Joint estimation of contemporary seed and pollen dispersal rates among plant populations

There are few statistical methods for estimating contemporary dispersal among plant populations. A maximum-likelihood procedure is introduced here that uses pre- and post-dispersal population samples of biparentally inherited genetic markers to jointly estimate contemporary seed and pollen immigration rates from a set of discrete external sources into a target population. Monte Carlo simulations indicate that accurate estimates and reliable confidence intervals can be obtained using this method for both pollen and seed migration rates at modest sample sizes (100 parents/population and 100 offspring) when population differentiation is moderate (F(ST) ≥ 0.1), or by increasing pre-dispersal samples (to about 500 parents/population) when genetic divergence is weak (F(ST) = 0.01). The method exhibited low sensitivity to the number of source populations and achieved good accuracy at affordable genetic resolution (10 loci with 10 equifrequent alleles each). Unsampled source populations introduced positive biases in migration rate estimates from sampled sources, although they were minor when the proportion of immigration from the latter was comparatively low. A practical application of the method to a metapopulation of the Australian resprouter shrub Banksia attenuata revealed comparable levels of directional seed and pollen migration among dune groups, and the estimate of seed dispersal was higher than a previous estimate based on conservative assignment tests. The method should be of interest to researchers and managers assessing broad-scale nonequilibrium seed and pollen gene flow dynamics in plants.     

Detecting populations in the 'ambiguous' zone: kinship-based estimation of population structure at low genetic divergence

Identifying population structure is one of the most common and important objectives of spatial analyses using population genetic data. Population structure is detected either by rejecting the null hypothesis of a homogenous distribution of genetic variation, or by estimating low migration rates. Issues arise with most current population genetic inference methods when the genetic divergence is low among putative populations. Low levels of genetic divergence may be as a result of either high ongoing migration or historic high migration but no current, ongoing migration. We direct attention to recent developments in the use of the tempo-spatial distribution of closely related individuals to detect population structure or estimate current migration rates. These 'kinship-based' approaches complement more traditional population-based genetic inference methods by providing a means to detect population structure and estimate current migration rates when genetic divergence is low. However, for kinship-based methods to become widely adopted, formal estimation procedures applicable to a range of species life histories are needed.     

A Fast Method that Uses Polygenic Scores to Estimate the Variance Explained by Genome-wide Marker Panels and the Proportion of Variants Affecting a Trait

Several methods have been proposed to estimate the variance in disease liability explained by large sets of genetic markers. However, current methods do not scale up well to large sample sizes. Linear mixed models require solving high-dimensional matrix equations, and methods that use polygenic scores are very computationally intensive. Here we propose a fast analytic method that uses polygenic scores, based on the formula for the non-centrality parameter of the association test of the score. We estimate model parameters from the results of multiple polygenic score tests based on markers with p values in different intervals. We estimate parameters by maximum likelihood and use profile likelihood to compute confidence intervals. We compare various options for constructing polygenic scores, based on nested or disjoint intervals of p values, weighted or unweighted effect sizes, and different numbers of intervals, in estimating the variance explained by a set of markers, the proportion of markers with effects, and the genetic covariance between a pair of traits. Our method provides nearly unbiased estimates and confidence intervals with good coverage, although estimation of the variance is less reliable when jointly estimated with the covariance. We find that disjoint p value intervals perform better than nested intervals, but the weighting did not affect our results. A particular advantage of our method is that it can be applied to summary statistics from single markers, and so can be quickly applied to large consortium datasets. Our method, named AVENGEME (Additive Variance Explained and Number of Genetic Effects Method of Estimation), is implemented in R software.     

Inferring recent migration rates from individual genotypes

We present a novel and straightforward method for estimating recent migration rates between discrete populations using multilocus genotype data. The approach builds upon a two-step sampling design, where individual genotypes are sampled before and after dispersal. We develop a model that estimates all pairwise backwards migration rates ( m_ij , the probability that an individual sampled in population i is a migrant from population j ) between a set of populations. The method is validated with simulated data and compared with the methods of BayesAss and Structure. First, we use data for an island model and then we consider more realistic data simulations for a metapopulation of the greater white-toothed shrew ( Crocidura russula ). We show that the precision and bias of estimates primarily depend upon the proportion of individuals sampled in each population. Weak sampling designs may particularly affect the quality of the coverage provided by 95% highest posterior density intervals. We further show that it is relatively insensitive to the number of loci sampled and the overall strength of genetic structure. The method can easily be extended and makes fewer assumptions about the underlying demographic and genetic processes than currently available methods. It allows backwards migration rates to be estimated across a wide range of realistic conditions.     

Estimation of migration rates from marker‐based parentage analysis

Coupled with rapid developments of efficient genetic markers, powerful population genetic methods were proposed to estimate migration rates (m) in natural populations in much broader spatial and temporal scales than the traditional mark‐release‐recapture (MRR) methods. Highly polymorphic (e.g. microsatellites) and genomic‐wide (e.g. SNPs) markers provide sufficient information to assign individuals to their populations or parents of origin and thereby to estimate directly m in a way similar to MRR. Such direct estimates of current migration rates are particularly useful in understanding the ecology and microevolution of wild populations and in managing the populations in the future. In this study, I proposed and implemented, in the software MigEst, a likelihood method to use marker‐based parentage assignments in jointly estimating m and candidate parent sampling proportions (x) in a subset of populations, investigated its power and accuracy using data simulated in various scenarios of population properties (e.g. the actual m, number, size and differentiation of populations) and sampling properties (e.g. the numbers of sampled parent candidates, offspring and markers), compared it with the population assignment approach implemented in the software BayesAss and demonstrated its usefulness by analysing a microsatellite data set from three natural populations of Brazilian bats. Simulations showed that MigEst provides unbiased and accurate estimates of m and performs better than BayesAss except when populations are highly differentiated with very small and ecologically insignificant migration rates. A valuable property of MigEst is that in the presence of unsampled populations, it gives good estimates of the rate of migration among sampled populations as well as of the rate of migration into each sampled population from the pooled unsampled populations.     

Evaluating the performance of a multilocus Bayesian method for the estimation of migration rates

Bayesian methods have become extremely popular in molecular ecology studies because they allow us to estimate demographic parameters of complex demographic scenarios using genetic data. Articles presenting new methods generally include sensitivity studies that evaluate their performance, but they tend to be limited and need to be followed by a more thorough evaluation. Here we evaluate the performance of a recent method, bayesass , which allows the estimation of recent migration rates among populations, as well as the inbreeding coefficient of each local population. We expand the simulation study of the original publication by considering multi-allelic markers and scenarios with varying number of populations. We also investigate the effect of varying migration rates and F _ST more thoroughly in order to identify the region of parameter space where the method is and is not able to provide accurate estimates of migration rate. Results indicate that if the demographic history of the species being studied fits the assumptions of the inference model, and if genetic differentiation is not too low ( F _ST ≥ 0.05), then the method can give fairly accurate estimates of migration rates even when they are fairly high (about 0.1). However, when the assumptions of the inference model are violated, accurate estimates are obtained only if migration rates are very low ( m  = 0.01) and genetic differentiation is high ( F _ST ≥ 0.10). Our results also show that using posterior assignment probabilities as an indication of how much confidence we can place on the assignments is problematical since the posterior probability of assignment can be very high even when the individual assignments are very inaccurate.     

Analysis of the Inheritance, Selection and Evolution of Growth Trajectories

We present methods for estimating the parameters of inheritance and selection that appear in a quantitative genetic model for the evolution growth trajectories and other "infinite-dimensional" traits that we recently introduced. Two methods for estimating the additive genetic covariance function are developed, a "full" model that fully fits the data and a "reduced" model that generates a smoothed estimate consistent with the sampling errors in the data. By decomposing the covariance function into its eigenvalues and eigenfunctions, it is possible to identify potential evolutionary changes in the population's mean growth trajectory for which there is (and those for which there is not) genetic variation. Algorithms for estimating these quantities, their confidence intervals, and for testing hypotheses about them are developed. These techniques are illustrated by an analysis of early growth in mice. Compatible methods for estimating the selection gradient function acting on growth trajectories in natural or domesticated populations are presented. We show how the estimates for the additive genetic covariance function and the selection gradient function can be used to predict the evolutionary change in a population's mean growth trajectory.     

Estimating population density from indirect sign: track counts and the Formozov–Malyshev–Pereleshin formula

For many purposes it is often desirable to estimate animal population densities over large areas. Where total counts are not possible and sightings are relatively rare, a range of methods exists to estimate densities from indirect sign. Such methods are frequently unreliable and usually require independent calibration or confirmation. We present an analytical method for estimating population density from track counts. The method, widely known in the Russian Federation but not in the English language scientific literature, requires counts of tracks of known age, together with estimates of animal daily travel distances. We use simulations to verify the theoretical basis of the approach and to indicate potential precision that may be achieved. We illustrate application of the approach using a large data set on ungulate track counts in the Russian Far East. We suggest that under most circumstances, nonparametric bootstrapping will be the most appropriate method for deriving estimates of confidence intervals about density estimates. As with other approaches to estimating density from indirect sign, the method that we discuss is vulnerable to violations of an array of underlying assumptions. However, it is easily applied and could represent an important method by which the relationship between indices of abundance and absolute density can be understood.     

Finding confidence limits on population growth rates

Recent concern with the survival of endangered species has renewed interest in estimating the growth rates of natural populations. Estimates of population growth rate are subject to uncertainties because of both sampling and experimental errors incurred when estimating rates of fecundity and survivorship. In recent years, a variety of methods have been proposed for placing confidence limits on estimated growth rates. The commonly used analytical approximation assumes that errors are relatively small. There are several computer-intensive methods, including methods based on jackknife and bootsrap procedures, that test the robustness of that approximation. In addition, several computer simulations of hypothetical populations have led to some generalizations about the performance of different methods. In general, it is possible to find confidence intervals for estimates of population growth rates but the appropriate method for doing so depends on the kind of data available and on the magnitude and correlation structure of the errors.     

Usefulness of single nucleotide polymorphism data for estimating population parameters

Single nucleotide polymorphism (SNP) data can be used for parameter estimation via maximum likelihood methods as long as the way in which the SNPs were determined is known, so that an appropriate likelihood formula can be constructed. We present such likelihoods for several sampling methods. As a test of these approaches, we consider use of SNPs to estimate the parameter Theta = 4N(e)micro (the scaled product of effective population size and per-site mutation rate), which is related to the branch lengths of the reconstructed genealogy. With infinite amounts of data, ML models using SNP data are expected to produce consistent estimates of Theta. With finite amounts of data the estimates are accurate when Theta is high, but tend to be biased upward when Theta is low. If recombination is present and not allowed for in the analysis, the results are additionally biased upward, but this effect can be removed by incorporating recombination into the analysis. SNPs defined as sites that are polymorphic in the actual sample under consideration (sample SNPs) are somewhat more accurate for estimation of Theta than SNPs defined by their polymorphism in a panel chosen from the same population (panel SNPs). Misrepresenting panel SNPs as sample SNPs leads to large errors in the maximum likelihood estimate of Theta. Researchers collecting SNPs should collect and preserve information about the method of ascertainment so that the data can be accurately analyzed.     

Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series

Dynamic invariants are often estimated from experimental time series with the aim of differentiating between different physical states in the underlying system. The most popular schemes for estimating dynamic invariants are capable of estimating confidence intervals, however, such confidence intervals do not reflect variability in the underlying dynamics. We propose a surrogate based method to estimate the expected distribution of values under the null hypothesis that the underlying deterministic dynamics are stationary. We demonstrate the application of this method by considering four recordings of human pulse waveforms in differing physiological states and show that correlation dimension and entropy are insufficient to differentiate between these states. In contrast, algorithmic complexity can clearly differentiate between all four rhythms.     

Robustness of coalescent estimators to between-lineage mutation rate variation

Data from HIV and from human neoplastic cells can show substantial between-lineage mutation rate variation even within a single population. Such variation may affect estimators of population quantities such as Theta = 4N(e)mu. Using simulated DNA data, I measured the effect of rate variation on recovery of Theta by the summary-statistic estimator of Watterson (Watterson GA. 1975. On the number of segregating sites in genetical systems without recombination. Theor Popul Biol. 7:256-276) and the coalescent maximum likelihood algorithm LAMARC (Kuhner MK. 2006. LAMARC 2.0: maximum likelihood and Bayesian estimation of population parameters. Bioinformatics. Advance Access doi: 10.1093/bioinformatics/btk051). Watterson's estimator showed a downward bias, as expected, with high values of Theta. LAMARC's mean estimate was accurate for all tested values of Theta and rate variation except for a downward bias when rate variation was maximal (i.e., the slow rate was zero). LAMARC had consistently narrower confidence intervals (CIs) than Watterson's estimator. Both methods tended to reject the truth too often when rate variation was 8x or greater and independent among branches, as well as when variation was 4x or greater and correlated among branches. In the case of Watterson's estimate, this excess rejection was fully attributable to variation among genealogies in the amount of total branch length associated with the fast and slow rates. However, in the case of LAMARC, some excess rejection was still observed even when between-genealogy variation was taken into account. Both estimators are robust to modest rate variation; however, their use should be coupled with a statistical test to rule out extreme rate variation as the resulting CIs may not be reliable.     

Quantifying population structure using the F-model

We review a model-based approach to estimate local population F(ST) 's that is based on the multinomial-Dirichlet distribution, the so-called F-model. As opposed to the standard method of estimating a single F(ST) value, this approach takes into account the fact that in most if not all realistic situations, local populations differ in their effective sizes and migration rates. Therefore, the use of this approach can help better describe the genetic structure of populations. Despite this obvious advantage, this method has remained largely underutilized by molecular ecologists. Thus, the objective of this review is to foster its use for studying the genetic structure of metapopulations. We present the derivation of the Bayesian formulation for the estimation of population-specific F(ST) 's based on the multinomial-Dirichlet distribution. We describe several recent applications of the F-model and present the results of a small simulation study that explains how the F-model can help better describe the genetic structure of populations.     

Estimating the degree of saturation in mutant screens

Large-scale screens for loss-of-function mutants have played a significant role in recent advances in developmental biology and other fields. In such mutant screens, it is desirable to estimate the degree of "saturation" of the screen (i.e., what fraction of the possible target genes has been identified). We applied Bayesian and maximum-likelihood methods for estimating the number of loci remaining undetected in large-scale screens and produced credibility intervals to assess the uncertainty of these estimates. Since different loci may mutate to alleles with detectable phenotypes at different rates, we also incorporated variation in the degree of mutability among genes, using either gamma-distributed mutation rates or multiple discrete mutation rate classes. We examined eight published data sets from large-scale mutant screens and found that credibility intervals are much broader than implied by previous assumptions about the degree of saturation of screens. The likelihood methods presented here are a significantly better fit to data from published experiments than estimates based on the Poisson distribution, which implicitly assumes a single mutation rate for all loci. The results are reasonably robust to different models of variation in the mutability of genes. We tested our methods against mutant allele data from a region of the Drosophila melanogaster genome for which there is an independent genomics-based estimate of the number of undetected loci and found that the number of such loci falls within the predicted credibility interval for our models. The methods we have developed may also be useful for estimating the degree of saturation in other types of genetic screens in addition to classical screens for simple loss-of-function mutants, including genetic modifier screens and screens for protein-protein interactions using the yeast two-hybrid method.     

Heard but not seen: an acoustic survey of the African forest elephant population at Kakum Conservation Area, Ghana

This study, designed to survey forest elephants ( Loxodonta africana cyclotis ) at Kakum Conservation Area, Ghana, is the first to apply acoustic methods to elephant abundance estimation and to compare results with independent survey estimates. Nine acoustic sensors gathered sound continuously for 38 days. Low-frequency calling rates have been established as useful elephant abundance indices at a Namibian watering hole and a central African forest clearing. In this study, we estimated elephant population size by applying an abundance index model and detection function developed in central Africa to data from simultaneous sampling periods on Kakum sensors. The sensor array recorded an average of 1.81 calls per 20-min sampling period from an effective detection area averaging 10.27 km². The resulting estimate of 294 elephants (95% CI: 259–329) falls within confidence bounds of recent dung-based surveys. An extended acoustic model, estimating the frequency with which elephants are silent when present, yields an estimate of 350 elephants (95% CI: 315–384). Acoustic survey confidence intervals are at least half as wide as those from dung-based surveys. This study demonstrates that acoustic surveying is a valuable tool for estimating elephant abundance, as well as for detecting other vocal species and anthropogenic noises that may be associated with poaching.     

A simulation study of three methods for estimating selective values and survival rates from recapture data

The methods ofManly (1973),Manly (1975) andManly (1977) for estimating survival rates and relative survival rates from recapture data have been compared by computer simulation. In the simulations batches of two types of animal were “released” at one point in “time” and recapture samples were taken at “daily” intervals from then on. The various methods of estimation were then used to estimate, the daily survival rates of type 1 and type 2 animals, and also the survival rate of the type 2 animals relative to the type 1 animals. Simulation experiments were designed to examine (a) the bias in estimates, (b) the relative precision of different methods of estimation, (c) the validity of confidence intervals for true parameter values, and (d) the effect on estimates of the failure of certain assumptions.     

Detecting Identity by Descent and Estimating Genotype Error Rates in Sequence Data

Existing methods for identity by descent (IBD) segment detection were designed for SNP array data, not sequence data. Sequence data have a much higher density of genetic variants and a different allele frequency distribution, and can have higher genotype error rates. Consequently, best practices for IBD detection in SNP array data do not necessarily carry over to sequence data. We present a method, IBDseq, for detecting IBD segments in sequence data and a method, SEQERR, for estimating genotype error rates at low-frequency variants by using detected IBD. The IBDseq method estimates probabilities of genotypes observed with error for each pair of individuals under IBD and non-IBD models. The ratio of estimated probabilities under the two models gives a LOD score for IBD. We evaluate several IBD detection methods that are fast enough for application to sequence data (IBDseq, Beagle Refined IBD, PLINK, and GERMLINE) under multiple parameter settings, and we show that IBDseq achieves high power and accuracy for IBD detection in sequence data. The SEQERR method estimates genotype error rates by comparing observed and expected rates of pairs of homozygote and heterozygote genotypes at low-frequency variants in IBD segments. We demonstrate the accuracy of SEQERR in simulated data, and we apply the method to estimate genotype error rates in sequence data from the UK10K and 1000 Genomes projects.     

Mitochondrial and nuclear genetic variation across calving lagoons in Eastern North Pacific gray whales (Eschrichtius robustus)

Accurate knowledge of population structure in cetaceans is critical for preserving and managing breeding habitat, particularly when habitat is not uniformly protected. Most eastern gray whales return to their major breeding range each winter along the Pacific coast of Baja California, Mexico, concentrating in 3 major calving lagoons, but it is unknown whether genetic differences exist between lagoons. Previous photo-identification studies and genetic studies suggest that gray whales may return to their natal lagoons to breed, potentially resulting in the buildup of genetic differences. However, an earlier genetic study used only one genetic marker and did not include samples from Bahia Magdalena, a major calving lagoon not currently designated as a wildlife refuge. To expand on this previous study, we collected genetic data from the mitochondrial control region (442 bp) and 9 microsatellite markers from 112 individuals across all 3 major calving lagoons. Our data suggest that migration rates between calving lagoons are high but that a small but significant departure from panmixia exists between Bahia Magdalena and Laguna San Ignacio (Fisher's Exact test, P < 0.0001; F(ST) = 0.006, P = 0.025). Coalescent simulations show that the lack of extensive population structure may result from the disruption of structure due to whaling. Another possibility is that rates of migration have always been high (>10% per generation). In addition, microsatellite data showed evidence of a severe population bottleneck. Eastern gray whales are still recovering from the impacts of whaling on their breeding grounds, and these populations should be protected and monitored for future genetic changes.     

Spatial and Space-Time Correlations in Systems of Subpopulations with Genetic Drift and Migration

The geographic distribution of genetic variation is an important theoretical and experimental component of population genetics. Previous characterizations of genetic structure of populations have used measures of spatial variance and spatial correlations. Yet a full understanding of the causes and consequences of spatial structure requires complete characterization of the underlying space-time system. This paper examines important interactions between processes and spatial structure in systems of subpopulations with migration and drift, by analyzing correlations of gene frequencies over space and time. We develop methods for studying important features of the complete set of space-time correlations of gene frequencies for the first time in population genetics. These methods also provide a new alternative for studying the purely spatial correlations and the variance, for models with general spatial dimensionalities and migration patterns. These results are obtained by employing theorems, previously unused in population genetics, for space-time autoregressive (STAR) stochastic spatial time series. We include results on systems with subpopulation interactions that have time delay lags (temporal orders) greater than one. We use the space-time correlation structure to develop novel estimators for migration rates that are based on space-time data (samples collected over space and time) rather than on purely spatial data, for real systems. We examine the space-time and spatial correlations for some specific stepping stone migration models. One focus is on the effects of anisotropic migration rates. Partial space-time correlation coefficients can be used for identifying migration patterns. Using STAR models, the spatial, space-time, and partial space-time correlations together provide a framework with an unprecedented level of detail for characterizing, predicting and contrasting space-time theoretical distributions of gene frequencies, and for identifying features such as the pattern of migration and estimating migration rates in experimental studies of genetic variation over space and time.     

JC virus evolution and its association with human populations

The ubiquitous human polyomavirus JC (JCV) is a small double-stranded DNA virus that establishes a persistent infection, and it is often transmitted from parents to children. There are at least 14 subtypes of the virus associated with different human populations. Because of its presumed codivergence with humans, JCV has been used as a genetic marker for human evolution and migration. Codivergence has also been used as a basis for estimating the rate of nucleotide substitution in JCV. We tested the hypothesis of host-virus codivergence by (i) performing a reconciliation analysis of phylogenetic trees of human and JCV populations and (ii) providing the first estimate of the evolutionary rate of JCV that is independent from the assumption of codivergence. Strikingly, our comparisons of JCV and human phylogenies provided no evidence for codivergence, suggesting that this virus should not be used as a marker for human population history. Further, while the estimated nucleotide substitution rate of JCV has large confidence intervals due to limited sampling, our analysis suggests that this virus may evolve nearly two orders of magnitude faster than predicted under the codivergence hypothesis.