A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Abstract

Analysis of linkage disequilibrium (r 2 =mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N e ) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N e based onr 2 for unlinked, diallelic gene loci are sharply biased downwards (N e =N<0:1 in some cases) if sample size (S) is less than true N e . The bias is shown to arise from inaccuracies in published formula for Eðr 2 Þ when S and/or N e are small. Empirically derived modifications to Eðr 2 Þ for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias inN e <5% in most cases). The modified method also performs well in estimating N e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affectN e , but if N has recently increased from a bottleneckN e can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N e in natural populations. However, a comprehensive assessment of performance ofr 2 with highly polymorphic markers such as microsatellites is needed.

Estimating contemporary effective population size in non-model species using linkage disequilibrium across thousands of loci

“…However, because these comparisons are not all independent, precision is greatly reduced from the theoretical value. Previously, this problem of assessing precision for the LD method has been pointed out and illustrated with small numbers of loci (Waples, 2006;Waples and Do, 2010). We show that the magnitude of this problem increases dramatically for genomics-scale data sets, to the extent that realized precision will be much less than predicted from standard models that assume complete independence among loci.…”

“…With genotypes coded in this way, r 2 is identical to Burrows' composite measure of linkage disequilibrium (r Δ ) (Weir, 1996;Zaykin, 2004). To mirror the approach implemented in the software LDNe (Waples and Do, 2008), where a sample-size adjustment factor of [S/(S − 1)] 2 was used (Weir, 1979), we multiplied each r 2 value by this term, subtracted the expected contribution from sampling error to obtain the adjusted r 2 ', and then calculatedN e as in Waples (2006).…”

“…This lack of independence between loci, coupled with the fact that each locus contributes to many pairwise r 2 measurements, is not accounted for when generating standard confidence intervals (CIs) around the mean r 2 orN e . To evaluate how much these effects reduce precision, we conducted a separate round of simulations and compared two measures of confidence: (1) nominal CIs aroundN e that assume all pairwise comparisons of loci are independent (Waples, 2006) and (2) empirical 95% intervals observed in the simulated data. Forward simulations of populations following a random Wright-Fisher mating model produce random variation in realized N e as the variance in reproductive success varies each generation, even if census size stays constant.…”

Long-term effective population size dynamics of an intensively monitored vertebrate population

“…To explore sensitivity, we also repeated the analysis with P crit = 0.01 and 0.05 while similarly applying the same criterion as above to ensure that single copy alleles were not counted. The 95% confidence intervals (CIs) were derived using the 'parametric' option that implements χ 2 approximation (Waples, 2006).…”

“…To test for differences in the effective population sizes of the three buzzard plumage morphs, we implemented the LD method (Hill, 1981;Waples, 2006;Waples and Do, 2010). For this analysis, it was necessary to pool individuals across years because of the low frequency of the dark morph.…”