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Effective population size
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Effective population size
The effective population size (Ne) is the size of an idealised population that would experience the same rate of genetic drift as the real population. Idealised populations are those where each locus evolves independently, following the assumptions of the neutral theory of molecular evolution. The effective population size is normally smaller than the census population size N. This can be due to chance events prevent some individuals from breeding, to occasional population bottlenecks, to background selection, and to genetic hitchhiking.
The same real population could have a different effective population size for different properties of interest, such as genetic drift (or more precisely, the speed of coalescence) over one generation vs. over many generations. Within a species, areas of the genome that have more genes and/or less genetic recombination tend to have lower effective population sizes, because of the effects of selection at linked sites. 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. Some versions of the effective population size are used in wildlife conservation.
In a rare experiment that directly measured genetic drift one generation at a time, in Drosophila populations of census size 16, the effective population size was 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.
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 4Ne, where is the mutation rate. The effective population size can therefore be estimated empirically by dividing the nucleotide diversity by 4. This captures the cumulative effects of genetic drift, genetic hitchhiking, and background selection over longer timescales. More advanced methods, permitting a changing effective population size over time, have also been developed.
The effective size measured to reflect these longer timescales may have little relationship to the number of individuals physically present in a population. 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. Sojourn times are proportional to N in neutral theory, but for alleles under selection, sojourn times are proportional to log(N). 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.
If the recombination map of recombination frequencies along chromosomes is known, Ne can be inferred from rP2 = 1 / (1+4Ne r), where rP is the Pearson correlation coefficient between loci. This expression can be interpreted as the probability that two lineages coalesce before one allele on either lineage recombines onto some third lineage.
The population size might not be constant over time, and thus neither might the effective population size (defined as coalescence speed). With a constant population size, we expect larger pairwise Hamming distance between sequences to be rarer. Under population expansion, an intermediate Hamming distance is instead most common; this is seen for humans. A skyline plot more directly describes coalescence speed over time. The pairwise sequential Markovian coalescent and multiple sequential Markovian coalescent take the average of skyline plots over many loci. An alternative approach infers effective population size over time, together with migration among populations, using the allele frequency spectrum, describing how often alleles are rare versus common. Yet another approach exploits runs of homozygosity to incorporate information from recombination events.
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Effective population size
The effective population size (Ne) is the size of an idealised population that would experience the same rate of genetic drift as the real population. Idealised populations are those where each locus evolves independently, following the assumptions of the neutral theory of molecular evolution. The effective population size is normally smaller than the census population size N. This can be due to chance events prevent some individuals from breeding, to occasional population bottlenecks, to background selection, and to genetic hitchhiking.
The same real population could have a different effective population size for different properties of interest, such as genetic drift (or more precisely, the speed of coalescence) over one generation vs. over many generations. Within a species, areas of the genome that have more genes and/or less genetic recombination tend to have lower effective population sizes, because of the effects of selection at linked sites. 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. Some versions of the effective population size are used in wildlife conservation.
In a rare experiment that directly measured genetic drift one generation at a time, in Drosophila populations of census size 16, the effective population size was 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.
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 4Ne, where is the mutation rate. The effective population size can therefore be estimated empirically by dividing the nucleotide diversity by 4. This captures the cumulative effects of genetic drift, genetic hitchhiking, and background selection over longer timescales. More advanced methods, permitting a changing effective population size over time, have also been developed.
The effective size measured to reflect these longer timescales may have little relationship to the number of individuals physically present in a population. 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. Sojourn times are proportional to N in neutral theory, but for alleles under selection, sojourn times are proportional to log(N). 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.
If the recombination map of recombination frequencies along chromosomes is known, Ne can be inferred from rP2 = 1 / (1+4Ne r), where rP is the Pearson correlation coefficient between loci. This expression can be interpreted as the probability that two lineages coalesce before one allele on either lineage recombines onto some third lineage.
The population size might not be constant over time, and thus neither might the effective population size (defined as coalescence speed). With a constant population size, we expect larger pairwise Hamming distance between sequences to be rarer. Under population expansion, an intermediate Hamming distance is instead most common; this is seen for humans. A skyline plot more directly describes coalescence speed over time. The pairwise sequential Markovian coalescent and multiple sequential Markovian coalescent take the average of skyline plots over many loci. An alternative approach infers effective population size over time, together with migration among populations, using the allele frequency spectrum, describing how often alleles are rare versus common. Yet another approach exploits runs of homozygosity to incorporate information from recombination events.