-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathmain-vignette.html
317 lines (284 loc) · 313 KB
/
main-vignette.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
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="author" content="Olivier François" />
<meta name="date" content="2018-01-15" />
<title>Simulating phenotypes and evaluating GWAS methods with naturalgwas</title>
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css">
div.sourceCode { overflow-x: auto; }
table.sourceCode, tr.sourceCode, td.lineNumbers, td.sourceCode {
margin: 0; padding: 0; vertical-align: baseline; border: none; }
table.sourceCode { width: 100%; line-height: 100%; }
td.lineNumbers { text-align: right; padding-right: 4px; padding-left: 4px; color: #aaaaaa; border-right: 1px solid #aaaaaa; }
td.sourceCode { padding-left: 5px; }
code > span.kw { color: #007020; font-weight: bold; } /* Keyword */
code > span.dt { color: #902000; } /* DataType */
code > span.dv { color: #40a070; } /* DecVal */
code > span.bn { color: #40a070; } /* BaseN */
code > span.fl { color: #40a070; } /* Float */
code > span.ch { color: #4070a0; } /* Char */
code > span.st { color: #4070a0; } /* String */
code > span.co { color: #60a0b0; font-style: italic; } /* Comment */
code > span.ot { color: #007020; } /* Other */
code > span.al { color: #ff0000; font-weight: bold; } /* Alert */
code > span.fu { color: #06287e; } /* Function */
code > span.er { color: #ff0000; font-weight: bold; } /* Error */
code > span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
code > span.cn { color: #880000; } /* Constant */
code > span.sc { color: #4070a0; } /* SpecialChar */
code > span.vs { color: #4070a0; } /* VerbatimString */
code > span.ss { color: #bb6688; } /* SpecialString */
code > span.im { } /* Import */
code > span.va { color: #19177c; } /* Variable */
code > span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code > span.op { color: #666666; } /* Operator */
code > span.bu { } /* BuiltIn */
code > span.ex { } /* Extension */
code > span.pp { color: #bc7a00; } /* Preprocessor */
code > span.at { color: #7d9029; } /* Attribute */
code > span.do { color: #ba2121; font-style: italic; } /* Documentation */
code > span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code > span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code > span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
</style>
<link href="data:text/css;charset=utf-8,body%20%7B%0Abackground%2Dcolor%3A%20%23fff%3B%0Amargin%3A%201em%20auto%3B%0Amax%2Dwidth%3A%20700px%3B%0Aoverflow%3A%20visible%3B%0Apadding%2Dleft%3A%202em%3B%0Apadding%2Dright%3A%202em%3B%0Afont%2Dfamily%3A%20%22Open%20Sans%22%2C%20%22Helvetica%20Neue%22%2C%20Helvetica%2C%20Arial%2C%20sans%2Dserif%3B%0Afont%2Dsize%3A%2014px%3B%0Aline%2Dheight%3A%201%2E35%3B%0A%7D%0A%23header%20%7B%0Atext%2Dalign%3A%20center%3B%0A%7D%0A%23TOC%20%7B%0Aclear%3A%20both%3B%0Amargin%3A%200%200%2010px%2010px%3B%0Apadding%3A%204px%3B%0Awidth%3A%20400px%3B%0Aborder%3A%201px%20solid%20%23CCCCCC%3B%0Aborder%2Dradius%3A%205px%3B%0Abackground%2Dcolor%3A%20%23f6f6f6%3B%0Afont%2Dsize%3A%2013px%3B%0Aline%2Dheight%3A%201%2E3%3B%0A%7D%0A%23TOC%20%2Etoctitle%20%7B%0Afont%2Dweight%3A%20bold%3B%0Afont%2Dsize%3A%2015px%3B%0Amargin%2Dleft%3A%205px%3B%0A%7D%0A%23TOC%20ul%20%7B%0Apadding%2Dleft%3A%2040px%3B%0Amargin%2Dleft%3A%20%2D1%2E5em%3B%0Amargin%2Dtop%3A%205px%3B%0Amargin%2Dbottom%3A%205px%3B%0A%7D%0A%23TOC%20ul%20ul%20%7B%0Amargin%2Dleft%3A%20%2D2em%3B%0A%7D%0A%23TOC%20li%20%7B%0Aline%2Dheight%3A%2016px%3B%0A%7D%0Atable%20%7B%0Amargin%3A%201em%20auto%3B%0Aborder%2Dwidth%3A%201px%3B%0Aborder%2Dcolor%3A%20%23DDDDDD%3B%0Aborder%2Dstyle%3A%20outset%3B%0Aborder%2Dcollapse%3A%20collapse%3B%0A%7D%0Atable%20th%20%7B%0Aborder%2Dwidth%3A%202px%3B%0Apadding%3A%205px%3B%0Aborder%2Dstyle%3A%20inset%3B%0A%7D%0Atable%20td%20%7B%0Aborder%2Dwidth%3A%201px%3B%0Aborder%2Dstyle%3A%20inset%3B%0Aline%2Dheight%3A%2018px%3B%0Apadding%3A%205px%205px%3B%0A%7D%0Atable%2C%20table%20th%2C%20table%20td%20%7B%0Aborder%2Dleft%2Dstyle%3A%20none%3B%0Aborder%2Dright%2Dstyle%3A%20none%3B%0A%7D%0Atable%20thead%2C%20table%20tr%2Eeven%20%7B%0Abackground%2Dcolor%3A%20%23f7f7f7%3B%0A%7D%0Ap%20%7B%0Amargin%3A%200%2E5em%200%3B%0A%7D%0Ablockquote%20%7B%0Abackground%2Dcolor%3A%20%23f6f6f6%3B%0Apadding%3A%200%2E25em%200%2E75em%3B%0A%7D%0Ahr%20%7B%0Aborder%2Dstyle%3A%20solid%3B%0Aborder%3A%20none%3B%0Aborder%2Dtop%3A%201px%20solid%20%23777%3B%0Amargin%3A%2028px%200%3B%0A%7D%0Adl%20%7B%0Amargin%2Dleft%3A%200%3B%0A%7D%0Adl%20dd%20%7B%0Amargin%2Dbottom%3A%2013px%3B%0Amargin%2Dleft%3A%2013px%3B%0A%7D%0Adl%20dt%20%7B%0Afont%2Dweight%3A%20bold%3B%0A%7D%0Aul%20%7B%0Amargin%2Dtop%3A%200%3B%0A%7D%0Aul%20li%20%7B%0Alist%2Dstyle%3A%20circle%20outside%3B%0A%7D%0Aul%20ul%20%7B%0Amargin%2Dbottom%3A%200%3B%0A%7D%0Apre%2C%20code%20%7B%0Abackground%2Dcolor%3A%20%23f7f7f7%3B%0Aborder%2Dradius%3A%203px%3B%0Acolor%3A%20%23333%3B%0Awhite%2Dspace%3A%20pre%2Dwrap%3B%20%0A%7D%0Apre%20%7B%0Aborder%2Dradius%3A%203px%3B%0Amargin%3A%205px%200px%2010px%200px%3B%0Apadding%3A%2010px%3B%0A%7D%0Apre%3Anot%28%5Bclass%5D%29%20%7B%0Abackground%2Dcolor%3A%20%23f7f7f7%3B%0A%7D%0Acode%20%7B%0Afont%2Dfamily%3A%20Consolas%2C%20Monaco%2C%20%27Courier%20New%27%2C%20monospace%3B%0Afont%2Dsize%3A%2085%25%3B%0A%7D%0Ap%20%3E%20code%2C%20li%20%3E%20code%20%7B%0Apadding%3A%202px%200px%3B%0A%7D%0Adiv%2Efigure%20%7B%0Atext%2Dalign%3A%20center%3B%0A%7D%0Aimg%20%7B%0Abackground%2Dcolor%3A%20%23FFFFFF%3B%0Apadding%3A%202px%3B%0Aborder%3A%201px%20solid%20%23DDDDDD%3B%0Aborder%2Dradius%3A%203px%3B%0Aborder%3A%201px%20solid%20%23CCCCCC%3B%0Amargin%3A%200%205px%3B%0A%7D%0Ah1%20%7B%0Amargin%2Dtop%3A%200%3B%0Afont%2Dsize%3A%2035px%3B%0Aline%2Dheight%3A%2040px%3B%0A%7D%0Ah2%20%7B%0Aborder%2Dbottom%3A%204px%20solid%20%23f7f7f7%3B%0Apadding%2Dtop%3A%2010px%3B%0Apadding%2Dbottom%3A%202px%3B%0Afont%2Dsize%3A%20145%25%3B%0A%7D%0Ah3%20%7B%0Aborder%2Dbottom%3A%202px%20solid%20%23f7f7f7%3B%0Apadding%2Dtop%3A%2010px%3B%0Afont%2Dsize%3A%20120%25%3B%0A%7D%0Ah4%20%7B%0Aborder%2Dbottom%3A%201px%20solid%20%23f7f7f7%3B%0Amargin%2Dleft%3A%208px%3B%0Afont%2Dsize%3A%20105%25%3B%0A%7D%0Ah5%2C%20h6%20%7B%0Aborder%2Dbottom%3A%201px%20solid%20%23ccc%3B%0Afont%2Dsize%3A%20105%25%3B%0A%7D%0Aa%20%7B%0Acolor%3A%20%230033dd%3B%0Atext%2Ddecoration%3A%20none%3B%0A%7D%0Aa%3Ahover%20%7B%0Acolor%3A%20%236666ff%3B%20%7D%0Aa%3Avisited%20%7B%0Acolor%3A%20%23800080%3B%20%7D%0Aa%3Avisited%3Ahover%20%7B%0Acolor%3A%20%23BB00BB%3B%20%7D%0Aa%5Bhref%5E%3D%22http%3A%22%5D%20%7B%0Atext%2Ddecoration%3A%20underline%3B%20%7D%0Aa%5Bhref%5E%3D%22https%3A%22%5D%20%7B%0Atext%2Ddecoration%3A%20underline%3B%20%7D%0A%0Acode%20%3E%20span%2Ekw%20%7B%20color%3A%20%23555%3B%20font%2Dweight%3A%20bold%3B%20%7D%20%0Acode%20%3E%20span%2Edt%20%7B%20color%3A%20%23902000%3B%20%7D%20%0Acode%20%3E%20span%2Edv%20%7B%20color%3A%20%2340a070%3B%20%7D%20%0Acode%20%3E%20span%2Ebn%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Efl%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Ech%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Est%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Eco%20%7B%20color%3A%20%23888888%3B%20font%2Dstyle%3A%20italic%3B%20%7D%20%0Acode%20%3E%20span%2Eot%20%7B%20color%3A%20%23007020%3B%20%7D%20%0Acode%20%3E%20span%2Eal%20%7B%20color%3A%20%23ff0000%3B%20font%2Dweight%3A%20bold%3B%20%7D%20%0Acode%20%3E%20span%2Efu%20%7B%20color%3A%20%23900%3B%20font%2Dweight%3A%20bold%3B%20%7D%20%20code%20%3E%20span%2Eer%20%7B%20color%3A%20%23a61717%3B%20background%2Dcolor%3A%20%23e3d2d2%3B%20%7D%20%0A" rel="stylesheet" type="text/css" />
</head>
<body>
<h1 class="title toc-ignore">Simulating phenotypes and evaluating GWAS methods with naturalgwas</h1>
<h4 class="author"><em>Olivier François</em></h4>
<h4 class="date"><em>2018-01-15</em></h4>
<div id="summary" class="section level4">
<h4>Summary</h4>
<p>Association studies of polygenic traits with genomic loci are notoriously difficult when those studies are conducted at large geographical scales. The difficulty arises as genotype frequencies often vary in geographic space and across distinct environments in a complex fashion. Those large-scale variations are known to yield false positives in association testing approaches. The R package <strong>naturalgwas</strong> allows researchers to simulate trait association from observed genotypes, modelling gene by environment interactions where environment is derived from a climate database. The R package includes an oracle method correcting false associations by using the true set of confounding variables. The simulated data and the oracle method can be used 1) to compare the ability of association methods to correctly remove confounding factors for a particular data set, 2) to evaluate power to detect causal variants, and 3) to assess the influence of various parameters including the number of causal variants, effect sizes and gene by environment interaction.</p>
<hr />
</div>
<div id="introduction" class="section level4">
<h4>Introduction</h4>
<p>This vignette presents a short tutorial on how to simulate phenotypes for “natural” organisms, and evaluate genome-wide association studies (GWAS) when field sampling has been performed at a large geographical scale. We illustrate the simulation approach with some phenotypic traits simulated from data of the plant species <em>Arabidopsis thaliana</em> (Atwell et al. 2010). To start with the R package <strong>naturalgwas</strong>, load the R functions in memory space as follows.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co">#install.packages("cate")</span>
<span class="co">#devtools::install_github("bcm-uga/lfmm")</span>
<span class="kw">library</span>(naturalgwas)</code></pre></div>
<div id="data-files" class="section level5">
<h5>Data files</h5>
<p>Running the main simulation function <strong>simu_pheno</strong>, and running the <strong>oracle</strong> method requires three files as input to the program: 1) a file encoding individual genotypes, 2) a file with individual geographic coordinates, and 3) a genetic map. Those data must be loaded in the R environment. The simulation could also work without geographic data by specifying a environmental variable. For example, we considered SNP data from the chromosome 5 of European accession/ecotypes of the plant species <em>A. thaliana</em>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">data</span>(A.thaliana)
genotype <-<span class="st"> </span>A.thaliana$genotype
chrpos <-<span class="st"> </span>A.thaliana$chrpos </code></pre></div>
<p>For SNPs, the <strong>genotype</strong> matrix encodes each individual genotype in a row. Each locus corresponds to a specific column. Genotypes are encoded as 0,1,2 for diploids, and 0,1 for haploids. Those numbers represent the number of reference or derived allele at each particular locus. <em>A. thaliana</em> is a diploid species with very high levels of inbreeding. In our example, 162 genotypes were encoded as haploids considering 53,859 SNPs from chromosome 5 (Atwell et al. 2010). Let’s print some genotypic values for three individuals at the first ten loci. We have a matrix of size 3 times 10 filled with 0 and 1 values.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">dim</span>(genotype)</code></pre></div>
<pre><code>## [1] 162 53859</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">genotype[<span class="kw">sample</span>(<span class="dv">162</span>, <span class="dv">3</span>),<span class="dv">1</span>:<span class="dv">10</span>]</code></pre></div>
<pre><code>## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
## [1,] 1 1 1 1 1 1 1 0 1 1
## [2,] 0 0 1 1 1 1 0 0 1 1
## [3,] 0 1 1 1 1 1 1 0 1 1</code></pre>
<p>The <strong>coordinate</strong> variable is a two-column matrix that contains longitude and latitude for each individual in the sample. Longitude (°E) and latitude (°N) must be encoded in the decimal format. Note that headers should be ignored when loading data into the R program. Let us show the location of the sampling sites in Europe (each point corresponds to an individual in the sample).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(maps)
coordinates <-<span class="st"> </span>A.thaliana$coord
<span class="kw">plot</span>(coordinates,
<span class="dt">pch =</span> <span class="dv">19</span>, <span class="dt">cex =</span> .<span class="dv">7</span>, <span class="dt">col =</span> <span class="st">"green4"</span>,
<span class="dt">xlab =</span> <span class="st">"Longitude (°E)"</span>,
<span class="dt">ylab =</span> <span class="st">"Latitude (°N)"</span>)
<span class="kw">map</span>(<span class="dt">add =</span> T, <span class="dt">interior =</span> <span class="ot">FALSE</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
</div>
<div id="simulating-artificial-phenotypes-from-real-genotypes" class="section level5">
<h5>Simulating artificial phenotypes from real genotypes</h5>
<p>For simulating artificial phenotypes from real genotypes and accounting for genotype by environment interactions, we need 1) a proxy variable for the enviromnent, 2) a reference set of weakly linked causal loci for which we wish to simulate trait association, 3) and a set of confounder factors typically arising from complex population structure and isolation-by-distance.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> env <-<span class="st"> </span><span class="kw">get_climate</span>(coordinates)
ref.set <-<span class="st"> </span><span class="kw">create_refset</span>(chrpos, <span class="dt">window =</span> <span class="dv">501</span>)
confounder <-<span class="st"> </span><span class="kw">create_factor</span>(genotype, <span class="dt">K =</span> <span class="dv">10</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>The above commands create an artificial environmental variable by combining 19 bioclimatic variables extracted from the ‘worldclim’ database, and they take a few minutes to download. The SNP reference set consists of picking one representant SNP in each window of size <strong>window</strong>. In the third line, 10 confounders are computed from the data. The confounders correspond to the first ten principal components of the genotype matrix using PCA from LEA (Frichot and Francois 2015). The PCA screeplot for the SNP data is displayed.</p>
<p>In addition, the <strong>create_factor</strong> function estimates the amount of residual variation in the data and an order of magnitude for effect sizes.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> confounder$sigma </code></pre></div>
<pre><code>## [1] 81.91204</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> confounder$base </code></pre></div>
<pre><code>## [1] 93.90588</code></pre>
<p>Simulation of phenotypic traits requires the following arguments: 1) a SNP genotype matrix, 2) a set of confounders created with <strong>create_factor</strong>, an environmental variable, a reference set of weakly linked SNPs created with <strong>create_refset</strong>, a number of causal SNPs to be drawn from the reference set, and values for effect size and GxE interaction parameters.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> n.causal <-<span class="st"> </span><span class="dv">6</span>
eff.size <-<span class="st"> </span><span class="fl">5.0</span>
sim <-<span class="st"> </span><span class="kw">simu_pheno</span>(A.thaliana$genotype,
confounder,
env,
ref.set, <span class="dt">ncausal =</span> n.causal,
<span class="dt">effect.size =</span> eff.size, <span class="dt">gxe =</span> .<span class="dv">5</span>)
ss <-<span class="st"> </span><span class="kw">sum</span>(<span class="kw">apply</span>(genotype[,sim$causal.set], <span class="dv">2</span>, var))
ss*(eff.size)^<span class="dv">2</span>*confounder$base^<span class="dv">2</span>/(ss*(eff.size)^<span class="dv">2</span>*confounder$base^<span class="dv">2</span> +<span class="st"> </span>confounder$sigma^<span class="dv">2</span> +<span class="st"> </span>confounder$base^<span class="dv">2</span>)
(ss*(eff.size)^<span class="dv">2</span>*confounder$base^<span class="dv">2</span> +<span class="st"> </span>confounder$sigma^<span class="dv">2</span>)/(ss*(eff.size)^<span class="dv">2</span>*confounder$base^<span class="dv">2</span> +<span class="st"> </span>confounder$sigma^<span class="dv">2</span> +<span class="st"> </span>confounder$base^<span class="dv">2</span>)</code></pre></div>
<p>In this simulation, a polygenic trait is associated with 6 causal variants, sampled from the SNP reference set. Each causal variant is associated with an effect size of 5 units. Gene by environment interactions are modelled by using the <em>env</em> variable created from ‘worldclim’.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> <span class="kw">hist</span>(<span class="kw">scale</span>(sim$phenotype), <span class="dt">main =</span> <span class="st">"Trait value"</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>To check whether the simulated trait displays any geographic variation, the trait variable can interpolated on a geographic map as follows.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> <span class="kw">library</span>(fields)
fit =<span class="st"> </span>fields::<span class="kw">Krig</span>(coordinates, <span class="kw">scale</span>(sim$phenotype), <span class="dt">theta =</span> <span class="dv">10</span>, <span class="dt">m =</span> <span class="dv">2</span>)
<span class="kw">surface</span>(fit, <span class="dt">extrap =</span> <span class="ot">TRUE</span>, <span class="dt">xlab =</span> <span class="st">"Longitude"</span>, <span class="dt">ylab =</span> <span class="st">"Latitude"</span>, <span class="dt">levels =</span> <span class="kw">c</span>(<span class="dv">0</span>))
<span class="kw">map</span>(<span class="dt">add =</span> <span class="ot">TRUE</span>, <span class="dt">interior =</span> F)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
</div>
<div id="running-the-oracle-method" class="section level5">
<h5>Running the oracle method</h5>
<p>Our next step is to perform a GWAS for the simulated phenotype, and to evaluate the relative power of methods to detect causal variants. To this objective, we use the ‘linear regression’ method as an oracle algorithm. The method is very close to the simulation model, and it becomes an oracle method when the true confounders are provided in arguments.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">pv.oracle <-<span class="st"> </span><span class="kw">oracle</span>(<span class="kw">scale</span>(sim$phenotype),
genotype,
confounder, <span class="dt">K =</span> <span class="dv">10</span>)$pv</code></pre></div>
<p>Now visualize the Manhattan plot for the oracle method. The vertical bars correspond to the causal variants in the simulation.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> <span class="kw">plot</span>(-<span class="kw">log10</span>(pv.oracle), <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">col =</span> <span class="st">"grey"</span>, <span class="dt">main =</span> <span class="st">"Manhattan plot (Oracle)"</span>)
<span class="kw">points</span>(sim$causal, -<span class="kw">log10</span>(pv.oracle)[sim$causal], <span class="dt">type =</span> <span class="st">"h"</span>, <span class="dt">lty =</span> <span class="dv">1</span>, <span class="dt">col =</span> <span class="st">"blue"</span>)
<span class="kw">abline</span>(-<span class="kw">log10</span>(<span class="fl">0.05</span>/<span class="kw">length</span>(pv.oracle)), <span class="dv">0</span>, <span class="dt">lty =</span> <span class="dv">2</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
</div>
<div id="heritability-and-mixed-linear-models" class="section level5">
<h5>Heritability and mixed linear models</h5>
<p>In this section, we used a mixed model approach and the R package <strong>rrBLUP</strong> to provide an heritability estimate for the simulated trait.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(rrBLUP)
G <-<span class="st"> </span>A.thaliana$genotype
<span class="kw">rownames</span>(G) <-<span class="st"> </span>A.thaliana$ecotype.id[,<span class="dv">1</span>]
data <-<span class="st"> </span><span class="kw">data.frame</span>(<span class="dt">y =</span> <span class="kw">scale</span>(sim$phenotype),
<span class="dt">gid =</span> A.thaliana$ecotype.id[,<span class="dv">1</span>])
<span class="co">#predict breeding values and compute h2</span>
kb <-<span class="st"> </span><span class="kw">kin.blup</span>(<span class="dt">data =</span> data,
<span class="dt">geno=</span><span class="st">"gid"</span>,
<span class="dt">pheno =</span> <span class="st">"y"</span>,
<span class="dt">K =</span> <span class="kw">A.mat</span>(G))
<span class="kw">cat</span>(<span class="st">"Heritability = "</span>, kb$Vg/(kb$Vg +<span class="st"> </span>kb$Ve), <span class="st">"</span><span class="ch">\n</span><span class="st">"</span>)</code></pre></div>
<pre><code>## Heritability = 0.9366343</code></pre>
<p>To provide a better estimate for the K matrix, we could use a latent factor model as follows.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">## fit latent factors using an LFMM
mod.lfmm <-<span class="st"> </span>lfmm::<span class="kw">lfmm_ridge</span>(<span class="dt">Y =</span> A.thaliana$genotype,
<span class="dt">X =</span> <span class="kw">scale</span>(sim$phenotype),
<span class="dt">K =</span> <span class="dv">6</span>)
Kinship <-<span class="st"> </span>mod.lfmm$U %*%<span class="st"> </span><span class="kw">t</span>(mod.lfmm$U)/<span class="kw">nrow</span>(mod.lfmm$U)
<span class="kw">rownames</span>(Kinship) <-<span class="st"> </span>A.thaliana$ecotype.id[,<span class="dv">1</span>]
## predict breeding values and compute h2
kb <-<span class="st"> </span><span class="kw">kin.blup</span>(<span class="dt">data =</span> data,
<span class="dt">geno=</span><span class="st">"gid"</span>,
<span class="dt">pheno =</span> <span class="st">"y"</span>,
<span class="dt">K =</span> Kinship)
<span class="kw">cat</span>(<span class="st">"Heritability = "</span>, kb$Vg/(kb$Vg +<span class="st"> </span>kb$Ve), <span class="st">"</span><span class="ch">\n</span><span class="st">"</span>)</code></pre></div>
<pre><code>## Heritability = 0.03081077</code></pre>
<p>The simulated trait does not exhibit a very high heritability value. Let us perform an association study by using a mixed linear model.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">geno <-<span class="st"> </span><span class="kw">t</span>(A.thaliana$genotype)
<span class="kw">colnames</span>(geno) <-<span class="st"> </span>A.thaliana$ecotype.id[,<span class="dv">1</span>]
G <-<span class="st"> </span><span class="kw">data.frame</span>(<span class="dt">marker =</span> <span class="dv">1</span>:<span class="kw">nrow</span>(A.thaliana$chrpos),
A.thaliana$chrpos,
geno,
<span class="dt">check.names =</span> <span class="ot">FALSE</span>)
pheno <-<span class="st"> </span><span class="kw">data.frame</span>(<span class="dt">line =</span> A.thaliana$ecotype.id[,<span class="dv">1</span>],
<span class="dt">y =</span> <span class="kw">scale</span>(sim$phenotype))
mlm <-<span class="st"> </span><span class="kw">GWAS</span>(<span class="dt">pheno =</span> pheno,
<span class="dt">geno =</span> G,
<span class="dt">K =</span> Kinship,
<span class="dt">n.PC =</span> <span class="dv">5</span>,
<span class="dt">plot =</span> <span class="ot">FALSE</span>)</code></pre></div>
<pre><code>## [1] "GWAS for trait: y"
## [1] "Variance components estimated. Testing markers."</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">## Manhattan plot
<span class="kw">plot</span>(mlm$y, <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">col =</span> <span class="st">"grey"</span>,
<span class="dt">ylab =</span> <span class="st">"-log10(pvalues)"</span>,
<span class="dt">main =</span> <span class="st">"Manhattan plot (mlm)"</span> )
<span class="kw">points</span>(sim$causal, mlm$y[sim$causal],
<span class="dt">type =</span> <span class="st">"h"</span>, <span class="dt">lty =</span> <span class="dv">1</span>, <span class="dt">col =</span> <span class="st">"green4"</span>)
<span class="kw">abline</span>(-<span class="kw">log10</span>(<span class="fl">0.05</span>/<span class="kw">length</span>(pv.oracle)), <span class="dv">0</span>, <span class="dt">lty =</span> <span class="dv">2</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>The results of a mixed linear model using the LFMM kinskip estimate are very close to the oracle method.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">qqplot</span>(-<span class="kw">log10</span>(pv.oracle), mlm$y, <span class="dt">col =</span> <span class="st">"grey"</span>, <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">ylab =</span><span class="st">"mlm scores"</span>)
<span class="kw">abline</span>(<span class="dv">0</span>,<span class="dv">1</span>, <span class="dt">col =</span> <span class="st">'green4'</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>Let us compare the results of method that estimate confounders at the same time as it computes association with phenotype. The <strong>cate</strong> method implements latent factor mixed models. Based on a principal component analysis of the genotype data, we evaluate that around <span class="math inline">\(K = 6\)</span> factors explain population structure, and 6 hidden factors are used in cate. In cate, the pvalues are computed as follows.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> pheno <-<span class="st"> </span><span class="kw">scale</span>(sim$phenotype)
pv.cate <-<span class="st"> </span>cate::<span class="kw">cate</span>( ~<span class="st"> </span>pheno,
<span class="dt">X.data =</span> <span class="kw">data.frame</span>(pheno),
<span class="dt">Y =</span> genotype,
<span class="dt">r =</span> <span class="dv">6</span>,
<span class="dt">calibrate =</span> <span class="ot">TRUE</span>)$beta.p.value</code></pre></div>
<p>Now let us visualize the Manhattan plot for the cate method and compare it to the Manhattan plot for the oracle method. The vertical bars correspond to the causal variants in the simulation.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> <span class="kw">plot</span>(-<span class="kw">log10</span>(pv.cate), <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">col =</span> <span class="st">"grey"</span>, <span class="dt">main =</span> <span class="st">"Manhattan plot (Latent factor model)"</span> )
<span class="kw">points</span>(sim$causal, -<span class="kw">log10</span>(pv.cate)[sim$causal], <span class="dt">type =</span> <span class="st">"h"</span>, <span class="dt">lty =</span> <span class="dv">1</span>, <span class="dt">col =</span> <span class="st">"orange"</span> )
<span class="kw">abline</span>(-<span class="kw">log10</span>(<span class="fl">0.05</span>/<span class="kw">length</span>(pv.oracle)), <span class="dv">0</span>, <span class="dt">lty =</span> <span class="dv">2</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>We eventually compare the results of the latent factor model with the oracle method.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> ## qqplot
<span class="kw">qqplot</span>(-<span class="kw">log10</span>(pv.oracle), -<span class="kw">log10</span>(pv.cate) , <span class="dt">pch =</span> <span class="dv">19</span>, <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">col =</span> <span class="st">"grey"</span> )
<span class="kw">abline</span>( <span class="dv">0</span>, <span class="dv">1</span>, <span class="dt">lwd =</span> <span class="dv">2</span>, <span class="dt">col =</span> <span class="st">"orange"</span> )</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>In this situation, the latent factor model and the oracle method performed similarly. Other testing methods could be evaluated similarly (glm, mixed models, etc). We compare the mixed modeling approach and cate below.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> ## qqplot
<span class="kw">qqplot</span>(mlm$y, -<span class="kw">log10</span>(pv.cate) , <span class="dt">pch =</span> <span class="dv">19</span>, <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">col =</span> <span class="st">"grey"</span> )
<span class="kw">abline</span>( <span class="dv">0</span>, <span class="dv">1</span>, <span class="dt">lwd =</span> <span class="dv">2</span>, <span class="dt">col =</span> <span class="st">"orange"</span> )</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
</div>
<div id="comparison-with-lfmm" class="section level5">
<h5>Comparison with LFMM</h5>
<p>For comparisons with <strong>cate</strong>, we also use <span class="math inline">\(K = 6\)</span> factors in <strong>lfmm</strong>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">lfmm.mod <-<span class="st"> </span>lfmm::<span class="kw">lfmm_ridge</span>(<span class="dt">Y =</span> genotype,
<span class="dt">X =</span> <span class="kw">scale</span>(sim$phenotype),
<span class="dt">K =</span> <span class="dv">6</span>)</code></pre></div>
<p>We compute the pvalues as follows</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> p <-<span class="st"> </span>lfmm::<span class="kw">lfmm_test</span>(<span class="dt">Y =</span> genotype,
<span class="dt">X =</span> <span class="kw">scale</span>(sim$phenotype),
<span class="dt">lfmm =</span> lfmm.mod,
<span class="dt">calibrate =</span> <span class="st">"gif"</span>)
pv.lfmm <-<span class="st"> </span>p$calibrated.pvalue</code></pre></div>
<p>Now let us visualize the Manhattan plots for <strong>lfmm</strong> and <strong>cate</strong>. The vertical bars correspond to the causal variants in the simulation.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> <span class="kw">plot</span>( -<span class="kw">log10</span>(pv.lfmm), <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">col =</span> <span class="st">"grey"</span>, <span class="dt">main =</span> <span class="st">"Manhattan plot (lfmm)"</span> )
<span class="kw">points</span>( sim$causal, -<span class="kw">log10</span>(pv.lfmm)[sim$causal], <span class="dt">type =</span> <span class="st">"h"</span>, <span class="dt">lty =</span> <span class="dv">1</span>, <span class="dt">col =</span> <span class="st">"blue"</span> )
<span class="kw">abline</span>(-<span class="kw">log10</span>(<span class="fl">0.05</span>/<span class="kw">length</span>(pv.oracle)), <span class="dv">0</span>, <span class="dt">lty =</span> <span class="dv">2</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>We eventually compare the results of the latent factor model with the oracle method.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> ## plot
<span class="kw">qqplot</span>(-<span class="kw">log10</span>(pv.oracle), -<span class="kw">log10</span>(pv.lfmm) , <span class="dt">pch =</span> <span class="dv">19</span>, <span class="dt">cex =</span> .<span class="dv">4</span>, <span class="dt">col =</span> <span class="st">"grey"</span> )
<span class="kw">abline</span>( <span class="dv">0</span>, <span class="dv">1</span>, <span class="dt">lwd =</span> <span class="dv">2</span>, <span class="dt">col =</span> <span class="st">"blue"</span> )</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
</div>
<div id="conditional-tests-lfmm" class="section level5">
<h5>conditional tests LFMM</h5>
<p>Based on previous analysis, we understood that only a handful of SNP could be detected with those simulation parameters. Here, we experimented <em>forward conditional tests</em>, in which the top hits are recursively included as covariates in an LFMM estimation/testing approach (12 cycles).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">cond.test <-<span class="st"> </span>lfmm::<span class="kw">forward_test</span>(<span class="dt">Y =</span> A.thaliana$genotype,
<span class="dt">X =</span> <span class="kw">scale</span>(sim$phenotype),
<span class="dt">K =</span> <span class="dv">6</span>,
<span class="dt">niter =</span> <span class="dv">12</span>)</code></pre></div>
<p>We compare the results with the truth.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># proposed candidates</span>
<span class="kw">cat</span>(<span class="st">"Candidate loci:"</span>)</code></pre></div>
<pre><code>## Candidate loci:</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">sort</span>(cond.test$candidates)</code></pre></div>
<pre><code>## [1] 8791 19536 19551 19588 19646 19663 19702 19703 19721 22796 26303
## [12] 34820</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># truth</span>
<span class="kw">cat</span>(<span class="st">"Causal SNPs:"</span>)</code></pre></div>
<pre><code>## Causal SNPs:</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">sim$causal.set</code></pre></div>
<pre><code>## [1] 8768 22796 26303 29309 34820 46844</code></pre>
</div>
</div>
<div id="package-reference" class="section level4">
<h4>Package reference</h4>
<ul>
<li>Francois O, Caye K (2017). naturalgwas: An R package for simulating phenotypes and evaluating GWAS methods with large-scale geographic sampling.</li>
</ul>
</div>
<div id="references" class="section level4">
<h4>References</h4>
<ul>
<li><p>Atwell S, Huang YS, Vilhjalmsson BJ, et al. (2010). Genome-wide association study of 107 phenotypes in <em>Arabidopsis thaliana</em> inbred lines. Nature 465, 627-631.</p></li>
<li><p>Francois O, Martins H, Caye K, Schoville SD (2016). Controlling false discoveries in genome scans for selection. Molecular Ecology 25, 454-469.</p></li>
<li><p>Frichot E, Francois O (2015). LEA: an R package for Landscape and Ecological Association studies. Methods in Ecology and Evolution 6(8), 925-929.</p></li>
</ul>
</div>
<!-- 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>