BIOL 4160

Evolution

Phil Ganter

301 Harned Hall

963-5782

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04 - Genetic Drift as an Evolutionary Force

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Genetic Drift

Random (chance) influence versus Deterministic influence

  • Inevitability of random influence
  • Adaptive versus non-adaptive evolution

Large numbers of random events occurring over long periods of time can be described mathematically, which makes it possible to predict the effect of drift on populations

  • One corollary to this is that population size is an important factor in making the predictions described above, a factor that always has an impact

In an infinite population, the outcome of an event is exactly what its probability predicts:

  • In an infinite population of fair coin tosses, 50% are heads and 50% are tails
  • In a finite population, random chance means that the actual outcome can differ from the expected
    • In a population of 100 coin tosses, 50 heads are expected but we would not feel  that the universe had come unraveled if we got 53 heads (or 46 heads)
  • The difference between expectation and outcome is the error due to sampling
    • Sampling is drawing a group of some size out of a larger (theoretically, infinite) population
    • If this does not seem true, then think of a sample of five coin tosses
      • expected outcome (50% heads) would mean that you get 2.5 heads, an impossibility as you can get 2 heads or 3, but not 2.5
      • Here the sample size is so small that you can see expectation from known probability is not always the outcome

Because all populations are finite in size, then each generation random chance will affect the proportion of each allele in the population

  • Hardy-Weinberg predicts no change, just like we predict 50% heads, but random chance alters this
  • The overall effect of these "wandering" allele frequencies is that allele frequencies will wander until they are caught in one of two "traps"
    • Fixation - when an allele's proportion hits 100%, no other alleles are left and we say that allele is "fixed" in the population

    Extinction - when an alleles proportion hits 0, it is lost from the population

As you can see, without migration or mutation, the number of heterozygous loci in a population will decrease over time

    Genetic Drift leads to a loss of genetic diversity

Some Impacts of Genetic Drift on Evolution

Genetic Drift leads to;

  • fixation and loss of alleles in populations
  • as individual loci become fixed, the overall genetic diversity declines
  • at a particular time, like the present, the probability of an allele becoming fixed is equal to its frequency at that time
    • a neutral mutation arises as a single copy of a gene in a population with a total of 2N (N = population size) copies of alleles at that locus (two copies for each diploid individual) so the probability of a mutation becoming fixed is 1/2N, which can be very small for large populations
    • a corollary of this is that, in a population with new mutations arising constantly, only 1/2N of them will ever be fixed (the rest will be lost)
  • evolution by drift occurs faster (% change per unit time) in small rather than large populations
    • a neutral mutation will take, on average, 4N generations to become fixed (if it does become fixed), which can be a long time in large populations!

Notice that population size is very important and deserves further consideration

  • If you count the size of a population (census the population) and use that figure as N, you are assuming that all individuals have the same chance of contributing genes to the next generation, which is often not a fair assumption
  • The actual number of breeding individuals is the Effective Population Size (Ne) - notice that Ne cannot be larger than N (the census size)
  • Some factors that can reduce N
    • Variation in the number progeny - through chance or because natural selection is favoring some progeny over others
    • Variation in the population sex ratio (away from 1:1)
    • Variation in population (census) size - when considering what happens over many generations, it is important to realize that chance events are more important during periods of low population numbers
      • Ne is usually closer to the minimum population size than the mean population size (it is always smaller than the mean)
      • There are two extremes of the effect of variation in population size:
        • Bottleneck Effect - when a population undergoes a crash, many alleles can be lost (think of a crash from 1,000 to 2 individuals - the large population may have had many, many alleles at a locus but the maximum number in the post-crash population is 4, as there were only two copies of the gene in each individual
        • Founder Effect - essentially the same as the bottleneck but it is not a crash but the effect of a small group of individuals (sometimes just one pregnant female) founding a new population

Neutral Theory

Neutralist-Selectionist Controversy

  • Selectionists saw adaptation and assumed that most variation at the genetic level had an effect on fitness
  • Neutralists felt that most genetic variation had no effect on the phenotype
  • The intensity of the controversy meant what it always means: both sides had data to back them up but not so much data that the other side had to give in
  • the result of such controversies is always the same:  both viewpoints are integrated into an overall understanding
  • evolutionary biology is in the process of integrating neutralism with selectionism
    • Most alleles are neutral (of equal fitness), some are harmful, and some are beneficial (selected)
    • Neutrality is useful
    • can be used to calibrate a "molecular clock" based on the rate at which new mutations arise and become fixed

Neutral mutation rate -u0

  • u0 is the rate of mutations at a locus per gamete per generation
  • most point mutations in a gene occur at unique sites (if they occur at the same site along the sequence, a new mutation would wipe out the presence of the previous mutation)
    • some sites may be functionally constrained because changing the base pair would change the codon and the amino acid at that site in the protein
    • if the amino acid is key to the function of the protein, any change may be harmful, not neutral (or, possibly helpful and still not neutral)
      • e.g. - an amino acid that is important to the catalytic function of the protein
  • The neutral mutation rate should equal the rate of fixation of mutations
    • fixation rate will underestimate the mutation rate to the degree than new mutations occur at the same site
    • estimation of  can be done if you compare two sequences in two species and can use the fossil record to date the time of the split (or, if you have genes in two allopatric populations and you can date the time of the population split and assume no migration)
      • the problem of multiple changes at one site again can invalidate this process and it gets worse as the time since the split increases
      • it is also possible to correct for the likelihood of multiple hits
  • Thus, at a locus, new mutations constantly occur and fixation (in the sense of an allele  being "fixed" at a frequency of zero) constantly removes alleles, which will produce a balance over time
    • The proportion of the population that are heterozygous at a locus is a way to measure the balance of these forces and will depend on the neutral fixation rate and the population size (which determines the rate of loss of alleles due to fixation) and are related as:

Drift and Flow

Genetic Drift within a population will move the population toward fixation of one allele at any locus

Gene Flow of alleles from other population will bring in alleles and counter the effect of drift

  • In populations where only drift and flow are occurring, these opposing forces produce an equilibrium where loss of alleles due to drift is balanced by gain of alleles through flow

F statistics can be used to predict the equilibrium point

  • We know that FST is related to the variation of allele frequency among populations from the lecture on genetic variation

  • FST is also approximately estimated with the formula below that relates it to population size and migration rate

  • Migration rates are notoriously hard to estimate as they can vary greatly in time and it is often impossible to determine which are immigrants and which are not
  • FST is often easier to measure as our ability to determine genotype becomes more accurate and facile

  • So, FST is often a better way to determine gene flow than direct methods such as you learn in ecology class (mark-recapture, for instance), if (and it's a big if) you can assume that other factors (selection, assortative mating, mutation) are insignificant in comparison to drift and flow.

Coalescence, Drift and Population History

Coalescent Theory is based on the idea that genes present in today's populations have a single ancestor some time in the past

  • This theory allows for migration among populations but only among known populations with known allele frequencies
  • Genes coming from some unknown source will invalidate the methodology.  Sources of such genes might be:
    • intraspecific - from unknown or unsampled populations of the same species
    • interspecific - new alleles arriving in a population by genetic exchange with another species - (Horizontal Gene Transfer)
  • Coalescent theory depends on the process of random loss of alleles due to genetic drift

At that time in the past when the ancestral allele existed, the population may have been (and almost surely was) composed of more that one allele but the other alleles lineages became extinct and, therefore, their descendants are not present in the current population

If one can assume that all of the alleles present in the population arose due to a mutation of a pre-existing allele in the population and that the rate of evolution is set by the mutational process and neutral theory (i. e. selection is not operating) then one can ask some interesting questions:

  • When did the ancestor of these alleles exist?
  • For subdivided populations with no migration, one can also ask about the maximal age of the populations
Last updated January 27, 2009