT HERE</span>
<span class="co"># ranef4.Migrmod <- nlme(MSD ~ asym / (1 + exp((xmidA - nDaysYr) / scale1)) +</span>
<span class="co"># (-asym /(1 + exp((xmidB - nDaysYr) / scale2))),</span>
<span class="co"># data = df,</span>
<span class="co"># fixed = list(asym + xmidA + xmidB + scale1 + scale2 ~ 1),</span>
<span class="co"># random = asym + xmidA + xmidB + scale1 + scale2 ~ 1 | MooseYrID,</span>
<span class="co"># start = c(asym = summary(ranef2.Migrmod)$tTable[1],</span>
<span class="co"># xmidA = summary(ranef2.Migrmod)$tTable[2],</span>
<span class="co"># xmidB = summary(ranef2.Migrmod)$tTable[3],</span>
<span class="co"># scale1 = 5,</span>
<span class="co"># scale2 = 10))</span>
<span class="co"># Mixed Migratory Model with distance and timing of Migration 1, and distance and timing of Migration 2, varying between individuals.</span>
mix.Migrmod <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span>asymA<span class="op">/</span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmidA <span class="op">-</span><span class="st"> </span>nDaysYr) <span class="op">/</span><span class="st"> </span>scale1)) <span class="op">+</span>
<span class="st"> </span>(<span class="op">-</span>asymB <span class="op">/</span>(<span class="dv">1</span> <span class="op">+</span><span class="st"> </span><span class="kw">exp</span>((xmidB <span class="op">-</span><span class="st"> </span>nDaysYr) <span class="op">/</span><span class="st"> </span>scale2))),
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> asymA <span class="op">+</span><span class="st"> </span>asymB <span class="op">+</span><span class="st"> </span>xmidA <span class="op">+</span><span class="st"> </span>xmidB <span class="op">+</span><span class="st"> </span>scale1 <span class="op">+</span><span class="st"> </span>scale2 <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> asymA <span class="op">+</span><span class="st"> </span>asymB <span class="op">+</span><span class="st"> </span>xmidA <span class="op">+</span><span class="st"> </span>xmidB <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">groups =</span> <span class="op">~</span>MooseYrID,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">asymA =</span> <span class="dv">10000</span>, <span class="dt">asymB =</span> <span class="dv">8000</span>, <span class="dt">xmidA =</span> <span class="dv">110</span>, <span class="dt">xmidB =</span> <span class="dv">300</span>, <span class="dt">scale1 =</span> <span class="dv">8</span>, <span class="dt">scale2 =</span> <span class="dv">12</span>))
<span class="co"># Nomad model</span>
linear <-<span class="st"> </span><span class="kw">nlme</span>(MSD <span class="op">~</span><span class="st"> </span><span class="dv">4</span> <span class="op">*</span><span class="st"> </span>D <span class="op">*</span><span class="st"> </span>nDaysYr,
<span class="dt">data =</span> df,
<span class="dt">fixed =</span> D <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">random =</span> D <span class="op">~</span><span class="st"> </span><span class="dv">1</span>,
<span class="dt">groups =</span> <span class="op">~</span>MooseYrID,
<span class="dt">start =</span> <span class="kw">c</span>(<span class="dt">D =</span> <span class="dv">3</span>))</code></pre></div>
<p><br></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># GOF indiv level</span>
<span class="co"># change this list below to include the model that fitted (with highest number of random effects) for each movement type</span>
HRMod <-<span class="st"> </span>asym.HRmod
NullMod <-<span class="st"> </span>null.HRmod
DispMod <-<span class="st"> </span>full.Dispmod
MigrMod <-<span class="st"> </span>ranef2.Migrmod
MigrModC <-<span class="st"> </span>mix.Migrmod
NomadMod <-<span class="st"> </span>linear</code></pre></div>
</div>
<div id="evaluate-model-fit" class="section level2">
<h2>Evaluate model fit</h2>
<p>This bit modified from script provided in Singh et al 2016.</p>
<ul>
<li><p>We first define a new function <code>cc_fun</code> that takes as arguments a single animal’s data, the model to evaluate, and the column of interest.</p></li>
<li><p>The we use dplyr to split the df by individual, apply the function to each animal and for all models, and combine the results</p></li>
</ul>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Now perform the calculations for the goodness of fit (i.e. concordance criterion).</span>
<span class="co"># Define a concordance criterion function that takes in:</span>
<span class="co"># a subsetted df (for an individual animal), a fitted model, and the column</span>
cc_fun <-<span class="st"> </span><span class="cf">function</span>(df_sub, mod, col) {
tmp_id <-<span class="st"> </span>df_sub[<span class="dv">1</span>, ]<span class="op">$</span>MooseYrID
tmp_msd <-<span class="st"> </span><span class="kw">as.numeric</span>(<span class="kw">as.matrix</span>(df_sub[, col]))
tmp_mod <-<span class="st"> </span><span class="kw">as.numeric</span>(<span class="kw">fitted</span>(mod)[<span class="kw">which</span>(<span class="kw">names</span>(<span class="kw">fitted</span>(mod)) <span class="op">==</span><span class="st"> </span>tmp_id)])
res <-<span class="st"> </span><span class="dv">1</span> <span class="op">-</span><span class="st"> </span>(<span class="kw">sum</span>((tmp_msd <span class="op">-</span><span class="st"> </span>tmp_mod) <span class="op">^</span><span class="st"> </span><span class="dv">2</span>)) <span class="op">/</span>
<span class="st"> </span>((<span class="kw">sum</span>((tmp_msd <span class="op">-</span><span class="st"> </span><span class="kw">mean</span>(tmp_msd)) <span class="op">^</span><span class="st"> </span><span class="dv">2</span>)) <span class="op">+</span>
<span class="st"> </span>(<span class="kw">sum</span>((tmp_mod <span class="op">-</span><span class="st"> </span><span class="kw">mean</span>(tmp_mod)) <span class="op">^</span><span class="st"> </span><span class="dv">2</span>)) <span class="op">+</span>
<span class="st"> </span>(<span class="kw">length</span>(tmp_msd) <span class="op">*</span><span class="st"> </span>((<span class="kw">mean</span>(tmp_msd) <span class="op">-</span><span class="st"> </span><span class="kw">mean</span>(tmp_mod)) <span class="op">^</span><span class="st"> </span><span class="dv">2</span>)))
<span class="kw">return</span>(res)
}
<span class="co"># Apply the CC function for each MooseYrID and model class</span>
moveClass <-<span class="st"> </span>df <span class="op">%>%</span>
<span class="st"> </span><span class="kw">group_by</span>(MooseYrID) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">do</span>(<span class="dt">cc_HRMod =</span> <span class="kw">cc_fun</span>(., HRMod, <span class="st">"MSD"</span>),
<span class="dt">cc_NullMod =</span> <span class="kw">cc_fun</span>(., NullMod, <span class="st">"MSD"</span>),
<span class="dt">cc_DispMod =</span> <span class="kw">cc_fun</span>(., DispMod, <span class="st">"MSD"</span>),
<span class="dt">cc_MigrMod =</span> <span class="kw">cc_fun</span>(., MigrMod, <span class="st">"MSD"</span>),
<span class="dt">cc_MigrModC =</span> <span class="kw">cc_fun</span>(., MigrModC, <span class="st">"MSD"</span>),
<span class="dt">cc_NomadMod =</span> <span class="kw">cc_fun</span>(., NomadMod, <span class="st">"MSD"</span>)) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">unnest</span>()
<span class="co"># Determine which model has the max CC for each animal</span>
maxcc1ID <-<span class="st"> </span>(<span class="kw">apply</span>(moveClass[, <span class="dv">2</span><span class="op">:</span><span class="dv">7</span>], <span class="dv">1</span>, which.max))
<span class="co"># Replace column index with model name</span>
moveClass<span class="op">$</span>bestMod.cc1ID <-<span class="st"> </span><span class="kw">factor</span>(<span class="kw">ifelse</span>(maxcc1ID <span class="op">==</span><span class="st"> </span><span class="dv">1</span>, <span class="st">"HRmod"</span>,
<span class="kw">ifelse</span>(maxcc1ID <span class="op">==</span><span class="st"> </span><span class="dv">2</span>, <span class="st">"NullMod"</span>,
<span class="kw">ifelse</span>(maxcc1ID <span class="op">==</span><span class="st"> </span><span class="dv">3</span>, <span class="st">"Dispmod"</span>,
<span class="kw">ifelse</span>(maxcc1ID <span class="op">==</span><span class="st"> </span><span class="dv">4</span>, <span class="st">"MigrMod"</span>,
<span class="kw">ifelse</span>(maxcc1ID <span class="op">==</span><span class="st"> </span><span class="dv">5</span>, <span class="st">"MigrModC"</span>,
<span class="kw">ifelse</span>(maxcc1ID <span class="op">==</span><span class="st"> </span><span class="dv">6</span>, <span class="st">"nomadMod"</span>, <span class="ot">NA</span>)))))))
<span class="co"># Also get the max CC value</span>
temp <-<span class="st"> </span><span class="kw">numeric</span>(<span class="kw">nrow</span>(moveClass))
<span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="kw">nrow</span>(moveClass)) {
temp[i] <-<span class="st"> </span><span class="kw">as.numeric</span>(moveClass[i, maxcc1ID[i] <span class="op">+</span><span class="st"> </span><span class="dv">1</span>])
}
moveClass<span class="op">$</span>bestMod.cc1 <-<span class="st"> </span>temp
<span class="co"># Also obtain the parameter estimates for the mixed migration model</span>
<span class="co"># Used below for filtering out bad fits and non-migratory animals</span>
coeffs <-<span class="st"> </span><span class="kw">coef</span>(MigrModC)
params <-<span class="st"> </span><span class="kw">bind_cols</span>(moveClass, coeffs)
<span class="co"># Join this back to original df</span>
df_smooth_fitted <-<span class="st"> </span><span class="kw">inner_join</span>(df, params)</code></pre></div>
<p><br></p>
<p>We can now plot the smoothed NSDs for each category of moose. Here, they are color coded by the concordance criterion. The poor-fitting models are darker.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Plot all models</span>
<span class="kw">ggplot</span>(df_smooth_fitted,
<span class="kw">aes</span>(<span class="dt">x =</span> plot_date, <span class="dt">y =</span> <span class="kw">sqrt</span>(MSD), <span class="dt">color =</span> bestMod.cc1)) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="kw">aes</span>(<span class="dt">group =</span> burst), <span class="dt">alpha =</span> <span class="fl">0.25</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Date"</span>, <span class="dt">y =</span> <span class="st">"Net displacement (km)</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">expand_limits</span>(<span class="dt">y =</span> <span class="dv">0</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">facet_wrap</span>(<span class="op">~</span>bestMod.cc1ID, <span class="dt">scales =</span> <span class="st">"free"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_color_gradientn</span>(<span class="dt">colours =</span> <span class="kw">viridis</span>(<span class="dv">10</span>)) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_datetime</span>(<span class="dt">date_labels =</span> <span class="st">"%b"</span>, <span class="dt">date_breaks =</span> <span class="st">"1 month"</span>,
<span class="dt">date_minor_breaks =</span> <span class="st">"1 month"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">theme</span>(<span class="dt">strip.background =</span> <span class="kw">element_blank</span>(),
<span class="dt">axis.text.x =</span> <span class="kw">element_text</span>(<span class="dt">angle =</span> <span class="dv">90</span>),
<span class="dt">panel.grid =</span> <span class="kw">element_blank</span>())</code></pre></div>
<p><img src="figures/moose-migration-repeatability/plot_all_nsd_models-1.png" width="1152" /></p>
<p><br></p>
</div>
</div>
<div id="remove-non-migrants" class="section level1">
<h1>Remove non-migrants</h1>
<p>Now, we must discard the non-migratory animals as well as those that are incorrectly identified as migrants (i.e., their NSD pattern does not show the exepcted “hump” pattern). This is necessary before fitting the final models. There is a fair bit of manual exploration involved here. To ease this, I created an NSD plotting function for examining individual NSD patterns in a given set of animals.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Function for obtaining plot labels</span>
get_labs <-<span class="st"> </span><span class="cf">function</span>(df, fil) {
labs <-<span class="st"> </span>df <span class="op">%>%</span>
<span class="st"> </span><span class="kw">ungroup</span>() <span class="op">%>%</span>
<span class="st"> </span><span class="kw">group_by</span>(MooseYrID) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">summarise</span>(<span class="dt">label =</span> <span class="kw">round</span>(<span class="kw">mean</span>(bestMod.cc1), <span class="dv">3</span>),
<span class="dt">y_lab =</span> (<span class="kw">max</span>(<span class="kw">sqrt</span>(NSDm)) <span class="op">-</span><span class="st"> </span><span class="kw">min</span>(<span class="kw">sqrt</span>(NSDm))) <span class="op">/</span><span class="st"> </span><span class="dv">2</span>) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">p_date =</span> <span class="kw">ymd</span>(<span class="st">"2000-09-01"</span>)) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">semi_join</span>(<span class="kw">filter_</span>(df, fil), <span class="dt">by =</span> <span class="st">"MooseYrID"</span>)
}
<span class="co"># Function for plotting individual NSDs with CC labels and migration timing</span>
plot_mig <-<span class="st"> </span><span class="cf">function</span>(df, lab) {
df_lines <-<span class="st"> </span>df <span class="op">%>%</span>
<span class="st"> </span><span class="kw">group_by</span>(MooseYrID) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">summarise</span>(<span class="dt">xmidA_d =</span> <span class="kw">as.POSIXct</span>(<span class="kw">ymd</span>(<span class="st">"2000-03-01"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">days</span>(<span class="kw">round</span>(<span class="kw">first</span>(xmidA), <span class="dv">0</span>))),
<span class="dt">xmidB_d =</span> <span class="kw">as.POSIXct</span>(<span class="kw">ymd</span>(<span class="st">"2000-03-01"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">days</span>(<span class="kw">round</span>(<span class="kw">first</span>(xmidB), <span class="dv">0</span>))))
lab<span class="op">$</span>p_date <-<span class="st"> </span><span class="kw">as.POSIXct</span>(lab<span class="op">$</span>p_date)
p <-<span class="st"> </span><span class="kw">ggplot</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="dt">data =</span> df,
<span class="kw">aes</span>(<span class="dt">x =</span> plot_date, <span class="dt">y =</span> <span class="kw">sqrt</span>(NSDm), <span class="dt">group =</span> burst),
<span class="dt">color =</span> <span class="st">"gray80"</span>, <span class="dt">size =</span> <span class="fl">0.7</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_path</span>(<span class="dt">data =</span> df,
<span class="kw">aes</span>(<span class="dt">x =</span> plot_date, <span class="dt">y =</span> <span class="kw">sqrt</span>(MSD), <span class="dt">group =</span> burst),
<span class="dt">size =</span> <span class="fl">0.7</span>, <span class="dt">color =</span> <span class="st">"dodgerblue4"</span>, <span class="dt">alpha =</span> <span class="fl">0.7</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"</span><span class="ch">\n</span><span class="st">Date"</span>, <span class="dt">y =</span> <span class="st">"Net displacement (km)</span><span class="ch">\n</span><span class="st">"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">expand_limits</span>(<span class="dt">y =</span> <span class="dv">0</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_label</span>(<span class="dt">data =</span> lab, <span class="kw">aes</span>(<span class="dt">x =</span> p_date, <span class="dt">y =</span> y_lab, <span class="dt">label =</span> label),
<span class="dt">size =</span> <span class="dv">2</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_vline</span>(<span class="dt">data =</span> df_lines, <span class="kw">aes</span>(<span class="dt">xintercept =</span> <span class="kw">as.numeric</span>(xmidA_d)), <span class="dt">lty =</span> <span class="dv">3</span>, <span class="dt">size =</span> <span class="fl">0.3</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">geom_vline</span>(<span class="dt">data =</span> df_lines, <span class="kw">aes</span>(<span class="dt">xintercept =</span> <span class="kw">as.numeric</span>(xmidB_d)), <span class="dt">lty =</span> <span class="dv">3</span>, <span class="dt">size =</span> <span class="fl">0.3</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">facet_wrap</span>(<span class="op">~</span>MooseYrID, <span class="dt">scales =</span> <span class="st">"free_y"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_x_datetime</span>(<span class="dt">date_labels =</span> <span class="st">"%b"</span>, <span class="dt">date_breaks =</span> <span class="st">"1 month"</span>,
<span class="dt">date_minor_breaks =</span> <span class="st">"1 month"</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_fc</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">theme</span>(<span class="dt">strip.background =</span> <span class="kw">element_blank</span>(),
<span class="dt">axis.text.x =</span> <span class="kw">element_text</span>(<span class="dt">angle =</span> <span class="dv">90</span>),
<span class="dt">panel.grid =</span> <span class="kw">element_blank</span>()) <span class="op">+</span>
<span class="st"> </span><span class="kw">coord_cartesian</span>()
<span class="kw">return</span>(p)
}</code></pre></div>
<p><br></p>
<div id="perform-the-filtering" class="section level2">
<h2>Perform the filtering</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Focus on migration models</span>
df_smooth_mig <-<span class="st"> </span><span class="kw">filter</span>(df_smooth_fitted,
bestMod.cc1ID <span class="op">%in%</span><span class="st"> </span><span class="kw">c</span>(<span class="st">"MigrMod"</span>, <span class="st">"MigrModC"</span>))
<span class="co"># See if any good models exist with cc below 0.85</span>
<span class="co"># Not really</span>
fil <-<span class="st"> </span><span class="kw">quote</span>(bestMod.cc1 <span class="op"><</span><span class="st"> </span><span class="fl">0.85</span>)