Evolution and conservation genetics

1. Evolution and conservation genetics

2. Neutral model of evolution • What governs heterogyzosity levels? • Neutral model of drift and mutation • Single population • Constant size • Drift occurs at rate 1/2N per generation • Mutation creates new or alternative alleles and prevents fixation of alleles

3. What model of mutation does a gene locus follow under the neutral model? • Infinite Alleles Model • Stepwise-Mutation Model

4. Infinite Alleles Model (IAM)(Crow-Kimura Model) • Average protein contains about 300 amino acids (900 nucleotides) • Mutations always occur to new alleles • Finite population size (drift) • How is loss of alleles due to drift balanced by new mutations Do allozymes really fall under a mutation-drift process?

5. What is the equilibrium heterozygosity predicted by IAM? F = probability that two alleles are both copies of the same ancestral allele (identical by descent) Probability that you are not identical by descent and neither allele has mutated Both alleles do not mutate Probability that two alleles are IBD. No mutation.

6. At equilibrium then… But we have two measures of homozygosity both measure the same thing thus equal each other Can you derive this? If H=1-F, then what is H at a mutation drift equilibrium?

7. Heterozygosity at a mutation drift equilibrium, given an IAM is… μ=0.001 When mutation rates are high and population size is held constant: higher equilibrium heterozygosity. When mutation rates are held constant then as population size increases: higher equilibrium heterozygosity μ=10-5 μ=10-7

8. Stepwise-mutation model (SMM)(Ohta and Kimura) Generated by slipped strand mispairing, mutations occur only at adjacent sites. Mutation can produce alleles already present in the population. Expect that the equilibrium level of heterozygosity under SMM to be lower than that of IAM.

9. Genetic diversity and population size What is the effect of “finite” population size on gene frequencies The various ways to mathematically study it Effective population size

10. Drift defined Random changes of gene frequencies among generations More important with Small population sizes Fluctuation in population size Low selection and migration Long time periods

11. A simple simulation of drift: “replicated outcomes” (mean frequency is dotted)

12. Buri’s (1956) classic genetic drift experiment showing the number of wildtype versus neutral mutant alleles in populations of 16 Drosophila followed through time: “gene frequency distribution”

13. Generalized effect of drift Allele frequencies do not change (much) on the landscape scale Within populations, drift decreases genetic variance Between populations, drift increases genetic variance Consider the following to simply illustrate the principle: In a Buri-like experiment on 4 lines of n=4 hermaphrodite snails, the frequency of an albinism allele was as follows at generations 2 and 6.

15. Observed vs. expected changes of mean and variance of gene frequency

16. Loss of heterozygosity due to drift

18. Buri used a population of size nine

19. Effective population size Governs random change of gene frequency, p Depends on several factors All those that reduce the size of the breeding population Ne = number of individuals in an ideal population which has the same magnitude of genetic drift as the actual population.

20. Wright-Fisher model Assume that the number of offspring is distributed as a Poisson variable with Mean = 2 ; Variance = 2 In this case, Ne = N No selection, Random mating, random number of offspring

21. Factors reducing N to Ne Only adults of reproductive age count Sex ratio Variation in size over time Variation in offspring number Inbreeding (self-fertilization)

22. Factors reducing N to Ne -- 1 Ne usually less than census population size Non-breeding individuals do not contribute juveniles “bachelor males” post-reproductives

23. Factors reducing N to Ne -- 2 different number of breeding individuals in the two sexes – one sex represented by a small number of breeding individuals example: Captive bred animals – only one male used for breeding

24. Different numbers of males and females Analogous to having two different population sizes Unequal sex ration

25. The effective population size is strongly influenced by the rarer of the two sexes.

26. Factors reducing N to Ne -- 3 Variation in number of offspring produced by different individuals Ne smaller when offspring numbers are more unequal Ne can be larger when variation in offspring number is reduced

27. V is the variance of reproductive success What is upper limit for effective population size?

29. Factors reducing N to Ne -- 4 • Variation of population size in different generations • Consider the effect on loss of variation caused by the specific population in size in generations 1, 2, 3, .... ,t. harmonic mean: occasional severe reductions in population size will predominate over long stretches of stable large population size in reducing variability

30. N=1000, 10, 1000

31. Factors reducing N to Ne -- 5 Self-fertilization causes increases of homozygosity (most extreme form of close inbreeding, or mating between relatives) f = fraction of loci in which both alleles are copies of an immediate ancestor Ne = N / (1+f)

33. Effective size in continuous populations What if there is one population, and mating occurs to nearby individuals progeny are dispersed a short distance “Neighborhood size” (Wright 1943) Number of individuals within which 95% of the alleles derive from the previous generation (twice the standard deviation of gene flow in one direction, … don’t worry about the formula…) Mainly applied to plants, Ne= 500-1000; why?

34. Estimation of effective population size Demographic data (variance of number of offspring, variation of population size direct… but usually difficult to obtain Can use genetic data reconstruct parentage of current population (paternity analysis, in a few weeks) temporal changes of gene frequency (need to separate from sampling variance) heterozygote excess, between few parents (only applicable to very small populations)

35. Heterozygosity vs. allele number as indicators of variation

36. Predicted Observed reduction of reduction of H = (1/N) Na =(8-n)/8 ______________________ (n) Rarer alleles are lost in bigger bottlenecks rarer genes lost faster than predicted by heterozygosity model!

37. These are special cases of genetic drift Especially important in conservation genetics Bottlenecks and founding effects

38. The Founder effect • New populations often started by small numbers of migrants (analogous to bottleneck) • Carry only a fraction of the genetic variability of the parental population • New populations tend to differ randomly both from the parent population and from each other, tend to be “inbred” • Applies to: • Invasive species • Island colonists • Examples… • Amish of Lancaster Co., PA (Ellis-van Creveld syndrome) • Pirates of Pitcairn Isle

40. The Cheetah bottleneck • 15,000 to 20,000 cats in the wild • All sampled cheetah share the same allozymes (Cohn 1996) • homozygosity of 100%, population 0% polymorphic • For genes mediating immune response, foreign skin is recognized as their own • Why? Two bottlenecks – 10,000 years ago and another in the last two centuries • Work of Stephen J. O’Brian and collaborators (Cat genome project)

44. Intrinsic rate of growth affects H after a bottleneck Dotted line: N=10 Solid line: N=2

45. Loss of alleles mainly depends on bottleneck size, not rate of growth following bottleneck

47. Genetics 144: 2001-2014 (December, 1996)

48. Heterozygosity excess:difference betweenthe observed heterozygosity and the heterozygosity expected from the observed number of alleles.

49. Journal of Heredity, 1998