class: center, middle, inverse, title-slide .title[ # BIO 345 Evolution: Genetic drift ] .author[ ###
Dylan Padilla
Spring, 2023
dpadil10@asu.edu
|
https://dylanpadilla.netlify.app/
] --- # 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[ ![](imgs/mechanisms.jpeg) ] .pull-right[ ] --- # What is <span style='color: purple;'>Evolution</span>? .pull-left[ ![](imgs/mechanisms.jpeg) ] .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> ๐๐ </center> --- # Online simulation [click here to follow along](https://cartwrig.ht/apps/genie/)<br><br> ๐๐งช๐ป