A method for detecting recent changes in contemporary effective population size from linkage disequilibrium at linked and unlinked loci

Abstract

Estimation of contemporary effective population size (Ne) from linkage disequilibrium (LD) between unlinked pairs of genetic markers has become an important tool in the field of population and conservation genetics. If data pertaining to physical linkage or genomic position are available for genetic markers, estimates of recombination rate between loci can be combined with LD data to estimate contemporary Ne at various times in the past. We extend the well-known, LD-based method of estimating contemporary Ne to include linkage information and show via simulation that even relatively small, recent changes in Ne can be detected reliably with a modest number of single-nucleotide polymorphism (SNP) loci. We explore several issues important to interpretation of the results and quantify the bias in estimates of contemporary Ne associated with the assumption that all loci in a large SNP data set are unlinked. The approach is applied to an empirical data set of SNP genotypes from a population of a marine fish where a recent, temporary decline in Ne is known to have occurred.

Figure 1

Estimates of N_e over time in the past for various demographic models, produced with LinkNe. Each panel represents a different starting effective population size (N_e). Confidence intervals are shown only for estimates from the most recent and most distant past. Time points within a plot are adjusted horizontally so that confidence intervals could be distinguished. (a) Trend lines for constant and decline models. (b) Trend lines for constant and expansion models. Upper confidence limits for estimates of N_e for the expansion to 5 × model and for starting N_e of 250, 500 and 1000 were truncated for clarity and are marked with an arrow to indicate that the interval extends beyond the limits of the plot.

Figure 2

Effect of sample-size (S) bias correction proposed by Waples (2006) on estimates of N_e over time. Estimates were produced with LinkNe. Solid lines represent estimates of N_e, with bias correction applied, for the constant population size model. Dashed lined represent estimates where r²_sample was measured as 1/S.

Figure 3

Effect of excluding rare alleles at various thresholds (0.10, 0.05, 0.02, 0.01 and 0), using the constant population model with N=250.

Figure 4

Effect of length of time between demographic change and sampling. (a) Results for decline to 25% of initial N_e of 250 when sampling was conducted 1, 2, 5, 10, 20 and 50 generations after a decline. (b) Results for an expansion to 2 × of initial N_e of 250 when sampling was conducted 1, 2, 5, 10, 20 and 50 generations post expansion.

Figure 5

Comparison of bias in measures of N_e using LinkNe and the LDNe method (as implemented in NeEstimator2). Bias was measured as the difference between the estimated and true N_e and is expressed a percentage of the true N_e. Estimates of N_e based on linkage disequilibrium can be biased downward when linked loci are assumed to be unlinked.

Figure 6

Results of analysis, using LinkNe, of a sample of red drum juveniles from Matagorda Bay, TX. (a) Trend line (dashed) for N_e produced using all sampled individuals and confidence interval (CI) of N_e when F₁ hatchery individuals are removed (shaded area). Note that when ‘wild' individuals are assessed, only the lower bounds of the CI are estimable from the data; for clarity, the CI is truncated at 10 000. (b) Trend line for F₁ hatchery-raised individuals, indicative of a large decline in N_e in the parental generation that consisted of hatchery brood stock.