Genetic drift
Genetic drift is random change in allele frequency caused by finite-population sampling. Unlike natural selection, it does not require one allele to have a systematic fitness advantage.
A finite sampling example
Suppose allele \(A\) currently has frequency
\[p=0.5.\]If the next generation contains only a small number of allele copies, it is unlikely that exactly half of them will always be \(A\). One replicate population may move to \(p=0.6\), another to \(p=0.4\), even when the alleles have identical fitness.
Expected change can be zero while realised change is not
Under neutral drift, the expected next allele frequency is often
\[\boxed{E[p_{n+1}\mid p_n]=p_n}.\]This does not mean
\[p_{n+1}=p_n\]in every population. It means that the average over many replicate populations equals the current frequency.
Why population size matters
Sampling variability becomes smaller when more allele copies are sampled. In a diploid Wright–Fisher population of \(N\) individuals, there are \(2N\) allele copies in each generation.
If the current frequency is \(p\), the next-generation frequency has conditional variance
\[\boxed{\operatorname{Var}(p_{n+1}\mid p_n=p)=\frac{p(1-p)}{2N}}.\]Thus drift is stronger when \(N\) is small.
Where drift is strongest in frequency space
The factor
\[p(1-p)\]is largest at \(p=1/2\) and tends to zero near \(p=0\) or \(p=1\). So the one-generation sampling variance is largest at intermediate allele frequencies.
Fixation and loss
Without mutation or migration, the boundary states
\[p=0\qquad\text{and}\qquad p=1\]are absorbing in standard neutral finite-population models.
If \(p=0\), allele \(A\) has been lost. If \(p=1\), it has become fixed.
Neutral fixation probability
For a neutral allele with initial frequency \(p_0\), the probability of eventual fixation is
\[\boxed{P(\text{fixation})=p_0}.\]Correspondingly,
\[\boxed{P(\text{loss})=1-p_0}.\]For a single new neutral copy in a diploid population of size \(N\),
\[p_0=\frac{1}{2N},\]so its fixation probability is \(1/(2N)\).
Drift does not have a preferred direction
Neutral drift can increase or decrease an allele frequency. The direction of a particular change is random.
Across many replicate populations, some alleles rise while others fall. Over time, however, more populations reach fixation or loss.
Loss of genetic variation
For two alleles with frequencies \(p\) and \(q=1-p\), expected heterozygosity is
\[\boxed{H=2pq=2p(1-p)}.\]Drift tends to reduce heterozygosity because replicate populations gradually move toward the absorbing states \(p=0\) and \(p=1\), where
\[H=0.\]Expected decline in heterozygosity
In the standard neutral diploid Wright–Fisher model, expected heterozygosity satisfies
\[\boxed{E[H_{n+1}]=\left(1-\frac{1}{2N}\right)E[H_n]}.\]Therefore smaller populations lose genetic variation more rapidly.
Effective population size
Real populations often do not behave genetically like an ideal population containing exactly the census number of individuals. Unequal reproductive success, changing population size or unequal sex ratios can alter the strength of drift.
This motivates the effective population size \(N_e\): the size of an idealised population that would experience approximately the same amount of drift as the real population.
Bottlenecks
A temporary sharp reduction in population size can cause strong drift. Even if the population later becomes large again, genetic variants lost during the bottleneck do not automatically return.
Founder effects
When a new population is established by a small number of individuals, its initial allele frequencies may differ substantially from those of the source population simply because the founders are a small sample.
Subsequent drift can amplify these differences.
Drift and selection together
Selection gives a systematic tendency, while drift adds random sampling variation. A beneficial allele is therefore not guaranteed to increase in every generation or even to survive when initially rare.
The relative importance of selection and drift depends on population size and the strength of selection.
Drift versus mutation
Drift removes variation through random fixation and loss, while mutation introduces new variation. In long-run population-genetic models, the observed amount of variation can reflect a balance between these opposing processes.
Drift versus migration
Independent drift can make separated populations genetically different. Migration can oppose this divergence by moving alleles between populations.
Deterministic models miss trajectory variability
A deterministic equation may predict a single allele-frequency trajectory. A stochastic drift model instead produces a probability distribution over possible future frequencies.
This makes questions such as fixation probability, extinction probability and time to absorption inherently stochastic.
What genetic drift is not
Genetic drift is not mutation, not natural selection and not simply measurement noise. It is biological randomness produced by finite reproductive sampling.
Transition to the Wright–Fisher model
The ideas above describe what drift does. The next lesson introduces the classical Wright–Fisher model, which specifies exactly how the \(2N\) allele copies in one generation are sampled to form the next generation.