-
Notifications
You must be signed in to change notification settings - Fork 51
/
Locus_Stats.html
1269 lines (1169 loc) · 52.4 KB
/
Locus_Stats.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
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<title>Locus stats, heterozygosity, HWE</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">Locus stats, heterozygosity, HWE</h1>
<h3 class="subtitle"><em>ZN Kamvar, SE Everhart, and NJ Grünwald</em></h3>
</div>
<p>A rigorous population genetic analysis looks closely at the data to assess quality and identify outliers or problems in the data such as erroneous allele calls. This chapter focuses on analysis on a per-locus level. While there are statistics that analyze populations across loci, it is important to analyze each locus independently to make sure that one locus is not introducing bias or spurious errors into the analysis.</p>
<blockquote>
<p><strong>Note:</strong> Many of these statistics are specific to co-dominant data.</p>
</blockquote>
<div id="locus-summary-statistics" class="section level2">
<h2>Locus summary statistics</h2>
<p>A quick way to assess quality of the data is to determine the number, diversity, expected heterozygosity, and evenness of the alleles at each locus. As an example, we will use data for the fungal-like protist <em>Phytophthora infestans</em> from <span class="citation">(Goss et al., 2014)</span>. First, we’ll use the function <code>locus_table</code> to get all of the statistics mentioned above. For documentation on this function type <code>?locus_table</code>. Here is a first look at each locus:</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 class="co"># Make sure poppr is loaded if you haven't done so already.</span></span>
<span id="cb1-2"><a href="#cb1-2"></a><span class="kw">library</span>(<span class="st">"magrittr"</span>) <span class="co"># We will also use magrittr for part of this chapter</span></span>
<span id="cb1-3"><a href="#cb1-3"></a><span class="kw">data</span>(<span class="st">"Pinf"</span>) <span class="co"># P. infestans data set from Mexico and South America</span></span>
<span id="cb1-4"><a href="#cb1-4"></a><span class="kw">locus_table</span>(Pinf)</span></code></pre></div>
<pre><code>##
## allele = Number of observed alleles
## 1-D = Simpson index
## Hexp = Nei's 1978 gene diversity
## ------------------------------------------</code></pre>
<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 can see here that we have a widely variable number of alleles per locus and that we actually have a single locus that only has two alleles, Pi33. This locus also has low diversity, low expected heterozygosity and is very uneven in allele distribution. This is a sign that this might be a phylogenetically uninformative locus, where we have two alleles and one is occurring at a minor frequency. We will explore analysis with and without this locus. Let’s first see if both of these alleles exist in both populations of this data set.</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">locus_table</span>(Pinf, <span class="dt">pop =</span> <span class="st">"North America"</span>)</span></code></pre></div>
<pre><code>##
## allele = Number of observed alleles
## 1-D = Simpson index
## Hexp = Nei's 1978 gene diversity
## ------------------------------------------</code></pre>
<pre><code>## summary
## locus allele 1-D Hexp Evenness
## Pi02 9.000 0.690 0.697 0.653
## D13 21.000 0.895 0.906 0.684
## Pi33 2.000 0.021 0.021 0.353
## Pi04 4.000 0.545 0.551 0.764
## Pi4B 5.000 0.596 0.603 0.736
## Pi16 6.000 0.425 0.430 0.498
## G11 15.000 0.824 0.833 0.625
## Pi56 3.000 0.335 0.338 0.647
## Pi63 3.000 0.310 0.313 0.568
## Pi70 2.000 0.203 0.205 0.595
## Pi89 11.000 0.627 0.634 0.549
## mean 7.364 0.497 0.503 0.607</code></pre>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1"></a><span class="kw">locus_table</span>(Pinf, <span class="dt">pop =</span> <span class="st">"South America"</span>)</span></code></pre></div>
<pre><code>##
## allele = Number of observed alleles
## 1-D = Simpson index
## Hexp = Nei's 1978 gene diversity
## ------------------------------------------</code></pre>
<pre><code>## summary
## locus allele 1-D Hexp Evenness
## Pi02 5.00 0.54 0.54 0.83
## D13 13.00 0.83 0.84 0.67
## Pi33 1.00 . .
## Pi04 4.00 0.61 0.62 0.81
## Pi4B 7.00 0.70 0.71 0.78
## Pi16 3.00 0.35 0.36 0.69
## G11 14.00 0.80 0.81 0.63
## Pi56 2.00 0.39 0.39 0.81
## Pi63 3.00 0.50 0.51 0.73
## Pi70 3.00 0.37 0.37 0.62
## Pi89 2.00 0.48 0.49 0.97
## mean 5.18 0.51 0.51 0.75</code></pre>
</div>
<div id="phylogenetically-uninformative-loci" class="section level2">
<h2>Phylogenetically uninformative loci</h2>
<p>We can see that the South American populations is fixed for one allele, thus it would not be a bad idea to remove that locus from downstream analyses. We can do this using the function <code>informloci</code>. This will remove loci that contain less than a given percentage of divergent individuals (the default is <span class="math inline">\(2/N\)</span>, where <span class="math inline">\(N\)</span> equals the number of individuals in the data set).</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1"></a><span class="kw">nLoc</span>(Pinf) <span class="co"># Let's look at our data set, note how many loci we have.</span></span></code></pre></div>
<pre><code>## [1] 11</code></pre>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1"></a>iPinf <-<span class="st"> </span><span class="kw">informloci</span>(Pinf)</span></code></pre></div>
<pre><code>## cutoff value: 2.32558139534884 % ( 2 samples ).</code></pre>
<pre><code>## MAF : 0.01</code></pre>
<pre><code>##
## Found 1 uninformative locus
## ============================
## 1 locus found with a cutoff of 2 samples :
## Pi33
## 0 loci found with MAF < 0.01</code></pre>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1"></a><span class="kw">nLoc</span>(iPinf) <span class="co"># Note that we have 1 less locus</span></span></code></pre></div>
<pre><code>## [1] 10</code></pre>
<p>So, how does this affect multi-locus based statistics? We can see immediately that it didn’t affect the number of multilocus genotypes, let’s take a look at the index of association:</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">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>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1"></a><span class="kw">poppr</span>(iPinf)</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 0.565 2.873 0.3446
## 2 North America 48 43 34.5 0.989 3.69 34.9 0.971 0.871 0.551 0.225 0.0255
## 3 Total 86 72 34.6 1.529 4.19 57.8 0.983 0.875 0.571 0.655 0.0750
## File
## 1 iPinf
## 2 iPinf
## 3 iPinf</code></pre>
<p>We can see that it increased ever so slightly for the “North America” and “Total” populations, but not the “South America” population as expected given the fixed alleles at locus P33.</p>
</div>
<div id="missing-data" class="section level2">
<h2>Missing data</h2>
<p>It is often important to asses the percentage of missing data. The <em>poppr</em> function <code>info_table</code> will help you visualize missing data so that you can assess how to treat these further using the function <code>missingno</code>. For this example, we will use the nancycats data set as it contains a wide variety of possibilities for missing data:</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1"></a><span class="kw">data</span>(nancycats)</span>
<span id="cb22-2"><a href="#cb22-2"></a><span class="kw">info_table</span>(nancycats, <span class="dt">plot =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<div class="figure">
<img src="Locus_Stats_files/figure-html/missing_table-1.png" alt="Plot of missing data" width="700px" />
<p class="caption">
Plot of missing data
</p>
</div>
<pre><code>## Locus
## Population fca8 fca23 fca43 fca45 fca77 fca78 fca90 fca96 fca37 Mean
## P01 0.200 . . . . . . . . 0.022
## P02 . . . . . . . . . .
## P03 . . . . . . . . . .
## P04 . . . . . . . . . .
## P05 . . . . . . . . . .
## P06 . . . . . . . . . .
## P07 0.357 . . . . . . . . 0.040
## P08 . . . . . . . . . .
## P09 . . . . . . . . . .
## P10 . . . . . . . . . .
## P11 0.150 . . 0.400 . . . 0.050 . 0.067
## P12 0.214 . . . . . . . . 0.024
## P13 . . . . . . . . . .
## P14 0.412 . . . . . . . . 0.046
## P15 . . . . . . . . . .
## P16 . . . . . . . . . .
## P17 . . . 1.000 . . . 0.615 . 0.179
## Total 0.084 . . 0.089 . . . 0.038 . 0.023</code></pre>
<p>Here we see a few things. The data set has an average of 2.34% missing data overall. More alarming, perhaps is the fact that population 17 has not been genotyped at locus fca45 at all and that locus fca8 shows missing data across many populations. Many analyses in <em>poppr</em> can be performed with missing data in place as it will be either considered an extra allele in the case of MLG calculations or will be interpolated to not contribute to the distance measure used for the index of association. If you want to specifically treat missing data, you can use the function <code>missingno</code> to remove loci or individuals, or replace missing data with zeroes or the average values of the locus.</p>
</div>
<div id="removing-loci-and-genotypes" class="section level2">
<h2>Removing loci and genotypes</h2>
<p>When removing loci or genotypes, you can specify a cutoff representing the percent missing to be removed. The default is <code>0.05</code> (5%).</p>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1"></a>nancycats <span class="op">%>%</span><span class="st"> </span><span class="kw">missingno</span>(<span class="st">"loci"</span>) <span class="op">%>%</span><span class="st"> </span><span class="kw">info_table</span>(<span class="dt">plot =</span> <span class="ot">TRUE</span>, <span class="dt">scale =</span> <span class="ot">FALSE</span>)</span></code></pre></div>
<pre><code>##
## Found 617 missing values.
##
## 2 loci contained missing values greater than 5%
##
## Removing 2 loci: fca8, fca45</code></pre>
<div class="figure">
<img src="Locus_Stats_files/figure-html/unnamed-chunk-2-1.png" alt="Plot of missing data" width="700px" />
<p class="caption">
Plot of missing data
</p>
</div>
<pre><code>## Locus
## Population fca23 fca43 fca77 fca78 fca90 fca96 fca37 Mean
## P01 . . . . . . . .
## P02 . . . . . . . .
## P03 . . . . . . . .
## P04 . . . . . . . .
## P05 . . . . . . . .
## P06 . . . . . . . .
## P07 . . . . . . . .
## P08 . . . . . . . .
## P09 . . . . . . . .
## P10 . . . . . . . .
## P11 . . . . . 0.0500 . 0.0071
## P12 . . . . . . . .
## P13 . . . . . . . .
## P14 . . . . . . . .
## P15 . . . . . . . .
## P16 . . . . . . . .
## P17 . . . . . 0.6154 . 0.0879
## Total . . . . . 0.0380 . 0.0054</code></pre>
<blockquote>
<p><strong>Advanced Users:</strong> when <code>scale = TRUE</code>, the color scale will be set so that the warmest color corresponds to the highest value.</p>
</blockquote>
<p>We only removed two loci. If we wanted to make sure we removed everything, we could set <code>cutoff = 0</code>.</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1"></a>miss <-<span class="st"> </span>nancycats <span class="op">%>%</span><span class="st"> </span><span class="kw">missingno</span>(<span class="st">"loci"</span>, <span class="dt">cutoff =</span> <span class="dv">0</span>) <span class="op">%>%</span><span class="st"> </span><span class="kw">info_table</span>(<span class="dt">plot =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<pre><code>##
## Found 617 missing values.
##
## 3 loci contained missing values greater than 0%
##
## Removing 3 loci: fca8, fca45, fca96</code></pre>
<pre><code>## No Missing Data Found!</code></pre>
<p>Again, removing individuals is also relatively easy:</p>
<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1"></a>miss <-<span class="st"> </span>nancycats <span class="op">%>%</span><span class="st"> </span><span class="kw">missingno</span>(<span class="st">"geno"</span>) <span class="op">%>%</span><span class="st"> </span><span class="kw">info_table</span>(<span class="dt">plot =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<pre><code>##
## Found 617 missing values.
##
## 38 genotypes contained missing values greater than 5%
##
## Removing 38 genotypes: N215, N216, N188, N189, N190, N191, N192, N298,
## N299, N300, N301, N302, N303, N304, N310, N195, N197, N198, N199, N200,
## N201, N206, N182, N184, N186, N282, N283, N288, N291, N292, N293, N294,
## N295, N296, N297, N281, N289, N290</code></pre>
<pre><code>## No Missing Data Found!</code></pre>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1"></a>miss <-<span class="st"> </span>nancycats <span class="op">%>%</span><span class="st"> </span><span class="kw">missingno</span>(<span class="st">"geno"</span>, <span class="dt">cutoff =</span> <span class="dv">0</span>) <span class="op">%>%</span><span class="st"> </span><span class="kw">info_table</span>(<span class="dt">plot =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<pre><code>##
## Found 617 missing values.
##
## 38 genotypes contained missing values greater than 0%
##
## Removing 38 genotypes: N215, N216, N188, N189, N190, N191, N192, N298,
## N299, N300, N301, N302, N303, N304, N310, N195, N197, N198, N199, N200,
## N201, N206, N182, N184, N186, N282, N283, N288, N291, N292, N293, N294,
## N295, N296, N297, N281, N289, N290
## No Missing Data Found!</code></pre>
<p>The function <code>missingno</code> removes individuals based on the percent of missing data relative to the number of loci. Let’s remove all individuals with 2 missing loci:</p>
<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb35-1"><a href="#cb35-1"></a>miss <-<span class="st"> </span>nancycats <span class="op">%>%</span></span>
<span id="cb35-2"><a href="#cb35-2"></a><span class="st"> </span><span class="kw">missingno</span>(<span class="st">"geno"</span>, <span class="dt">cutoff =</span> <span class="dv">2</span><span class="op">/</span><span class="kw">nLoc</span>(nancycats)) <span class="op">%>%</span></span>
<span id="cb35-3"><a href="#cb35-3"></a><span class="st"> </span><span class="kw">info_table</span>(<span class="dt">plot =</span> <span class="ot">TRUE</span>)</span></code></pre></div>
<div class="figure">
<img src="Locus_Stats_files/figure-html/unnamed-chunk-5-1.png" alt="Plot of missing data" width="700px" />
<p class="caption">
Plot of missing data
</p>
</div>
<p>We only found one individual in population 11.</p>
<!--
Replacing missing data
----
Replacement of missing data occurs for each allele over all loci. It will
replace all missing data in your data set. There are two options: replacement of
missing data with zeroes, in fact recoding these as another allelic state, or
replacement of missing data with the average allele frequency observed.
Note that the first population in the data set has 20% missing data
at the first locus. Here is the un-replaced data for reference:
```r
nan1 <- popsub(nancycats, 1, drop = TRUE) # Dropping alleles not in that population.
tab(nan1[loc = "fca8"])
```
```
## fca8.133 fca8.135 fca8.137 fca8.143
## N215 NA NA NA NA
## N216 NA NA NA NA
## N217 0 1 0 1
## N218 1 1 0 0
## N219 1 1 0 0
## N220 0 1 0 1
## N221 0 2 0 0
## N222 0 1 0 1
## N223 0 0 1 1
## N224 0 2 0 0
```
```r
nanzero <- missingno(nancycats, "zero")
```
```
##
## Replaced 617 missing values.
```
```r
tab(popsub(nanzero, 1, drop = TRUE)[loc = "fca8"])
```
```
## fca8.133 fca8.135 fca8.137 fca8.143
## N215 0 0 0 0
## N216 0 0 0 0
## N217 0 1 0 1
## N218 1 1 0 0
## N219 1 1 0 0
## N220 0 1 0 1
## N221 0 2 0 0
## N222 0 1 0 1
## N223 0 0 1 1
## N224 0 2 0 0
```
The `NA`s have been replaced with zeroes. Now let's look at what happens when we
replace with `"mean"`.
> Note: We get a warning with this command that says `@tab does not contain integers`.
> This is because the `genind` object should only contain counts of alleles, but
> replacing missing data with the mean will give decimal numbers (aka numeric).
```r
nanmean <- missingno(nancycats, "mean")
```
```
##
## Replaced 617 missing values.
```
```r
tab(popsub(nanmean, 1, drop = TRUE)[loc = "fca8"])
```
```
## Warning in validityMethod(object): @tab does not contain integers; as of
## adegenet_2.0-0, numeric values are no longer used
## Warning in validityMethod(object): @tab does not contain integers; as of
## adegenet_2.0-0, numeric values are no longer used
```
```
## fca8.117 fca8.119 fca8.121 fca8.123 fca8.127 fca8.129
## N215 0.004608295 0.004608295 0.02764977 0.1336406 0.004608295 0.0921659
## N216 0.004608295 0.004608295 0.02764977 0.1336406 0.004608295 0.0921659
## N217 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## N218 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## N219 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## N220 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## N221 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## N222 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## N223 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## N224 0.000000000 0.000000000 0.00000000 0.0000000 0.000000000 0.0000000
## fca8.131 fca8.133 fca8.135 fca8.137 fca8.139 fca8.141 fca8.143
## N215 0.1013825 0.1520737 0.483871 0.3824885 0.124424 0.1889401 0.202765
## N216 0.1013825 0.1520737 0.483871 0.3824885 0.124424 0.1889401 0.202765
## N217 0.0000000 0.0000000 1.000000 0.0000000 0.000000 0.0000000 1.000000
## N218 0.0000000 1.0000000 1.000000 0.0000000 0.000000 0.0000000 0.000000
## N219 0.0000000 1.0000000 1.000000 0.0000000 0.000000 0.0000000 0.000000
## N220 0.0000000 0.0000000 1.000000 0.0000000 0.000000 0.0000000 1.000000
## N221 0.0000000 0.0000000 2.000000 0.0000000 0.000000 0.0000000 0.000000
## N222 0.0000000 0.0000000 1.000000 0.0000000 0.000000 0.0000000 1.000000
## N223 0.0000000 0.0000000 0.000000 1.0000000 0.000000 0.0000000 1.000000
## N224 0.0000000 0.0000000 2.000000 0.0000000 0.000000 0.0000000 0.000000
## fca8.145 fca8.147 fca8.149
## N215 0.05069124 0.01382488 0.03225806
## N216 0.05069124 0.01382488 0.03225806
## N217 0.00000000 0.00000000 0.00000000
## N218 0.00000000 0.00000000 0.00000000
## N219 0.00000000 0.00000000 0.00000000
## N220 0.00000000 0.00000000 0.00000000
## N221 0.00000000 0.00000000 0.00000000
## N222 0.00000000 0.00000000 0.00000000
## N223 0.00000000 0.00000000 0.00000000
## N224 0.00000000 0.00000000 0.00000000
```
Notice that there are a lot more alleles than there were originally. This is
because the procedure is performed over the entire data set, not by population.
Let's look at what happens if we perform the same routine on the subset data.
```r
nan1 <- nancycats %>% popsub(1, drop = TRUE) %>% missingno("mean")
```
```
##
## Replaced 8 missing values.
```
```r
tab(nan1[loc = "fca8"])
```
```
## fca8.133 fca8.135 fca8.137 fca8.143
## N215 0.25 1.125 0.125 0.5
## N216 0.25 1.125 0.125 0.5
## N217 0.00 1.000 0.000 1.0
## N218 1.00 1.000 0.000 0.0
## N219 1.00 1.000 0.000 0.0
## N220 0.00 1.000 0.000 1.0
## N221 0.00 2.000 0.000 0.0
## N222 0.00 1.000 0.000 1.0
## N223 0.00 0.000 1.000 1.0
## N224 0.00 2.000 0.000 0.0
```
-->
</div>
<div id="hardy-weinberg-equilibrium" class="section level2">
<h2>Hardy-Weinberg equilibrium</h2>
<p>Next, let’s determine if our populations are in Hardy-Weinberg equilibrium. We will again use the nancycats data to test for HWE using the function <code>hw.test()</code> from the <em>pegas</em> package. This will compute the <span class="math inline">\(\chi^2\)</span> statistic over the entire data set and compute two P-values, one analytical and one derived from permutations:</p>
<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb36-1"><a href="#cb36-1"></a><span class="kw">library</span>(<span class="st">"pegas"</span>)</span>
<span id="cb36-2"><a href="#cb36-2"></a>(nanhwe.full <-<span class="st"> </span><span class="kw">hw.test</span>(nancycats, <span class="dt">B =</span> <span class="dv">1000</span>)) <span class="co"># performs 1000 permuatations</span></span></code></pre></div>
<pre><code>## chi^2 df Pr(chi^2 >) Pr.exact
## fca8 395.80006 120 0.000000e+00 0
## fca23 239.34221 55 0.000000e+00 0
## fca43 434.33397 45 0.000000e+00 0
## fca45 66.11849 36 1.622163e-03 0
## fca77 270.52066 66 0.000000e+00 0
## fca78 402.80002 28 0.000000e+00 0
## fca90 217.19836 66 0.000000e+00 0
## fca96 193.36764 66 1.965095e-14 0
## fca37 291.00731 153 1.209777e-10 0</code></pre>
<p>We can see here that both the analytical p-value and permuted p-value show that we have confidence that all loci are not under the null expectation of HWE. This makes sense given that these data represent 17 populations of cats. If we wanted to check what the HWE statistic for each population is, we should first separate the populations with the function <code>seppop()</code>. For this exercise, we will only focus on the analytical p-value by setting <code>B = 0</code>.</p>
<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1"></a>(nanhwe.pop <-<span class="st"> </span><span class="kw">seppop</span>(nancycats) <span class="op">%>%</span><span class="st"> </span><span class="kw">lapply</span>(hw.test, <span class="dt">B =</span> <span class="dv">0</span>))</span></code></pre></div>
<pre><code>## $P01
## chi^2 df Pr(chi^2 >)
## fca8 5.135802 6 0.526517306
## fca23 26.049383 10 0.003674334
## fca43 12.922449 10 0.228040169
## fca45 2.716049 3 0.437506757
## fca77 28.122449 15 0.020815001
## fca78 0.400000 1 0.527089257
## fca90 13.924320 10 0.176471694
## fca96 3.071074 3 0.380796192
## fca37 10.156250 3 0.017283597
##
## $P02
## chi^2 df Pr(chi^2 >)
## fca8 29.86239 15 1.242747e-02
## fca23 23.22222 10 9.955382e-03
## fca43 27.20034 6 1.328128e-04
## fca45 12.21716 15 6.625229e-01
## fca77 86.16667 45 2.152672e-04
## fca78 11.50468 6 7.397613e-02
## fca90 56.75227 15 9.039990e-07
## fca96 92.07157 15 4.066747e-13
## fca37 13.17284 15 5.889498e-01
##
## $P03
## chi^2 df Pr(chi^2 >)
## fca8 39.720000 21 0.008041715
## fca23 45.600000 28 0.019163551
## fca43 14.206612 15 0.509920497
## fca45 4.752066 10 0.907112985
## fca77 11.148148 10 0.346093040
## fca78 31.544379 15 0.007422415
## fca90 9.470000 10 0.488153481
## fca96 4.860000 6 0.561890682
## fca37 13.481481 6 0.035996207
##
## $P04
## chi^2 df Pr(chi^2 >)
## fca8 64.30391 45 0.0308567389
## fca23 30.85879 28 0.3233864330
## fca43 10.77193 15 0.7685881191
## fca45 26.58116 21 0.1851504896
## fca77 35.34014 21 0.0259007804