Conservation Genetics

, 7:167 | Cite as

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

  • Robin S. WaplesEmail author


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.


computer simulations mating systems non-ideal populations precision sample size temporal method 



I thank Gordon Luikart and Phillip England for bringing this bias to my attention and François Balloux for sharing an unpublished manuscript. Eric Anderson, Mark Beaumont, François Bonhomme, Craig Busack, Phillip England, Oscar Gaggiotti, Bill Hill, Gordon Luikart, Peter Smouse, David Tallmon, Bruce Weir, and two anonymous reviewers provided useful discussions and/or comments on earlier drafts. I am grateful to Geof Givens for suggesting the algorithm for generating an overdispersed Poisson distribution and to Craig Busack for pointing out the subtleties regarding the correction to \(E(\hat{r}^2)\) for permanent pair bonding. A major part of this research was conducted while the author was a visiting scientist at LECA, and I am grateful to Gordon Luikart and Pierre Taberlet for making that possible.


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Laboratoire d’Ecologie Alpine (LECA), Génomique des Populations et BiodiversitéUniversité Joseph FourierGrenobleFrance‰

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