Effective population size

The effective population size is the number of individuals that an idealised population would need to have in order for some specified quantity of interest to be the same in the idealised population as in the real population. Idealised populations are based on unrealistic but convenient simplifications such as random mating, simultaneous birth of each new generation, constant population size, and equal numbers of children per parent. In some simple scenarios, the effective population size is the number of breeding individuals in the population. However, for most quantities of interest and most real populations, the census population size N of a real population is usually larger than the effective population size Ne. The same population may have multiple effective population sizes, for different properties of interest, including for different genetic loci. The effective population size is the number of individuals that an idealised population would need to have in order for some specified quantity of interest to be the same in the idealised population as in the real population. Idealised populations are based on unrealistic but convenient simplifications such as random mating, simultaneous birth of each new generation, constant population size, and equal numbers of children per parent. In some simple scenarios, the effective population size is the number of breeding individuals in the population. However, for most quantities of interest and most real populations, the census population size N of a real population is usually larger than the effective population size Ne. The same population may have multiple effective population sizes, for different properties of interest, including for different genetic loci. The effective population size is most commonly measured with respect to the coalescence time. In an idealised diploid population with no selection at any locus, the expectation of the coalescence time in generations is equal to twice the census population size. The effective population size is measured as within-species genetic diversity divided by four times the mutation rate μ {displaystyle mu } , because in such an idealised population, the heterozygosity is equal to 4 N μ {displaystyle 4Nmu } . In a population with selection at many loci and abundant linkage disequilibrium, the coalescent effective population size may not reflect the census population size at all, or may reflect its logarithm. The concept of effective population size was introduced in the field of population genetics in 1931 by the American geneticist Sewall Wright. Depending on the quantity of interest, effective population size can be defined in several ways. Ronald Fisher and Sewall Wright originally defined it as 'the number of breeding individuals in an idealised population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration'. More generally, an effective population size may be defined as the number of individuals in an idealised population that has a value of any given population genetic quantity that is equal to the value of that quantity in the population of interest. The two population genetic quantities identified by Wright were the one-generation increase in variance across replicate populations (variance effective population size) and the one-generation change in the inbreeding coefficient (inbreeding effective population size). These two are closely linked, and derived from F-statistics, but they are not identical. Today, the effective population size is usually estimated empirically with respect to the sojourn or coalescence time, estimated as the within-species genetic diversity divided by the mutation rate, yielding a coalescent effective population size. Another important effective population size is the selection effective population size 1/scritical, where scritical is the critical value of the selection coefficient at which selection becomes more important than genetic drift. In Drosophila populations of census size 16, the variance effective population size has been measured as equal to 11.5. This measurement was achieved through studying changes in the frequency of a neutral allele from one generation to another in over 100 replicate populations. For coalescent effective population sizes, a survey of publications on 102 mostly wildlife animal and plant species yielded 192 Ne/N ratios. Seven different estimation methods were used in the surveyed studies. 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. A genealogical analysis of human hunter-gatherers (Eskimos) determined the effective-to-census population size ratio for haploid (mitochondrial DNA, Y chromosomal DNA), and diploid (autosomal DNA) loci separately: the ratio of the effective to the census population size was estimated as 0.6–0.7 for autosomal and X-chromosomal DNA, 0.7–0.9 for mitochondrial DNA and 0.5 for Y-chromosomal DNA. References missingIn the Wright-Fisher idealized population model, the conditional variance of the allele frequency p ′ {displaystyle p'} , given the allele frequency p {displaystyle p} in the previous generation, is Let var ^ ( p ′ ∣ p ) {displaystyle {widehat {operatorname {var} }}(p'mid p)} denote the same, typically larger, variance in the actual population under consideration. The variance effective population size N e ( v ) {displaystyle N_{e}^{(v)}} is defined as the size of an idealized population with the same variance. This is found by substituting var ^ ( p ′ ∣ p ) {displaystyle {widehat {operatorname {var} }}(p'mid p)} for var ⁡ ( p ′ ∣ p ) {displaystyle operatorname {var} (p'mid p)} and solving for N {displaystyle N} which gives