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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>BIO 345 Evolution: Genetic drift</title>
<meta charset="utf-8" />
<meta name="author" content=" Dylan Padilla Spring, 2023 dpadil10@asu.edu | https://dylanpadilla.netlify.app/" />
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class: center, middle, inverse, title-slide
.title[
# BIO 345 Evolution: Genetic drift
]
.author[
### <br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/> Dylan Padilla <br/> Spring, 2023 <br /> <svg viewBox="0 0 512 512" style="position:relative;display:inline-block;top:.1em;fill:red;height:1em;" xmlns="http://www.w3.org/2000/svg"> <path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg> <a href="mailto:dpadil10@asu.edu" class="email">dpadil10@asu.edu</a> | <svg viewBox="0 0 512 512" style="position:relative;display:inline-block;top:.1em;fill:red;height:1em;" xmlns="http://www.w3.org/2000/svg"> <path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"></path></svg> <a href="https://dylanpadilla.netlify.app/" class="uri">https://dylanpadilla.netlify.app/</a>
]
---
# Announcements
- Leading recitaions
1. Genetic drift
--
2. Game theory
--
3. Speciation
<br><br>
--
- Let's do this as interactive as possible!
---
# Outline
<br/><br/>
- Mechanisms of evolution
--
- Hardy-Weinberg equilibrium
--
- Discuss genetic drift
--
- Genetic drift examples
---
# What is <span style='color: purple;'>Evolution</span>?
---
# What is <span style='color: purple;'>Evolution</span>?
.pull-left[
]
.pull-right[
]
---
# What is <span style='color: purple;'>Evolution</span>?
.pull-left[
]
.pull-right[
<center>
<img src = "imgs/pop-gen-environment.png" width = "450" height = "450">
</center>
]
---
# Hardy-Weinberg Equilibrium
.pull-left[
<br><br><br>
<center>
What happens when nothing is happening?
</center>
]
.pull-right[
<center>
<img src = "imgs/HW.png" width = "520" height = "450">
</center>
]
---
# Hardy-Weinberg Equilibrium
.pull-left[
<center>
<img src = "imgs/assumptions.png" width = "520" height = "450">
</center>
]
.pull-right[
]
---
# Hardy-Weinberg Equilibrium
.pull-left[
<center>
<img src = "imgs/assumptions.png" width = "520" height = "450">
</center>
]
.pull-right[
<br><br><br>
<center>
These assumptions are not met by real populations, but reality is often close enough to the theory to allow accurate predictions to be made based on the H-W equilibrium
</center>
]
---
# Hardy-Weinberg Equilibrium
<span style='color: purple;'>With random mating and no evolution, allele frequencies do not change from one generation to the next</span>
.pull-left[
<center>
<img src = "imgs/punnet.png" width = "420" height = "400">
</center>
]
.pull-right[
<center>
\[f(A_1)=36\%+24\%=60\% \]
\[f(A_2)=16\%+24\%=40\% \]
Expressed as `\(p\)` and `\(q:\)`
\[f(A_1)=p^2+pq\]
\[f(A_2)=q^2+pq\]
</center>
]
---
# Genetic drift
<br><br>
- Changes in allele frequency that results from the random sampling of individuals from generation to generation in a finite population
<br>
--
- Increases the homozygosity of a population (i.e., increases AA or aa, decreases Aa)
<br>
--
- Reduction of genetic variation within a given population can increase the differences between populations of the same species
---
# Bottleneck effect
## <span style='color: purple;'>Fluctuating Population Size</span>
<img src="index_files/figure-html/unnamed-chunk-1-1.png" width="45%" style="display: block; margin: auto;" />
---
# Founder effect
<br>
<center>
<img src = "imgs/founder-effect.jpeg" width = "700" height = "400"><br>
</center>
---
# Why is drift very important?
<span style='color: purple;'>The neutal theory of evolution</span>
.pull-left[
<center>
<img src = "imgs/kimura.png" width = "360" height = "400"><br>
Motoo Kimura
</center>
]
.pull-right[
1. "claims that most of DNA sequence difference between alleles within a population or between species are due to neutral mutations"<br><br><br><br><br><br>
2. Under this model, genetic mutations insert genetic variation into populations and are countered by the process of genetic drift which eliminates genetic variation from populations
]
---
# Let's see an example
```r
Ne <- c(60, 64, 48, 34, 22, 60, 46, 38, 24, 10)
chrom <- 2 * Ne
p = .6
q = 1 - p
gen <- 100
matrix <- array(NA, dim = c(100, 10))
```
---
```r
head(matrix)
```
```
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] NA NA NA NA NA NA NA NA NA NA
[2,] NA NA NA NA NA NA NA NA NA NA
[3,] NA NA NA NA NA NA NA NA NA NA
[4,] NA NA NA NA NA NA NA NA NA NA
[5,] NA NA NA NA NA NA NA NA NA NA
[6,] NA NA NA NA NA NA NA NA NA NA
```
```r
matrix[1, ] <- round(rep(chrom*p, 1))
head(matrix)
```
```
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 72 77 58 41 26 72 55 46 29 12
[2,] NA NA NA NA NA NA NA NA NA NA
[3,] NA NA NA NA NA NA NA NA NA NA
[4,] NA NA NA NA NA NA NA NA NA NA
[5,] NA NA NA NA NA NA NA NA NA NA
[6,] NA NA NA NA NA NA NA NA NA NA
```
---
```r
set.seed(1094)
for(i in 2:gen){
for(j in 1:10){
matrix[i, j] <- rbinom(n = 1, size = chrom, prob = matrix[i-1, j]/chrom)
}
}
dat <- as.data.frame(matrix)
head(dat)
```
```
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
1 72 77 58 41 26 72 55 46 29 12
2 75 79 51 45 24 64 54 44 33 6
3 75 87 52 38 23 59 57 41 37 4
4 79 86 56 41 29 52 56 48 39 3
5 79 92 68 37 34 56 62 45 31 3
6 78 101 74 45 37 55 52 50 33 6
```
---
```r
for(i in 1:ncol(dat)){
dat[ , i] <- round(dat[i]/chrom[i], 1)
}
head(dat)
```
```
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
1 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
2 0.6 0.6 0.5 0.7 0.5 0.5 0.6 0.6 0.7 0.3
3 0.6 0.7 0.5 0.6 0.5 0.5 0.6 0.5 0.8 0.2
4 0.7 0.7 0.6 0.6 0.7 0.4 0.6 0.6 0.8 0.1
5 0.7 0.7 0.7 0.5 0.8 0.5 0.7 0.6 0.6 0.1
6 0.7 0.8 0.8 0.7 0.8 0.5 0.6 0.7 0.7 0.3
```
---
.pull-left[
<br><br><br><br>
```r
dat$gen <- 1:100
par(las = 1)
plot(rep(NA, 100), type = "n", ylim = c(0, 1), ylab = "Allele frequency", xlab = "Generation")
lines(V1 ~ gen, data = dat, type = "l", lwd = 1.5, col = "gray", ylim = c(0, 1), ylab = "Allele frequency", xlab = "Generation")
lines(V2 ~ gen, data = dat, lwd = 1.5, col = "black")
lines(V6 ~ gen, data = dat, lwd = 1.5, col = "gray", lty = 2)
lines(V7 ~ gen, data = dat, lwd = 1.5, lty = 2)
legend("bottomleft", legend = c("pop1", "pop2", "pop6", "pop7"), col = c("gray", "black", "gray", "black"), lty = c(1, 1, 2, 2), lwd = 1.5, bty = "n")
```
]
.pull-right[
<img src="index_files/figure-html/unnamed-chunk-7-1.png" style="display: block; margin: auto;" />
]
---
# Summary
- Though natural selection is a major driver of evolution in populations, there are other processes that result in genetic changes as well
--
- Genetic drift is a random process meaning that there is no selective pressure needed for certain alleles to increase or decrease in a population
--
- Large fluctuations in allele frequencies are more common in small populations
--
- Genetic drift can have major effects when a population is sharply reduced in size by a natural disaster (bottleneck effect) or when a small group splits off from the main population to found a colony (founder effect)
<br>
<center>
😎👍
</center>
---
# Online simulation
[click here to follow along](https://cartwrig.ht/apps/genie/)<br><br>
📊🧪💻
</textarea>
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