Estimating Effective Population Size from Linkage Disequilibrium between Unlinked Loci: Theory and Application to Fruit Fly Outbreak Populations

Abstract

There is a substantial literature on the use of linkage disequilibrium (LD) to estimate effective population size using unlinked loci. The estimates are extremely sensitive to the sampling process, and there is currently no theory to cope with the possible biases. We derive formulae for the analysis of idealised populations mating at random with multi-allelic (microsatellite) loci. The ‘Burrows composite index’ is introduced in a novel way with a ‘composite haplotype table’. We show that in a sample of diploid size , the mean value of or from the composite haplotype table is biased by a factor of , rather than the usual factor for a conventional haplotype table. But analysis of population data using these formulae leads to estimates that are unrealistically low. We provide theory and simulation to show that this bias towards low estimates is due to null alleles, and introduce a randomised permutation correction to compensate for the bias. We also consider the effect of introducing a within-locus disequilibrium factor to , and find that this factor leads to a bias in the estimate. However this bias can be overcome using the same randomised permutation correction, to yield an altered with lower variance than the original , and one that is also insensitive to null alleles. The resulting formulae are used to provide estimates on 40 samples of the Queensland fruit fly, Bactrocera tryoni, from populations with widely divergent expectations. Linkage relationships are known for most of the microsatellite loci in this species. We find that there is little difference in the estimated values from using known unlinked loci as compared to using all loci, which is important for conservation studies where linkage relationships are unknown.

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

“…In contrast, in the Queensland fruit fly (Bactrocera tryoni), Sved et al (2013) did not find a consistent change inN e across a set of~30 microsatellite loci when co-located loci were excluded. This difference may be due to increased number of loci in this study, and/or the simplified nature of simulated data, both of which can tend to reduce noise in estimates.…”

“…Other methods have computed a weighted mean based on allele frequencies, number of alleles and/or missing data (for example, Peel et al, 2013;Sved et al, 2013), but here we simulate only bi-allelic loci without missing data and did not compute a weighted mean. Alleles observed in low numbers (⩽2) provide little information on LD and can upwardly bias estimates of r 2 (Waples and Do, 2010), so we excluded loci with an observed minor allele frequency of o0.05 in each replicate.…”

“…We used a hybrid of two different formulas for E(r 2 ): equation 2 in Weir and Hill (1980) and equation 3 in Sved and Feldman (1973). The Sved and Feldman formula is incorrect for unlinked loci (c = 0.5) (Sved et al, 2013), while the Weir and Hill (1980) formula produces non-sensical values (E(r 2 )41) for closely linked loci. a For a simulated population size of 50, no sample size of 100 is possible, and replication across sample sizes of 50 is not meaningful.…”

Pudong White pig: a unique genetic resource disclosed by sequencing data

“…The N e estimation procedure first emerged over 40 years ago (Sved et al, 1971), and has now been improved to allow estimates based on high throughput SNP data from, Xiao, Zhang, Sun, Wang and Pan for example, SNP chips or NGS technology, based on different algorithms (Waples and Do, 2008;Sved et al, 2013). In this study, N e values were calculated using SNeP software (Barbato et al, 2015), which allows the analysis of large data sets.…”

Census and contemporary effective population size of two populations of the protected Spanish Moon Moth (Graellsia isabellae)

“…Firstly, we expect data errors to be negligible, as two researchers independently performed the allele calling and 10% of the samples of the project were randomly regenotyped. Nevertheless, our conclusion of moderate-large N e for Puebla is not jeopardised by this possibility, as null alleles bias towards low N e when estimated with the LD method (Sved et al, 2013). Despite having excluded locus GI18 from analyses involving Puebla, we cannot rule out a slight effect of null alleles, a well-known phenomenon in Lepidoptera (e.g.…”