ZOOL 304

Analysis of Genetic Drift

• Outside link:  Genetic drift
   
• INTRODUCTION:  Key points regarding genetic drift
   

• For a readable discussion of history, assumptions, and limitations of models in population genetics, see:
        John Wakeley (2005) The limits of theoretical population genetics, Genetics 169: 1-7.

The following notes (and quoted section headings) are adapted from Chapter 6 of Mark Ridley's textbook, EVOLUTION, 2nd ed. (1996), Blackwell Science, Inc., Cambridge MA. ISBN 0-86542-495-0.

• Random sampling.
• Genetic drift.
• The founder effect.
• Allele substitution by drift.
• No "equilibrium" in small populations.
• The "march to homozygosity."
• Polymorphism resulting from neutral mutation and drift.
• Effective population size.

Introduction

• We often introduce population genetics using models, such as the Hardy-Weinberg equilibrium, which assumes large populations in which drift is unimportant.  Note that in any finite population, the Hardy-Weinberg model gives an expectation (i.e., a most probable outcome) rather than a deterministic prediction.
• To analyze genetic drift, we assume that alleles are neutral so that selection is unimportant.  
• In real life, we must remember that drift AND selection are both important.  Even when alleles appear neutral, small differences in selection coefficient may in fact exist, so selection must never be completely disregarded.  But drift can override weak selection if a populations is sufficiently small, so drift can never be ignored either.

Key points regarding genetic drift.

• Allele frequencies fluctuate at random, but eventually become fixed.
• Neutral genetic variation in a population is eventually lost to drift.
• Initially similar sub-populations will diverge in allele frequencies, and may eventually become fixed for different alleles (depending on gene flow).
• The probability, at any given time, that an allele will eventually become fixed equals the frequency of the allele at that time.
• Note that these statements all refer to statistical expectations (i.e., most probable outcomes) rather than deterministic predictions.
• The rate at which these events occur is greater for small populations. The size that matters is the effective population size.
  • For an allele which eventually becomes fixed, the average time to reach fixation in a population of size N, is 4N generations.
  • Drift decreases heterozygosity by 1 / 2N per generation.

"Successive generations are a random sample from the parental gene pool."

• Note that for finite populations, the idealized Hardy-Weinberg model gives an expectation (i.e., a most probable outcome) rather than a deterministic prediction.
• For example, if we were to sample 10 gametes at random from a gene pool in which A and a alleles have frequency 0.5, the most likely outcome would be 5 of each, for frequencies of 0.5 A and 0.5 a in the next generation.  That is, indeed, the Hardy-Weinberg expectation.
• But do note that the most-likely Hardy-Weinberg expectation can be quite improbable.  The probability of the most likely outcome is actually less than 1 in 4 for this particular case of 10 gametes.
• The probability that an actual random sample will exactly match the most likely expected outcome actually becomes lower, the bigger sample (although the relative size of the probable discrepency grows smaller.)
• Understand that random samples are NOT selection.

• Three processes - drift, founder effect, and inbreeding -- all operate most strongly in small populations.  And all reduce heterozygosity.
  • Drift occurs gradually over many generations in a stable population.
  • The founder effect results from a single small sample when a population is first founded.
  • Inbreeding can reduce the effective size of a population.
• The combination of drift in conjunction with neutral mutation creates and maintains allele polymorphism.

"The frequency of alleles with the same fitness will change at random through time in a process called genetic drift."

• We give this name, genetic drift, to the effect of random changes in allele frequency, because even though it is itself a random process it leads to definite expectations when many loci or many populations are considered.

"A small founder population may have a nonrepresentative sample of the ancestral population's genes."

• This founder effect is the result of a single small random sample.
• The founder effect is not the same as genetic drift, since drift is cumulative change over many generations.
• Both drift and founder effect result from random sampling.
• A sizable population with a high frequency of a deleterious allele can be explained by the founder effect, by considering that founder allele frequencies can be maintained during population growth (by standard Hardy-Weinberg expectation), while selection may take many generations to reduce the frequency of the deleterious allele (especially if it is recessive with respect to fitness).

"One gene can be substituted for another by random drift."

• This is a fundamental concept.  When averaged over many loci and many populations, random genetic drift turns out to be a very effective agency for evolutionary change (but not for adaptation).
• In a diploid population of N individuals, there are 2N genes at a given locus.  Consider what can happen to a new, neutral mutation.  ("Neutral" means that it has no selective advantage or disadvantage.)
  • A new mutation, present as only single copy in the population, has a frequency of 1 / (2N).
  • The chance that a new neutral mutation will be lost from the population by chance alone is (2N - 1) / (2N), or (equivalent expression) 1 - 1 / 2N. If N is very large, this chance is nearly one (a probability of one is certainty).
  • The chance that a new neutral mutation will eventually be fixed in the population is 1 / 2N.  If N is very large, this chance is very small (near zero).
• That chance that any particular new neutral mutation is fixed is therefore low.  But what happens if new neutral mutations are continually introduced into the populations at rate u per gene per generation?
  • With 2N genes at any given locus in the population, in every generation there will be (on average) 2Nu new mutations.
  • Each of those alleles will be fixed with probability 1 / (2N).
  • Multiplying, we get 2Nu times 1 / (2N) = u per generation as the rate at which new alleles at each locus are fixed in a population.
  • Random drift thus leads to an expectation of a very definite average rate of neutral evolution by mutation and allele replacement.
• Remember.  Drift is evolution, but drift is NOT selection.  Allele replacement by drift is not adaptive.

"The Hardy-Weinberg 'equilibrium' is not an equilibrium in a small population.."

• The Hardy-Weinberg model does give the most likely expectation for gene frequencies at each generation.
• But, as noted above, in real populations this most likely expectation is actually quite improbable (like an unskillfully-thrown dart hitting the bull's-eye).
• Each bit of "noise", departing from the Hardy-Weinberg expectation, resets the gene frequencies for the next generation.
• So there is no "equilibrium", there is random drift with no stability until one or another (neutral) allele is fixed.
• Of course, selection, which is a deterministic process, can override drift if alleles do not all have equivalent fitness.

"Neutral drift over time produces a march to homozygosity."

• A so-called "march to homozygosity" is itself a probabilistic expectation, not a deterministic process such as the word "march" would imply.
• The "march to homozygosity" is predictable on average, when many alleles at many loci are considered.  But any particular allele will "drift" rather than "march" to homozygosity (or loss).
• To make the concept a bit more intuitive, consider a locus at which there are as many different alleles as there were genes in the population.  Then the odds that each and every one of these alleles would be passed along so that there would be exactly one of each in the next generation, would be fantastically low.  In such a case, some loss of heterozygosity would indeed be expected at every generation (and, of course, with any loss of heterozygosity, there is a gain in homozygosity).

"A calculable amount of polymorphism will exist in a population because of neutral mutation."

• This is an essential concept for understanding the Neutral Theory of molecular evolution.
• The process of genetic drift leads to eventual homozygosity, IF no new alleles are introduced (and, of course, only in the absence of a deterministic process like selection that maintains polymorphism).
• But IF there is a continual supply of new neutral alleles (i.e., mutation), then drift assures the likelihood that some fraction of those alleles will increase in frequency and thereby increase the overall heterozygosity.
• Because there are so many genetic loci, so many ways to produce neutral alleles, and so much time for drift to operate, the statistical predictions of drift lead to very reliable conclusions.

Effective population size.

• Actual population count is NOT the same as the theoretical effective population size.  Reasons include:
  • Some countable individuals may not breed, for a wide variety of biological reasons, such as polygyny (in which a few males mate with "harems" of many females while many other males fail to mate altogether).
  • Individuals may vary significantly in fertility, even if all do reproduce.
  • Population size may vary from generation to generation, with significant "bottlenecks" of low population size.
  • Subdivided population or non-random mating may accelerate inbreeding over the expectation of panmixus.
• The effective population size is usually smaller than actual population count.  Effective population size will be smaller than census size if:
  • Some individuals do not breed.
  • Individuals vary greatly in number of progeny.
  • Numbers of males and females are not equal.
  • Generations overlap.
  • Population size fluctuates.
  • Mating is not panmictic, which may result from:
    • Subdivided population structure.
    • Geographic distance.
    • Mating among relatives (in the extreme case, self-fertilization).
• The effective population size is the size for which expected heterozygosity matches observed heterozygosity.
  • Any factor which decreases effective population size will decrease the expected heterozygosity (or, equivalently, increase the homozygosity, or inbreeding) of the actual population.
• Effective population size significantly affects the expectations of drift, founder effect, and march to homozygosity.

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