Precision and accuracy of divergence time estimates from STR and SNPSTR variation

Inference of intraspecific population divergence patterns typically requires genetic data for molecular markers with relatively high mutation rates. Microsatellites, or short tandem repeat (STR) polymorphisms, have proven informative in many such investigations. These markers are characterized, however, by high levels of homoplasy and varying mutational properties, often leading to inaccurate inference of population divergence. A SNPSTR is a genetic system that consists of an STR polymorphism closely linked (typically < 500 bp) to one or more single-nucleotide polymorphisms (SNPs). SNPSTR systems are characterized by lower levels of homoplasy than are STR loci. Divergence time estimates based on STR variation (on the derived SNP allele background) should, therefore, be more accurate and precise. We use coalescent-based simulations in the context of several models of demographic history to compare divergence time estimates based on SNPSTR haplotype frequencies and STR allele frequencies. We demonstrate that estimates of divergence time based on STR variation on the background of a derived SNP allele are more accurate (3% to 7% bias for SNPSTR versus 11% to 20% bias for STR) and more precise than STR-based estimates, conditional on a recent SNP mutation. These results hold even for models involving complex demographic scenarios with gene flow, population expansion, and population bottlenecks. Varying the timing of the mutation event generating the SNP revealed that estimates of divergence time are sensitive to SNP age, with more recent SNPs giving more accurate and precise estimates of divergence time. However, varying both mutational properties of STR loci and SNP age demonstrated that multiple independent SNPSTR systems provide less biased estimates of divergence time. Furthermore, the combination of estimates based separately on STR and SNPSTR variation provides insight into the age of the derived SNP alleles. In light of our simulations, we interpret estimates from data for human populations.     

Likelihood analysis of ongoing gene flow and historical association

Abstract.— We develop a Monte Carlo-based likelihood method for estimating migration rates and population divergence times from data at unlinked loci at which mutation rates are sufficiently low that, in the recent past, the effects of mutation can be ignored. The method is applicable to restriction fragment length polymorphisms (RFLPs) and single nucleotide polymorphisms (SNPs) sampled from a subdivided population. The method produces joint maximum-likelihood estimates of the migration rate and the time of population divergence, both scaled by population size, and provides a framework in which to test either for no ongoing gene flow or for population divergence in the distant past. We show the method performs well and provides reasonably accurate estimates of parameters even when the assumptions under which those estimates are obtained are not completely satisfied. Furthermore, we show that, provided that the number of polymorphic loci is sufficiently large, there is some power to distinguish between ongoing gene flow and historical association as causes of genetic similarity between pairs of populations.     

Do complex population histories drive higher estimates of substitution rate in phylogenetic reconstructions?

Our curiosity about biodiversity compels us to reconstruct the evolutionary past of species. Molecular evolutionary theory now allows parameterization of mathematically sophisticated and detailed models of DNA evolution, which have resulted in a wealth of phylogenetic histories. But reconstructing how species and population histories have played out is critically dependent on the assumptions we make, such as the clock-like accumulation of genetic differences over time and the rate of accumulation of such differences. An important stumbling block in the reconstruction of evolutionary history has been the discordance in estimates of substitution rate between phylogenetic and pedigree-based studies. Ancient genetic data recovered directly from the past are intermediate in time scale between phylogenetics-based and pedigree-based calibrations of substitution rate. Recent analyses of such ancient genetic data suggest that substitution rates are closer to the higher, pedigree-based estimates. In this issue, Navascués & Emerson (2009) model genetic data from contemporary and ancient populations that deviate from a simple demographic history (including changes in population size and structure) using serial coalescent simulations. Furthermore, they show that when these data are used for calibration, we are likely to arrive at upwardly biased estimates of mutation rate.     

Heterogeneity of microsatellite mutations within and between loci,and implications for human demographic histories.

Microsatellites have been widely used to reconstruct human evolution. However, the efficient use of these markers relies on information regarding the process producing the observed variation. Here, we present a novel approach to the locus-by-locus characterization of this process. By analyzing somatic mutations in cancer patients, we estimated the distributions of mutation size for each of 20 loci. The same loci were then typed in three ethnically diverse population samples. The generalized stepwise mutation model was used to test the predicted relationship between population and mutation parameters under two demographic scenarios: constant population size and rapid expansion. The agreement between the observed and expected relationship between population and mutation parameters, even when the latter are estimated in cancer patients, confirms that somatic mutations may be useful for investigating the process underlying population variation. Estimated distributions of mutation size differ substantially amongst loci, and mutations of more than one repeat unit are common. A new statistic, the normalized population variance, is introduced for multilocus estimation of demographic parameters, and for testing demographic scenarios. The observed population variation is not consistent with a constant population size. Time estimates of the putative population expansion are in agreement with those obtained by other methods.     

Detecting population growth, selection and inherited fertility from haplotypic data in humans

The frequency of a rare mutant allele and the level of allelic association between this allele and one or several closely linked markers are frequently measured in genetic epidemiology. Both quantities are related to the time elapsed since the appearance of the mutation in the population and the intrinsic growth rate of the mutation (which may be different from the average population growth rate). Here, we develop a method that uses these two kinds of genetic data to perform a joint estimation of the age of the mutation and the minimum growth rate that is compatible with its present frequency. In absence of demographic data, it provides a useful estimate of population growth rate. When such data are available, contrasts among estimates from several loci allow demographic processes, affecting all loci similarly, to be distinguished from selection, affecting loci differently. Testing these estimates on populations for which data are available for several disorders shows good congruence with demographic data in some cases whereas in others higher growth rates are obtained, which may be the result of selection or hidden demographic processes.     

Known unknowns in an imperfect world: incorporating uncertainty in recruitment estimates using multi‐event capture–recapture models

Studying the demography of wild animals remains challenging as several of the critical parts of their life history may be difficult to observe in the field. In particular, determining with certainty when an individual breeds for the first time is not always obvious. This can be problematic because uncertainty about the transition from a prebreeder to a breeder state – recruitment – leads to uncertainty in vital rate estimates and in turn in population projection models. To avoid this issue, the common practice is to discard imperfect data from the analyses. However, this practice can generate a bias in vital rate estimates if uncertainty is related to a specific component of the population and reduces the sample size of the dataset and consequently the statistical power to detect effects of biological interest. Here, we compared the demographic parameters assessed from a standard multistate capture–recapture approach to the estimates obtained from the newly developed multi‐event framework that specifically accounts for uncertainty in state assessment. Using a comprehensive longitudinal dataset on southern elephant seals, we demonstrated that the multi‐event model enabled us to use all the data collected (6639 capture–recapture histories vs. 4179 with the multistate model) by accounting for uncertainty in breeding states, thereby increasing the precision and accuracy of the demographic parameter estimates. The multi‐event model allowed us to incorporate imperfect data into demographic analyses. The gain in precision obtained has important implications in the conservation and management of species because limiting uncertainty around vital rates will permit predicting population viability with greater accuracy.     

Maximum-likelihood estimation of demographic parameters using the frequency spectrum of unlinked single-nucleotide polymorphisms

A maximum-likelihood method for demographic inference is applied to data sets consisting of the frequency spectrum of unlinked single-nucleotide polymorphisms (SNPs). We use simulation analyses to explore the effect of sample size and number of polymorphic sites on both the power to reject the null hypothesis of constant population size and the properties of two- and three-dimensional maximum-likelihood estimators (MLEs). Large amounts of data are required to produce accurate demographic inferences, particularly for scenarios of recent growth. Properties of the MLEs are highly dependent upon the demographic scenario, as estimates improve with a more ancient time of growth onset and smaller degree of growth. Severe episodes of growth lead to an upward bias in the estimates of the current population size, and that bias increases with the magnitude of growth. One data set of African origin supports a model of mild, ancient growth, and another is compatible with both constant population size and a variety of growth scenarios, rejecting greater than fivefold growth beginning >36,000 years ago. Analysis of a data set of European origin indicates a bottlenecked population history, with an 85% population reduction occurring approximately 30,000 years ago.     

The mid-depth method and HIV-1: a practical approach for testing hypotheses of viral epidemic history.

We introduce the mid-depth method, a practical approach for testing hypotheses of demographic history using genealogies reconstructed from sequence data. The relative positions of internal nodes within a genealogy contain information about past population dynamics. We explain how this information can be used to (1) test the null hypothesis of constant population size and (2) estimate the growth rate and current population size of an exponentially growing population. Simulation tests indicate that, as expected, estimates of exponential growth rates are sometimes biased. The mid-depth method is computationally rapid and does not require knowledge of the sample's mutation rate. However, it does assume that the reconstructed genealogy is correct and is therefore best suited to the analysis of variation-rich viral data sets. When applied to HIV-1 sequence data, the mid-depth method provides phylogenetic evidence of different exponential growth rates for subtypes A and B. We posit that this difference in growth rate reflects the different transmission routes and epidemiological histories of the two subtypes.     

Statistical guidelines for detecting past population shifts using ancient DNA

Populations carry a genetic signal of their demographic past, providing an opportunity for investigating the processes that shaped their evolution. Our ability to infer population histories can be enhanced by including ancient DNA data. Using serial-coalescent simulations and a range of both quantitative and temporal sampling schemes, we test the power of ancient mitochondrial sequences and nuclear single-nucleotide polymorphisms (SNPs) to detect past population bottlenecks. Within our simulated framework, mitochondrial sequences have only limited power to detect subtle bottlenecks and/or fast post-bottleneck recoveries. In contrast, nuclear SNPs can detect bottlenecks followed by rapid recovery, although bottlenecks involving reduction of less than half the population are generally detected with low power unless extensive genetic information from ancient individuals is available. Our results provide useful guidelines for scaling sampling schemes and for optimizing our ability to infer past population dynamics. In addition, our results suggest that many ancient DNA studies may face power issues in detecting moderate demographic collapses and/or highly dynamic demographic shifts when based solely on mitochondrial information.     

Detection of reduction in population size using data from microsatellite loci

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.     

Soft Selective Sweeps in Complex Demographic Scenarios

Adaptation from de novo mutation can produce so-called soft selective sweeps, where adaptive alleles of independent mutational origin sweep through the population at the same time. Population genetic theory predicts that such soft sweeps should be likely if the product of the population size and the mutation rate toward the adaptive allele is sufficiently large, such that multiple adaptive mutations can establish before one has reached fixation; however, it remains unclear how demographic processes affect the probability of observing soft sweeps. Here we extend the theory of soft selective sweeps to realistic demographic scenarios that allow for changes in population size over time. We first show that population bottlenecks can lead to the removal of all but one adaptive lineage from an initially soft selective sweep. The parameter regime under which such “hardening” of soft selective sweeps is likely is determined by a simple heuristic condition. We further develop a generalized analytical framework, based on an extension of the coalescent process, for calculating the probability of soft sweeps under arbitrary demographic scenarios. Two important limits emerge within this analytical framework: In the limit where population-size fluctuations are fast compared to the duration of the sweep, the likelihood of soft sweeps is determined by the harmonic mean of the variance effective population size estimated over the duration of the sweep; in the opposing slow fluctuation limit, the likelihood of soft sweeps is determined by the instantaneous variance effective population size at the onset of the sweep. We show that as a consequence of this finding the probability of observing soft sweeps becomes a function of the strength of selection. Specifically, in species with sharply fluctuating population size, strong selection is more likely to produce soft sweeps than weak selection. Our results highlight the importance of accurate demographic estimates over short evolutionary timescales for understanding the population genetics of adaptation from de novo mutation.     

Estimating divergence times from DNA sequences

The patterns of genetic variation within and among individuals and populations can be used to make inferences about the evolutionary forces that generated those patterns. Numerous population genetic approaches have been developed in order to infer evolutionary history. Here, we present the “Two-Two (TT)” and the “Two-Two-outgroup (TTo)” methods; two closely related approaches for estimating divergence time based in coalescent theory. They rely on sequence data from two haploid genomes (or a single diploid individual) from each of two populations. Under a simple population-divergence model, we derive the probabilities of the possible sample configurations. These probabilities form a set of equations that can be solved to obtain estimates of the model parameters, including population split times, directly from the sequence data. This transparent and computationally efficient approach to infer population divergence time makes it possible to estimate time scaled in generations (assuming a mutation rate), and not as a compound parameter of genetic drift. Using simulations under a range of demographic scenarios, we show that the method is relatively robust to migration and that the TTo method can alleviate biases that can appear from drastic ancestral population size changes. We illustrate the utility of the approaches with some examples, including estimating split times for pairs of human populations as well as providing further evidence for the complex relationship among Neandertals and Denisovans and their ancestors.     

Microsatellite mutations and inferences about human demography

Microsatellites have been widely used as tools for population studies. However, inference about population processes relies on the specification of mutation parameters that are largely unknown and likely to differ across loci. Here, we use data on somatic mutations to investigate the mutation process at 14 tetranucleotide repeats and carry out an advanced multilocus analysis of different demographic scenarios on worldwide population samples. We use a method based on less restrictive assumptions about the mutation process, which is more powerful to detect departures from the null hypothesis of constant population size than other methods previously applied to similar data sets. We detect a signal of population expansion in all samples examined, except for one African sample. As part of this analysis, we identify an "anomalous" locus whose extreme pattern of variation cannot be explained by variability in mutation size. Exaggerated mutation rate is proposed as a possible cause for its unusual variation pattern. We evaluate the effect of using it to infer population histories and show that inferences about demographic histories are markedly affected by its inclusion. In fact, exclusion of the anomalous locus reduces interlocus variability of statistics summarizing population variation and strengthens the evidence in favor of demographic growth.     

Joint estimation of migration rate and effective population size using the island model

Using the island model of population demography, I report that the demographic parameters migration rate and effective population size can be jointly estimated with equilibrium probabilities of identity in state calculated using a sample of genotypes collected at a single point in time from a single generation. The method, which uses moment-type estimators, applies to dioecious populations in which females and males have identical demography and monoecious populations with no selfing and requires that offspring genotypes are sampled following reproduction and prior to migration. I illustrate the estimation procedure using the infinite-island model with no mutation and the finite-island model with three kinds of mutation models. In the infinite-island model with no mutation, the estimators can be expressed as simple functions of estimates of the F-statistic parameters F(IT) and F(ST). In the finite-island model with mutation among k alleles, mutation rate, migration rate, and effective population size can be simultaneously estimated. The estimates of migration rate and effective population size are somewhat robust to violations in assumptions that may arise in empirical applications such as different kinds of mutation models and deviations from temporal equilibrium.     

Population bottlenecks and Pleistocene human evolution

We review the anatomical and archaeological evidence for anearly population bottleneck in humans and bracket the time whenit could have occurred. We outline the subsequent demographicchanges that the archaeological evidence of range expansionsand contractions address, and we examine how inbreeding effectivepopulation size provides an alternative view of past populationsize change. This addresses the question of other, more recent,population size bottlenecks, and we review nonrecombining andrecombining genetic systems that may reflect them. We examinehow these genetic data constrain the possibility of significantpopulation size bottlenecks (i.e., of sufficiently small sizeand/or long duration to minimize genetic variation in autosomaland haploid systems) at several different critical times inhuman history. Different constraints appear in nonrecombiningand recombining systems, and among the autosomal loci most areincompatible with any Pleistocene population size expansions.Microsatellite data seem to show Pleistocene population sizeexpansions, but in aggregate they are difficult to interpretbecause different microsatellite studies do not show the sameexpansion. The archaeological data are only compatible witha few of these analyses, most prominently with data from Aluelements, and we use these facts to question whether the viewof the past from analysis of inbreeding effective populationsize is valid. Finally, we examine the issue of whether inbreedingeffective population size provides any reasonable measure ofthe actual past size of the human species. We contend that ifthe evidence of a population size bottleneck early in the evolutionof our lineage is accepted, most genetic data either lack theresolution to address subsequent changes in the human populationor do not meet the assumptions required to do so validly. Itis our conclusion that, at the moment, genetic data cannot disprovea simple model of exponential population growth following abottleneck 2 MYA at the origin of our lineage and extendingthrough the Pleistocene. Archaeological and paleontologicaldata indicate that this model is too oversimplified to be anaccurate reflection of detailed population history, and thereforewe find that genetic data lack the resolution to validly reflectmany details of Pleistocene human population change. However,there is one detail that these data are sufficient to address.Both genetic and anthropological data are incompatible withthe hypothesis of a recent population size bottleneck. Suchan event would be expected to leave a significant mark acrossnumerous genetic loci and observable anatomical traits, butwhile some subsets of data are compatible with a recent populationsize bottleneck, there is no consistently expressed effect thatcan be found across the range where it should appear, and thisabsence disproves the hypothesis.     

Environmental stochasticity and extinction risk in a population of a small songbird, the great tit

Using a long-term demographic data set, we estimated the separate effects of demographic and environmental stochasticity in the growth rate of the great tit population in Wytham Wood, United Kingdom. Assuming logistic density regulation, both the demographic (sigma2d = 0.569) and environmental (sigma2e = 0.0793) variance, with interactions included, were significantly greater than zero. The estimates of the demographic variance seemed to be relatively insensitive to the length of the study period, whereas reliable estimates of the environmental variance required long time series (at least 15 yr of data). The demographic variance decreased significantly with increasing population density. These estimates are used in a quantitative analysis of the demographic factors affecting the risk of extinction of this population. The very long expected time to extinction of this population (approximately 10(19) yr) was related to a relatively large population size (>/=120 pairs during the study period). However, for a given population size, the expected time to extinction was sensitive to both variation in population growth rate and environmental stochasticity. Furthermore, the form of the density regulation strongly affected the expected time to extinction. Time to extinction decreased when the maximum density regulation approached K. This suggests that estimates of viability of small populations should be given both with and without inclusion of density dependence.     

The observed range for temporal mean-variance scaling exponents can be explained by reproductive correlation

The mean-variance scaling relationship known as Taylor's power law has been well documented empirically over the past four decades but a general theoretical explanation for the phenomenon does not exist. Here we provide an explanation that relates empirical patterns of temporal mean-variance scaling to individual level reproductive behavior. Initially, we review the scaling behavior of population growth models to establish theoretical limits for the scaling exponent b that is in agreement with the empirically observed range (1≤b≤2). We go on to show that the degree of reproductive covariance among individuals determines the scaling exponent b. Independent reproduction results in an exponent of one, while completely correlated reproduction results in the upper limit of two. Intermediate exponents, which are common empirically, can be generated through the decay of reproductive covariance with increasing population size. Finally, we describe how the link between reproductive correlation and the scaling exponent provides a way to infer properties of individual-level reproductive behavior, such as the relative influence of demographic stochasticity, from a macroecological pattern.     

Effects of recent population bottlenecks on reconstructing the demographic history of prairie-chickens

Current methods of DNA sequence analysis attempt to reconstruct historical patterns of population structure and growth from contemporary samples. However, these techniques may be influenced by recent population bottlenecks, which have the potential to eliminate lineages that reveal past changes in demography. One way to examine the performance of these demographic methods is to compare samples from populations before and after recent bottlenecks. We compared estimates of demographic history from populations of greater prairie-chickens (Tympanuchus cupido) before and after recent bottlenecks using four common methods (nested clade analysis [NCA], Tajima's D, mismatch distribution, and MDIV). We found that NCA did not perform well in the presence of bottleneck events, although it did recover some genetic signals associated with increased isolation and the extinction of intermediate populations. The majority of estimates for Tajima's D, including those from bottlenecked populations, were not significantly different from zero, suggesting our data conformed to neutral expectations. In contrast, mismatch distributions including the raggedness index were more likely to identify recently bottlenecked populations with this data set. Estimates of population mutation rate (theta), population divergence time (t), and time to the most recent common ancestor (TMRCA) from MDIV were similar before and after bottlenecks; however, estimates of gene flow (M) were significantly lower in a few cases following a bottleneck. These results suggest that caution should be used when assessing demographic history from contemporary data sets, as recently fragmented and bottlenecked populations may have lost lineages that affect inferences of their demographic history.     

Genomic data detect corresponding signatures of population size change on an ecological time scale in two salamander species

Understanding the demography of species over recent history (e.g. <100 years) is critical in studies of ecology and evolution, but records of population history are rarely available. Surveying genetic variation is a potential alternative to census‐based estimates of population size, and can yield insight into the demography of a population. However, to assess the performance of genetic methods, it is important to compare their estimates of population history to known demography. Here, we leveraged the exceptional resources from a wetland with 37 years of amphibian mark–recapture data to study the utility of genetically based demographic inference on salamander species with documented population declines (Ambystoma talpoideum) and expansions (A. opacum), patterns that have been shown to be correlated with changes in wetland hydroperiod. We generated ddRAD data from two temporally sampled populations of A. opacum (1993, 2013) and A. talpoideum (1984, 2011) and used coalescent‐based demographic inference to compare alternate evolutionary models. For both species, demographic model inference supported population size changes that corroborated mark–recapture data. Parameter estimation in A. talpoideum was robust to our variations in analytical approach, while estimates for A. opacum were highly inconsistent, tempering our confidence in detecting a demographic trend in this species. Overall, our robust results in A. talpoideum suggest that genome‐based demographic inference has utility on an ecological scale, but researchers should also be cognizant that these methods may not work in all systems and evolutionary scenarios. Demographic inference may be an important tool for population monitoring and conservation management planning.