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
Models of Gene flow • Island models • Stepping stone models • Isolation by distance models
Gene flow • Homogenizes the populations within a species (unopposed by other forces) • Rate of gene flow = m • A1 varies among populations (pi) resident • the average allele frequency in source population is p (i.e. immigrant coming from) • within population i (pi), a proportion of m of the gene copies enter from other populations, and the frequency is p
m = migrant Source pi p resident Gene flow
Gene flow • A proportion (1-m) of the gene copies are non-immigrants and among these the frequency is pi • After 1 generation the populations new allele freq (p’) is: pi’ = pi(1-m) + pm or pi’ = pi-pim + pm So........Δp = m(p – pi)
m = 0.001 p=0.3 p=0.1 resident Source 1 in a 1000 is a migrant Gene flow
Gene flow Δpi = m(p-pi) = 0.001(0.3-0.1) =.0002 pi’ = pi(1-m) + pm = 0.1(1-0.001)+0.3*0.001 =0.1002
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
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
Gene flow and Drift • Fst must reach an equilibrium between drift and gene flow • Thus Fst= 1 / (4Nm + 1)
Gene flow • We can rearrange Fst= 1 / (4Nm + 1) so that we can estimate the average # of immigrants into a population per generation Nm = 1 / (Fst – 1) • Notice! This tells us that the higher the rate of gene flow, the more similar the allele frequencies between populations • Conversely, observing a strong divergence indicates that the balance between gene flow and drift is tipped toward drift
Estimating Fst • Direct estimates of gene flow • Mark-recapture studies... • Indirect estimates of gene flow • Alleles used to calculate Fst are neutral • Allele frequencies must have reached equilibrium between gene flow and drift
Gene Flow Example! • Water snakes of Lake Erie • Nerodia sipedon • Live on mainland and on several islands • Color pattern variable • Strongly banded to unbanded • Banding controlled by a single locus with two alleles • Banded is dominant over unbanded • On mainland most snakes are banded • On island many are unbanded
Gene Flow... • Water snakes of Lake Erie • Banding pattern due to natural selection • On islands snakes bask on rocks • On mainland stay closer to vegetation • Why is the unbanded allele not fixed on islands? • Banded snakes migrate from mainland each generation • Bring banded alleles to island gene pool • Migration works in opposition to natural selection
Conservation Genetics • Westermeier’s hypothesis • Destruction of prairie did two things • Reduced population size • Fragmented remaining population • Remaining prairie chickens were trapped in two islands in seas of farmland • Genetic drift caused decline in heterozygosity • Inbreeding depression occurred
Conservation Genetics • Accumulation of deleterious recessives leads to reduction in population size • Effectiveness of genetic drift is increased • Speed and proportion of deleterious mutations going to fixation increases • Population size decreases more • Mutational Meltdown (synergistic interaction between mutation, pop. Size and drift)
Conservation Genetics • Prairie chickens caught in mutational meltdown • Reproductive success decreased • Hatching success low • Birds had fallen into extinction vortex • Birds needed gene flow
Conservation Genetics • In 1992 conservationists trapped birds from Minnesota, Kansas, and Nebraska and moved them to Jasper County, Illinois • Hatching rate increased and population began to grow • Migration, genetic drift, and nonrandom mating all contributed to fate of Illinois greater prairie chickens
Conclusions about Gene Flow • Certain taxa display substantial gene flow over long distances • But on average the level of gene flow is greatly restricted over short distances • Implies local populations can diverge substantially due to drift • Thus, species can adapt to local conditions!!!!
Neutrality • A new mutation takes 4Ne to be fixed • What happens if you have a large Ne? • Ne = 2000 fixation in 8000 gens. • Ne = 1000 fixation in 4000 gens. • Ne = 500 fixation in 2000 gens.
Neutrality • In larger populations (larger Ne) fixation may take a very long long time! • Other mutations arise in the interim
Additional mutations arise! • For example, if the mutation rate is 10-9 (=substitutions per site per gamete per generation) • Given a gene is 1000 nucleotides long... • What is our mutation rate over this gene/gamete/generation? • 10-6 if we have Ne = 1000 (with 2N gene copies) • 10-6(mutations/gene) X 2000(=2N) X 4000(generations)= 8 mutations per gene over 4000 generations!!!
Additional mutations arise! • Given an estimated 8 mutations in a gene over 4000 generations • And the probability that a new mutation will be fixed 1/2Ne • There will be a STEADY substitution of alleles • Therefore: in such large effective populations, we generally expect at least moderate levels of polymorphism (multiple alleles per loci) given our calculations above!
What have we assumed during these calculations? • In calculating the preceding stats for mutation and allele generation we assumed NO selection for or against particular alleles • We therefore assumed they were selectively NEUTRAL....
The Assumption of Neutrality • Mayr: • “It is unlikely that two genes would have identical selective values under all conditions that they must exist in a population Thus, cases of neutral polymorphisms do not exist, it then appears that random fixation is of negligible evolutionary importance”
The Assumtion of Neutrality • Lewontin and Hubby (1966) • “Natural selection could not maintain so much genetic variation.” Suggested that much of the variation is selectively neutral. • M. Kimura (1968) • Demonstrated similar rates of evolution between lineages. Concluded that such a constancy could not be maintained by natural selection, must instead be by mutation and genetic drift.
The Neutral Theory of Molecular Evolution • Contends that: • a small minority of mutations in DNA sequences are advantageous and are fixed by Natural Selection and although some are disadvantageous and are eliminated by “purifying” Selection... • the great majority of mutations that are fixed are effectively neutral with respect to fitness, and are fixed by genetic drift
The Neutral Theory of Molecular Evolution • Most genetic variation is selectively neutral and lacks adaptive significance • BUT, this is not to say that phenotypic change evolves by genetic drift!..... Instead, phenotypic characters evolve by natural selection • The neutral theory acknowledges that many mutations are deleterious and are eliminated by natural selection • It holds that MOST of the variation we see at the molecular level is neutral and has no adaptive role (i.e. No effect on fitness)
The Neutral Theory of Molecular Evolution • Neutral Mutation Rate u0 = f0ut • Certain alleles are effectively neutral • No benefit or hindrance to fitness or so small it is not a problem (eg. s=0.001) • In other words, the mutant allele is so similar to other alleles in fitness that changes in its frequency are governed by drift alone, not by natural selection!
The Neutral Theory of Molecular Evolution • Small population (500) and s=0.001 • simulations show that most variation is due to drift... • But, in a large population (5000), natural selection will be more important since the power of drift decreases (given the large pop. size) • Thus, an allele may be effectively neutral in one population but not in another, simply due to the Ne
The Neutral Theory of Molecular Evolution • Examples (Genetic constraints, codons) • The amino acid Leucine is encoded by 6 possible codons: Here we can envision that changing the DNA sequence to any one of the 6 possible Leucine codons would be unlikely to have any effects on fitness or even phenotype! CUU CUC CUA CUG UUA UUG
Types of DNA Substitution Synonymous VS. Nonsynonymous DNA1 = AAA GCT CAT GTA GAA DNA2 = AAG GCT GAT GTA GAA Protein1 = Lys Ala His Val Glu Protein2 = Lys Ala Asp Val Glu Synonymous mutation Nonsynonymous mutation
Substitutions in DNA • Mutations occur at the 3rd position most frequently and 2nd most infrequently • Neutral mutation rate would be greatest in DNA seq. that is not transcribed and has known function (e.g. Pseudogenes, introns, spacers, etc.)
Substitutions in DNA • The number of new mutations is u0 * 2Ne • We know that a mutation will become fixed at a frequency of p, which equals 1/2Ne since 2Ne gene copies might mutate
Substitutions in DNA • The number of neutral mutations that will someday become fixed is 2Neu0 * 1/2Ne • This can be reduced to u0 (which is the neutral mutation rate) • This rate of mutation is theoretically constant and equals the neutral mutation rate!!!!! • Most molecular polymorphisms are selectively neutral
Variation Loss VS Gain • If a locus evolves purely by drift, all variation will be ultimately lost (F=1, autozygous) • What happens if a mutation arises……it becomes allozygous (F<1) • Steady State – a balance between the rate of loss of variation by genetic drift and by the rate of gain of variation by mutation
Alleles Continually Arise By Mutation! • We have just demonstrated that new alleles arise continuously via mutation • Many are lost by genetic drift, but others drift higher and get fixed over 4Ne generations. • Remember allele freqs. sum to 1 so previously common alleles have drifted lower and are ultimately lost
Steady Turnover in Alleles • Over time we generally see a steady turnover in alleles • The level of variation (H) remains about the same and is Higher in Large populations, Lower in Small populations • Thus, there must be a positive correlation between heterozygosity at a locus and its rate of evolution…
Variation within & among Species • Nonsynonymous and Synonymous changes in protein coding sequence • expect the ratio of Ks:Ka to be 1:1 or less (due to purifying selection) • (eg. adh loci)
Rates of Molecular Evolution • What do we expect to see…. • We would expect that rates of evolution are greatest at DNA positions that, when altered, are least likely to effect function…
Neutralist debate • The fight between selection and drift • Population Structure and gene trees
Coalescence • If you have a population that is divided by something and there is no gene flow between populations what will eventually happen over time? • Ultimately, all the gene copies in each will be descendants of one of the copies that was included in each population at the time of isolation • Each population will have a monophyletic gene tree (or is at least likely to, given enough time)
Coalescent Theory • Coalescent Theory tells us that under certain conditions the Gene tree may not match the Species tree