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# POPULATION GENETICS GENE 612

Texas A&M

GPA 3.54

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This 13 page Class Notes was uploaded by Elvera Macejkovic V on Wednesday October 21, 2015. The Class Notes belongs to GENE 612 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/225933/gene-612-texas-a-m-university in Genetics (Graduate Group) at Texas A&M University.

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Date Created: 10/21/15

GENE 612 Population Genetics Week 7 Tuesday Announcements Exams coming back by email today and next few days as I finish off the remainder We Genetic drift stochastic allele frequency change cumulative effect of sampling error in gene segregation and subsequent genetic events Fisher genetic drift or sampling error was viewed as mere noise creating variance in genotype frequencies Viewed it as inhibitory to selection preventing or hindering adaptive evolution Wright viewed genetic drift as key way to create shifts in the genefreq structure of populations allowing them to take alternative evolutionary trajectories as driven by selection sidebaron adaptive landscapes When is GD relatively more important 0 Low population size low Ne actually 0 Low selection and migration 0 Long time periods 0 Cyclic populations ie uctuation in population size 0 Hidden genetic variance Sampling error may lead to local abundance of rare alleles termed a founder e ect The concept applies not only to founders per se but bottleneck survivors founders of resurgency Examples 0 Amish of Lancaster Co PA Ellisvan Creveld syndrome 0 Pirates of Pitcairn Isle tails unconfirmed rumor 0 Blue Koonzes of KY Note similarity with effects of inbreeding Also sampling error and inbreeding often occur together 7 39 10 05 u 04 Figure 62 Allelic fre quency over time for four 0 2 PW solid lines of WWW of size 29 The man e n of and A1 for the our 00 Plun tu 393 indicated it bmkm line by At right Buri s 1956 classic genetic drift experiment showing the number of wildtype versus neutral mutant alleles in populations of 16 Drosophila followed through time Note the unfortunate removal of populations from the graph once they became xedibut see raw data below from Buri 1956 Generatlnn Consider a simple simulation Fig 62 G eneralian m rw y m rn n n v vurvr39 nvv v I v 0 2 4 6 81012 4161320222426283032 Number of bw75 genes GOTO Excel demo Bun s Why or why not emplncal expenment VVlth a Monte Carlo simulatlon Do your results t WMW 1 up u u n u H m n m w m 2 u u u m n u n m n u Suggested study Create a biallelic simulation like that in Fig 62 above to mg u 5quot 1 Consider the generalized effects of drift 0 Allele frequencies do not change much on the landscape scale 0 Within populations a rift decreases genetic variance 0 Between populations a rift increases genetic variance 0 Consider the following to simply illustrate the principle In a Burilike experiment on 4 lines of n4 hermaphrodite snails the frequency of an albinism allele was as follows at generations 2 and 6 Generation 2 Generation 6 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 variance 267 variance 2133 In in both cases p2 p6 05 but 62 267 and 66 213 In the examples so far we typically started at p q 05 We saw that the probability of a given allele being fixed was 05 for a given population In general terms the probability of an allele being fixed by drift is equal to its initial frequency Denoting the probability an allele will be fixed as u then ufixation of A2 q0 Eq 61 If we start at qo it follows that qo of the populations will fix for A2 so if averaging across populations qt will still be equal to qo But as previously stated the variance will increase over this timecourse Genetic Drift and Effective Polmla on Size 020 b 0 1B Expected 39 0 Observed Figure 64 The ob 0 12 served and expected I mean a and variance 0 03 I in allelic frequency in 39 the cmhnent of Burl m4 1956 True expected Variance was generated 000 I I I I I I n J I r I using Expression 643 and 0 2 4 a B m 12 14 16 13 39 popula on sin of nine Genem on Variance in allele frequencies among populations at time Iis calculated as vqt poqo 11 IZNJ Eq 64a Prelude to next week s topic What is the main reason natural populations not so extremely divergent always xed for one allele or another as these examples all suggest Recall the suggested problem from last week Modify your Levene model so that when a given environment occurs inbreeding becomes more common than in other environments Consider that the very factors causing increased inbreeding might reduce population size Thus there might be joint effects of drift and inbreeding What are the effects of inbreeding versus drift Generation To summarize I o Drift decreases Vql genetic variance Within pops declines Ih M l lI liA J o Drift increases Vq variance among pops increases 0 0h qo q stays same at landscape level agabdowww a m awn Aj 39 y y v ozasa1o121 1 Number 01 aw geneg uA1 010 0 Note that the actual values for families of 16 are plotted with those predicted for samples of 9 flies using Eq 64a Expected 0 Observed Why do the data for samples of 16 ies fit those eXpected from samples of size 9 est of line for 16 inserted at left in green Generation Note that although Hedrick says Ne9 provides a better fit I know other sources that claim Nel 15 give the best fit your homestudy problem will allow you to settle the matter So genetic drift leads ultimately to xation at neutral loci with the rate being determined by sample size Flg 015 A 1generanon Sgeneralions 44 l ZOQeneralIons 1 Frequency So let s consider the issue of population size in more detail Skipping the challenging but fascinating derivation on p 233 the eXpected heterozygosity at generation Iis Ht 1 IZNYHO Eq 63b consider this relationship with N l N 00 it may also be useful to calculate Hm which equals 1 12NHt Ht 1 l2NtH0 can also be written in terms of a log eXpectation Ht HoetZN and solved for t as t 2NlnX Where X is a proportion of original heterozygosity that remains ie HtHo Eq 65b gives the expected time to xation of an allele with an initial frequency of q Tqo mournc101 clo Why does this equation depend on both sample size and initial allele freq Note read over development of Eq 65b p 234239 but you only need understand it in principle A particularly good thought exercise is to imagine how selection would be incorporated into the transition matrix in Table 62 Methinks there is much ado over N When might low N occur in nature 0 founder events invasion of new habitat o bottlenecks catastrophes 0 chronic low population sizes probably not common why Founder events and catastrophes What is the probability of polymorphism R given a founder event or rebound from catastrophe 10 0 a 0 m 0 a 0 r0 Fig 67 onbabilily 01 polymorphism R 391 2 3 4 5 6 7 8 9 70 Number 0 founders N The number of founders or bottleneck survivors has an eXponential effect on the number of alleles going into a newborn population It is assumed that the population quickly grows but the rate of growth further determines how much polymorphism is likely in generations hence Speci cally the previous graph gave us starting conditions onlyihez at the reductionbirth event Given that starting point what happens to hez over time Since heterozygosity is lost each generation while the population size is low the intrinsic rate of increase of the population largely determines the long term trajectory of freqhez Fig 68 0 Solid N02 Dotted N010 Average helelczygoslly Recall that r is the rate of increase in a population from Ch 1 The trajectories of alternative populations drift in random directions This implies differentiation between populations will be achieved Fig 69 06 0 B 10 1 04 TN Note Hedrick s formula for D over time Eq 66 XaXis is the fraction of original heterozygosity remaining Try N oo Effective population size Recall the loss of effect of drift was more pronounced in the y example than the expectation under population sizes of 16 055 Expacled o Observed Generation The fact that the expected curve for N9 t the observed values better than Nl6 the actual population size used in the experiment suggested that not all 16 individuals were actually breeding Why might this be What does this imply for the practical issues of pop gen and pop bio counting individuals not adequate must know sex ratio must know breeding system must know demographics 0 000 But all our equations rely on N Whatever shall we do We can apply a correction to N to create Ne so that all formulae using N remain viable Thus our new population estimate allows us to return to our cozy thinking about ideal populations Three approaches to calculating NE 0 inbreeding o variance 0 eigenvalue Count the number of organisms and estimate the f 62 or Ahez Compare observed to eXpected patterns and assuming deviation is due to NeltN as in Buri s y example Ne must be 9 because the pattern did not fit that eXpected if Ne truly were 16 Next time finish Ne discussion and get into population structure Ch 7

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