An evaluation of the methods to estimate effective population size from measures of linkage disequilibrium

Abstract

In 1971, John Sved derived an approximate relationship between linkage disequilibrium (LD) and effective population size for an ideal finite population. This seminal work was extended by Sved and Feldman (Theor Pop Biol 4, 129, 1973) and Weir and Hill (Genetics 95, 477, 1980) who derived additional equations with the same purpose. These equations yield useful estimates of effective population size, as they require a single sample in time. As these estimates of effective population size are now commonly used on a variety of genomic data, from arrays of single nucleotide polymorphisms to whole genome data, some authors have investigated their bias through simulation studies and proposed corrections for different mating systems. However, the cause of the bias remains elusive. Here, we show the problems of using LD as a statistical measure and, analogously, the problems in estimating effective population size from such measure. For that purpose, we compare three commonly used approaches with a transition probability‐based method that we develop here. It provides an exact computation of LD. We show here that the bias in the estimates of LD and effective population size are partly due to low‐frequency markers, tightly linked markers or to a small total number of crossovers per generation. These biases, however, do not decrease when increasing sample size or using unlinked markers. Our results show the issues of such measures of effective population based on LD and suggest which of the method here studied should be used in empirical studies as well as the optimal distance between markers for such estimates.

A method to estimate effective population size from linkage disequilibrium when generations overlap

“…Our results show that using the linked identity by descent provides better estimates, which is in agreement with our earlier work (Garcia-Cortes et al 2019). We have further compared our exact results with those obtained via simulations, using multinomial distributions, and have obtained a very good agreement between them.…”

“…Following Sved (1971); Sved & Feldman (1973) and earlier work (Garcia-Cortes et al 2019), we have derived here exact equations for linkage disequilibrium in populations with overlapping generations. Combining this result with life-history parameters, we have inferred the number of newborns per generation, N 0 , which in turn, can be used to estimate effective population size, a key parameter in evolutionary and conservation studies.…”

“…4 are in line with our previous results. We had shown for non-overlapping generations that the estimator of Weir & Hill (1980) was downward biased (Garcia-Cortes et al 2019). In Table 4 we observe a similar trend, where the results obtained with Ne estimator, based on the estimator developed by Weir & Hill (1980), are smaller than those obtained with our method.…”

“…Q is the probability of joint IBD without replacement, while L is the probability of joint IBD, but allowing for replacement. Earlier work has shown that L , as derived in Sved & Feldman (1973), provides better estimations of E [ r 2 ] (Garcia-Cortes et al 2019).…”

“…By inverting the system of equations derived, we can then estimate the cohort size and the effective population size from genetic data. Furthermore, we take advantage of our previous research (Garcia-Cortes et al 2019), to show the importance of dealing appropiately with frequencies or probabilities, and how they lead to very different results. Finally, we apply our method to publicly available data from the white-crowned sparrow ( Zonotrichia leucophrys , Lipshutz et al 2017).…”