5.1 Genetic drift #
The study of Genetic drift provides fundamental principles governing cellular architecture, molecular interactions, and physiological regulation.
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5.1.1 Sampling in a Wright–Fisher population #
Genetic drift is allele-frequency change from sampling error in a finite population. In the Wright–Fisher model, N diploids carry 2N copies at an autosomal locus. The next generation is a random draw of 2N copies from the current frequency p. The variance of the new frequency is p(1 − p)/(2N), largest at intermediate p and larger, for a given p, when N is small.
If a draw ever hits 0 or 1, and there is no mutation, the population stays there. Fixation is absorption at 1, loss at 0. Every neutral allele in a finite population is eventually fixed or lost. The probability that a neutral allele is the one fixed equals its current frequency. A new mutant therefore fixes with probability 1/(2N). Drift is a random walk with two traps, not a blur around a stable mean.
Conditional on fixation, a new neutral allele takes on the order of 4Ne generations to get there. Isolated populations with the same selection and no migrants therefore become different at neutral loci. Different alleles get trapped.
5.1.2 Effective size #
Census size, N, is a head count. Effective size, Ne, is the size of an ideal Wright–Fisher population that would drift at the same rate as the real one. Ne is almost always smaller than N.
Fluctuating size pulls long-term Ne towards the harmonic mean of the generation sizes, which is dominated by the small generations. A population that is huge for ninety-nine years and tiny in the hundredth has an Ne closer to the crash than an ordinary average suggests. With Nm breeding males and Nf breeding females, Ne is about 4 Nm Nf / (Nm + Nf). One male and a hundred females give Ne near 4, not near 101. If the variance V in offspring number exceeds the ideal (about 2, matching a mean of 2 in a constant diploid population), Ne is about 4N / (V + 2), below N. Overlapping generations and structure usually push Ne down further.
Ne/N is not a constant. For many animals it is often on the order of one tenth, and it varies widely. The useful question is which reducing factor is severe: a harem, a crash, or a few adults supplying most of the offspring.
5.1.3 Founders and bottlenecks #
A founder effect is the sample carried by the few colonists who start a population. A bottleneck is a crash in a population that already exists. Rare alleles are missed first. Heterozygosity falls. Allele number falls faster than heterozygosity and recovers only by mutation or immigration, on a timescale of order Ne generations.
The northern elephant seal was hunted in the nineteenth century to a very small remnant and later recovered in head count. Diversity stayed low relative to the southern elephant seal, which did not pass through the same crash. That is a bottleneck in heterozygosity, not a demonstration that bottlenecks cause adaptation. Mayr’s stronger claim, that founder events trigger genetic revolutions which found species, is not established. The frequency shift itself is ordinary drift at small N.
Census size can rebound in a few generations while Ne, averaged through the crash, stays small. A head count used as if it were Ne overestimates resistance to further drift and to inbreeding.
5.2 Gene flow #
5.2.1 Migration homogenises #
Gene flow is the movement of alleles among populations by migrants who breed. Each generation a fraction m of local gene copies is replaced from elsewhere, and the local frequency moves towards the source. With no selection and no mutation, gene flow erases the differences drift builds.
In the island model, equilibrium differentiation at a neutral locus is about FST = 1 / (1 + 4 Ne m). FST is Wright’s measure of how different populations are, relative to the variation inside them. When Ne m is much greater than 1, neutral frequencies stay similar. When it is much less than 1, drift differentiates them. “About one migrant per generation prevents complete neutral differentiation” is this equation, not a field law. It assumes the island model at equilibrium, and it applies to neutral markers. It is not a rule of management: one migrant may homogenise neutral markers and do nothing for a population that is failing demographically. Loci under strong selection can stay different at migration rates that erase neutral differences.
5.2.2 Migration against selection #
Where selection differs among places, migration and selection oppose each other. A locally favoured allele is swamped if migrants arrive faster than selection increases it, and maintained if selection is strong relative to m. The stable pattern is a cline: the allele common in the habitat that favours it, rare outside, with the width of the transition set by dispersal distance and by the strength of selection.
Gene flow can also deliver an allele that selection then spreads. That is adaptive introgression. Chapter 11’s Tibetan case is one. “Migration” does not say whether the arriving allele is helpful. The fitnesses decide after it arrives.
A phenotypic difference between two places may be plasticity, genetic divergence, or both. A transplant or a common garden separates them. If the difference vanishes when both populations are reared in both places, neither selection nor drift has been shown to have changed them. If it persists, the cause of the genetic difference is still open. Drift and selection both produce genetic differences.
5.3 Non-random mating #
5.3.1 Inbreeding changes who is homozygous #
Inbreeding is mating between relatives. It raises the chance that the two alleles in an individual are identical by descent. The inbreeding coefficient, F, is that probability. Genotype frequencies become p²(1 − F) + pF, 2pq(1 − F), and q²(1 − F) + qF. Heterozygotes fall by the factor (1 − F). Allele frequencies do not move. Inbreeding rearranges genotypes given p. It is not a force on p. One generation of random mating, if it can be arranged, restores Hardy–Weinberg proportions.
Assortative mating sorts by phenotype, not by pedigree. Positive assortment increases homozygosity at the loci that build the trait being sorted on. It does not make the whole genome homozygous the way a pedigree of cousin marriages does, and it can contribute to reproductive isolation. Neither process, alone, changes allele frequencies.
Structure imitates inbreeding in a pooled sample. If two populations with different p are combined, and Hardy–Weinberg is calculated from the average p, heterozygotes are fewer than predicted. This is the Wahlund effect. The deficit is twice the variance of p among the groups. A reported excess of homozygotes is ambiguous until structure is ruled out.
5.3.2 Inbreeding depression #
Inbreeding depression is the fall in fitness that often comes with increased homozygosity. Under the dominance explanation, rare deleterious alleles that are partly recessive are exposed in homozygotes. Under overdominance, heterozygotes are intrinsically fitter and inbreeding makes them rarer. The dominance explanation accounts for most of the depression that has been dissected. Heterozygote advantage exists — sickle cell is the clear case — and it is not the main cost of routine inbreeding.
Inbreeding itself did not change allele frequencies. Selection on the newly exposed homozygotes can change them afterwards. That second step is selection. Purging, the removal of deleterious alleles once they are exposed, is real and incomplete: many alleles are only partly exposed, and mutation keeps adding new ones.
Small populations both drift and inbreed. Drift changes p. Inbreeding, given p, changes the proportion of homozygotes. A bottleneck can do both at once, because the survivors are few and related. Calling that event only “drift”, or only “inbreeding”, drops half of what happened to the genotypes.
5.4 Key terms, summary, and self-check #
Key terms. Genetic drift; fixation; effective population size; harmonic mean; founder effect; bottleneck; gene flow; FST; cline; inbreeding coefficient; assortative mating; Wahlund effect; inbreeding depression.
Summary. Drift is binomial sampling of 2N copies, stronger at small N, and it ends in fixation or loss with probability equal to current frequency for a neutral allele. Ne matches that rate for a real population and is reduced by crashes, unequal sex ratio, and high variance in family size. Neutral fixation takes on the order of 4Ne generations. Migration pulls populations together and, in a simple model, keeps neutral FST low when Ne m is large; local selection can resist that pull or be swamped by it. Inbreeding raises homozygosity according to F, does not change allele frequencies, and exposes deleterious recessives.
Self-check.
1. A neutral allele is at frequency 0.2. What is its probability of eventual fixation, and why does the sampling variance shrink as N grows?
2. A population is founded by one breeding male and twenty breeding females. Why is Ne far below 21?
3. Why does a single crash dominate long-term Ne?
4. A sample has fewer heterozygotes than Hardy–Weinberg predicts. Give two explanations that are not selection.
5. Under what condition does migration stop a locally favoured allele from being maintained? Does “one migrant per generation” decide it?
