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First_Steps.html
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<a class="navbar-brand" href="index.html">Population genetics and genomics in R</a>
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<a href="TOC.html">Table of contents</a>
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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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<li>
<a href="First_Steps.html">First steps</a>
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<li>
<a href="Population_Strata.html">Population strata and clone correction</a>
</li>
<li>
<a href="Locus_Stats.html">Locus-based statistics and missing data</a>
</li>
<li>
<a href="Genotypic_EvenRichDiv.html">Genotypic evenness, richness, and diversity</a>
</li>
<li>
<a href="Linkage_disequilibrium.html">Linkage disequilibrium</a>
</li>
<li>
<a href="Pop_Structure.html">Population structure</a>
</li>
<li>
<a href="Minimum_Spanning_Networks.html">Minimum Spanning Networks</a>
</li>
<li>
<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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Part III
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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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<li>
<a href="analysis_of_genome.html">Analysis of genomic data</a>
</li>
<li>
<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="intro_vcf.html">Introduction</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="analysis_of_genome.html">Analysis of genome data</a>
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<a href="reading_vcf.html">VCF data</a>
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<a href="gbs_analysis.html">Analysis of GBS data</a>
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About
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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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<div class="fluid-row" id="header">
<h1 class="title toc-ignore">First Analysis</h1>
<h3 class="subtitle"><em>ZN Kamvar, SE Everhart and NJ Grünwald</em></h3>
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<p>This chapter introduces basic use of and navigation in <em>poppr</em> as well as good practices when starting an analysis. We take a glance at the genotypic diversity observed in populations and allelic frequencies observed in your loci by population. Both of these are good first steps to eliminate data entry errors, check for missing/rare data, and make sure all loci conform to expectations given your analyses.</p>
<p>For these examples, we will be using the data set <code>Pinf</code> that is already built into <em>poppr</em> containing 86 individuals of the polyploid data for <em>Phytophthora infestans</em> genotyped over 11 microsatellite loci <span class="citation">(Goss et al., 2014)</span>.</p>
<div id="the-genotype-accumulation-curve" class="section level2">
<h2>The genotype accumulation curve</h2>
<p>A genotype accumulation curve is a tool that allows you to assess how much power you have to discriminate between unique individuals given a random sample of <span class="math inline">\(n\)</span> loci. This analysis is particularly important for clonal organisms to confirm that a plateau has been reached in the number of loci necessary to discriminate individuals. Below, we will analyze the <code>Pinf</code> data set.</p>
<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>(<span class="st">"poppr"</span>)</span>
<span id="cb1-2"><a href="#cb1-2"></a><span class="kw">data</span>(<span class="st">"Pinf"</span>) <span class="co"># Load the data</span></span>
<span id="cb1-3"><a href="#cb1-3"></a>Pinf <span class="co"># We expect a maximum of 72 Multilocus Genotypes</span></span></code></pre></div>
<pre><code>##
## This is a genclone object
## -------------------------
## Genotype information:
##
## 72 multilocus genotypes
## 86 tetraploid individuals
## 11 codominant loci
##
## Population information:
##
## 2 strata - Continent, Country
## 2 populations defined - South America, North America</code></pre>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1"></a>gac <-<span class="st"> </span><span class="kw">genotype_curve</span>(Pinf, <span class="dt">sample =</span> <span class="dv">1000</span>, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<div class="figure">
<img src="First_Steps_files/figure-html/unnamed-chunk-2-1.png" alt="Genotype accumulation curve" width="672" />
<p class="caption">
Genotype accumulation curve
</p>
</div>
<p>We specified <code>sample = 1000</code> in our function call. This means that for each boxplot, <span class="math inline">\(n\)</span> loci were randomly sampled 1000 times in order to create the distribution. Since this data has been curated, we can see that we have reached the plateau with 11 loci. Try seeing what happens when you use a data set of sexual populations such as <code>microbov</code> or <code>nancycats</code>. Also, what happens when you use dominant AFLP data such as <code>Aeut</code>?</p>
</div>
<div id="allele-frequencies-missing-data-and-ploidy" class="section level2">
<h2>Allele frequencies, missing data, and ploidy</h2>
<p>A good first step after loading data is to look for missing data, rare alleles and overall quality of your data:</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1"></a><span class="kw">data</span>(<span class="st">"Pinf"</span>)</span>
<span id="cb4-2"><a href="#cb4-2"></a>(pinflt <-<span class="st"> </span><span class="kw">locus_table</span>(Pinf))</span></code></pre></div>
<pre><code>## summary
## locus allele 1-D Hexp Evenness
## Pi02 10.000 0.633 0.637 0.663
## D13 25.000 0.884 0.889 0.587
## Pi33 2.000 0.012 0.012 0.322
## Pi04 4.000 0.578 0.582 0.785
## Pi4B 7.000 0.669 0.672 0.707
## Pi16 6.000 0.403 0.406 0.507
## G11 21.000 0.839 0.844 0.544
## Pi56 3.000 0.361 0.363 0.707
## Pi63 3.000 0.413 0.415 0.641
## Pi70 3.000 0.279 0.281 0.580
## Pi89 11.000 0.615 0.619 0.578
## mean 8.636 0.517 0.520 0.602</code></pre>
<p>We see that we have anywhere from 2 to 25 microsatellite alleles per locus. Locus D13 has the highest Simpson diversity (0.884) and Pi04 has the most evenly distirbuted alleles (0.785). We also observe between 1-10% missing data in the ‘North America’ population:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1"></a><span class="kw">info_table</span>(Pinf, <span class="dt">type =</span> <span class="st">"missing"</span>, <span class="dt">plot =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<div class="figure">
<img src="First_Steps_files/figure-html/unnamed-chunk-4-1.png" alt="Missing data plot" width="1152" />
<p class="caption">
Missing data plot
</p>
</div>
<pre><code>## Locus
## Population Pi02 D13 Pi33 Pi04 Pi4B Pi16 G11 Pi56 Pi63 Pi70 Pi89 Mean
## South America . . . . . . . . . . . .
## North America . 0.104 . . . 0.062 . . 0.021 . 0.021 0.019
## Total . 0.058 . . . 0.035 . . 0.012 . 0.012 0.011</code></pre>
<p>If your data consists of polyploid SSR markers, you would code the unobserved alleles as ‘0’. The <code>Pinf</code> data set is a perfect example of this. It is a subset of a slightly larger tetraploid data set. In this example, each row represents an isolate and each column represents a locus:</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">tail</span>(<span class="kw">genind2df</span>(Pinf, <span class="dt">sep =</span> <span class="st">"/"</span>))</span></code></pre></div>
<pre><code>## pop Pi02 D13 Pi33
## PiPE22 South America 000/000/160/160 000/000/142/144 000/000/203/203
## PiPE23 South America 000/000/160/160 000/000/140/140 000/000/203/203
## PiPE24 South America 000/000/160/160 000/000/142/144 000/000/203/203
## PiPE25 South America 000/000/160/160 000/000/142/144 000/000/203/203
## PiPE26 South America 000/000/162/162 000/000/142/142 000/000/203/203
## PiPE27 South America 000/000/154/160 000/000/136/138 000/000/203/203
## Pi04 Pi4B Pi16 G11
## PiPE22 000/000/166/170 000/000/213/217 000/000/176/178 000/152/162/200
## PiPE23 000/000/166/170 000/000/213/217 000/000/176/178 000/152/160/200
## PiPE24 000/000/166/170 000/000/213/217 000/000/176/178 000/152/162/200
## PiPE25 000/000/166/170 000/000/213/217 000/000/176/178 000/152/162/200
## PiPE26 000/000/166/170 000/000/205/217 000/000/176/178 000/000/156/166
## PiPE27 000/000/166/170 000/000/213/217 000/000/176/178 000/152/170/200
## Pi56 Pi63 Pi70 Pi89
## PiPE22 000/000/176/176 000/148/151/157 000/000/189/192 000/000/179/179
## PiPE23 000/000/176/176 000/148/151/157 000/000/189/192 000/000/179/179
## PiPE24 000/000/176/176 000/148/151/157 000/000/189/192 000/000/179/179
## PiPE25 000/000/176/176 000/148/151/157 000/000/189/192 000/000/179/179
## PiPE26 000/000/176/176 000/000/157/157 000/000/192/195 000/000/179/181
## PiPE27 000/000/176/176 000/148/151/157 000/000/189/192 000/000/179/179</code></pre>
<p>The <code>genind2df()</code> function transforms the data from genind object into a dataframe and adds ‘/’ as separators between alleles at each locus. Note how missing allelles are coded as ‘000’.</p>
<p>To observe the different levels of ploidy in your data, use the function <code>info_table</code> with the argument <code>type = "ploidy"</code>:</p>
<blockquote>
<p>Notice you can change the colors of the plot by setting a “low” color and a “high” color.</p>
</blockquote>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1"></a>Pinf.ploidy <-<span class="st"> </span><span class="kw">info_table</span>(Pinf, <span class="dt">type =</span> <span class="st">"ploidy"</span>, <span class="dt">plot =</span> <span class="ot">TRUE</span>, <span class="dt">low =</span> <span class="st">"black"</span>, <span class="dt">high =</span> <span class="st">"orange"</span>)</span></code></pre></div>
<div class="figure" style="text-align: center">
<img src="First_Steps_files/figure-html/unnamed-chunk-6-1.png" alt="Plot of ploidy" width="480" />
<p class="caption">
Plot of ploidy
</p>
</div>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1"></a><span class="kw">tail</span>(Pinf.ploidy)</span></code></pre></div>
<pre><code>## Loci
## Samples Pi02 D13 Pi33 Pi04 Pi4B Pi16 G11 Pi56 Pi63 Pi70 Pi89
## PiPE22 2 2 2 2 2 2 3 2 3 2 2
## PiPE23 2 2 2 2 2 2 3 2 3 2 2
## PiPE24 2 2 2 2 2 2 3 2 3 2 2
## PiPE25 2 2 2 2 2 2 3 2 3 2 2
## PiPE26 2 2 2 2 2 2 2 2 2 2 2
## PiPE27 2 2 2 2 2 2 3 2 3 2 2</code></pre>
<p>Note that ploidy varies between 2 and 3 among individuals and loci.</p>
<p>You are now able to assess the quality of your data and examine allelic diversity in your populations.</p>
</div>
<div id="calculating-genotypic-diversity" class="section level2">
<h2>Calculating genotypic diversity</h2>
<p>Let us get a first impression of the diversity found in this data using the summary function, <code>poppr</code>:</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1"></a><span class="kw">poppr</span>(Pinf)</span></code></pre></div>
<pre><code>## Pop N MLG eMLG SE H G lambda E.5 Hexp Ia rbarD
## 1 South America 38 29 29.0 0.000 3.27 23.3 0.957 0.883 0.513 2.873 0.3446
## 2 North America 48 43 34.5 0.989 3.69 34.9 0.971 0.871 0.503 0.223 0.0240
## 3 Total 86 72 34.6 1.529 4.19 57.8 0.983 0.875 0.520 0.652 0.0717
## File
## 1 Pinf
## 2 Pinf
## 3 Pinf</code></pre>
<p>We can see statistics printed for each individual and the total population. The fields you see in the output include:</p>
<table>
<colgroup>
<col width="8%" />
<col width="91%" />
</colgroup>
<thead>
<tr class="header">
<th>Abbreviation</th>
<th>Statistic</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><code>Pop</code></td>
<td>Population name.</td>
</tr>
<tr class="even">
<td><code>N</code></td>
<td>Number of individuals observed.</td>
</tr>
<tr class="odd">
<td><code>MLG</code></td>
<td>Number of multilocus genotypes (MLG) observed.</td>
</tr>
<tr class="even">
<td><code>eMLG</code></td>
<td>The number of expected MLG at the smallest sample size ≥ 10 based on rarefaction</td>
</tr>
<tr class="odd">
<td><code>SE</code></td>
<td>Standard error based on eMLG.</td>
</tr>
<tr class="even">
<td><code>H</code></td>
<td>Shannon-Wiener Index of MLG diversity <span class="citation">(Shannon, 2001)</span>.</td>
</tr>
<tr class="odd">
<td><code>G</code></td>
<td>Stoddart and Taylor’s Index of MLG diversity <span class="citation">(Stoddart & Taylor, 1988)</span>.</td>
</tr>
<tr class="even">
<td><code>lambda</code></td>
<td>Simpson’s Index <span class="citation">(Simpson, 1949)</span>.</td>
</tr>
<tr class="odd">
<td><code>E.5</code></td>
<td>Evenness, <span class="math inline">\(E_5\)</span> <span class="citation">(Pielou, 1975; Ludwig & Reynolds, 1988; Grünwald et al., 2003)</span>.</td>
</tr>
<tr class="even">
<td><code>Hexp</code></td>
<td>Nei’s unbiased gene diversity <span class="citation">(Nei, 1978)</span>.</td>
</tr>
<tr class="odd">
<td><code>Ia</code></td>
<td>The index of association, <span class="math inline">\(I_A\)</span> <span class="citation">(Brown, Feldman & Nevo, 1980; Smith et al., 1993)</span>.</td>
</tr>
<tr class="even">
<td><code>rbarD</code></td>
<td>The standardized index of association, <span class="math inline">\(\bar{r}_d\)</span> [@].</td>
</tr>
</tbody>
</table>
<p>What does all this mean? Both populations have a similar number of individuals (<span class="math inline">\(N\)</span> = 38 and 48) sampled. However, one population has 29 and the other 43 <span class="math inline">\(MLG\)</span> while both populations together have combined 86 <span class="math inline">\(MLG\)</span>. Genotypic diversity (either <span class="math inline">\(H\)</span> or <span class="math inline">\(G\)</span>) is higher in population 2 than population 1, while evenness is similar. Let’s ignore <span class="math inline">\(I_A\)</span> and <span class="math inline">\(\bar{r}_d\)</span> for now, as these are measures of linkage disequilibrium that will be covered in <a href="Linkage_disequilibrium.html">Chapter 4</a>.</p>
<p>Next, let’s calculate <span class="math inline">\(MLG\)</span> for each population, e.g. “South America” and “North America” populations:</p>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1"></a>P.tab <-<span class="st"> </span><span class="kw">mlg.table</span>(Pinf)</span></code></pre></div>
<div class="figure">
<img src="First_Steps_files/figure-html/unnamed-chunk-8-1.png" alt="Multilocus Genotype Table" width="672" />
<p class="caption">
Multilocus Genotype Table
</p>
</div>
<p>The figures provide histograms to see how evenly <span class="math inline">\(MLGs\)</span> are distributed within each population. Both populations have genotypes that occur a few times and only a few genotypes that occur more than 2 times (as expected from the high <span class="math inline">\(E_5\)</span> discussed above). Try this analysis on other published data sets such as that of the root rot pathogen <em>Aphanomyces euteiches</em>, stored in <em>poppr</em> as <code>Aeut</code>. See if you can produce similar tables and graphs and compare it to the published paper <span class="citation">(Grünwald & Hoheisel, 2006)</span>.</p>
</div>
<div id="conclusions" class="section level2">
<h2>Conclusions</h2>
<p>Going through many of these steps will give you a valuable first look at your data. These analyses can give you insight into what methods you are able to use in your analysis. The genotype curve can tell you if you’ve sampled enough loci (or if you have over sampled) and <code>info_table</code> provides a nice visualization to aid assessing whether or not there are missing data in your sample. For clonal populations, the genotypic diversity table is valuable for informing you of how to clone-correct populations, which we will tackle in the <a href="Population_Strata.html">next chapter</a>.</p>
</div>
<div id="references" class="section level2">
<h2>References</h2>
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</div>
<div id="ref-goss2014irish">
<p>Goss EM., Tabima JF., Cooke DEL., Restrepo S., Fry WE., Forbes GA., Fieland VJ., Cardenas M., Grünwald NJ. 2014. The Irish potato famine pathogen <em>phytophthora infestans</em> originated in central mexico rather than the andes. <em>Proceedings of the National Academy of Sciences</em> 111:8791–8796. Available at: <a href="http://www.pnas.org/content/early/2014/05/29/1401884111.abstract">http://www.pnas.org/content/early/2014/05/29/1401884111.abstract</a></p>
</div>
<div id="ref-grunwald2003">
<p>Grünwald NJ., Goodwin SB., Milgroom MG., Fry WE. 2003. Analysis of genotypic diversity data for populations of microorganisms. <em>Phytopathology</em> 93:738–746. Available at: <a href="http://apsjournals.apsnet.org/doi/abs/10.1094/PHYTO.2003.93.6.738">http://apsjournals.apsnet.org/doi/abs/10.1094/PHYTO.2003.93.6.738</a></p>
</div>
<div id="ref-grunwald2006hierarchical">
<p>Grünwald NJ., Hoheisel G-A. 2006. Hierarchical analysis of diversity, selfing, and genetic differentiation in populations of the oomycete <em>aphanomyces euteiches</em>. <em>Phytopathology</em> 96:1134–1141. Available at: <a href="http://apsjournals.apsnet.org/doi/abs/10.1094/PHYTO-96-1134">http://apsjournals.apsnet.org/doi/abs/10.1094/PHYTO-96-1134</a></p>
</div>
<div id="ref-ludwig1988statistical">
<p>Ludwig JA., Reynolds JF. 1988. <em>Statistical ecology: A primer in methods and computing</em>. Wiley.com.</p>
</div>
<div id="ref-nei1978estimation">
<p>Nei M. 1978. Estimation of average heterozygosity and genetic distance from a small number of individuals. <em>Genetics</em> 89:583–590. Available at: <a href="http://www.genetics.org/content/89/3/583.abstract">http://www.genetics.org/content/89/3/583.abstract</a></p>
</div>
<div id="ref-pielou1975ecological">
<p>Pielou EC. 1975. <em>Ecological diversity</em>. Wiley New York.</p>
</div>
<div id="ref-shannon2001mathematical">
<p>Shannon CE. 2001. A mathematical theory of communication. <em>ACM SIGMOBILE Mobile Computing and Communications Review</em> 5:3–55. Available at: <a href="http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf">http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf</a></p>
</div>
<div id="ref-simpson1949measurement">
<p>Simpson EH. 1949. Measurement of diversity. <em>Nature</em> 163:688. Available at: <a href="http://dx.doi.org/10.1038/163688a0">http://dx.doi.org/10.1038/163688a0</a></p>
</div>
<div id="ref-smith1993clonal">
<p>Smith JM., Smith NH., O’Rourke M., Spratt BG. 1993. How clonal are bacteria. <em>Proceedings of the National Academy of Sciences</em> 90:4384–4388. Available at: <a href="http://www.pnas.org/content/90/10/4384">http://www.pnas.org/content/90/10/4384</a></p>
</div>
<div id="ref-stoddart1988genotypic">
<p>Stoddart JA., Taylor JF. 1988. Genotypic diversity: Estimation and prediction in samples. <em>Genetics</em> 118:705–711. Available at: <a href="http://www.genetics.org/content/118/4/705">http://www.genetics.org/content/118/4/705</a></p>
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