Estimation of effective population size in continuously distributed populations: there goes the neighborhood

Abstract

Use of genetic methods to estimate effective population size (N e ) is rapidly increasing, but all approaches make simplifying assumptions unlikely to be met in real populations. In particular, all assume a single, unstructured population, and none has been evaluated for use with continuously distributed species. We simulated continuous populations with local mating structure, as envisioned by Wright's concept of neighborhood size (NS), and evaluated performance of a single-sample estimator based on linkage disequilibrium (LD), which provides an estimate of the effective number of parents that produced the sample (N b ). Results illustrate the interacting effects of two phenomena, drift and mixture, that contribute to LD. Samples from areas equal to or smaller than a breeding window produced estimates close to the NS. As the sampling window increased in size to encompass multiple genetic neighborhoods, mixture LD from a two-locus Wahlund effect overwhelmed the reduction in drift LD from incorporating offspring from more parents. As a consequence,N b never approached the global N e , even when the geographic scale of sampling was large. Results indicate that caution is needed in applying standard methods for estimating effective size to continuously distributed populations. Heredity (2013) 111, 189-199; doi:10.1038/hdy.2013; published online 8 May 2013Keywords: genetic monitoring; inbreeding; isolation-by-distance; linkage disequilibrium; wahlund effect; wright's neighborhood INTRODUCTIONThe concept of effective population size (N e ) provides a way to quantify the evolutionary changes caused by random processes in finite populations (Charlesworth, 2009). Since its formal definition by Wright (1931) as the size of an ideal population that has played the same rate of genetic drift as an actual population of interest, N e has a central role in studies of evolution and ecology. In addition to directly affecting the rates of loss of neutral genetic variability and frequency change of neutral alleles, N e mediates the effectiveness of migration and selection, which are predictable in large populations but can be overwhelmed by drift in small ones.The original concept of N e envisaged a single population or a series of semi-discrete populations connected by limited migration. In many species, however, individuals are distributed more or less continuously across large landscapes, and matings occur more frequently among spatially proximal individuals. This type of demography produces a pattern of 'isolation-by-distance' (IBD; Wright, 1943), in which genetic differentiation increases with distance, but there are no distinct breaks or discrete subunits within the global population. Species distributed in this fashion pose a particular challenge in applying the concept of effective population size. For example, recent research using the coalescent (for example, Barton and Wilson, 1995;Wilkins, 2004) has shown that evolutionary processes in continuously distributed populations exhibit both a short-term dynamic that is strong...

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

“…Population structure As population structure can cause inaccuracies in N e estimation (Waples and England, 2011;Neel et al, 2013;Gilbert and Whitlock, 2015), we used two approaches to test for the presence of cryptic population structure within the study area. Arguably the most versatile tests of population structure need not rely on knowledge of where individuals were sampled.…”

The effect of neighborhood size on effective population size in theory and in practice

“…N e is the effective number of individuals within the whole population, defined as the size of an ideal population affected by random genetic sampling at the same rate as the population being studied (Wright, 1931(Wright, ,1938, whereas N n is the effective number of individuals within an area of a population (the neighborhood) defined such that the parents of a focal individual can be considered to be genetically representative of the neighborhood's occupants (Wright, 1946). To avoid confusion, the notation N n is used for the neighborhood number instead of N b (Slatkin and Barton, 1989) as N b has been used for the effective number of breeders in a given year in species with overlapping generations (Waples, 2005), and, more generally, for the effective number of parents producing the sample used in the estimation of N e when there is temporal or spatial population structure (Neel et al, 2013).…”

“…During the initial nonequilibrium phase (he used the first 15 generations), while the genetic structure was being established, estimates of N e (using the decline in heterozygosity) were closely related to N n , but later, when the genetic structure of the population had equilibrated, the estimates of N e were more influenced by N. However, Kawata (1995) found that at these late stages the estimated N e was always less than or equal to the population size, a result conflicting with Equation (4). Neel et al (2013) also simulated a neighborhood-structured population, estimating N e with a single-sample estimator (based on linkage disequilibrium). Like Kawata (1995), they found that under some conditions (in their case, when the genetic sampling was at the scale of a single neighborhood) the estimated N e was close to N n .…”

“…Second, the two previous studies showed that, under some conditions in populations with significant spatial genetic structure, traditional estimators of N e can lead to substantial underestimates closer to N n than the expected N e . Furthermore, Neel et al (2013) concluded that single-sample estimates of N e will generally result in an underestimation of the true N e , and raised the question of whether this bias also applies to the more traditional two-sample temporal method (see Waples, 1989). If the temporal method underestimates the true N e to a degree similar to that revealed by the simulation estimates of Neel et al (2013) using a single-sample linkage disequilibrium method, then this might account for many of the unusually low estimates of N e /N reported in the literature.…”

“…Understanding the extent to which spatial genetic structure is expected to increase (or decrease) N e is important in predicting the effect of factors such as habitat loss on the long-term genetic composition of populations using the theoretical links between ecological/demographic factors and N e (Nunney and Elam, 1994). It is also important in evaluating genetic estimates of N e , given the concern over substantial bias noted by Neel et al (2013). Documenting this bias across the available genetic estimators is the first step in moving toward a resolution of the problem.…”