Genetic drift and population size

Genetic drift and population size

However this result appears to have been widely interpreted as meaning that the magnitude of the effects of genetic drift do not depend on population size.

However this notion apparently equates "genetic drift" with "the evolution of neutral alleles".

Genetic drift and near neutral alleles

The conclusion about the effect of population size on genetic drift is reversed.

If near-neutral alleles are considered, in can be seen that the probability of fixation of such alleles due to genetic drift depends critically on the population size.

Genetic drift simulation

So - to illuminate the issue - I performed a computer simulation of genetic drift of near-neutral alleles.

The simulation modelled the effect of population size on the probability of fixation of slightly-deleterious alleles.

Methodology

• Population size;
• Probability of fixation;
• Relative fitness of deleterious mutants;

The initial population always consisted of 50% mutants.

The population size during each run was kept fixed.

Individuals were chosen for reproduction and death at random.

Mutant indivduals had a reduced chance of successful reproduction - as specified by the "relative mutatant fitness" parameter.

The probability of fixation was calulated by performing each run 150 times - and seeing on what proportion of the runs the deleterious mutant allele reached fixation.

Each run continued until the mutant alleles either reached fixation - or were totally eliminated from the population.

Results

The graph has an element of noise - since the simulation was stochastic - and the runs were only repeated 150 times.

The first, white line represents mutants with a relative fitness of 1.0. This is the classical case of neutral alleles.

As predicted by theory, in this case, the probability of fixation of the mutant alleles does not depend on the population size.

The other lines represent the fate of near-neutral alleles.

As can be clearly seen, the probability of them reaching fixation due to the effect of genetic drift varies a good deal as the size of the population varies. Alleles furthest from neutrality are the most powerfully affected.

Discussion

The result illustrates that the effects of genetic drift on allele fixation typically depend on the population size - except in the case where the allele in question is exactly neutral.

This is intuitively obvious - since the cumulative effects of selection have longer to produce their effects in larger populations.

Exact neutrality is rare

However exact neutrality is so rare as to be practically non-existent.

Even junk DNA can affect reproductive success - since its sequence affects how restriction enzymes in viruses attach to it - since it can sometimes be expressed if stop codons get mutated - since duplicating different sequences required different nutrients - and so on.

The ubiquitous nature of near-neutrality means that the classical result of independence from population size is not of much practical significance.

In the real world, the magnitude of genetic drift - as measured by the rate of fixation of alleles it produces - is critically a function of the size of the population.

In a large population, an allele is much less likely to be effectively "neutral" in the first place - and so the predictions of neutral theory are likely to be relevant at a much smaller number of loci.

This is basically why you get founder effects in small populations and more stability in larger ones - there are fewer effectively-neutral alleles (and thus reduced possibilities for genetic drift) in larger populations.

References

1. Neutral Theory and effective population size