[1] Idealised populations are those following simple one-locus models that comply with assumptions of the neutral theory of molecular evolution.
The effective population size is normally smaller than the census population size N, partly because chance events prevent some individuals from breeding, and partly due to background selection and genetic hitchhiking.
[4] This measurement was achieved through studying changes in the frequency of a neutral allele from one generation to another in over 100 replicate populations.
More commonly, effective population size is estimated indirectly by comparing data on current within-species genetic diversity to theoretical expectations.
According to the neutral theory of molecular evolution, an idealised diploid population will have a pairwise nucleotide diversity equal to 4
The effective population size can therefore be estimated empirically by dividing the nucleotide diversity by 4
More advanced methods, permitting a changing effective population size over time, have also been developed.
[6] The effective size measured to reflect these longer timescales may have little relationship to the number of individuals physically present in a population.
[7] Measured effective population sizes vary between genes in the same population, being low in genome areas of low recombination and high in genome areas of high recombination.
Genetic hitchhiking can cause neutral mutations to have sojourn times proportional to log(N): this may explain the relationship between measured effective population size and the local recombination rate.
[6] A survey of publications on 102 mostly wildlife animal and plant species yielded 192 Ne/N ratios.
Accordingly, the ratios ranged widely from 10-6 for Pacific oysters to 0.994 for humans, with an average of 0.34 across the examined species.
[14][15] This limit to selection in a real population may be captured in a toy Wright-Fisher simulation through the appropriate choice of Ne.
[18] Today, the effective population size is usually estimated empirically with respect to the amount of within-species genetic diversity divided by the mutation rate, yielding a coalescent effective population size that reflects the cumulative effects of genetic drift, background selection, and genetic hitchhiking over longer time periods.
[14] In the Wright-Fisher idealized population model, the conditional variance of the allele frequency
When N is large, Ne approximately equals N, so this is usually trivial and often ignored: If population size is to remain constant, each individual must contribute on average two gametes to the next generation.
The vast majority of individuals may have no offspring, and the next generation stems only from a small number of individuals, so The effective population size is then smaller, and given by: Note that if the variance of k is less than 2, Ne is greater than N. In the extreme case of a population experiencing no variation in family size, in a laboratory population in which the number of offspring is artificially controlled, Vk = 0 and Ne = 2N.
[20] For the idealized population, the inbreeding coefficients follow the recurrence equation Using Panmictic Index (1 − F) instead of inbreeding coefficient, we get the approximate recurrence equation The difference per generation is The inbreeding effective size can be found by solving This is When organisms live longer than one breeding season, effective population sizes have to take into account the life tables for the species.
Further, define the following age structure characteristics: The generation time is calculated as Then, the inbreeding effective population size is[21] Similarly, the inbreeding effective number can be calculated for a diploid population with discrete age structure.