Genetic drift and population size
Genetic drift and population size
Long ago it was proved that the rate of fixation of neutral
alleles in a population was effectively independent of the
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
What is the effect of considering the fates of near
neutral alleles in genetic drift?
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
It appears to be widely thought that size of the effects of
genetic drift do not depend on the size of the population.
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.
The simulation plotted the results of varying three variables:
Organisms were modelled as being either normal or mutated.
- 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.
The results are illustrated by the following graph:
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
The other lines represent the fate of near-neutral
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.
Firstly, note that selection is not responsible for the
fixation of any of the deleterious mutations in
this experiment. That is because the mutant alleles were all
deleterious. Selection favours extinction of the
mutant alleles - not their fixation. The only force
that could make these alleles reach fixation is genetic
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
Exact neutrality is rare
If exactly neutral alleles were rare, this result might not be
seen as being of great significance.
However exact neutrality is so rare as to be practically
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.
- Neutral Theory and effective population size