Estimating quantitative genetic parameters in wild populations: a comparison of pedigree and genomic approaches

The estimation of quantitative genetic parameters in wild populations is generally limited by the accuracy and completeness of the available pedigree information. Using relatedness at genomewide markers can potentially remove this limitation and lead to less biased and more precise estimates. We estimated heritability, maternal genetic effects and genetic correlations for body size traits in an unmanaged long‐term study population of Soay sheep on St Kilda using three increasingly complete and accurate estimates of relatedness: (i) Pedigree 1, using observation‐derived maternal links and microsatellite‐derived paternal links; (ii) Pedigree 2, using SNP‐derived assignment of both maternity and paternity; and (iii) whole‐genome relatedness at 37 037 autosomal SNPs. In initial analyses, heritability estimates were strikingly similar for all three methods, while standard errors were systematically lower in analyses based on Pedigree 2 and genomic relatedness. Genetic correlations were generally strong, differed little between the three estimates of relatedness and the standard errors declined only very slightly with improved relatedness information. When partitioning maternal effects into separate genetic and environmental components, maternal genetic effects found in juvenile traits increased substantially across the three relatedness estimates. Heritability declined compared to parallel models where only a maternal environment effect was fitted, suggesting that maternal genetic effects are confounded with direct genetic effects and that more accurate estimates of relatedness were better able to separate maternal genetic effects from direct genetic effects. We found that the heritability captured by SNP markers asymptoted at about half the SNPs available, suggesting that denser marker panels are not necessarily required for precise and unbiased heritability estimates. Finally, we present guidelines for the use of genomic relatedness in future quantitative genetics studies in natural populations.     

Controlling population evolution in the laboratory to evaluate methods of historical inference

Natural populations of known detailed past demographic history are extremely valuable to evaluate methods of historical inference, yet are extremely rare. As an alternative approach, we have generated multiple replicate microsatellite data sets from laboratory-cultured populations of a gonochoric free-living nematode, Caenorhabditis remanei, that were constrained to pre-defined demographic histories featuring different levels of migration among populations or bottleneck events of different magnitudes. These data sets were then used to evaluate the performances of two recently developed population genetics methods, BayesAss+, that estimates recent migration rates among populations, and Bottleneck, that detects the occurrence of recent bottlenecks. Migration rates inferred by BayesAss+ were generally over-estimates, although these were often included within the confidence interval. Analyses of data sets simulated in-silico, using a model mimicking the laboratory experiments, produced less biased estimates of the migration rates, and showed increased efficiency of the program when the number of loci and sampled genotypes per population was higher. In the replicates for which the pre-bottleneck laboratory-cultured populations did not significantly depart from a mutation/drift equilibrium, an important assumption of the program Bottleneck, only a portion of the bottleneck events were detected. This result was confirmed by in-silico simulations mirroring the laboratory bottleneck experiments. More generally, our study demonstrates the feasibility, and highlights some of the limits, of the approach that consists in generating molecular genetic data sets by controlling the evolution of laboratory-reared nematode populations, for the purpose of validating methods inferring population history.     

Measuring Gene Flow among Populations Having High Levels of Genetic Fragmentation

We present an analysis of the genetic structures of 22 species of salamanders, with regard to levels of gene flow among populations. We estimate the gene flow parameter, Nm (the product of the effective population number and rate of migration among populations) using two alternative methods described by Wright and Slatkin. For most species, these two methods give approximately congruent estimates of Nm; when estimates differ, the method of Wright produces values slightly larger than those derived by the method of Slatkin. We analyze these results in light of independently derived historical inferences of the fragmentation of populations. This analysis suggests that the Nm values calculated from protein polymorphisms may contain information more relevant to historical patterns of gene exchange than to the current population dynamics; moderately large values of Nm may be calculated for species containing populations known to be no longer exchanging genes. Application of a method for estimating the maximum possible rate of gene exchange among populations indicates that, for most species studied here, gene flow among populations probably is no greater than the mutation rate. We suggest that most plethodontid species cannot be viewed as units whose cohesion is maintained by continuing gene exchange. Furthermore, we suggest that phenotypic uniformity among populations is not easily explained by hypotheses of continual stabilizing selection and propose that future work concentrate upon clarification of the genetic and epigenetic factors conferring self-maintenance or autopoietic properties on living systems.     

Comparison of confidence intervals for adjusted attributable risk estimates under multinomial sampling

The epidemiologic concept of the adjusted attributable risk is a useful approach to quantitatively describe the importance of risk factors on the population level. It measures the proportional reduction in disease probability when a risk factor is eliminated from the population, accounting for effects of confounding and effect-modification by nuisance variables. The computation of asymptotic variance estimates for estimates of the adjusted attributable risk is often done by applying the delta method. Investigations on the delta method have shown, however, that the delta method generally tends to underestimate the standard error, leading to biased confidence intervals. We compare confidence intervals for the adjusted attributable risk derived by applying computer intensive methods like the bootstrap or jackknife to confidence intervals based on asymptotic variance estimates using an extensive Monte Carlo simulation and within a real data example from a cohort study in cardiovascular disease epidemiology. Our results show that confidence intervals based on bootstrap and jackknife methods outperform intervals based on asymptotic theory. Best variants of computer intensive confidence intervals are indicated for different situations.     

Field surveys of capercaillie (<Emphasis Type="Italic">Tetrao urogallus</Emphasis>) in the Swiss Alps underestimated local abundance of the species as revealed by genetic analyses of non-invasive samples

An increasing number of species are becoming threatened by habitat loss and fragmentation. Therefore, solid estimates of the species’ abundance in the remaining populations are required to develop suitable conservation measures and to monitor their effectiveness. The capercaillie (Tetrao urogallus L.) has experienced a dramatic decline in central Europe and has disappeared from large areas of its former natural range. In Switzerland, the species’ distribution, habitat requirements and demographic status were studied and evaluated in an attempt to support appropriate management decisions to conserve the species. National surveys of the capercaillie in Switzerland have traditionally been obtained from male counts at leks. However, individual attendance to the lek is sex- and age-specific. Thus, male counts at leks may provide a biased estimate of local population sizes. In the present study, we compared two alternative indirect methods to estimate the sizes of local populations at eight study sites situated in the Alps and Prealps of Switzerland. We first assessed the sizes of local populations from the observed density and distribution of direct and indirect evidence of the species’ presence during field surveys. Feather and faeces samples collected during field surveys were genotyped at twelve nuclear microsatellite loci and a sex-specific nuclear gene fragment. Individual genotypes were used as genetic tags to estimate the sizes of the eight local populations using an urn model developed for small populations. The index of local population sizes assessed from field surveys was lower than the number of unique genotypes at each study site, which itself underestimated the abundances of populations in most cases. Based on our results, the genetic tagging method appeared to be less biased than the field survey method. However, an alternative faeces sampling scheme, resulting in 2–3 genotypings per individual, could further improve the accuracy of the size estimates of local populations. Our study confirms that genetic tagging methods are a valuable tool to estimate the sizes of local populations and to monitor the response of rare and elusive species to management actions.     

Estimating Abundance of an Unmarked,Low-Density Species using Cameras

Estimating abundance of wildlife populations can be challenging and costly, especially for species that are difficult to detect and that live at low densities, such as cougars (Puma concolor). Remote, motion-sensitive cameras are a relatively efficient monitoring tool, but most abundance estimation techniques using remote cameras rely on some or all of the population being uniquely identifiable. Recently developed methods estimate abundance from encounter rates with remote cameras and do not require identifiable individuals. We used 2 methods, the time-to-event and space-to-event models, to estimate the density of 2 cougar populations in Idaho, USA, over 3 winters from 2016–2019. We concurrently estimated cougar density using the random encounter model (REM), an existing camera-based method for unmarked populations, and genetic spatial capture recapture (SCR), an established method for monitoring cougar populations. In surveys for which we successfully estimated density using the SCR model, the time-to-event estimates were more precise and showed comparable variation between survey years. The space-to-event estimates were less precise than the SCR estimates and were more variable between survey years. Compared to REM, time-to-event was more precise and consistent, and space-to-event was less precise and consistent. Low sample sizes made the space-to-event and SCR models inconsistent from survey to survey, and non-random camera placement may have biased both of the camera-based estimators high. We show that camera-based estimators can perform comparably to existing methods for estimating abundance in unmarked species that live at low densities. With the time- and space-to-event models, managers could use remote cameras to monitor populations of multiple species at broader spatial and temporal scales than existing methods allow. © 2020 The Wildlife Society.     

Parentage assignment detects frequent and large-scale dispersal in water voles

Estimating the rate and scale of dispersal is essential for predicting the dynamics of fragmented populations, yet empirical estimates are typically imprecise and often negatively biased. We maximized detection of dispersal events between small, subdivided populations of water voles (Arvicola terrestris) using a novel method that combined direct capture-mark-recapture with microsatellite genotyping to identify parents and offspring in different populations and hence infer dispersal. We validated the method using individuals known from trapping data to have dispersed between populations. Local populations were linked by high rates of juvenile dispersal but much lower levels of adult dispersal. In the spring breeding population, 19% of females and 33% of males had left their natal population of the previous year. The average interpopulation dispersal distance was 1.8 km (range 0.3-5.2 km). Overall, patterns of dispersal fitted a negative exponential function. Information from genotyping increased the estimated rate and scale of dispersal by three- and twofold, respectively, and hence represents a powerful tool to provide more realistic estimates of dispersal parameters.     

Design and Analysis of Line Transect Surveys for Primates

Line transect surveys are widely used for estimating abundance of primate populations. The method relies on a small number of key assumptions, and if these are not met, substantial bias may occur. For a variety of reasons, primate surveys often do not follow what is generally considered to be best practice, either in survey design or in analysis. The design often comprises too few lines (sometimes just 1), subjectively placed or placed along trails, so lacks both randomization and adequate replication. Analysis often involves flawed or inefficient models, and often uses biased estimates of the locations of primate groups relative to the line. We outline the standard method, emphasizing the assumptions underlying the approach. We then consider options for when it is difficult or impossible to meet key assumptions. We explore the performance of these options by simulation, focusing particularly on the analysis of primate group sizes, where many of the variations in survey methods have been developed. We also discuss design issues, field methods, analysis, and potential alternative methodologies for when standard line transect sampling cannot deliver reliable abundance estimates.     

Can population growth rates vary with the spatial scale at which they are measured?

1.  The ratio of successive population censuses is often assumed to reflect population growth rates. We identify three simple potential sources of bias in the estimation of population growth rates that relate to either the total number of censused individuals or the spatial areas over which censuses are conducted.
2.  The commonly used method of adding a constant to time series data to avoid problems caused by division by zero can lead to underestimation of growth rates at low densities in increasing populations.
3.  Variances associated with density estimates can lead to positive bias in estimation of growth rates when populations are distributed in ephemeral patches. The spatial variance and spatio-temporal covariance in bank vole census data suggest that this bias could be severe when small trapping grids are used. Use of logged estimators of growth rate avoids this problem.
4.  Using census data from non-randomly placed trapping grids that are smaller than twice the maximum range of natal dispersal to estimate population growth rates can lead to negatively biased estimates, particularly at low population densities.
5.  These three sources of bias are evaluated as explanations for scale-dependent changes in the estimates of growth rates identified in populations of snowshoe hare ( Lepus americanus ), bank voles ( Clethrionomys glareolus ) and lemmings ( Lemmus lemmus ).     

Concordant genetic estimators of migration reveal anthropogenically enhanced source-sink population structure in the river sculpin, Cottus gobio

River systems are vulnerable to natural and anthropogenic habitat fragmentation and will often harbor populations deviating markedly from simplified theoretical models. We investigated fine-scale population structure in the sedentary river fish Cottus gobio using microsatellites and compared migration estimates from three FST estimators, a coalescent maximum-likelihood method and Bayesian recent migration analyses. Source-sink structure was evident via asymmetry in migration and genetic diversity with smaller upstream locations emigration biased and larger downstream subpopulations immigration biased. Patterns of isolation by distance suggested that the system was largely, but not entirely, in migration-drift equilibrium, with headwater populations harboring a signal of past colonizations and in some cases also recent population bottlenecks. Up- vs. downstream asymmetry in population structure was partly attributable to the effects of flow direction, but was enhanced by weirs prohibiting compensatory upstream migration. Estimators of migration showed strong correspondence, at least in relative terms, especially if pairwise FST was used as an indirect index of relative gene flow rather than being translated to Nm. Since true parameter values are unknown in natural systems, comparisons among estimators are important, both to determine confidence in estimates of migration and to validate the performance of different methods.     

Abundance of rare and elusive species: Empirical investigation of closed versus spatially explicit capture–recapture models with lynx as a case study

Effective conservation and management require reliable monitoring methods and estimates of abundance to prioritize human and financial investments. Camera trapping is a non-invasive sampling method allowing the use of capture–recapture (CR) models to estimate abundance while accounting for the difficulty of detecting individuals in the wild. We investigated the relative performance of standard closed CR models and spatially explicit CR models (SECR) that incorporate spatial information in the data. Using simulations, we considered 4 scenarios comparing low versus high detection probability and small versus large populations and contrasted abundance estimates obtained from both approaches. Standard CR and SECR models both provided minimally biased abundance estimates, but precision was improved when using SECR models. The associated confidence intervals also provided better coverage than their non-spatial counterpart. We concluded SECR models exhibit better statistical performance than standard closed CR models and allow for sound management strategies based on density maps of activity centers. To illustrate the comparison, we considered the Eurasian lynx (Lynx lynx) as a case study that provided the first abundance estimates of a local population in France. © 2012 The Wildlife Society.     

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.     

Line Transect Sampling of Primates: Can Animal-to-Observer Distance Methods Work?

Line transect sampling is widely used for estimating abundance of primate populations. Researchers commonly use animal-to-observer distances (AODs) in analysis, in preference to perpendicular distances from the line, which is in marked contrast with standard practice for other applications of line transect sampling. We formalize the mathematical shortcomings of approaches based on AODs, and show that they are likely to give strongly biased estimates of density. We review papers that claim good performance for the method, and explore this performance through simulations. These confirm strong bias in estimates of density using AODs. We conclude that AOD methods are conceptually flawed, and that they cannot in general provide valid estimates of density.     

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.     

A genome-wide departure from the standard neutral model in natural populations of Drosophila

We analyze nucleotide polymorphism data for a large number of loci in areas of normal to high recombination in Drosophila melanogaster and D. simulans (24 and 16 loci, respectively). We find a genome-wide, systematic departure from the neutral expectation for a panmictic population at equilibrium in natural populations of both species. The distribution of sequence-based estimates of 2Nc across loci is inconsistent with the assumptions of the standard neutral theory, given the observed levels of nucleotide diversity and accepted values for recombination and mutation rates. Under these assumptions, most estimates of 2Nc are severalfold too low; in other words, both species exhibit greater intralocus linkage disequilibrium than expected. Variation in recombination or mutation rates is not sufficient to account for the excess of linkage disequilibrium. While an equilibrium island model does not seem to account for the data, more complicated forms of population structure may. A proper test of alternative demographic models will require loci to be sampled in a more consistent fashion.     

Testing marker-based estimates of heritability in the wild

Marker-based estimates of heritability are an attractive alternative to pedigree-based methods for estimating quantitative genetic parameters in field studies where it is difficult or impossible to determine relationships and pedigrees. Here I test the ability of the marker-based method to estimate heritability of a suite of traits in a wild population of bighorn sheep (Ovis canadensis) using marker data from 32 microsatellite loci. I compared marker-based estimates with estimates obtained using a pedigree and the animal model. Marker-based estimates of heritability were imprecise and downwardly biased. The high degree of uncertainty in marker-based estimates suggests that the method may be sufficient to detect the presence of genetic variance for highly heritable traits, but not sufficiently reliable to estimate genetic parameters.     

A Comparison of Methods to Measure Fitness in Escherichia coli

In order to characterize the dynamics of adaptation, it is important to be able to quantify how a population’s mean fitness changes over time. Such measurements are especially important in experimental studies of evolution using microbes. The Long-Term Evolution Experiment (LTEE) with Escherichia coli provides one such system in which mean fitness has been measured by competing derived and ancestral populations. The traditional method used to measure fitness in the LTEE and many similar experiments, though, is subject to a potential limitation. As the relative fitness of the two competitors diverges, the measurement error increases because the less-fit population becomes increasingly small and cannot be enumerated as precisely. Here, we present and employ two alternatives to the traditional method. One is based on reducing the fitness differential between the competitors by using a common reference competitor from an intermediate generation that has intermediate fitness; the other alternative increases the initial population size of the less-fit, ancestral competitor. We performed a total of 480 competitions to compare the statistical properties of estimates obtained using these alternative methods with those obtained using the traditional method for samples taken over 50,000 generations from one of the LTEE populations. On balance, neither alternative method yielded measurements that were more precise than the traditional method.     

The impact of homologous recombination on the generation of diversity in bacteria

The imprint of demographic and selective processes on bacterial population structure needs to be evaluated as deviation from the expectations of an appropriate null neutral model. We explore the impact of varying the population mutation and recombination rates theta and rho on ideal populations, using a recently developed model of neutral drift at multiple loci. This model may be fitted to experimental data to provide estimates of these parameters, and we do so for seven bacterial species (Neisseria meningitidis, Streptococcus pneumoniae, Streptococcus pyogenes, Staphylococcus aureus, Helicobacter pylori, Burkholderia pseudomallei and Bacillus cereus), illustrating that bacterial species vary extensively in these fundamental parameters. Historically, the influence of recombination has often been estimated through its influence on the Index of Association I(A). We show that this may be relatively insensitive to changes in either mutation or recombination rates. It is known that biased sampling can lead to artificially high estimates of I(A). We therefore provide a method of precisely separating the effects of such bias and true linkage between alleles. We also demonstrate that by fitting the neutral model to experimental data, more informative and precise estimates of the relative roles of recombination and mutation may be obtained.     

Statewide and local recruitment of mourning doves in Missouri

Intensive harvests have the potential to greatly affect local mourning dove (Zenaida macroura) populations, a popular gamebird and songbird. To evaluate if recruitment was commensurate with harvest, we applied a ratio-based method to estimate local and statewide mourning dove recruitment across 7 public hunting areas in Missouri from 2005 to 2011. We estimated recruitment from preharvest adult sex ratios and harvest age ratios that incorporated various methods to address potential inherent biases (e.g., bias in the adults of unknown sex in preharvest samples, bias in unknown age wings, and local differential vulnerability; DV). Data from 356 radio-marked doves revealed a DV rate, where hatch year doves were, on average 2.7× more likely to be harvested than adult doves. Recruitment estimates for local areas were highly variable and in some cases, biologically unrealistic (e.g., >10 offspring/female), because of small preharvest sample sizes. However, data pooled statewide provided recruitment estimates of 3.1 offspring/female (±0.3 SE) or 4.1 offspring/female (±0.3 SE), assuming samples of unknown sex doves were female biased or male biased, respectively. Although statewide estimates agree with directly observed rates, the sex ratios and differential vulnerability comprising them vary considerably from what has been previously assumed. Whether preharvest sex ratios are biased from trapping methods has 2 important implications; either regional approaches have overestimated recruitment or the number of females in Missouri's population is much less than originally thought. Because each of these scenarios are important to understanding the effects of regional harvest management on Missouri's dove population, they highlight the importance of a better understanding of biases involved in estimating recruitment. © 2012 The Wildlife Society.     

Comparing relative rates of pollen and seed gene flow in the island model using nuclear and organelle measures of population structure

We describe a method for comparing nuclear and organelle population differentiation (F(ST)) in seed plants to test the hypothesis that pollen and seed gene flow rates are equal. Wright's infinite island model is used, with arbitrary levels of self-fertilization and biparental organelle inheritance. The comparison can also be applied to gene flow in animals. Since effective population sizes are smaller for organelle genomes than for nuclear genomes and organelles are often uniparentally inherited, organelle F(ST) is expected to be higher at equilibrium than nuclear F(ST) even if pollen and seed gene flow rates are equal. To reject the null hypothesis of equal seed and pollen gene flow rates, nuclear and organelle F(ST)'s must differ significantly from their expected values under this hypothesis. Finite island model simulations indicate that infinite island model expectations are not greatly biased by finite numbers of populations (>/=100 subpopulations). The power to distinguish dissimilar rates of pollen and seed gene flow depends on confidence intervals for fixation index estimates, which shrink as more subpopulations and loci are sampled. Using data from the tropical tree Corythophora alta, we rejected the null hypothesis that seed and pollen gene flow rates are equal but cannot reject the alternative hypothesis that pollen gene flow is 200 times greater than seed gene flow.