We demonstrate that the mean ratio of the number of alleles to the range in allele size, which we term M, calculated from a population sample of microsatellite loci, can be used to detect reductions in population size. Using simulations, we show that, for a general class of mutation models, the value of M decreases when a population is reduced in size. The magnitude of the decrease is positively correlated with the severity and duration of the reduction in size. We also find that the rate of recovery of M following a reduction in size is positively correlated with post-reduction population size, but that recovery occurs in both small and large populations. This indicates that M can distinguish between populations that have been recently reduced in size and those which have been small for a long time. We employ M to develop a statistical test for recent reductions in population size that can detect such changes for more than 100 generations with the post-reduction demographic scenarios we examine. We also compute M for a variety of populations and species using microsatellite data collected from the literature. We find that the value of M consistently predicts the reported demographic history for these populations. This method, and others like it, promises to be an important tool for the conservation and management of populations that are in need of intervention or recovery.

Detection of reduction in population size using data from microsatellite loci.

Distributions of pairwise differences often called "mismatch distributions" have been extensively used to estimate the demographic parameters of past population expansions. However, these estimations relied on the assumption that all mutations occurring in the ancestry of a pair of genes lead to observable differences (the infinite-sites model). This mutation model may not be very realistic, especially in the case of the control region of mitochondrial DNA, where this methodology has been mostly applied. In this article, we show how to infer past demographic parameters by explicitly taking into account a finite-sites model with heterogeneity of mutation rates. We also propose an alternative way to derive confidence intervals around the estimated parameters, based on a bootstrap approach. By checking the validity of these confidence intervals by simulations, we find that only those associated with the timing of the expansion are approximately correctly estimated, while those around the population sizes are overly large. We also propose a test of the validity of the estimated demographic expansion scenario, whose proper behavior is verified by simulation. We illustrate our method with human mitochondrial DNA, where estimates of expansion times are found to be 10-20% larger when taking into account heterogeneity of mutation rates than under the infinite-sites model.

https://www.genetics.org/content/genetics/152/3/1079.full.pdf

Estimation of Past Demographic Parameters From the Distribution of Pairwise Differences When the Mutation Rates Vary Among Sites: Application to Human Mitochondrial DNA

Although highly variable loci, such as microsatellite loci, are revolutionizing both evolutionary and conservation biology, data from these loci need to be carefully evaluated. First, because these loci often have very high within-population heterozygosity, the magnitude of differentiation measures may be quite small. For example, maximum GST values for populations with no common alleles at highly variable loci may be small and are at maximum less than the average within-population homozygosity. As a result, measures that are variation independent are recommended for highly variable loci. Second, bottlenecks or a reduction in population size can generate large genetic distances in a short time for these loci. In this case, the genetic distance may be corrected for low variation in a population and tests to detect bottlenecks are advised. Third, statistically significant differences may not reflect biologically meaningful differences both because the patterns of adaptive loci may not be correlated with highly variable loci and statistical power with these markers is so high. As an example of this latter effect, the statistical power to detect a one-generation bottleneck of different sizes for different numbers of highly variable loci is discussed. All of these concerns need to be incorporated in the utilization and interpretation of patterns of highly variable loci for both evolutionary and conservation biology.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1558-5646.1999.tb03767.x

Perspective: highly variable loci and their interpretation in evolution and conservation.

Identifying recently bottlenecked populations (populations severely reduced in size) is important because bottlenecks can increase demographic stochasticity, rate of inbreeding, loss of genetic variation, and fixation of deleterious alleles and, thereby, reduce adaptive potential and increase the probability of population extinction (Frankel & Soulé 1981; Lande 1988, 1994; Leberg 1990; Hedrick & Miller 1992; Mills & Smouse 1994; Frankham 1995 a , 1995 b ; but see Bryant et al. 1986; Goodnight 1987). Unfortunately, it is usually difficult to determine if a population has recently experienced a bottleneck because historical population sizes and levels of genetic variation are seldom known. We developed a statistical test (a sign test for heterozygosity excess) for detecting recent historical bottlenecks using allele frequency data (Cornuet & Luikart 1996). The test requires no data on historical population sizes or levels of genetic variation; it requires only measurements of allele frequencies from 5 to 20 polymorphic loci in a sample of approximately 20-30 individuals. The test has reasonable statistical power when applied to allele frequency data sets generated by computer simulations (Cornuet & Luikart 1996). The performance of the test, however, must be evaluated by means of empirical data from natural populations before it can be used with confidence. Our objectives were to (1) explain to conservation biologists the principle of the sign test for detecting heterozygosity excess and (2) evaluate the reliability of the test by analyzing 56 allozyme and 37 microsatellite data sets from bottlenecked and nonbottlenecked natural populations.

Empirical Evaluation of a Test for Identifying Recently Bottlenecked Populations from Allele Frequency Data

The population structure of domesticated species is influenced by the natural history of the populations of predomesticated ancestors, as well as by the breeding system and complexity of the breeding practices exercised by humans. Within Oryza sativa, there is an ancient and well-established divergence between the two major subspecies, indica and japonica, but finer levels of genetic structure are suggested by the breeding history. In this study, a sample of 234 accessions of rice was genotyped at 169 nuclear SSRs and two chloroplast loci. The data were analyzed to resolve the genetic structure and to interpret the evolutionary relationships between groups. Five distinct groups were detected, corresponding to indica, aus, aromatic, temperate japonica, and tropical japonica rices. Nuclear and chloroplast data support a closer evolutionary relationship between the indica and the aus and among the tropical japonica, temperate japonica, and aromatic groups. Group differences can be explained through contrasting demographic histories. With the availability of rice genome sequence, coupled with a large collection of publicly available genetic resources, it is of interest to develop a population-based framework for the molecular analysis of diversity in O. sativa.

https://www.genetics.org/content/genetics/169/3/1631.full.pdf

Genetic Structure and Diversity in Oryza sativa L.

When a population experiences a reduction of its effective size, it generally develops a heterozygosity excess at selectively neutral loci, i.e., the heterozygosity computed from a sample of genes is larger than the heterozygosity expected from the number of alleles found in the sample if the population were at mutation drift equilibrium. The heterozygosity excess persists only a certain number of generations until a new equilibrium is established. Two statistical tests for detecting a heterozygosity excess are described. They require measurements of the number of alleles and heterozygosity at each of several loci from a population sample. The first test determines if the proportion of loci with heterozygosity excess is significantly larger than expected at equilibrium. The second test establishes if the average of standardized differences between observed and expected heterozygosities is significantly different from zero. Type I and II errors have been evaluated by computer simulations, varying sample size, number of loci, bottleneck size, time elapsed since the beginning of the bottleneck and level of variability of loci. These analyses show that the most useful markers for bottleneck detection are those evolving under the infinite allele model (IAM) and they provide guidelines for selecting sample sizes of individuals and loci. The usefulness of these tests for conservation biology is discussed.

https://www.genetics.org/content/genetics/144/4/2001.full.pdf

Jean Marie Cornuet

Papers

Description and Power Analysis of Two Tests for Detecting Recent Population Bottlenecks from Allele Frequency Data