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

Abstract

Analysis of linkage disequilibrium ($\hat{r}^2$=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 on $\hat{r}^2$ for unlinked, diallelic gene loci are sharply biased downwards ($\hat{N}_{\rm e}/N <0.1$ 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 $E(\hat{r}^2)$ when S and/or N _e are small. Empirically derived modifications to $E(\hat{r}^2)$ for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in $\hat{N}_{\rm e}<5$% 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 affect $\hat{N}_{\rm e}$, but if N has recently increased from a bottleneck $\hat{N}_{\rm e}$ 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 of $\hat{r}^2$ with highly polymorphic markers such as microsatellites is needed.