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Part I
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<a href="Introduction.html">Introduction</a>
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<a href="Getting_ready_to_use_R.html">Getting ready to use R</a>
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Part II
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<a href="Data_Preparation.html">Data preparation</a>
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<a href="First_Steps.html">First steps</a>
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<li>
<a href="Population_Strata.html">Population strata and clone correction</a>
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<li>
<a href="Locus_Stats.html">Locus-based statistics and missing data</a>
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<li>
<a href="Genotypic_EvenRichDiv.html">Genotypic evenness, richness, and diversity</a>
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<a href="Linkage_disequilibrium.html">Linkage disequilibrium</a>
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<a href="Pop_Structure.html">Population structure</a>
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<a href="Minimum_Spanning_Networks.html">Minimum Spanning Networks</a>
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<a href="AMOVA.html">AMOVA</a>
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<a href="DAPC.html">Discriminant analysis of principal components (DAPC)</a>
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<a href="intro_vcf.html">Population genomics and HTS</a>
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<a href="reading_vcf.html">Reading VCF data</a>
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<a href="analysis_of_genome.html">Analysis of genomic data</a>
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<a href="gbs_analysis.html">Analysis of GBS data</a>
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<a href="clustering_plot.html">Clustering plot</a>
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<a href="reading_vcf.html">VCF data</a>
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<a href="quality_control.html">Quality control</a>
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<a href="gbs_analysis.html">Analysis of GBS data</a>
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<a href="reading_vcf.html">VCF data</a>
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<a href="quality_control.html">Quality control</a>
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<a href="gbs_analysis.html">Analysis of GBS data</a>
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Appendices
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<a href="funpendix.html">Function glossary</a>
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<a href="background_functions.html">Background_functions</a>
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<a href="https://github.com/grunwaldlab/Population_Genetics_in_R/">Source Code</a>
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<h1 class="title toc-ignore">gst_gbs_data</h1>
<h4 class="author">Javier F. Tabima</h4>
<h4 class="date">7/14/2017</h4>
</div>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1"></a><span class="kw">library</span>(vcfR)</span>
<span id="cb1-2"><a href="#cb1-2"></a><span class="kw">library</span>(poppr)</span>
<span id="cb1-3"><a href="#cb1-3"></a><span class="kw">library</span>(ape)</span>
<span id="cb1-4"><a href="#cb1-4"></a><span class="kw">library</span>(RColorBrewer)</span>
<span id="cb1-5"><a href="#cb1-5"></a><span class="kw">library</span>(reshape2)</span>
<span id="cb1-6"><a href="#cb1-6"></a><span class="kw">library</span>(ggplot2)</span>
<span id="cb1-7"><a href="#cb1-7"></a><span class="kw">library</span>(knitcitations)</span>
<span id="cb1-8"><a href="#cb1-8"></a>bib <-<span class="st"> </span><span class="kw">read.bibtex</span>(<span class="st">"bibtexlib.bib"</span>)</span>
<span id="cb1-9"><a href="#cb1-9"></a>pop.data <-<span class="st"> </span><span class="kw">read.table</span>(<span class="st">"population_data.gbs.txt"</span>, <span class="dt">sep =</span> <span class="st">"</span><span class="ch">\t</span><span class="st">"</span>, <span class="dt">header =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1"></a>rubi.VCF <-<span class="st"> </span><span class="kw">read.vcfR</span>(<span class="st">"prubi_gbs.vcf.gz"</span>)</span></code></pre></div>
<pre><code>## Scanning file to determine attributes.
## File attributes:
## meta lines: 9460
## header_line: 9461
## variant count: 615
## column count: 103
##
Meta line 1000 read in.
Meta line 2000 read in.
Meta line 3000 read in.
Meta line 4000 read in.
Meta line 5000 read in.
Meta line 6000 read in.
Meta line 7000 read in.
Meta line 8000 read in.
Meta line 9000 read in.
Meta line 9460 read in.
## All meta lines processed.
## gt matrix initialized.
## Character matrix gt created.
## Character matrix gt rows: 615
## Character matrix gt cols: 103
## skip: 0
## nrows: 615
## row_num: 0
##
Processed variant: 615
## All variants processed</code></pre>
<div id="additional-step-2-calculating-population-structure-using-f_st" class="section level2">
<h2>Additional step 2: Calculating population structure using <span class="math inline">\(F_{ST}\)</span></h2>
<p>A standard way to calculate population structure in population genetics is using the fixation index (<span class="math inline">\(F_{ST}\)</span>) proposed by Sewall Wright <span class="citation">(Wright, 1949, p. @wright1978evolution)</span>.</p>
<p>The fixation index measures population differentiation due to genetic structure, and is based on the variance of the allele frequencies between populations. <span class="math inline">\(F_{ST}\)</span> values can be calculated for any molecular marker.</p>
<p>The R package <em>vcfR</em> includes a function to calculate differentiation measures from VCF data. The function <code>genetic_diff()</code> includes options for Nei’s <span class="math inline">\(G_{ST}\)</span> <span class="citation">(Nei, 1973)</span>, including Hedrick’s <span class="math inline">\(G'_{ST}\)</span> correction for high allelism <span class="citation">(Hedrick, 2005)</span> , as well as Jost’s <span class="math inline">\(D\)</span> <span class="citation">(Jost, 2008)</span>.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1"></a>myDiff <-<span class="st"> </span><span class="kw">genetic_diff</span>(rubi.VCF, <span class="kw">as.factor</span>(pop.data<span class="op">$</span>State), <span class="dt">method =</span> <span class="st">"nei"</span>)</span>
<span id="cb4-2"><a href="#cb4-2"></a>knitr<span class="op">::</span><span class="kw">kable</span>(<span class="kw">t</span>(<span class="kw">as.matrix</span>(<span class="kw">round</span>(<span class="kw">colMeans</span>(myDiff[,<span class="kw">c</span>(<span class="dv">3</span><span class="op">:</span><span class="dv">10</span>,<span class="dv">13</span>)], <span class="dt">na.rm =</span> <span class="ot">TRUE</span>), <span class="dt">digits =</span> <span class="dv">3</span>))))</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="right">Hs_CA</th>
<th align="right">Hs_OR</th>
<th align="right">Hs_WA</th>
<th align="right">Ht</th>
<th align="right">n_CA</th>
<th align="right">n_OR</th>
<th align="right">n_WA</th>
<th align="right">Gst</th>
<th align="right">Gprimest</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">0.048</td>
<td align="right">0.054</td>
<td align="right">0.059</td>
<td align="right">0.062</td>
<td align="right">62.179</td>
<td align="right">44.25</td>
<td align="right">72.943</td>
<td align="right">0.056</td>
<td align="right">0.084</td>
</tr>
</tbody>
</table>
<p>The calculation of Nei´s <span class="math inline">\(G_{ST}\)</span> and Hedrick´s <span class="math inline">\(G'_{ST}\)</span> indicate that there is a low degree of population differentiation across states in the western USA. <span class="math inline">\(F_{ST}\)</span> values have a range from 0 (no genetic structure) to 1 (complete population structure). (However, an unbiased estimate may be slightly negative.) Hedrick´s <span class="math inline">\(G'_{ST}\)</span> index rescales Nei´s <span class="math inline">\(G_{ST}\)</span> values into a range from 0 to 1 for loci with many alleles. These indices can be thought of as analogs to <span class="math inline">\(F_{ST}\)</span> values.</p>
<p>While <span class="math inline">\(F_{ST}\)</span> range from 0 to 1, they do not scale linearly. That is, two populations with an <span class="math inline">\(F_{ST}\)</span> of 0.5 should not be interpreted as being 50% differentiated. Wright suggested the following guidelines for <span class="math inline">\(F_{ST}\)</span> values <span class="citation">(Wright, 1978)</span>:</p>
<ul>
<li><span class="math inline">\(F_{ST}\)</span> values from 0 to 0.05: Little genetic differentiation</li>
<li><span class="math inline">\(F_{ST}\)</span> values from 0.05 to 0.15: Moderate genetic differentiation</li>
<li><span class="math inline">\(F_{ST}\)</span> values from 0.15 to 0.25: Great genetic differentiation</li>
<li><span class="math inline">\(F_{ST}\)</span> values greater than 0.25: Very great genetic differentiation</li>
</ul>
<p>These guidelines are valid for our <span class="math inline">\(G'_{ST}\)</span> values as well. For a more extensive discussion on the interpretation of <span class="math inline">\(F_{ST}\)</span> values, we recommend chapter 4 in <span class="citation">Hartl & Clark (2007)</span>.</p>
<p>Both measurements of population differentiation for <em>P. rubi</em> show a moderate degree of differentiation among populations (Hedrick´s <span class="math inline">\(G'_{ST}\)</span> = 0.084).</p>
<p>However, these results from the population differentiation calculation are obtained by estimating the mean for each of the indices in the function. Each variant has its own estimation for each index in the <code>genetic_diff</code> function. We can visualize the distribution of indices across all variant positions using a violin plot:</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1"></a>dpf <-<span class="st"> </span><span class="kw">melt</span>(myDiff[,<span class="kw">c</span>(<span class="dv">3</span><span class="op">:</span><span class="dv">6</span>,<span class="dv">10</span>,<span class="dv">13</span>)], <span class="dt">varnames=</span><span class="kw">c</span>(<span class="st">'Index'</span>, <span class="st">'Sample'</span>), <span class="dt">value.name =</span> <span class="st">'Depth'</span>, <span class="dt">na.rm=</span><span class="ot">TRUE</span>)</span></code></pre></div>
<pre><code>## No id variables; using all as measure variables</code></pre>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1"></a>p <-<span class="st"> </span><span class="kw">ggplot</span>(dpf, <span class="kw">aes</span>(<span class="dt">x=</span>variable, <span class="dt">y=</span>Depth)) <span class="op">+</span><span class="st"> </span><span class="kw">geom_violin</span>(<span class="dt">fill=</span><span class="st">"#8dd3c7"</span>, <span class="dt">adjust =</span> <span class="fl">2.8</span>)</span>
<span id="cb7-2"><a href="#cb7-2"></a>p <-<span class="st"> </span>p <span class="op">+</span><span class="st"> </span><span class="kw">xlab</span>(<span class="st">""</span>)</span>
<span id="cb7-3"><a href="#cb7-3"></a>p <-<span class="st"> </span>p <span class="op">+</span><span class="st"> </span><span class="kw">ylab</span>(<span class="st">""</span>)</span>
<span id="cb7-4"><a href="#cb7-4"></a>p <-<span class="st"> </span>p <span class="op">+</span><span class="st"> </span><span class="kw">theme_bw</span>()</span>
<span id="cb7-5"><a href="#cb7-5"></a>p <-<span class="st"> </span>p <span class="op">+</span><span class="st"> </span><span class="kw">scale_y_continuous</span>(<span class="dt">breaks=</span><span class="kw">seq</span>(<span class="fl">0.05</span>, <span class="fl">0.95</span>, <span class="dt">by=</span><span class="fl">0.1</span>))</span>
<span id="cb7-6"><a href="#cb7-6"></a>p <-<span class="st"> </span>p <span class="op">+</span><span class="st"> </span><span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="kw">c</span>(<span class="fl">0.05</span>, <span class="fl">0.15</span>, <span class="fl">0.25</span>), <span class="dt">color =</span> <span class="st">"#B22222"</span>, <span class="dt">lwd =</span> <span class="dv">1</span>)</span>
<span id="cb7-7"><a href="#cb7-7"></a></span>
<span id="cb7-8"><a href="#cb7-8"></a>p</span></code></pre></div>
<p><img src="GST_gbs_analysis_files/figure-html/unnamed-chunk-4-1.png" width="672" /></p>
<p>The violin plot shows a high abundance of variants with low values for each index, indicating that the low values of population differentiation are common in our analysis. Nonetheless, we see a number of outlier variants in the high ends of the distribution. These variants represent sites in the genome under high differentiation. We can visualize these results by plotting the value of the index of interest (in this example, Hedrick´s <span class="math inline">\(G'_{ST}\)</span>) against the position in the genome. These “Manhattan plots” allow visualization of differentiation along a portion of the genome:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1"></a><span class="kw">plot</span>(<span class="dv">1</span><span class="op">:</span><span class="kw">nrow</span>(myDiff), myDiff<span class="op">$</span>Gprimest, <span class="dt">xlab =</span> <span class="st">""</span>, <span class="dt">ylab =</span> <span class="st">""</span>, <span class="dt">xaxt =</span> <span class="st">"n"</span>, </span>
<span id="cb8-2"><a href="#cb8-2"></a> <span class="dt">pch =</span> <span class="dv">21</span>, <span class="dt">bg =</span> <span class="kw">as.factor</span>(myDiff<span class="op">$</span>CHROM), <span class="dt">yaxt=</span><span class="st">'n'</span>)</span>
<span id="cb8-3"><a href="#cb8-3"></a><span class="kw">abline</span>(<span class="dt">h=</span><span class="dv">0</span>)</span>
<span id="cb8-4"><a href="#cb8-4"></a><span class="kw">title</span>(<span class="dt">ylab =</span> <span class="kw">expression</span>(<span class="st">"G'"</span>[ST]))</span>
<span id="cb8-5"><a href="#cb8-5"></a><span class="kw">abline</span>(<span class="dt">h=</span><span class="kw">c</span>(<span class="fl">0.05</span>, <span class="fl">0.15</span>, <span class="fl">0.25</span>), <span class="dt">col =</span> <span class="st">"#B22222"</span>)</span>
<span id="cb8-6"><a href="#cb8-6"></a><span class="kw">axis</span>(<span class="dt">side=</span><span class="dv">2</span>, <span class="dt">at=</span><span class="kw">seq</span>(<span class="fl">0.05</span>, <span class="fl">0.95</span>, <span class="dt">by=</span><span class="fl">0.1</span>), <span class="dt">las=</span><span class="dv">2</span>)</span>
<span id="cb8-7"><a href="#cb8-7"></a><span class="kw">title</span>(<span class="dt">xlab =</span> <span class="st">"Position"</span>, <span class="dt">line =</span> <span class="dv">1</span>)</span></code></pre></div>
<p><img src="GST_gbs_analysis_files/figure-html/unnamed-chunk-5-1.png" width="672" /></p>
<p>We observe that the majority of variants have very low values of Hedrick´s <span class="math inline">\(G'_{ST}\)</span>, as expected from previous results. However, there are positions in the genome with high Hedrick´s <span class="math inline">\(G'_{ST}\)</span> values. Note however, that GBS data is very different than whole genome sequence data, as the variants that are obtained by GBS do not represent long stretches of the genome but only fragments scattered throughout the genome. We would need variant calls for a whole genome to find regions of divergence.</p>
<div id="refs" class="references">
<div id="ref-hartl2007">
<p>Hartl D., Clark A. 2007. <em>Principles of population genetics</em>. Sinauer Associates, Incorporated. Available at: <a href="http://books.google.com/books?id=SB1vQgAACAAJ">http://books.google.com/books?id=SB1vQgAACAAJ</a></p>
</div>
<div id="ref-hedrick2005standardized">
<p>Hedrick PW. 2005. A standardized genetic differentiation measure. <em>Evolution</em> 59:1633–1638. Available at: <a href="http://dx.doi.org/10.1111/j.0014-3820.2005.tb01814.x">http://dx.doi.org/10.1111/j.0014-3820.2005.tb01814.x</a></p>
</div>
<div id="ref-jost2008gst">
<p>Jost L. 2008. <span class="math inline">\(G_{ST}\)</span> And its relatives do not measure differentiation. <em>Molecular Ecology</em> 17:4015–4026. Available at: <a href="http://dx.doi.org/10.1111/j.1365-294X.2008.03887.x">http://dx.doi.org/10.1111/j.1365-294X.2008.03887.x</a></p>
</div>
<div id="ref-nei1973analysis">
<p>Nei M. 1973. Analysis of gene diversity in subdivided populations. <em>Proceedings of the National Academy of Sciences</em> 70:3321–3323. Available at: <a href="http://www.pnas.org/content/70/12/3321.abstract">http://www.pnas.org/content/70/12/3321.abstract</a></p>
</div>
<div id="ref-wright1949genetical">
<p>Wright S. 1949. The genetical structure of populations. <em>Annals of Eugenics</em> 15:323–354. Available at: <a href="http://dx.doi.org/10.1111/j.1469-1809.1949.tb02451.x">http://dx.doi.org/10.1111/j.1469-1809.1949.tb02451.x</a></p>
</div>
<div id="ref-wright1978evolution">
<p>Wright S. 1978. Evolution and the genetics of populations. Vol. 4. Variability within and among natural populations. <em>University of Chicago Press, Chicago, IL, USA</em>. Available at: <a href="http://www.press.uchicago.edu/ucp/books/book/chicago/E/bo3642015.html">http://www.press.uchicago.edu/ucp/books/book/chicago/E/bo3642015.html</a></p>
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