Biology subjects

Waples, R. S.

Publications and source records attributed to Waples, R. S..

16 recordsLinked to original sources

bioRxiv2026

An exact formula for the contribution of sampling error to r2, a common measure of linkage disequilibrium

Interest in quantifying linkage disequilibrium (LD, non-random associations of alleles at different loci) has skyrocketed in recent years as researchers have focused on use of LD in genome-wide association studies (GWAS), for studying historical demography, and for estimating effective population size (Ne). The most widely used LD metric is r2 = the squared correlation of alleles at a pair of loci. Despite a half century of efforts, developing an unbiased expectation of r2 as a function of the many factors that can affect it (physical linkage, genetic drift, selection, migration, mutation, mating systems) remains elusive. Furthermore, even when all of these other factors are absent, empirical estimates of r2 are upwardly biased by sampling a finite number (S) of individuals, and that must be accounted for if one wants to focus on the desired signal of LD. Previous approaches to estimate [Formula] have been shown to be biased to greater or lesser degrees. The purpose of this short paper is to demonstrate that a simple and apparently exact expression for [Formula] does exist for the special case where sampling error is the only factor contributing to r2, in which case [Formula] = 1/(S - 1). When other factors contribute heavily to LD, [Formula] shrinks toward 0 as empirical r2 [->] 1. However, for estimating contemporary Ne with unlinked markers, empirical r2 will generally be small and 1/(S - 1) will provide a robust estimate of [Formula].

evolutionary biology↗

bioRxiv2026

Extremely low effective population size in a captive-bred population: partial mitigation through management practices

1Effective population size (Ne) is a critical parameter for evaluating the evolutionary and persistence potential of endangered populations and for designing sustainable conservation strategies. Captive breeding and release programs are widely used across taxa to reduce risk of extinction when natural reproduction is insufficient or no longer possible, making it essential to assess their consequences. We used the case study of the landlocked Saimaa salmon (Salmo salar), one of the most critically en-dangered salmonid populations in Europe, with unique evolutionary significance due to its isolation from other populations since the last glaciation. Using long-term demographic data (1969-2024) from wild-caught founders of a captive breeding and release program, we estimated the effective population size under multiple scenarios of variance in reproductive success. Across scenarios, Ne ranged from 33 to 81 individuals, representing 32%-75% of the census size. Captive breeding practices aimed at equalizing parental contributions during fertilization and early life stages increased Ne by 12% compared to natural reproductive conditions. However, variation in survival after early developmental stages, typically beyond direct management control, remained a key determinant of Ne. Despite recent increases in the number of founders, the population remains genetically vulnerable due to historical bottlenecks. These results highlight that while captive breeding programs can partially mitigate genetic risks, their effectiveness depends critically on both controlled and uncontrolled sources of variance in reproductive success. Strengthening such programs may require combining breeding management with habitat restoration and, where appropriate, genetic rescue to ensure the long-term evolutionary potential of such unique and endangered populations.

evolutionary biology↗

bioRxiv2026

Extreme male reproductive skew limits effective population size in American Standardbred horses

Standardbred horses are widely used for harness racing in North America, Europe, Australia, and New Zealand. In the U.S., two gaits (Pacers and Trotters) are genetically differentiated at a level typical for different horse breeds. We used the complete pedigree for all registered American Standardbred foals born 1970-2014 (>200K Trotters and >500K Pacers) to calculate annual and lifetime reproductive skew and its consequences for the effective number of breeders per year (Nb) and effective size per generation (Ne). With rare exceptions, females can only produce 0 or 1 foal per year, which limits annual and lifetime variance in offspring number. These constraints do not apply to males: with humans (rather than horses) deciding who breeds with whom, and how often, the most prolific stud regularly sires well over 100 foals each year and often over 1000 across its lifetime. Male reproductive skew increased over time in both gaits, with the most prolific studs producing 20% or more of all foals sired by members of their birth cohort. Although each gait in the U.S. is represented by tens of thousands of adult horses at any given time, male Ne is typically in the low hundreds, which drives the overall Ne/N ratio to or below 0.01--a value often considered to be "tiny." Ne/N ratios this low have rarely been reported for large mammals and generally are thought to apply primarily to some marine species with very high fecundity. When Ne/N is this low, even large populations can experience substantial erosion of genetic diversity.

evolutionary biology↗

bioRxiv2025

Anthropocene genetic diversity loss in the marine tropics

Genetic diversity is a crucial component of biodiversity, and as such, its maintenance and preservation is of high conservation concern. Tropical environments are undergoing intense rates of environmental change, and these changes may be driving large declines in genetic diversity. However, data on genetic diversity are highly skewed towards temperate regions. The degree to which diversity loss has occurred in tropical species, particularly marine species, remains an open and important question. Here, we directly compare genomic data from modern and museum collections of two commercially-harvested nearshore marine fishes (Equulites laterofenestra and Gazza minuta) gathered from a single location in the Philippines, spanning a century of intense environmental change. These data reveal a marked loss in genetic diversity and evidence for multiple orders of magnitude reductions in effective population size (Ne) in both species, indicating substantial genomic erosion. Such a decline highlights the long-lasting genomic consequences of anthropogenic activity and sheds light on an, until-now, invisible loss of diversity from the most biodiverse ocean region. Significance StatementRecent reports have shown that genetic diversity in marine fishes has declined either slightly or not at all during the Anthropocene. However, almost all studies investigating marine genetic diversity loss have been from temperate latitudes, whereas tropical marine environments experience some of the most intense human impacts. Here, we directly compare genomic data from modern and historical specimens of two commercially-harvested fishes from the Philippines. We show that marine species in the tropics have already lost substantial genetic diversity and may have undergone severe bottlenecks over the past century. These results shine a light on the previously invisible loss of genetic diversity in the most biodiverse region of the ocean, and they emphasize the evolutionary consequences of the Anthropocene.

ecology↗

bioRxiv2025

Combining multiple genetic estimates of Ne

Researchers often use multiple genetic methods to estimate contemporary effective population size (Ne), but few formally combine estimates despite potential benefits for increasing precision. Maximizing benefits requires an optimal, inverse-variance weighting scheme. Methods should be estimating the same parameter, which can be appropriate either for estimates using the same method applied to different time periods, or estimates using different methods applied to the same time period. Previous approaches focused on [Formula] for weighting, but that is problematical because [Formula] is highly skewed and can be infinitely large. A new approach is described using weights inversely proportional to [Formula], which is the drift signal that [Formula] estimation methods respond to. The distribution of [Formula] is close to normal even when [Formula] assumes extreme values. Benefits are maximized under three general conditions: estimators have approximately equal variances; they are uncorrelated or have weak positive correlations; individual estimates have low precision (i.e., if data are limited and/or true Ne is large). Analytical and numerical results demonstrate that: (1) existing theory allows robust estimates of [Formula] for the temporal and LD methods, which provide independent information about Ne - both of which facilitate optimally combining those methods; (2) estimates for the LD and sibship methods are essentially uncorrelated when data are limited but can be strongly positively correlated in genomics-scale datasets. General theory predicting [Formula] for the sibship method is lacking, but values for specific scenarios have been published. New software (CO_SCPLOWOMBOC_SCPLOWNO_SCPLOWEC_SCPLOW) is introduced to calculate combined estimates.

evolutionary biology↗

bioRxiv2024

Practical considerations regarding estimating Ne when generations overlap

Researchers studying species in nature often find it challenging to apply methods based on simplistic models of reality. Here I consider how some real-world complications influence demographic estimates of effective population size (Ne) when generations overlap. The most widely-used model (by Hill) expresses Ne as a function of variance in lifetime reproductive output (LRO) of the N1 members of a newborn cohort. Hills model assumes stable age structure and constant population size, in which case mean [Formula]. In real-world applications, researchers often ask whether unbiased estimates can be obtained under the following conditions: (1) When [Formula] for empirical data; (2) If cohorts are defined at a later age than newborns; (3) If survival to age at sexual maturity () is not random; (4) When some or all null parents (those with LRO=0) are not sampled. Using analytical methods and computer simulations, I show that: (1) Because variance in offspring number is positively correlated with the mean, [Formula] will be biased using raw data when [Formula], but this bias can be overcome by rescaling var(LRO) to its expected value when [Formula]. (2) The cohort can be defined at any age [≤], provided that (a) LRO data cover the full lifespan (e.g., production of newborns by newborns, or production of adults by adults), and (b) survival to age is random. (3) If juvenile survival is family-correlated, defining cohorts at age avoids upward bias in [Formula] that occurs if newborn cohorts are used. (4) Missing some or all null parents has no effect on [Formula], provided that data are rescaled to [Formula].

evolutionary biology↗

bioRxiv2024

MAXTEMP: A method to maximize precision of the temporal method for estimating Ne in genetic monitoring programs

We introduce a new software program, MAXTEMP, that maximizes precision of the temporal method for estimating effective population size (Ne) in genetic monitoring programs, which are increasingly used to systematically track changes in global biodiversity. Scientists and managers are typically most interested in Ne for individual generations, either to match with single-generation estimates of census size (N) or to evaluate consequences of specific management actions or environmental events. Systematically sampling every generation produces a time series of single-generation estimates of temporal [Formula], which can then be used to estimate Ne; however, these estimates have relatively low precision because each reflects just a single episode of genetic drift. Systematic sampling also produces an array of multigenerational temporal estimates that collectively contain a great deal of information about genetic drift that, however, can be difficult to interpret. Here we show how additional information contained in multigenerational temporal estimates can be leveraged to increase precision of [Formula] for individual generations. Using information from one additional generation before and after a target generation can reduce the standard deviation of [Formula] by up to 50%, which not only tightens confidence intervals around [Formula] but also reduces the incidence of extreme estimates. Practical application of MAXTEMP is illustrated with data for a long-term genetic monitoring program for California delta smelt. A second feature of MAXTEMP, which allows one to estimate Ne in an unsampled generation using a combination of temporal and single-sample estimates of Ne from sampled generations, is also described and evaluated.

genetics↗

bioRxiv2023

Robustness of the overlapping-generation method of Hill for calculating Ne to extreme violations of model assumptions

For species with overlapping generations, the most widely-used method to calculate effective population size (Ne) is Hills, the key parameter for which is lifetime variance in offspring number (Vk*). Hills model assumes stable age structure and constant abundance, and sensitivity to those assumptions has been evaluated previously. Here I evaluate robustness of Hills model to extreme patterns of reproductive success, whose effects have not been previously examined: 1) very strong reproductive skew; 2) strong temporal autocorrelations in individual reproductive success; and 3) strong covariance of individual reproduction and survival. Genetic drift (loss of heterozygosity and increase in allele-frequency variance) was simulated in age-structured populations using methods that: generated no autocorrelations or covariances (Model NoCor); or created strong positive (Model Positive) or strong negative (Model Negative) temporal autocorrelations in reproduction and covariances between reproduction and survival. Compared to Model NoCor, the other models led to greatly elevated or reduced Vk*, and hence greatly reduced or elevated Ne, respectively. A new index is introduced ({rho},+), which is the correlation between 1) the number of offspring produced by each individual at the age at maturity (), and 2) the total number of offspring produced during the rest of their lifetimes. Mean {rho},+ was {approx}0 under Model NoCor, strongly positive under Model Positive, and strongly negative under Model Negative. Even under the most extreme reproductive scenarios in Models Positive and Negative, when Vk* was calculated from the realized population pedigree and used to calculate Ne in Hills model, the result accurately predicted the rate of genetic drift in simulated populations. These results held for scenarios where age-specific reproductive skew was random (variance{approx}mean) and highly overdispersed (variance up to 20 times the mean). Collectively, these results are good news for researchers as they demonstrate the robustness of Hills model even to extreme repro0ductive scenarios.

evolutionary biology↗

bioRxiv2022

Null models for the Opportunity for Selection

Crows Opportunity for Selection (I=variance in relative fitness) is an important albeit controversial eco-evolutionary concept, particularly regarding the most appropriate null model(s). Here we treat this topic in a comprehensive way by considering opportunities for both fertility selection (If) and viability selection (Im) for discrete generations, both seasonal and lifetime reproductive success in age-structured species, and for experimental designs that include either a full or partial life cycle, with complete enumeration or random subsampling. For each scenario, a null model that includes random demographic stochasticity can be constructed that follows Crows initial formulation that I=If+Im. The two components of I are qualitatively different. Whereas an adjusted If ({Delta}If) can be computed that accounts for random demographic stochasticity in offspring number, Im cannot be similarly adjusted in the absence of data on phenotypic traits under viability selection. Including as potential parents some individuals that die before reproductive age produces an overall, zero-inflated-Poisson null model. It is always important to remember that (1) Crows I represents only the opportunity for selection and not selection itself, and (2) the species biology can lead to random stochasticity in offspring number that is either overdispersed or underdispersed compared to the Poisson (Wright-Fisher) expectation.

evolutionary biology↗

bioRxiv2022

Partitioning variance in reproductive success, within years and across lifetimes

Variance in reproductive success ([Formula], with k=number of offspring) plays a large role in determining the rate of genetic drift and the scope within which selection acts. Various frameworks have been proposed to parse factors that contribute to [Formula], but none has focused on age-specific values of [Formula], which indicate the degree to which reproductive skew is overdispersed (compared to the random Poisson expectation) among individuals of the same age and sex. Here, an ANOVA sums-of-squares framework is used to partition variance in annual and lifetime reproductive success into between-group and within-group components. For annual reproduction, the between-age effect depends on age-specific fecundity (bx), but relatively few empirical data are available on the within-age effect, which depends on{phi} x. By defining groups by age-at-death rather than age, the same ANOVA framework can be used to partition variance in lifetime reproductive success into between-group, within-group, and longevity components. Analyses of simulated data and worked examples for black bears and great tits illustrate the methods and show that the largely-neglected within-age effect a) typically represents a substantial component of the overall variance (even under a null model of random reproductive success), and b) can dominate the overall variance when{phi} x>1.

evolutionary biology↗

bioRxiv2022

THEWEIGHT: A simple and flexible algorithm for simulating non-ideal, age-structured populations

O_LIThe Wright-Fisher model, which directs how matings occur and how genes are transmitted across generations, has long been a lynchpin of evolutionary biology. This model is elegantly simple, analytically tractable, and easy to implement, but it has one serious limitation: essentially no real species satisfies its many assumptions. With growing awareness of the importance of jointly considering both ecology and evolution in eco-evolutionary models, this limitation has become more apparent, causing many researchers to search for more realistic simulation models. C_LIO_LIA recently described variation retains most of the Wright-Fisher simplicity but provides greater flexibility to accommodate departures from model assumptions. This generalized Wright-Fisher model relaxes the assumption that all individuals have identical expected reproductive success by introducing a vector of parental weights w that specifies relative probabilities different individuals have of producing offspring. With parental weights specified this way, expectations of key demographic parameters are simple functions of w. This allows researchers to quantitatively predict the consequences of non-Wright-Fisher features incorporated into their models. C_LIO_LIAn important limitation of the Wright-Fisher model is that it assumes discrete generations, whereas most real species are age-structured. Here I show how an algorithm (TO_SCPLOWHEC_SCPLOWWO_SCPLOWEIGHTC_SCPLOW) that implements the generalized Wright-Fisher model can be used to model evolution in age-structured populations with overlapping generations. Worked examples illustrate simulation of seasonal and lifetime reproductive success and show how the user can pick vectors of weights expected to produce a desired level of reproductive skew or a desired Ne/N ratio. Alternatively, weights can be associated with heritable traits to provide a simple, quantitative way to model natural selection. Using TO_SCPLOWHEC_SCPLOWWO_SCPLOWEIGHTC_SCPLOW, it is easy to generate positive or negative correlations of individual reproductive success over time, thus allowing explicit modeling of common biological processes like skip breeding and persistent individual differences. C_LIO_LICode is provided to implement basic features of TO_SCPLOWHEC_SCPLOWWO_SCPLOWEIGHTC_SCPLOW and applications described here. However, required coding changes to the Wright-Fisher model are modest, so the real value of the new algorithm is to encourage users to adopt its features into their own or others models. C_LI

evolutionary biology↗

bioRxiv2021

Relative precision of the sibship and LD methods for estimating effective population size with genomics-scale datasets

Computer simulations were used to compare relative precision of two widely-used single-sample methods for estimating effective population size (Ne)--the sibship method and the linkage-disequilibrium (LD) method. Emphasis is on performance when thousands of gene loci are used, which now can easily be achieved even for non-model species. Results show that unless Ne is very small, if at least 500-2000 diallelic loci are used, precision of the LD method is higher than the maximum possible precision for the sibship method, which occurs when all sibling relationships have been correctly identified. Results also show that when precision is high for both methods, their estimates of effective population size are high and positively correlated, which limits additional gains in precision that might be obtained by combining information from the two estimators.

genetics↗

bioRxiv2021

Close-kin methods to estimate census size and effective population size

The last two decades have witnessed rapid developments and increasing interest in use of (1) genetic methods to estimate effective population size (Ne) and (2) close-kin mark-recapture (CKMR) methods to estimate abundance based on the incidence of close relatives. Whereas Ne estimation methods have been applied to a wide range of taxa, all CKMR applications to date have been for aquatic species. These two fields of inquiry have developed largely independently, and this is unfortunate because deeper insights can be gained by joint evaluation of eco-evolutionary processes. In this synthesis, we use simple analytical models and simulated pedigree data to illustrate how various factors (life-history traits; patterns of variation in individual reproductive success; experimental design; stochasticity; marker type) can affect performance of the estimators. We show that the Ne/N ratio and the probability of a close-kin match both depend on a vector of parental weights that specify relative probabilities that different individuals will produce offspring. Although age-specific vital rates are central to both methodologies, for CKMR they can potentially bias abundance estimates unless properly accounted for, whereas they represent the signals of genetic drift that Ne estimation methods depend upon. Coordinating Ne and CKMR estimation methods using the same or overlapping datasets would facilitate joint evaluation of both the ecological and evolutionary consequences of abundance.

evolutionary biology↗

bioRxiv2020

Pseudoreplication in genomics-scale datasets

In genomics-scale datasets, loci are closely packed within chromosomes and hence provide correlated information. Averaging across loci as if they were independent creates pseudoreplication, which reduces the effective degrees of freedom (df) compared to the nominal degrees of freedom, df. This issue has been known for some time, but consequences have not been systematically quantified across the entire genome. Here we measured pseudoreplication (quantified by the ratio df/df) for a common metric of genetic differentiation (FST) and a common measure of linkage disequilibrium between pairs of loci (r2). Based on data simulated using models (SLiM and msprime) that allow efficient forward-in-time and coalescent simulations while precisely controlling population pedigrees, we estimated df and df/df by measuring the rate of decline in the variance of mean FST and mean r2 as more loci were used. For both indices, df increases with Ne and genome size, as expected. However, even for large Ne and large genomes, df for mean r2 plateaus after a few thousand loci, and a variance components analysis indicates that the limiting factor is uncertainty associated with sampling individuals rather than genes. Pseudoreplication is less extreme for FST, but df/df [≤]0.01 can occur in datasets using tens of thousands of loci. Commonly-used block-jackknife methods consistently overestimated var(FST), producing very conservative confidence intervals. Predicting df based on our modeling results as a function of Ne, L, S, and genome size provides a robust way to quantify precision associated with genomics-scale datasets.

genetics↗

bioRxiv2020

An estimator of the Opportunity for Selection that is independent of mean fitness

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crows Opportunity for Selection (I), which is the variance in relative fitness [Formula]. Crows I has been widely used but remains controversial because it depends on mean offspring number in a sample [Formula]. Here I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crows I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance [Formula] to its expected value at a fixed [Formula] removes dependence of I on mean offspring number, but the result still depends on choice of [Formula]. A new index is introduced, [Formula], which makes I independent of sample [Formula] without the need for variance rescaling. {Delta}I has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. {Delta}I can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.

evolutionary biology↗

bioRxiv2016

What can genomics tell us about the success of enhancement programs in anadromous Chinook salmon? A comparative analysis across four generations

Population enhancement through the release of cultured organisms can be an important tool for marine restoration. However, there has been considerable debate about whether releases effectively contribute to conservation and harvest objectives, and whether cultured organisms impact the fitness of wild populations. Pacific salmonid hatcheries on the West Coast of North America represent one of the largest enhancement programs in the world. Molecular-based pedigree studies on one or two generations have contributed to our understanding of the fitness of hatchery-reared individuals relative to wild individuals, and tend to show that hatchery fish have lower reproductive success. However, interpreting the significance of these results can be challenging because the long-term genetic and ecological effects of releases on supplemented populations are unknown. Further, pedigree studies have been opportunistic, rather than hypothesis driven, and have not provided information on \"best case\" management scenarios. Here, we present a comparative, experimental approach based on genome-wide surveys of changes in diversity in two hatchery lines founded from the same population. We demonstrate that gene flow with wild individuals can reduce divergence from the wild source population over four generations. We also report evidence for consistent genetic changes in a closed hatchery population that can be explained by both genetic drift and domestication selection. The results of this study suggest that genetic risks can be minimized over at least four generations with appropriate actions, and provide empirical support for a decision-making framework that is relevant to the management of hatchery populations.

evolutionary biology↗