-
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathindex.html
More file actions
537 lines (485 loc) · 21.2 KB
/
index.html
File metadata and controls
537 lines (485 loc) · 21.2 KB
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
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<title>reveal.js</title>
<link rel="stylesheet" href="dist/reset.css">
<link rel="stylesheet" href="dist/reveal.css">
<link rel="stylesheet" href="dist/theme/black.css">
<!-- Theme used for syntax highlighted code -->
<link rel="stylesheet" href="plugin/highlight/monokai.css">
<style>
.mermaid-container {
max-height: 800px; /* Adjust this based on your layout */
overflow-y: auto;
padding: 1em;
background-color: #1e1e1e; /* optional dark background */
border-radius: 8px;
}
</style>
</head>
<body>
<div class="reveal">
<div class="slides">
<section>
<div class="mermaid-container">
<pre class="mermaid">
%%{init: {'theme': 'dark', 'themeVariables': { 'fontSize': '18px' }}}%%
classDiagram
class DBConnector {
-conn: Sql
+connect(): Sql
+disconnect(): void
}
class VariantFilteringDBConnector {
+getRegionsFromFeatures(): String
}
class CompletionMessage {
+completionMessage: Map
+initCompletionMessage(): void
+writeCompletionJson(): void
+addCompletionMessageField(): void
}
class WorkflowVariantFiltering {
-params: Map
-final_vcf: Map
-sampleDiscordance: Map
+getConnection(): VariantFilteringDBConnector
+registerMessageHandlers(): void
+setFinalVcf(): void
...
}
class SharedStockNamesByStudy {
-tgdrs: List
-studiesNames: Map
-preservedStudiesNames: Map
-sampleMetaData: Map
-sampleTgdrs: Map
+readSharedSamples(): void
+retainHighestSample(): Map
+getStandardName(): Set
+renameStudiesNames(): void
+removeFirstHyphenInstance(): String
+createSampleWithDuplicateStudiesObject(): Maps
+buildSampleNamesQuery(List tgdrs): String
+getPairwiseComparison(): Map
}
VariantFilteringDBConnector --|> DBConnector : extends
WorkflowVariantFiltering ..> VariantFilteringDBConnector : uses
WorkflowVariantFiltering ..> CompletionMessage : uses
</pre>
</div>
</section>
<section>
<p style="letter-spacing: 2px;">| <strong>Analysis Panel</strong> | <strong>Landscape Genomics</strong> | <strong>Demo</strong> |</p>
<img src="https://treegenesdb.org/sites/all/modules/custom_modules/cartogratree_landing/images/cp_header_2024.jpg">
</section>
<section>
<h2>Analysis Panel Overview</h2>
<div class="mermaid-container">
<pre class="mermaid">
%%{init: {'theme': 'dark', 'themeVariables': { 'darkMode': true, 'fontSize': '30px'}}}%%
flowchart LR
subgraph VCF Processing
A1{Selected Multiple Studies} --> |YES|A[VCF Sample Overlap] --> B[Genotype Overlap] --> C[Merge VCFs] --> D[VCF Filtering]
A1{Selected Multiple Studies} --> D[VCF Filtering]
end
subgraph MeteData
E1[Phenotypic Data]
E2[Environmental Data]
end
subgraph Analysis
D[VCF Filtering] --> F1[Population Structure]
D[VCF Filtering] --> F2[Genome-Wide Association Study]
E1[Phenotypic Data] --> F2[Genome-Wide Association Study]
E2[Environmental Data] --> F2[Genome-Wide Association Study]
end
</pre>
</div>
</section>
<section>
<h2>NextFlow</h2>
<p>Workflow management software</p>
<div style="display: grid; grid-template-columns: 1fr 1fr; gap: 20px; max-width: 800px; margin: 40px auto;">
<div style="background-color: #e0e0e0; color: #000; border-radius: 12px; padding: 20px; display: flex; align-items: center; font-size: 1.2em;">
<!-- Reproducible Icon -->
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" height="40" width="40" style="margin-right: 15px;"><!--!Font Awesome Free 6.7.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2025 Fonticons, Inc.-->
<path d="M0 224c0 17.7 14.3 32 32 32s32-14.3 32-32c0-53 43-96 96-96l160 0 0 32c0 12.9 7.8 24.6 19.8 29.6s25.7 2.2 34.9-6.9l64-64c12.5-12.5 12.5-32.8 0-45.3l-64-64c-9.2-9.2-22.9-11.9-34.9-6.9S320 19.1 320 32l0 32L160 64C71.6 64 0 135.6 0 224zm512 64c0-17.7-14.3-32-32-32s-32 14.3-32 32c0 53-43 96-96 96l-160 0 0-32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9l-64 64c-12.5 12.5-12.5 32.8 0 45.3l64 64c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6l0-32 160 0c88.4 0 160-71.6 160-160z"/>
</svg>
<span>Reproducible</span>
</div>
<div style="background-color: #e0e0e0; color: #000; border-radius: 12px; padding: 20px; display: flex; align-items: center; font-size: 1.2em;">
<!-- Concurrency Icon -->
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 576 512" width="40" height="40" style="margin-right: 15px;"><!--!Font Awesome Free 6.7.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2025 Fonticons, Inc.-->
<path d="M269.5 69.9c11.1-7.9 25.9-7.9 37 0C329 85.4 356.5 96 384 96c26.9 0 55.4-10.8 77.4-26.1c0 0 0 0 0 0c11.9-8.5 28.1-7.8 39.2 1.7c14.4 11.9 32.5 21 50.6 25.2c17.2 4 27.9 21.2 23.9 38.4s-21.2 27.9-38.4 23.9c-24.5-5.7-44.9-16.5-58.2-25C449.5 149.7 417 160 384 160c-31.9 0-60.6-9.9-80.4-18.9c-5.8-2.7-11.1-5.3-15.6-7.7c-4.5 2.4-9.7 5.1-15.6 7.7c-19.8 9-48.5 18.9-80.4 18.9c-33 0-65.5-10.3-94.5-25.8c-13.4 8.4-33.7 19.3-58.2 25c-17.2 4-34.4-6.7-38.4-23.9s6.7-34.4 23.9-38.4C42.8 92.6 61 83.5 75.3 71.6c11.1-9.5 27.3-10.1 39.2-1.7c0 0 0 0 0 0C136.7 85.2 165.1 96 192 96c27.5 0 55-10.6 77.5-26.1zm37 288C329 373.4 356.5 384 384 384c26.9 0 55.4-10.8 77.4-26.1c0 0 0 0 0 0c11.9-8.5 28.1-7.8 39.2 1.7c14.4 11.9 32.5 21 50.6 25.2c17.2 4 27.9 21.2 23.9 38.4s-21.2 27.9-38.4 23.9c-24.5-5.7-44.9-16.5-58.2-25C449.5 437.7 417 448 384 448c-31.9 0-60.6-9.9-80.4-18.9c-5.8-2.7-11.1-5.3-15.6-7.7c-4.5 2.4-9.7 5.1-15.6 7.7c-19.8 9-48.5 18.9-80.4 18.9c-33 0-65.5-10.3-94.5-25.8c-13.4 8.4-33.7 19.3-58.2 25c-17.2 4-34.4-6.7-38.4-23.9s6.7-34.4 23.9-38.4c18.1-4.2 36.2-13.3 50.6-25.2c11.1-9.4 27.3-10.1 39.2-1.7c0 0 0 0 0 0C136.7 373.2 165.1 384 192 384c27.5 0 55-10.6 77.5-26.1c11.1-7.9 25.9-7.9 37 0zm0-144C329 229.4 356.5 240 384 240c26.9 0 55.4-10.8 77.4-26.1c0 0 0 0 0 0c11.9-8.5 28.1-7.8 39.2 1.7c14.4 11.9 32.5 21 50.6 25.2c17.2 4 27.9 21.2 23.9 38.4s-21.2 27.9-38.4 23.9c-24.5-5.7-44.9-16.5-58.2-25C449.5 293.7 417 304 384 304c-31.9 0-60.6-9.9-80.4-18.9c-5.8-2.7-11.1-5.3-15.6-7.7c-4.5 2.4-9.7 5.1-15.6 7.7c-19.8 9-48.5 18.9-80.4 18.9c-33 0-65.5-10.3-94.5-25.8c-13.4 8.4-33.7 19.3-58.2 25c-17.2 4-34.4-6.7-38.4-23.9s6.7-34.4 23.9-38.4c18.1-4.2 36.2-13.3 50.6-25.2c11.1-9.5 27.3-10.1 39.2-1.7c0 0 0 0 0 0C136.7 229.2 165.1 240 192 240c27.5 0 55-10.6 77.5-26.1c11.1-7.9 25.9-7.9 37 0z"/>
</svg>
<span>Concurrency</span>
</div>
<div style="background-color: #e0e0e0; color: #000; border-radius: 12px; padding: 20px; display: flex; align-items: center; font-size: 1.2em;">
<!-- Portable Icon -->
<svg xmlns="http://www.w3.org/2000/svg" width="60" height="60" style="margin-right: 50px;" viewBox="0 0 640 512"><!--!Font Awesome Free 6.7.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2025 Fonticons, Inc.-->
<path d="M0 32C0 14.3 14.3 0 32 0L48 0c44.2 0 80 35.8 80 80l0 288c0 8.8 7.2 16 16 16l464 0c17.7 0 32 14.3 32 32s-14.3 32-32 32l-66.7 0c1.8 5 2.7 10.4 2.7 16c0 26.5-21.5 48-48 48s-48-21.5-48-48c0-5.6 1-11 2.7-16l-197.5 0c1.8 5 2.7 10.4 2.7 16c0 26.5-21.5 48-48 48s-48-21.5-48-48c0-5.6 1-11 2.7-16L144 448c-44.2 0-80-35.8-80-80L64 80c0-8.8-7.2-16-16-16L32 64C14.3 64 0 49.7 0 32zM432 96l0-40c0-4.4-3.6-8-8-8l-80 0c-4.4 0-8 3.6-8 8l0 40 96 0zM288 96l0-40c0-30.9 25.1-56 56-56l80 0c30.9 0 56 25.1 56 56l0 40 0 224-192 0 0-224zM512 320l0-224 16 0c26.5 0 48 21.5 48 48l0 128c0 26.5-21.5 48-48 48l-16 0zM240 96l16 0 0 224-16 0c-26.5 0-48-21.5-48-48l0-128c0-26.5 21.5-48 48-48z"/>
</svg>
<span>Portable</span>
</div>
<div style="background-color: #e0e0e0; color: #000; border-radius: 12px; padding: 20px; display: flex; align-items: center; font-size: 1.2em;">
<div style="width: 120; height: 60px; display: flex; justify-content: center; align-items: center; margin-right: 15px; overflow: hidden;">
<img src="https://raw.githubusercontent.com/nf-core/logos/master/nf-core-logos/nf-core-logo.svg"
alt="nf-core logo"
style="width: 120%; height: auto; object-fit: contain;">
</div>
<span>Community</span>
</div>
</div>
</section>
<section>
<section>
<h3>Landscape Genomics</h3>
<p>Aims to understand how environmental heterogeneity influences the distribution of genetic diversity.</p>
<img src="./assets/UpperMedway_10m_115points.jpg" width="700" height="500">
</section>
<section>
<h3>Population Structure</h3>
<p>Patterns of genetic variation within and between individuals</p>
<ul>
<li>Isolation by distance</li>
<li>Genetic drift</li>
<li>Selection</li>
</ul>
</section>
<section style="display: flex; flex-direction: column; align-items: center;">
<h3>Genome-wide association study (GWAS)</h3>
<p>Examines the relationship between different genotypes and specific traits or environments.</p>
<div style="display: flex; gap: 20px; justify-content: center; flex-wrap: wrap; margin-top: 1em;">
<img src="./assets/GWAS-SimplifiedGenotypeVsEffect.png"
alt="GWAS Simplified Genotype vs Effect"
style="max-width: 250px; max-height: 600px; object-fit: contain; background-color: white; padding: 10px; border-radius: 8px;">
<img src="./assets/manhattan.png"
alt="Manhattan Plot"
style="max-width: 500px; max-height: 600px; object-fit: contain;">
</div>
</section>
<section>
<h3>Genetic Offset</h3>
<p>Difference between the current genetic makeup to the genetic makeup predicted to be optimal for future environmental conditions</p>
<div style="display: flex; justify-content: center; margin-top: 20px;">
<img src="./assets/landscape_genomics_eucalyptus.jpg"
alt="Landscape Genomics Eucalyptus"
style="max-width: 600px; max-height: 600px; object-fit: contain;">
</div>
</section>
</section>
<section>
<h3>TPPS submission enables seamless integration of studies</h3>
<p>Allowing for analysis of large datasets in the analysis panel</p>
<div style="display: grid; grid-template-columns: 1fr 1fr; gap: 20px; max-width: 800px; margin: 40px auto;">
<div style="background-color: #e0e0e0; color: #000; border-radius: 12px; padding: 20px; display: flex; align-items: center; font-size: 1.2em;">
<p><strong>Mega:</strong> Integration of raw data </p>
</div>
<div style="background-color: #e0e0e0; color: #000; border-radius: 12px; padding: 20px; display: flex; align-items: center; font-size: 1.2em;">
<p><strong>Meta:</strong> Integration of summary results</p>
</div>
</div>
</section>
<section>
<section>
<h3>Demo With <i>Populus trichocarpa</i></h3>
<table>
<thead>
<tr>
<th>Study</th>
<th>Samples</th>
<th>Genotypes</th>
<th>Phenotypes</th>
</tr>
</thead>
<tbody>
<tr>
<td>Geraldes et al. 2008</td>
<td>55</td>
<td>32,000</td>
<td>0</td>
</tr>
<tr>
<td>Mckown et al. 2013</td>
<td>555</td>
<td>0</td>
<td>400</td>
</tr>
<tr>
<td>Mckown et al. 2014</td>
<td>555</td>
<td>28,000</td>
<td>0</td>
</tr>
</tbody>
</table>
</section>
<section>
<h3>Genotype Assay</h3>
<p>A cost effective way to obtain tens of thousands of mutations</p>
<img src="./assets/microarray.jpg"
alt="DNA MicroArray"
style="max-width: 500px; max-height: 600px; object-fit: contain;">
</section>
<section>
<h3>Filter and Select studies in cartograplant</h3>
<video controls autoplay style="max-width: 100%; height: auto;">
<source src="./assets/NATC-FilteringAndSelectingStudies.mp4" type="video/mp4">
<p>Your browser does not support the video tag.</p>
</video>
</section>
</section>
<section>
<section>
<h3>Panel 1: Workspace</h3>
<p>Responsible for file management:</p>
<ul>
<li>Create new workspace directory</li>
<li>Upload files from local machine</li>
<li>Stores output from workflows</li>
<li>Delete Files</li>
</ul>
</section>
<section>
<video controls autoplay style="max-width: 100%; height: auto;">
<source src="../assets/NATC-Workspace.mp4" type="video/mp4">
</video>
</section>
</section>
<section>
<section>
<h3>Panel 2: Study-Context</h3>
<div class="mermaid-container">
<pre class="mermaid">
%%{init: {'theme': 'dark', 'themeVariables': { 'darkMode': true }}}%%
flowchart LR
A[VCF] --> B{Are there clones?}
dbid1[(Database)] --> B
B --> |NO| C[Do nothing]
B --> |YES| D[Rename Samples]
</pre>
</div>
<div>
<table style="font-size:2.0vw">
<thead>
<tr>
<th>Study 1</th>
<th>Study 2</th>
<th>Study 3</th>
<th>Standard Name</th>
</tr>
</thead>
<tbody>
<tr>
<td>GLCA-26-1</td>
<td>GLCA26-1</td>
<td>GLCA26-1</td>
<td>sample05</td>
</tr>
<tr>
<td>HFCA-20-2</td>
<td>Null</td>
<td>Null</td>
<td>sample06</td>
</tr>
</tbody>
</div>
</table>
</section>
<section>
<video autoplay controls style="max-width: 100%; height: auto;">
<source src="../assets/NATC-StudyContext.mp4" type="video/mp4">
<p>Your browser does not support the video tag.</p>
</video>
</section>
</section>
<section>
<section>
<h3>Panel 3: Filter By Traits</h3>
<p>Select phenotypes of interest for upload into workspace</p>
<ul>
<li>Determine total counts</li>
<li>Redundancy analysis based on x>1 phenotypes</li>
</ul>
</section>
<section>
<img src="./assets/NATC-filterByTraits.png" alt="Filter By Traits" style="max-width: 100%; height: auto;">
</section>
<section>
<h3>Phenotype File Output Format</h3>
<div style="overflow-x: auto; max-width: 100%;">
<table style="font-size: 2.0vw; width: 100%; border-collapse: collapse; margin: 20px 0;">
<thead>
<tr>
<th>phenotype_id</th>
<th>phenotype_name</th>
<th>plant_accession</th>
<th>study_accession</th>
<th>year</th>
<th>value</th>
</tr>
</thead>
<tbody>
<tr>
<td>8880144</td>
<td>change in plant height</td>
<td>TGDR1904-ALAA20-1</td>
<td>TGDR1904</td>
<td>2009</td>
<td>194.7</td>
</tr>
</tbody>
</table>
</div>
</section>
</section>
<section>
<section>
<h3>Panel 4: Study Markers Overlap</h3>
<ol>
<li>Marker Overlap</li>
<li>Genotype concordance</li>
<li>Merge VCF's</li>
</ol>
</section>
<section>
<h3>Genotype Quality Control</h3>
<video controls autoplay style="max-width: 100%; height: auto;">
<source src="./assets/NATC-StudyMarkerOverlap.mp4" type="video/mp4">
<p>Your browser does not support the video tag.</p>
</video>
</section>
</section>
<section>
<section>
<h3>Panel 5: Variant Filtering</h3>
<img src="./assets/NGS-Pipeline.png" alt="NGS Pipeline" style="max-width: 100%; height: auto;">
</section>
<section>
<img src="./assets/NATC-variantFiltering.png" alt="Variant Filtering" style="max-width: 100%; height: auto;">
</section>
</section>
<section>
<section>
<h3>Panel 6: Population Structure</h3>
<div class="mermaid-container">
<pre class="mermaid">
%%{init: {'theme': 'dark', 'themeVariables': { 'darkMode': true, 'fontSize': '40px'}}}%%
flowchart LR
A[VCF] --> B(Convert into Plink format)
B --> C[Prune for linkage disequilibrium]
C --> D[Measure Population Structure K=2]
C --> K2[Measure Population Structure K=3]
C --> K3[Measure Population Structure K=4]
D --> E{Has lowest cross-validation error?}
K2 --> E
K3 --> E
E --> |YES|F[Plot Population Structure]
</pre>
</div>
</section>
<section>
<h3>Linkage disequilibrium</h3>
<p>Non-random associate of alleles at different loci on a chromosome</p>
<div style="background-color: #e0e0e0; color: #000; border-radius: 12px; padding: 20px; display: flex; align-items: center;">
<img src="./assets/linkageDisequilibrium.png" alt="Linkage Disequilibrium" style="max-width: 100%; height: auto;">
</div>
</section>
<section>
<img src="./assets/NATC-PopulationStructure.png" alt="Population Structure" style="max-width: 100%; height: auto;">
</section>
</section>
<section>
<section>
<h3>Panel 7: Choose Environments</h3>
<p>multicollinearity: describes a high correlation of two or more independent variables</p>
<p></p>
</section>
<section>
<video autoplay controls style="max-width: 100%; height: auto;">
<source src="./assets/NATC-EnvironmentalData.mov" type="video/mp4">
<p>Your browser does not support the video tag.</p>
</video>
</section>
</section>
<section>
<section>
<h3>Panel 8: Run Analysis</h3>
<p>Perform G x P and G x E associations</p>
</section>
<section>
<h3>Linear Model (LM) in GEMMA</h3>
<img src="./assets/NATC-gemmalm.png" alt="Gemma Linear Model" style="max-width: 100%; height: auto;">
</section>
<section>
<h3>Spurious correlation</h3>
<img src="./assets/spurious_association.jpg" alt="Spurious Association" style="max-width: 100%; height: auto;">
</section>
<section>
<h3>Linear Mixed Model (LMM) in GEMMA</h3>
<p>
$$ \mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{u} + \boldsymbol{\epsilon} $$
</p>
<ul>
<li>\( \mathbf{y} \): vector of phenotypes</li>
<li>\( \mathbf{X} \): matrix of fixed effects (e.g., SNPs, covariates)</li>
<li>\( \boldsymbol{\beta} \): vector of fixed-effect coefficients</li>
<li>\( \mathbf{Z} \): incidence matrix for random effects</li>
<li>\( \mathbf{u} \sim \mathcal{N}(0, \mathbf{K}\sigma^2_g) \): random genetic effects with kinship matrix \( \mathbf{K} \)</li>
<li>\( \boldsymbol{\epsilon} \sim \mathcal{N}(0, \mathbf{I}\sigma^2_e) \): residual errors</li>
</ul>
</section>
<section>
<h3>Kinship Matrix</h3>
<p>Measure the degree of relatedness between samples</p>
<img src="./assets/kinshipMatrix.png" alt="Kinship Matrix" style="max-width: 90%; height: 500px;">
</section>
<section>
<h3>Linear Mixed Model (LMM) in GEMMA</h3>
<img src="./assets/NATC-gemmalmm.png" alt="Gemma Linear Mixed Model" style="max-width: 100%; height: auto;">
</section>
<section>
<h3>Linear Mixed Model (LMM) in LEA</h3>
<p>
$$ \mathbf{Y} = \mathbf{X}\boldsymbol{\beta} + \mathbf{U}\mathbf{V}^\top + \boldsymbol{\epsilon} $$
</p>
<ul>
<li>\( \mathbf{Y} \): matrix of genotypes (individuals × loci)</li>
<li>\( \mathbf{X} \): matrix of environmental variables (individuals × predictors)</li>
<li>\( \boldsymbol{\beta} \): matrix of effect sizes (predictors × loci)</li>
<li>\( \mathbf{U} \): matrix of latent factors (individuals × K)</li>
<li>\( \mathbf{V} \): matrix of factor loadings (loci × K)</li>
<li>\( \boldsymbol{\epsilon} \sim \mathcal{N}(0, \sigma^2) \): residual noise</li>
</ul>
</section>
<section>
<h3>Linear Mixed Model (LMM) in LEA</h3>
<img src="./assets/NATC-lealmm.png" alt="LEA Linear Mixed Model" style="max-width: 100%; height: auto;">
</section>
</section>
<section>
<img src="./assets/acknowledgements.png" alt="Acknowledgments" style="max-width: 100%; height: auto;">
</section>
</div>
</div>
<script src="dist/reveal.js"></script>
<script src="plugin/notes/notes.js"></script>
<script src="plugin/markdown/markdown.js"></script>
<script src="plugin/highlight/highlight.js"></script>
<script src="plugin/mermaid/mermaid.js"></script>
<script src="plugin/math/math.js"></script>
<script>
// More info about initialization & config:
// - https://revealjs.com/initialization/
// - https://revealjs.com/config/
Reveal.initialize({
hash: true,
navigationMode: 'default',
// Learn about plugins: https://revealjs.com/plugins/
plugins: [ RevealMarkdown, RevealHighlight, RevealNotes, RevealMermaid, RevealMath.KaTeX ],
});
</script>
</body>
</html>