Novel multilocus measure of linkage disequilibrium to estimate past effective population size

Abstract

Linkage disequilibrium (LD) between densely spaced, polymorphic genetic markers in humans and other species contains information about historical population size. Inferring past population size is of interest both from an evolutionary perspective (e.g., testing the "out of Africa" hypothesis of human evolution) and to improve models for mapping of disease and quantitative trait genes. We propose a novel multilocus measure of LD, the chromosome segment homozygosity (CSH). CSH is defined for a specific chromosome segment, up to the full length of the chromosome. In computer simulations CSH was generally less variable than the r(2) measure of LD, and variability of CSH decreased as the number of markers in the chromosome segment was increased. The essence and utility of our novel measure is that CSH over long distances reflects recent effective population size (N), whereas CSH over small distances reflects the effective size in the more distant past. We illustrate the utility of CSH by calculating CSH from human and dairy cattle SNP and microsatellite marker data, and predicting N at various times in the past for each species. Results indicated an exponentially increasing N in humans and a declining N in dairy cattle. CSH is a valuable statistic for inferring population histories from haplotype data, and has implications for mapping of disease loci.

Figure 1.

(A) CSH and r² from the simulated data set. Results are averaged over all haplotype regions of a given length, and over 200 replicates. (B) Coefficient of variation of r² and CSH over all haplotype regions of the same length, across 200 replicates. (C) CSH from the data simulated with either an infinite alleles model or a stepwise mutation model. Results are averaged over all haplotype regions of a given length, and over 200 replicates.

Figure 1.

(A) CSH and r² from the simulated data set. Results are averaged over all haplotype regions of a given length, and over 200 replicates. (B) Coefficient of variation of r² and CSH over all haplotype regions of the same length, across 200 replicates. (C) CSH from the data simulated with either an infinite alleles model or a stepwise mutation model. Results are averaged over all haplotype regions of a given length, and over 200 replicates.

Figure 1.

(A) CSH and r² from the simulated data set. Results are averaged over all haplotype regions of a given length, and over 200 replicates. (B) Coefficient of variation of r² and CSH over all haplotype regions of the same length, across 200 replicates. (C) CSH from the data simulated with either an infinite alleles model or a stepwise mutation model. Results are averaged over all haplotype regions of a given length, and over 200 replicates.

Figure 2.

Chromosomal homozygosity for different lengths of chromosome (given the recombination rate) for populations: (A) CONS (constant population size), (B) LINI (linearly increasing population size), (C) LIND (linearly decreasing population size), and (D) EXPI (exponentially increasing population size). The expected value of chromosomal homozygosity, 1/(4Nc + 1), is given on each graph for the maximum and minimum population sizes of each population. Standard error bars indicate variation among the 50 replicates.

Figure 2.

Chromosomal homozygosity for different lengths of chromosome (given the recombination rate) for populations: (A) CONS (constant population size), (B) LINI (linearly increasing population size), (C) LIND (linearly decreasing population size), and (D) EXPI (exponentially increasing population size). The expected value of chromosomal homozygosity, 1/(4Nc + 1), is given on each graph for the maximum and minimum population sizes of each population. Standard error bars indicate variation among the 50 replicates.

Figure 3.

Simulated and estimated effective population size over time for four populations; (CONST) constant population size from 0 to 6050 generations ago; (LINI) increase in population size in the last 50 generations from 1000 to 5000; (LIND) decrease in population size in the last 50 generations from 1000 to 100; (EXPI) increase in population size in the last 50 generations from 1000 to 11290. SIM and EST identify the simulated and estimated population sizes for each population.

Figure 4.

(A) Chromosomal homozygosity for increasing lengths of haplotype from the data of Moffat et al. (2000). The upper (solid) line is the expected CSH when the effective population size is 5000. The lower (dashed) line is the expected CSH when the effective population size is 15,000. (B) Effective population size of the human population ancestral to the sample used, up to 2000 generations ago. (C) Chromosomal homozygosity from the dairy cattle data set. Also plotted are the expected values of CSH when N = 1000 and N = 250. (D) Effective population size of the dairy cattle population ancestral to the sample used, up to 167 generations ago.

Figure 4.

(A) Chromosomal homozygosity for increasing lengths of haplotype from the data of Moffat et al. (2000). The upper (solid) line is the expected CSH when the effective population size is 5000. The lower (dashed) line is the expected CSH when the effective population size is 15,000. (B) Effective population size of the human population ancestral to the sample used, up to 2000 generations ago. (C) Chromosomal homozygosity from the dairy cattle data set. Also plotted are the expected values of CSH when N = 1000 and N = 250. (D) Effective population size of the dairy cattle population ancestral to the sample used, up to 167 generations ago.