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Population Structure and Drift

Population Structure and Drift. Chapter 11. Conservation Genetics. Illinois Greater Prairie Chicken Tympanuchus cupido pinnatus 200 years ago Illinois was covered with prairie with millions of greater prairie chickens Introduction of steel plow decimated prairie habitat

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Population Structure and Drift

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  1. Population Structure and Drift Chapter 11

  2. Conservation Genetics • Illinois Greater Prairie Chicken • Tympanuchus cupido pinnatus • 200 years ago Illinois was covered with prairie with millions of greater prairie chickens • Introduction of steel plow decimated prairie habitat • By 1994 there were less than 50 greater prairie chickens left • Two remnant populations

  3. Conservation Genetics • Ban on hunting began in 1933 • In 1960s the two populations were established as sanctuaries • In 1970s bird numbers increased • By mid-1970s population began to crash again • In 1994 only 6 males were left • Why did population decline when habitat was restored?

  4. Random Genetic Drift • In finite populations, allele frequencies can fluctuate by chance • e.g. populations heavily structured by geography  mating not random

  5. Random Genetic Drift • Consequence • the replacement of old alleles by new ones proceeds in a random fashion not influenced by natural selection • NONADAPTIVE evolution! • Allele frequencies CAN & DO change from 1 generation to the next

  6. What are the two MOST important causes of allele substitutions or evolution in populations • Random Genetic Drift • Natural Selection

  7. Coalescence • Given enough time, all gene copies in a population are ultimately descended from a single ancestral gene copy • However, this is also affected by: • Mutation • Immigration • Natural Selection

  8. EXAMPLE OF COALESCENCE

  9. Coalescence • Implies that the average degree of relationship among individuals increases with the passage of time • Thus becomes monomorphic, becomes fixed (freq. of 1.0)

  10. Coalescence • If we have alleles pand q where p=0.5 and q=0.5 • What would be the probability that allele q is passed on to the next generation? • If we have alleles pand q where p=0.9 and q=0.1 • A population will eventually become monomorphic and this equals the initial frequency of that allele

  11. Coalescence • How long does it take? • The mean time back to common ancestry of all gene copies in the population is 2N generations • Consider the probability of q being passed to the next generation when there was a small number of mating individuals....say 10...???

  12. Genetic Drift • Alleles fluctuate at random, and eventually become fixed • Genetic variation is lost • Initially similar populations diverge in allele frequency, and may become fixed for different alleles (all individuals homozygous) • The probability, at time t, that an allele will eventually become fixed equals the frequency of the allele at that time • The rate at which these events occur is greater, the smaller the population

  13. N = 4 N = 40 N = 400

  14. Drift Simulator • http://darwin.eeb.uconn.edu/simulations/drift.html

  15. Evolution by Genetic Drift • In an adult population there are 2N gene copies • The variance in allele frequencies: V = p (1-p) / 2N (where 2 refers to the diploid condition and N refers to the size of the population) What is this telling us?

  16. Evolution by Genetic Drift is FASTER in small populations • The smaller the N (pop. size) the greater the genetic variance from generation to generation! • The probability, at time t, that an allele will ultimately become fixed equals its frequency at that time. • If a new mutation arises in a population, the probability it will be fixed in that population at time t is: pt = ½ N this is the likelihood of reaching p=1 (fixation) • Clearly, if the population is small, fixation will occur faster

  17. Evolution by Drift • Random walk of the drunk • The probability, at time t, that an allele will ultimately be fixed equals it frequency (pt) at that time.

  18. Structured Populations • The Concept of Demes and metapopulations

  19. Structured Populations

  20. Structured Populations • Demes and metapopulations • the equation to predict the probability of a new mutation becoming fixed is still ½ N • if k=# of populations • 2Nk=total # gene copies in population • Overall number of populations fixed for p: • pk(2N) [where 2N = #genes per population)

  21. Structured Populations • frequency of, say the allele p, is summed over all metapopulations p2Nk / 2Nk • This equals p, the initial frequency!

  22. Structured Populations • Thus one consequence of drift is the smaller the population size, the shorter the average time to fixation • For diploid populations, a newly arisen neutral allele mutation takes (on average) 4N generations to become fixed

  23. Heterozygosity • Heterozygosity is maximal when all alleles are equal (p=0.5 and q=0.5) • Alleles may drift from low frequency to high frequency or even fixation in which case: • Heterozygosity initially increases (as the frequencies start to approach 50% p and q) then starts to decrease as one of the two alleles drift toward fixation • In a metapopulation, different alleles become fixed in different demes (or metapopulations) each of which declines in Heterozygosity • Alleles may drift from low frequency to high frequency or even fixation

  24. Heterozygosity and Drift • During this process in a metapopulation or deme system of structured populations, heterozygosity and homozygosity retain apparent H-W equilibrium genotype frequencies within each population BUT the metapopulation suffers a net DECREASE in Heterozygosity!

  25. What is Predicted based on Genetic Drift Simulations... p = 0.5 q = 0.5 N = 16 2N = 32 Estimates fixation by 19 generations!

  26. The Real Experimental Data

  27. Effective population size  Ne • The reality of population ecology and demography can affect the reality of chance mating within populations, decreasing the effective population size • Variation in number of progeny • skewed sex ratios • overlapping generations • fluctuations in population size

  28. Genetic Drift • Experimental study on Drosophila • Average heterozygosity fell over time • Decrease in heterozygosity did not match predictions exactly • Fell at rate predicted for population size of 9, not 16!!! • Effective population size was only 9 • Some individuals could have died • Some males may have been rejected by females • Theory of genetic drift can make testable predictions about behavior of alleles in finite populations

  29. Founder Effects • Genetic bottlenecks population going through a population crash, followed by a population increase This has massive consequences on the size of the gene pool after population increase, and thus, drastically affects Ne

  30. FounderEffects N = number of founders r = pop. increase WE SEE: if “r” is small, Heterozygosity declines faster!

  31. Inbreeding • Autozygous • homozygous only and identical by descent • Allozygous • either homozygous or heterozygous but not identical by descent • An inbred population is one in which the probability that an individual is autozygous is greater, as a consequence of mating among relatives, than in a panmictic population

  32. Inbreeding Inbreeding coeffecient = F  the probability that an individual taken at random from a population that is autozygous • F is the fraction that is autozygous and 1-F is the fraction that is allozygous

  33. Inbreeding • With two alleles A1 and A2 with frequencies p and q  the probability that an individual is allozygous and A1A1 = (1-F)p2 • A1A2 = (1-F)2pq  the fraction of heterozygotes (although by definition, they are allozygous) • A2A2 = (1-F)q2 • Thus the fraction that is autozygous and A1A1 = F(p) and thus, A2A2 = F(q)

  34. Inbreeding • Notice, the frequency of homozygotes is higher! • F increases over generations • Frequency of Heterozygosity is ½ in each successive generation

  35. Genetic Consequences of Inbreeding • Inbreeding redistributes the alleles to the homozygous condition  genotype freqs. change but allele frequencies do not change • Genetic variance of a phenotypic character within a population is usually increased • inbreeding depression  increase in homozygous recessive alleles (likely to increase deleterious phenotypes) • Inbreeding promotes linkage disequilibrium  nonrandom association of alleles at different loci

  36. Genetic Drift VS Inbreeding • Genetic Drift • Allele frequencies change • Inbreeding • Allele frequencies do not change but genotype frequencies (homozygous vs. heterozygotes) DO change!

  37. Gene flow • Natural populations of a species typically are not completely isolated, but instead exchange genes with one another to a greater or lesser extent • Gene flow, if unopposed by other factors, homogenizes a population

  38. Models of Gene flow • Island models • Stepping stone models • Isolation by distance models

  39. Gene flow • Homogenizes the populations within a species (unopposed by other forces) • Rate of gene flow = m • A1 varies among populations (pi) resident • pi and the average allele frequency is p (source) • within population i (pi), a proportion of m of the gene copies enter from other populations, and the frequency is p

  40. Gene flow p p m resident Source

  41. Gene flow • A proportion 1-m of the gene copies are non-immigrants and among these the frequency is p • After 1 generation the populations new allele freq (p’) is: p’ = p(1-m) + pm or p’ = p-pm + pm So........Δp = m(p – p)

  42. Gene flow p=0.3 p=0.1 m=0.001 resident Source 1 in a 1000 is a migrant

  43. Gene flow Δp = m(p-p) = 0.001(0.3-0.1) =.0002 p’ = p(1-m) + pm = 0.1(1-0.001)+0.3*0.001 =0.1002

  44. Equilibrium Frequency • Equilibrium frequency is found by setting p’ = 0 (or Δp = 0), which is where p’ is not changing between generations and is, thus, in equilibrium So... Δp = 0 = m(p-p) thus p = p Therefore, each population will ultimately attain the same allele frequencies showing that gene flow homogenizes populations

  45. Gene flow and drift • In the absence of gene flow populations tend to diverge due to drift • Fst = fraction of autozygotes in a sub-population at time t • Another way to look at this is that Fst is a measure of the observed variation in allele frequency among populations Fst= 1- (1-½N)t see page 315, box 11.D

  46. Gene flow and Drift • Fst must reach an equilibrium between drift and gene flow • Thus Fst= 1 / (4Nm + 1)

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