Effective population size

Abstract

What is it? An aid to calculation in population genetics, introduced by Sewall Wright. The rate of change of the genetic make-up of a population by genetic drift – fluctuations in allele frequencies caused by random sampling – is inversely related to the effective population size, Ne. Ne is measured with reference to an ideal ‘Wright–Fisher’ population. This has a fixed number of N diploid breeding individuals, with no distinction of sex. Each new generation is formed by sampling genes randomly from the parents of the previous generation. The rate at which selectively neutral variability is lost from the population is then equal to 1/(2N). In the messier real world, there may be two different sexes, population size may change, individuals may differ in their reproductive success and there may be overlapping generations. If you are clever enough, you can write down an expression for the rate of drift per generation in such cases. This is then equated to 1/(2Ne). Ne is usually substantially smaller than the census number of breeding individuals.Why is it useful? Genetic drift is a major factor in DNA sequence evolution. To make sense of the data, we need evolutionary models which include genetic drift. By plugging Ne into the relevant equations, we can write down general expressions, instead of having to work out new results for each type of population. For example, a favourable new mutation which increases the fitness of its carriers by a small amount s has a chance of spreading of 2(Ne/N)s in a population of size N and effective size Ne. Reducing Ne relative to N thus reduces the chance that a favourable mutation will spread.Similarly, the chance that a deleterious mutation can get fixed against selection is increased by a reduction in Ne, and approaches the value for a neutral mutation when |Nes|⪡1. The equilibrium level of within-population variability for neutral or nearly-neutral variants is controlled by the product of the mutation rate and Ne, so that Ne plays an important role in the interpretation of data on single nucleotide polymorphisms, a major focus of contemporary human genetics.What influences Ne? If population size changes, the long-term value of Ne, which controls the level of neutral variability, is the harmonic mean (reciprocal of the mean of the reciprocals) of the series of values for each generation. A population that has recently expanded, like our own, has a much smaller Ne than indicated by its current size. In the human case, levels of variability indicate that Ne is close to 10,000, reflecting the population size in the remote past. Ne is affected by mode of inheritance, so that X-linked, Y-linked and organelle genes each have their own Ne values, which differ from that for autosomal genes. Ne is also influenced by natural or artificial selection, which induce heritable variation in fitness. Selection at sites linked to a gene under study may greatly reduce its Ne value. This means that genomic regions with low levels of genetic recombination, where genes tend to be tightly linked to each other, may have lower than average levels of variability and adaptation.