-
Notifications
You must be signed in to change notification settings - Fork 51
/
Copy pathDAPC.html
815 lines (741 loc) · 40.4 KB
/
DAPC.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<title>Discriminant analysis of principal components (DAPC)</title>
<script src="site_libs/jquery-1.11.3/jquery.min.js"></script>
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link href="site_libs/bootstrap-3.3.5/css/sandstone.min.css" rel="stylesheet" />
<script src="site_libs/bootstrap-3.3.5/js/bootstrap.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/html5shiv.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/respond.min.js"></script>
<script src="site_libs/navigation-1.1/tabsets.js"></script>
<script src="site_libs/accessible-code-block-0.0.1/empty-anchor.js"></script>
<link href="site_libs/anchor-sections-1.0/anchor-sections.css" rel="stylesheet" />
<script src="site_libs/anchor-sections-1.0/anchor-sections.js"></script>
<!-- Global Site Tag (gtag.js) - Google Analytics -->
<script async src="https://www.googletagmanager.com/gtag/js?id=UA-107144798-3"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments)};
gtag('js', new Date());
gtag('config', 'UA-107144798-3');
</script>
<style type="text/css">
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
span.underline{text-decoration: underline;}
div.column{display: inline-block; vertical-align: top; width: 50%;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
</style>
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css" data-origin="pandoc">
code.sourceCode > span { display: inline-block; line-height: 1.25; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode { white-space: pre; position: relative; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
code.sourceCode { white-space: pre-wrap; }
code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ background-color: #f8f8f8; }
@media screen {
code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ef2929; } /* Alert */
code span.an { color: #8f5902; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #c4a000; } /* Attribute */
code span.bn { color: #0000cf; } /* BaseN */
code span.cf { color: #204a87; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4e9a06; } /* Char */
code span.cn { color: #000000; } /* Constant */
code span.co { color: #8f5902; font-style: italic; } /* Comment */
code span.cv { color: #8f5902; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #8f5902; font-weight: bold; font-style: italic; } /* Documentation */
code span.dt { color: #204a87; } /* DataType */
code span.dv { color: #0000cf; } /* DecVal */
code span.er { color: #a40000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #0000cf; } /* Float */
code span.fu { color: #000000; } /* Function */
code span.im { } /* Import */
code span.in { color: #8f5902; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #204a87; font-weight: bold; } /* Keyword */
code span.op { color: #ce5c00; font-weight: bold; } /* Operator */
code span.ot { color: #8f5902; } /* Other */
code span.pp { color: #8f5902; font-style: italic; } /* Preprocessor */
code span.sc { color: #000000; } /* SpecialChar */
code span.ss { color: #4e9a06; } /* SpecialString */
code span.st { color: #4e9a06; } /* String */
code span.va { color: #000000; } /* Variable */
code span.vs { color: #4e9a06; } /* VerbatimString */
code span.wa { color: #8f5902; font-weight: bold; font-style: italic; } /* Warning */
</style>
<script>
// apply pandoc div.sourceCode style to pre.sourceCode instead
(function() {
var sheets = document.styleSheets;
for (var i = 0; i < sheets.length; i++) {
if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
try { var rules = sheets[i].cssRules; } catch (e) { continue; }
for (var j = 0; j < rules.length; j++) {
var rule = rules[j];
// check if there is a div.sourceCode rule
if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") continue;
var style = rule.style.cssText;
// check if color or background-color is set
if (rule.style.color === '' && rule.style.backgroundColor === '') continue;
// replace div.sourceCode by a pre.sourceCode rule
sheets[i].deleteRule(j);
sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
}
}
})();
</script>
<style type="text/css">
pre:not([class]) {
background-color: white;
}
</style>
<style type="text/css">
h1 {
font-size: 34px;
}
h1.title {
font-size: 38px;
}
h2 {
font-size: 30px;
}
h3 {
font-size: 24px;
}
h4 {
font-size: 18px;
}
h5 {
font-size: 16px;
}
h6 {
font-size: 12px;
}
.table th:not([align]) {
text-align: left;
}
</style>
<link rel="stylesheet" href="styles.css" type="text/css" />
<style type = "text/css">
.main-container {
max-width: 940px;
margin-left: auto;
margin-right: auto;
}
code {
color: inherit;
background-color: rgba(0, 0, 0, 0.04);
}
img {
max-width:100%;
}
.tabbed-pane {
padding-top: 12px;
}
.html-widget {
margin-bottom: 20px;
}
button.code-folding-btn:focus {
outline: none;
}
summary {
display: list-item;
}
</style>
<style type="text/css">
/* padding for bootstrap navbar */
body {
padding-top: 61px;
padding-bottom: 40px;
}
/* offset scroll position for anchor links (for fixed navbar) */
.section h1 {
padding-top: 66px;
margin-top: -66px;
}
.section h2 {
padding-top: 66px;
margin-top: -66px;
}
.section h3 {
padding-top: 66px;
margin-top: -66px;
}
.section h4 {
padding-top: 66px;
margin-top: -66px;
}
.section h5 {
padding-top: 66px;
margin-top: -66px;
}
.section h6 {
padding-top: 66px;
margin-top: -66px;
}
.dropdown-submenu {
position: relative;
}
.dropdown-submenu>.dropdown-menu {
top: 0;
left: 100%;
margin-top: -6px;
margin-left: -1px;
border-radius: 0 6px 6px 6px;
}
.dropdown-submenu:hover>.dropdown-menu {
display: block;
}
.dropdown-submenu>a:after {
display: block;
content: " ";
float: right;
width: 0;
height: 0;
border-color: transparent;
border-style: solid;
border-width: 5px 0 5px 5px;
border-left-color: #cccccc;
margin-top: 5px;
margin-right: -10px;
}
.dropdown-submenu:hover>a:after {
border-left-color: #ffffff;
}
.dropdown-submenu.pull-left {
float: none;
}
.dropdown-submenu.pull-left>.dropdown-menu {
left: -100%;
margin-left: 10px;
border-radius: 6px 0 6px 6px;
}
</style>
<script>
// manage active state of menu based on current page
$(document).ready(function () {
// active menu anchor
href = window.location.pathname
href = href.substr(href.lastIndexOf('/') + 1)
if (href === "")
href = "index.html";
var menuAnchor = $('a[href="' + href + '"]');
// mark it active
menuAnchor.parent().addClass('active');
// if it's got a parent navbar menu mark it active as well
menuAnchor.closest('li.dropdown').addClass('active');
});
</script>
<!-- tabsets -->
<style type="text/css">
.tabset-dropdown > .nav-tabs {
display: inline-table;
max-height: 500px;
min-height: 44px;
overflow-y: auto;
background: white;
border: 1px solid #ddd;
border-radius: 4px;
}
.tabset-dropdown > .nav-tabs > li.active:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li.active:before {
content: "";
border: none;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs > li.active {
display: block;
}
.tabset-dropdown > .nav-tabs > li > a,
.tabset-dropdown > .nav-tabs > li > a:focus,
.tabset-dropdown > .nav-tabs > li > a:hover {
border: none;
display: inline-block;
border-radius: 4px;
background-color: transparent;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li {
display: block;
float: none;
}
.tabset-dropdown > .nav-tabs > li {
display: none;
}
</style>
<!-- code folding -->
</head>
<body>
<div class="container-fluid main-container">
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="index.html">Population genetics and genomics in R</a>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="TOC.html">Table of contents</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Part I
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="Introduction.html">Introduction</a>
</li>
<li>
<a href="Getting_ready_to_use_R.html">Getting ready to use R</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Part II
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="Data_Preparation.html">Data preparation</a>
</li>
<li>
<a href="First_Steps.html">First steps</a>
</li>
<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>
</li>
<li>
<a href="DAPC.html">Discriminant analysis of principal components (DAPC)</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Part III
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="intro_vcf.html">Population genomics and HTS</a>
</li>
<li>
<a href="reading_vcf.html">Reading VCF data</a>
</li>
<li>
<a href="analysis_of_genome.html">Analysis of genomic data</a>
</li>
<li>
<a href="gbs_analysis.html">Analysis of GBS data</a>
</li>
<li>
<a href="clustering_plot.html">Clustering plot</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Workshops
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li class="dropdown-submenu">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">ICPP</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="workshop_icpp.html">Preparation</a>
</li>
<li>
<a href="intro_vcf.html">Introduction</a>
</li>
<li>
<a href="reading_vcf.html">VCF data</a>
</li>
<li>
<a href="quality_control.html">Quality control</a>
</li>
<li>
<a href="gbs_analysis.html">Analysis of GBS data</a>
</li>
<li>
<a href="analysis_of_genome.html">Analysis of genome data</a>
</li>
</ul>
</li>
<li class="dropdown-submenu">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">APS Southern Division</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="workshop_southernAPS.html">Preparation</a>
</li>
<li>
<a href="intro_vcf.html">Introduction</a>
</li>
<li>
<a href="reading_vcf.html">VCF data</a>
</li>
<li>
<a href="quality_control.html">Quality control</a>
</li>
<li>
<a href="gbs_analysis.html">Analysis of GBS data</a>
</li>
</ul>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
About
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="Authors.html">Authors</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Appendices
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="intro_to_R.html">Introduction to R</a>
</li>
<li>
<a href="Data_sets.html">Data sets</a>
</li>
<li>
<a href="funpendix.html">Function glossary</a>
</li>
<li>
<a href="background_functions.html">Background_functions</a>
</li>
<li>
<a href="https://github.com/grunwaldlab/Population_Genetics_in_R/">Source Code</a>
</li>
</ul>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
<div class="fluid-row" id="header">
<h1 class="title toc-ignore">Discriminant analysis of principal components (DAPC)</h1>
<h3 class="subtitle"><em>NJ Grünwald, ZN Kamvar, and SE Everhart</em></h3>
</div>
<div id="introduction" class="section level1">
<h1>Introduction</h1>
<p>Often we want to infer population structure by determining the number of clusters (groups) observed without prior knowledge. Several approaches can be used to infer groups such as for example K-means clustering, Bayesian clustering using STRUCTURE, and multivariate methods such as Discriminant Analysis of Principal Components (DAPC) <span class="citation">(Pritchard, Stephens & Donnelly, 2000; Jombart, Devillard & Balloux, 2010; Grünwald & Goss, 2011)</span>. A STRUCTURE-like approach assumes that markers are not linked and that populations are panmictic <span class="citation">(Pritchard et al., 2000)</span>. To use model-free methods K-means clustering based on genetic distance or DAPC are more convenient approaches for populations that are clonal or partially clonal. Here we explore DAPC further.</p>
</div>
<div id="dapc-analysis-of-the-h3n2-influenza-strains" class="section level1">
<h1>DAPC analysis of the H3N2 influenza strains</h1>
<p>DAPC was pioneered by Jombart and colleagues <span class="citation">(Jombart et al., 2010)</span> and can be used to infer the number of clusters of genetically related individuals. In this multivariate statistical approach variance in the sample is partitioned into a between-group and within- group component, in an effort to maximize discrimination between groups. In DAPC, data is first transformed using a principal components analysis (PCA) and subsequently clusters are identified using discriminant analysis (DA). This tutorial is based on the <a href="http://adegenet.r-forge.r-project.org/files%20/tutorial-dapc.pdf">vignette</a> written by Thibaut Jombart. We encourage the user to explore this vignette further. The vignette can also be opened within R by executing <code>adegenetTutorial("dapc")</code>.</p>
<p>We will use the seasonal influenza dataset H3N2 data containing 1903 isolates genotyped for 125 SNPs located in the hemagglutinin segment. This dataset as well as the <code>dapc()</code> function is part of the <a href="http://adegenet.r-forge.r-project.org"><em>adegenet</em></a> package.</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="co"># DAPC requires the adegenet package. Let's load this package:</span></span>
<span id="cb1-2"><a href="#cb1-2"></a><span class="kw">library</span>(<span class="st">"adegenet"</span>)</span>
<span id="cb1-3"><a href="#cb1-3"></a><span class="kw">data</span>(H3N2) <span class="co"># load the H3N2 influenza data. Type ?H3N2 for more info.</span></span>
<span id="cb1-4"><a href="#cb1-4"></a><span class="kw">pop</span>(H3N2) <-<span class="st"> </span>H3N2<span class="op">$</span>other<span class="op">$</span>epid</span>
<span id="cb1-5"><a href="#cb1-5"></a>dapc.H3N2 <-<span class="st"> </span><span class="kw">dapc</span>(H3N2, <span class="dt">var.contrib =</span> <span class="ot">TRUE</span>, <span class="dt">scale =</span> <span class="ot">FALSE</span>, <span class="dt">n.pca =</span> <span class="dv">30</span>, <span class="dt">n.da =</span> <span class="kw">nPop</span>(H3N2) <span class="op">-</span><span class="st"> </span><span class="dv">1</span>)</span>
<span id="cb1-6"><a href="#cb1-6"></a><span class="kw">scatter</span>(dapc.H3N2, <span class="dt">cell =</span> <span class="dv">0</span>, <span class="dt">pch =</span> <span class="dv">18</span><span class="op">:</span><span class="dv">23</span>, <span class="dt">cstar =</span> <span class="dv">0</span>, <span class="dt">mstree =</span> <span class="ot">TRUE</span>, <span class="dt">lwd =</span> <span class="dv">2</span>, <span class="dt">lty =</span> <span class="dv">2</span>)</span></code></pre></div>
<p><img src="DAPC_files/figure-html/unnamed-chunk-2-1.png" width="960" /></p>
<p>The <code>dapc()</code> arguments we used refer to:</p>
<ul>
<li>the dataset H3N2</li>
<li><code>var.contrib</code> this is set to <code>TRUE</code>, meaning that we want to retain the variables contributing to the analysis in our output. We will use this later to see which loci are responsible for separating populations.</li>
<li><code>center</code> this is set to <code>FALSE</code>, indicating that we do not want the data to be rescaled so the mean = 0.</li>
<li><code>n.pca</code> is the number of axes retained in the Principal Component Analysis (PCA). By default, it is set to <code>NULL</code>.</li>
<li><code>n.da</code> is the number of axes retained in the Discriminant Analysis (DA). By default, it is set to <code>NULL</code>.</li>
</ul>
<blockquote>
<p>It is important to set <code>n.pca = NULL</code> when you analyze your data because the number of principal components retained has a large effect on the outcome of the data. See the section below for a statistical method called cross- validation as an aid for choosing <code>n.pca</code></p>
</blockquote>
<p>The <code>scatter()</code> function is part of the <em>ade4</em> package and plots results of a DAPC analysis.</p>
<p>As you can see, each year between 2001 to 2005 is a cluster of H3N2 strains separated by axis 1. In contrast, axis 2 separates the strains observed in the 2006 cluster from the clusters observed during 2001-5, indicating that the strains observed in 2006 are genetically distinct.</p>
<p>Next, let’s assess if there are alleles that most differentiate the 2006 cluster from those in other years.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1"></a><span class="kw">set.seed</span>(<span class="dv">4</span>)</span>
<span id="cb2-2"><a href="#cb2-2"></a>contrib <-<span class="st"> </span><span class="kw">loadingplot</span>(dapc.H3N2<span class="op">$</span>var.contr, <span class="dt">axis =</span> <span class="dv">2</span>, <span class="dt">thres =</span> <span class="fl">0.07</span>, <span class="dt">lab.jitter =</span> <span class="dv">1</span>)</span></code></pre></div>
<p><img src="DAPC_files/figure-html/unnamed-chunk-3-1.png" width="960" /></p>
<p>It looks like SNPs at position 399 and 906 are involved. Let’s check this further by looking at allele frequencies by year:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1"></a>temp <-<span class="st"> </span><span class="kw">seploc</span>(H3N2) <span class="co"># seploc {adegenet} creates a list of individual loci.</span></span>
<span id="cb3-2"><a href="#cb3-2"></a>snp906 <-<span class="st"> </span><span class="kw">tab</span>(temp[[<span class="st">"906"</span>]]) <span class="co"># tab {adegenet} returns a matrix of genotypes</span></span>
<span id="cb3-3"><a href="#cb3-3"></a>snp399 <-<span class="st"> </span><span class="kw">tab</span>(temp[[<span class="st">"399"</span>]])</span>
<span id="cb3-4"><a href="#cb3-4"></a></span>
<span id="cb3-5"><a href="#cb3-5"></a><span class="co"># The following two commands find the average allele frequencies per population</span></span>
<span id="cb3-6"><a href="#cb3-6"></a>(freq906 <-<span class="st"> </span><span class="kw">apply</span>(snp906, <span class="dv">2</span>, <span class="cf">function</span>(e) <span class="kw">tapply</span>(e, <span class="kw">pop</span>(H3N2), mean, <span class="dt">na.rm =</span> <span class="ot">TRUE</span>)))</span></code></pre></div>
<pre><code>## 906.c 906.t
## 2001 0.000000000 1.0000000
## 2002 0.000000000 1.0000000
## 2003 0.000000000 1.0000000
## 2004 0.000000000 1.0000000
## 2005 0.002155172 0.9978448
## 2006 0.616071429 0.3839286</code></pre>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1"></a>(freq399 <-<span class="st"> </span><span class="kw">apply</span>(snp399, <span class="dv">2</span>, <span class="cf">function</span>(e) <span class="kw">tapply</span>(e, <span class="kw">pop</span>(H3N2), mean, <span class="dt">na.rm =</span> <span class="ot">TRUE</span>)))</span></code></pre></div>
<pre><code>## 399.c 399.t
## 2001 0.000000000 1.0000000
## 2002 0.000000000 1.0000000
## 2003 0.000000000 1.0000000
## 2004 0.001848429 0.9981516
## 2005 0.002079002 0.9979210
## 2006 0.357142857 0.6428571</code></pre>
<p>Note that a new allele appeared in 2005 for SNP locus 906 and 2004 for locus 399 separating populations along axis 2.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1"></a><span class="co"># First, set the plotting parameters</span></span>
<span id="cb7-2"><a href="#cb7-2"></a><span class="co"># mfrow = number of columns, rows</span></span>
<span id="cb7-3"><a href="#cb7-3"></a><span class="co"># mar = plot margin size</span></span>
<span id="cb7-4"><a href="#cb7-4"></a><span class="co"># las = axis label style (3: always vertical)</span></span>
<span id="cb7-5"><a href="#cb7-5"></a><span class="kw">par</span>(<span class="dt">mfrow =</span> <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="dt">mar =</span> <span class="kw">c</span>(<span class="dv">5</span>, <span class="dv">4</span>, <span class="dv">4</span>, <span class="dv">0</span>) <span class="op">+</span><span class="st"> </span><span class="fl">0.1</span>, <span class="dt">las =</span> <span class="dv">3</span>)</span>
<span id="cb7-6"><a href="#cb7-6"></a></span>
<span id="cb7-7"><a href="#cb7-7"></a><span class="kw">matplot</span>(freq906, <span class="dt">pch =</span> <span class="kw">c</span>(<span class="st">"c"</span>, <span class="st">"t"</span>), <span class="dt">type =</span> <span class="st">"b"</span>,</span>
<span id="cb7-8"><a href="#cb7-8"></a> <span class="dt">xlab =</span> <span class="st">"year"</span>, <span class="dt">ylab =</span> <span class="st">"allele frequency"</span>, <span class="dt">main =</span> <span class="st">"SNP # 906"</span>,</span>
<span id="cb7-9"><a href="#cb7-9"></a> <span class="dt">xaxt =</span> <span class="st">"n"</span>, <span class="dt">cex =</span> <span class="fl">1.5</span>)</span>
<span id="cb7-10"><a href="#cb7-10"></a><span class="kw">axis</span>(<span class="dt">side =</span> <span class="dv">1</span>, <span class="dt">at =</span> <span class="dv">1</span><span class="op">:</span><span class="dv">6</span>, <span class="dt">lab =</span> <span class="dv">2001</span><span class="op">:</span><span class="dv">2006</span>)</span>
<span id="cb7-11"><a href="#cb7-11"></a></span>
<span id="cb7-12"><a href="#cb7-12"></a><span class="kw">matplot</span>(freq399, <span class="dt">pch =</span> <span class="kw">c</span>(<span class="st">"c"</span>, <span class="st">"t"</span>), <span class="dt">type =</span> <span class="st">"b"</span>,</span>
<span id="cb7-13"><a href="#cb7-13"></a> <span class="dt">xlab =</span> <span class="st">"year"</span>, <span class="dt">ylab =</span> <span class="st">"allele frequency"</span>, <span class="dt">main =</span> <span class="st">"SNP #399"</span>,</span>
<span id="cb7-14"><a href="#cb7-14"></a> <span class="dt">xaxt =</span> <span class="st">"n"</span>, <span class="dt">cex =</span> <span class="fl">1.5</span>)</span>
<span id="cb7-15"><a href="#cb7-15"></a><span class="kw">axis</span>(<span class="dt">side =</span> <span class="dv">1</span>, <span class="dt">at =</span> <span class="dv">1</span><span class="op">:</span><span class="dv">6</span>, <span class="dt">lab =</span> <span class="dv">2001</span><span class="op">:</span><span class="dv">2006</span>)</span></code></pre></div>
<p><img src="DAPC_files/figure-html/unnamed-chunk-5-1.png" width="960" /></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="co"># Now we reset the plotting parameters to default</span></span>
<span id="cb8-2"><a href="#cb8-2"></a><span class="kw">par</span>(<span class="dt">mfrow =</span> <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">1</span>), <span class="dt">mar =</span> <span class="kw">c</span>(<span class="dv">5</span>, <span class="dv">4</span>, <span class="dv">4</span>, <span class="dv">2</span>) <span class="op">+</span><span class="st"> </span><span class="fl">0.1</span>, <span class="dt">las =</span> <span class="dv">0</span>)</span></code></pre></div>
<p>This plot nicely illustrates the effect of mutation, followed by selection or drift in the seasonal H3N2 influenza virus.</p>
</div>
<div id="cross-validation-dapc-analysis-of-phytophthora-ramorum-from-forests-and-nurseries" class="section level1">
<h1>Cross validation: DAPC analysis of <em>Phytophthora ramorum</em> from forests and nurseries</h1>
<p>Above we showed a nice example of a story that shows how two loci can drastically influence an epidemic. Next we will spend some time establishing what the appropriate number of principal components (PC) is for the analysis. It is important to carefully choose the correct number of PCs so as to include most sources of variation explained by an appropriate number of PCs retained. One way of ensuring that you have selected the correct number of PCs is to do cross-validation. This is a procedure in which you leave out a certain percentage of your data, run DAPC, and then see if the data that was left out is correctly placed into the population.</p>
<p>Since the H3N2 data set is quite large, we will use <em>Phytophthora ramorum</em> data from nurseries in California and Oregon <span class="citation">(Goss et al., 2009)</span> and forests in Curry County, Oregon <span class="citation">(Kamvar et al., 2015)</span>. These data represent the Sudden Oak Death epidemic in Curry County, OR from 2001-2014 separated into different watershed regions. In <span class="citation">Kamvar et al. (2015)</span>, the “Hunter Creek (HunterCr)” population was shown to be the result of a second introduction, likely from nurseries. Part of the evidence to support this conclusion came from DAPC results. Here, we will recreate the process of cross validation and reporting.</p>
<p>If we run the function <code>xvalDapc()</code> with default parameters, it will run 30 replicates of cross-validation for a number of PCs less than the total number of alleles in the data. This is a good way to get an idea of where to focus more intense cross-validation runs:</p>
<blockquote>
<p>By default <code>xvalDapc()</code> needs two parameters: 1. The genotype matrix, 2. The population factors.</p>
</blockquote>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1"></a><span class="kw">library</span>(<span class="st">"poppr"</span>)</span>
<span id="cb9-2"><a href="#cb9-2"></a><span class="kw">data</span>(<span class="st">"Pram"</span>, <span class="dt">package =</span> <span class="st">"poppr"</span>)</span>
<span id="cb9-3"><a href="#cb9-3"></a>Pram</span></code></pre></div>
<pre><code>##
## This is a genclone object
## -------------------------
## Genotype information:
##
## 98 multilocus genotypes
## 729 diploid individuals
## 5 codominant loci
##
## Population information:
##
## 3 strata - SOURCE, YEAR, STATE
## 9 populations defined -
## Nursery_CA, Nursery_OR, JHallCr_OR, ..., Winchuck_OR, ChetcoMain_OR, PistolRSF_OR</code></pre>
<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">set.seed</span>(<span class="dv">999</span>)</span>
<span id="cb11-2"><a href="#cb11-2"></a>pramx <-<span class="st"> </span><span class="kw">xvalDapc</span>(<span class="kw">tab</span>(Pram, <span class="dt">NA.method =</span> <span class="st">"mean"</span>), <span class="kw">pop</span>(Pram))</span></code></pre></div>
<p><img src="DAPC_files/figure-html/unnamed-chunk-6-1.png" width="960" /></p>
<p>You can see that we have a peak around 15 PC. From here, we can narrow the search by specifying the number of PC to try with <code>n.pca</code> and centering it around 15, and doing 1000 replicates each (Note, this will take a long time).</p>
<blockquote>
<p>Windows users: change parallel to “snow”.</p>
</blockquote>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1"></a><span class="kw">set.seed</span>(<span class="dv">999</span>)</span>
<span id="cb12-2"><a href="#cb12-2"></a><span class="kw">system.time</span>(pramx <-<span class="st"> </span><span class="kw">xvalDapc</span>(<span class="kw">tab</span>(Pram, <span class="dt">NA.method =</span> <span class="st">"mean"</span>), <span class="kw">pop</span>(Pram),</span>
<span id="cb12-3"><a href="#cb12-3"></a> <span class="dt">n.pca =</span> <span class="dv">10</span><span class="op">:</span><span class="dv">20</span>, <span class="dt">n.rep =</span> <span class="dv">1000</span>,</span>
<span id="cb12-4"><a href="#cb12-4"></a> <span class="dt">parallel =</span> <span class="st">"multicore"</span>, <span class="dt">ncpus =</span> 4L))</span></code></pre></div>
<p><img src="DAPC_files/figure-html/Pramhide-1.png" width="960" /></p>
<pre><code>## user system elapsed
## 176.473 9.777 47.494</code></pre>
<p>We can see that it’s basically a flat line all the way. If we take a look at the object, we see that 16 PCs give us the highest percent of correctly predicted subsamples with the lowest error.</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1"></a><span class="kw">names</span>(pramx) <span class="co"># The first element are all the samples</span></span></code></pre></div>
<pre><code>## [1] "Cross-Validation Results"
## [2] "Median and Confidence Interval for Random Chance"
## [3] "Mean Successful Assignment by Number of PCs of PCA"
## [4] "Number of PCs Achieving Highest Mean Success"
## [5] "Root Mean Squared Error by Number of PCs of PCA"
## [6] "Number of PCs Achieving Lowest MSE"
## [7] "DAPC"</code></pre>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1"></a>pramx[<span class="op">-</span><span class="dv">1</span>]</span></code></pre></div>
<pre><code>## $`Median and Confidence Interval for Random Chance`
## 2.5% 50% 97.5%
## 0.09179837 0.11054024 0.13281445
##
## $`Mean Successful Assignment by Number of PCs of PCA`
## 10 11 12 13 14 15 16 17
## 0.6483115 0.6484877 0.6460399 0.6459813 0.6563492 0.6673671 0.6733597 0.6704714
## 18 19 20
## 0.6703640 0.6692078 0.6670846
##
## $`Number of PCs Achieving Highest Mean Success`
## [1] "16"
##
## $`Root Mean Squared Error by Number of PCs of PCA`
## 10 11 12 13 14 15 16 17
## 0.3534834 0.3531600 0.3557343 0.3558209 0.3456140 0.3344596 0.3285616 0.3315655
## 18 19 20
## 0.3315402 0.3324705 0.3349063
##
## $`Number of PCs Achieving Lowest MSE`
## [1] "16"
##
## $DAPC
## #################################################
## # Discriminant Analysis of Principal Components #
## #################################################
## class: dapc
## $call: dapc.data.frame(x = as.data.frame(x), grp = ..1, n.pca = ..2,
## n.da = ..3)
##
## $n.pca: 16 first PCs of PCA used
## $n.da: 8 discriminant functions saved
## $var (proportion of conserved variance): 0.984
##
## $eig (eigenvalues): 881.9 207.4 97.39 57.36 49.03 ...
##
## vector length content
## 1 $eig 8 eigenvalues
## 2 $grp 729 prior group assignment
## 3 $prior 9 prior group probabilities
## 4 $assign 729 posterior group assignment
## 5 $pca.cent 38 centring vector of PCA
## 6 $pca.norm 38 scaling vector of PCA
## 7 $pca.eig 33 eigenvalues of PCA
##
## data.frame nrow ncol content
## 1 $tab 729 16 retained PCs of PCA
## 2 $means 9 16 group means
## 3 $loadings 16 8 loadings of variables
## 4 $ind.coord 729 8 coordinates of individuals (principal components)
## 5 $grp.coord 9 8 coordinates of groups
## 6 $posterior 729 9 posterior membership probabilities
## 7 $pca.loadings 38 16 PCA loadings of original variables
## 8 $var.contr 38 8 contribution of original variables</code></pre>
<p>We also have a DAPC object that we can plot comparable to figure 4 in <span class="citation">Kamvar et al. (2015)</span>:</p>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1"></a><span class="kw">scatter</span>(pramx<span class="op">$</span>DAPC, <span class="dt">col =</span> <span class="kw">other</span>(Pram)<span class="op">$</span>comparePal, <span class="dt">cex =</span> <span class="dv">2</span>, <span class="dt">legend =</span> <span class="ot">TRUE</span>,</span>
<span id="cb18-2"><a href="#cb18-2"></a> <span class="dt">clabel =</span> <span class="ot">FALSE</span>, <span class="dt">posi.leg =</span> <span class="st">"bottomleft"</span>, <span class="dt">scree.pca =</span> <span class="ot">TRUE</span>,</span>
<span id="cb18-3"><a href="#cb18-3"></a> <span class="dt">posi.pca =</span> <span class="st">"topleft"</span>, <span class="dt">cleg =</span> <span class="fl">0.75</span>, <span class="dt">xax =</span> <span class="dv">1</span>, <span class="dt">yax =</span> <span class="dv">2</span>, <span class="dt">inset.solid =</span> <span class="dv">1</span>)</span></code></pre></div>
<p><img src="DAPC_files/figure-html/unnamed-chunk-8-1.png" width="960" /></p>
<p>We can see that this shows the clear separation of Hunter Creek from the rest of the epidemic, providing evidence that this population arose from a separate introduction.</p>
</div>
<div id="conclusions" class="section level1">
<h1>Conclusions</h1>
<p>DAPC is a wonderful tool for exploring structure of populations based on PCA and DA without making assumptions of panmixia. Thus, this technique provides a robust alternative to Bayesian clustering methods like STRUCTURE <span class="citation">(Pritchard et al., 2000)</span> that should not be used for clonal or partially clonal populations.</p>
<p>DAPC analysis is inherently interactive and cannot be scripted <em>a priori</em>. Please refer to the <a href="https://github.com/thibautjombart/adegenet/blob/master/tutorials/tutorial-dapc.pdf">vignette</a> written by Thibaut Jombart for a more interactive analysis.</p>
</div>
<div id="references" class="section level1 unnumbered">
<h1>References</h1>
<div id="refs" class="references">
<div id="ref-goss2009population">
<p>Goss EM., Larsen M., Chastagner GA., Givens DR., Grünwald NJ. 2009. Population genetic analysis infers migration pathways of phytophthora ramorum in us nurseries. <em>PLoS Pathog</em> 5:e1000583. Available at: <a href="http://dx.doi.org/10.1371/journal.ppat.1000583">http://dx.doi.org/10.1371/journal.ppat.1000583</a></p>
</div>
<div id="ref-grunwald2011evolution">
<p>Grünwald NJ., Goss EM. 2011. Evolution and population genetics of exotic and re-emerging pathogens: Novel tools and approaches. <em>Annual Review of Phytopathology</em> 49:249–267. Available at: <a href="http://www.annualreviews.org/doi/abs/10.1146/annurev-phyto-072910-095246?journalCode=phyto">http://www.annualreviews.org/doi/abs/10.1146/annurev-phyto-072910-095246?journalCode=phyto</a></p>
</div>
<div id="ref-jombart2010discriminant">
<p>Jombart T., Devillard S., Balloux F. 2010. Discriminant analysis of principal components: A new method for the analysis of genetically structured populations. <em>BMC genetics</em> 11:94. Available at: <a href="http://www.biomedcentral.com/1471-2156/11/94">http://www.biomedcentral.com/1471-2156/11/94</a></p>
</div>
<div id="ref-kamvar2015spatial">
<p>Kamvar Z., Larsen M., Kanaskie A., Hansen E., Grünwald N. 2015. Spatial and temporal analysis of populations of the sudden oak death pathogen in oregon forests. <em>Phytopathology</em> 105:982–989. Available at: <a href="http://dx.doi.org/10.1094/PHYTO-12-14-0350-FI">http://dx.doi.org/10.1094/PHYTO-12-14-0350-FI</a></p>
</div>
<div id="ref-pritchard2000inference">
<p>Pritchard JK., Stephens M., Donnelly P. 2000. Inference of population structure using multilocus genotype data. <em>Genetics</em> 155:945–959. Available at: <a href="http://www.genetics.org/content/155/2/945.abstract">http://www.genetics.org/content/155/2/945.abstract</a></p>
</div>
</div>
</div>
</div>
<script>
// add bootstrap table styles to pandoc tables
function bootstrapStylePandocTables() {
$('tr.odd').parent('tbody').parent('table').addClass('table table-condensed');
}
$(document).ready(function () {
bootstrapStylePandocTables();
});
</script>
<!-- tabsets -->
<script>
$(document).ready(function () {
window.buildTabsets("TOC");
});
$(document).ready(function () {
$('.tabset-dropdown > .nav-tabs > li').click(function () {
$(this).parent().toggleClass('nav-tabs-open')
});
});
</script>
<!-- code folding -->
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement("script");
script.type = "text/javascript";
script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
document.getElementsByTagName("head")[0].appendChild(script);
})();
</script>
</body>
</html>