Estimation of population allele frequencies from next‐generation sequencing data: pool‐versus individual‐based genotyping

Molecular markers produced by next‐generation sequencing (NGS) technologies are revolutionizing genetic research. However, the costs of analysing large numbers of individual genomes remain prohibitive for most population genetics studies. Here, we present results based on mathematical derivations showing that, under many realistic experimental designs, NGS of DNA pools from diploid individuals allows to estimate the allele frequencies at single nucleotide polymorphisms (SNPs) with at least the same accuracy as individual‐based analyses, for considerably lower library construction and sequencing efforts. These findings remain true when taking into account the possibility of substantially unequal contributions of each individual to the final pool of sequence reads. We propose the intuitive notion of effective pool size to account for unequal pooling and derive a Bayesian hierarchical model to estimate this parameter directly from the data. We provide a user‐friendly application assessing the accuracy of allele frequency estimation from both pool‐ and individual‐based NGS population data under various sampling, sequencing depth and experimental error designs. We illustrate our findings with theoretical examples and real data sets corresponding to SNP loci obtained using restriction site–associated DNA (RAD) sequencing in pool‐ and individual‐based experiments carried out on the same population of the pine processionary moth (Thaumetopoea pityocampa). NGS of DNA pools might not be optimal for all types of studies but provides a cost‐effective approach for estimating allele frequencies for very large numbers of SNPs. It thus allows comparison of genome‐wide patterns of genetic variation for large numbers of individuals in multiple populations.     

Structural learning and integrative decomposition of multi‐view data

The increased availability of multi‐view data (data on the same samples from multiple sources) has led to strong interest in models based on low‐rank matrix factorizations. These models represent each data view via shared and individual components, and have been successfully applied for exploratory dimension reduction, association analysis between the views, and consensus clustering. Despite these advances, there remain challenges in modeling partially‐shared components and identifying the number of components of each type (shared/partially‐shared/individual). We formulate a novel linked component model that directly incorporates partially‐shared structures. We call this model SLIDE for Structural Learning and Integrative DEcomposition of multi‐view data. The proposed model‐fitting and selection techniques allow for joint identification of the number of components of each type, in contrast to existing sequential approaches. In our empirical studies, SLIDE demonstrates excellent performance in both signal estimation and component selection. We further illustrate the methodology on the breast cancer data from The Cancer Genome Atlas repository.     

An integrated population model for a long‐lived ungulate: more efficient data use with Bayesian methods

We develop an integrated population model for Svalbard reindeer Rangifer tarandus platyrhynchus, and demonstrate how this type of model can be used to extract more information from the data and separate different sources of variability in population estimates. Our model combines individual mark–recapture data with population counts and harvesting data within a Bayesian model framework, and accounts for observation error, environmental and demographic stochasticity, and age structure. From this model we obtain annual estimates of age‐specific population size, survival and fecundity. The model provides estimates of age structure at a finer scale than that found in the census data, and enables us to estimate survival for the period before calves are first caught and marked, i.e. before they enter the individual mark–recapture data. The modeling framework provides an improved approach to studying age‐structured populations that are imperfectly censused and where the demography of only a sample of individuals is known. We use data from independent censuses of the same population to evaluate population estimates obtained from the model, and show that it is successful at correcting for different types of observation error. Based on our model results, we suggest that allocating resources to the collection of supplementary mark–recapture data could improve the reliability of population projections more than making regular population censuses as exhaustive as possible. Our work demonstrates how integrated Bayesian population modeling can be used to increase the amount of information extracted from collections of data, identifying and disentangling sources of variation in individual performance and population size. This represents an important step towards increasing the predictive ability of population growth models for long‐lived species experiencing changes in environmental conditions and harvesting regimes.     

Modeling Inter‐Subject Variability in fMRI Activation Location: A Bayesian Hierarchical Spatial Model

Summary The aim of this article is to develop a spatial model for multi‐subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi‐subject data, some work on spatial modeling of single‐subject data, and some recent work on spatial modeling of multi‐subject data. However, there has been no work on spatial models that explicitly account for inter‐subject variability in activation locations. In this article, we use the idea of activation centers and model the inter‐subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical framework which allows us to draw inferences at all levels: the population level, the individual level, and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question that is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass‐univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.     

Range Expansion and Population Dynamics of an Invasive Species: The Eurasian Collared-Dove (Streptopelia decaocto)

Invasive species offer ecologists the opportunity to study the factors governing species distributions and population growth. The Eurasian Collared-Dove (Streptopelia decaocto) serves as a model organism for invasive spread because of the wealth of abundance records and the recent development of the invasion. We tested whether a set of environmental variables were related to the carrying capacities and growth rates of individual populations by modeling the growth trajectories of individual populations of the Collared-Dove using Breeding Bird Survey (BBS) and Christmas Bird Count (CBC) data. Depending on the fit of our growth models, carrying capacity and growth rate parameters were extracted and modeled using historical, geographical, land cover and climatic predictors. Model averaging and individual variable importance weights were used to assess the strength of these predictors. The specific variables with the greatest support in our models differed between data sets, which may be the result of temporal and spatial differences between the BBS and CBC. However, our results indicate that both carrying capacity and population growth rates are related to developed land cover and temperature, while growth rates may also be influenced by dispersal patterns along the invasion front. Model averaged multivariate models explained 35–48% and 41–46% of the variation in carrying capacities and population growth rates, respectively. Our results suggest that widespread species invasions can be evaluated within a predictable population ecology framework. Land cover and climate both have important effects on population growth rates and carrying capacities of Collared-Dove populations. Efforts to model aspects of population growth of this invasive species were more successful than attempts to model static abundance patterns, pointing to a potentially fruitful avenue for the development of improved invasive distribution models.     

Estimating occupancy dynamics for large‐scale monitoring networks: amphibian breeding occupancy across protected areas in the northeast United States

Regional monitoring strategies frequently employ a nested sampling design where a finite set of study areas from throughout a region are selected and intensive sampling occurs within a subset of sites within the individual study areas. This sampling protocol naturally lends itself to a hierarchical analysis to account for dependence among subsamples. Implementing such an analysis using a classic likelihood framework is computationally challenging when accounting for detection errors in species occurrence models. Bayesian methods offer an alternative approach for fitting models that readily allows for spatial structure to be incorporated. We demonstrate a general approach for estimating occupancy when data come from a nested sampling design. We analyzed data from a regional monitoring program of wood frogs (Lithobates sylvaticus) and spotted salamanders (Ambystoma maculatum) in vernal pools using static and dynamic occupancy models. We analyzed observations from 2004 to 2013 that were collected within 14 protected areas located throughout the northeast United States. We use the data set to estimate trends in occupancy at both the regional and individual protected area levels. We show that occupancy at the regional level was relatively stable for both species. However, substantial variation occurred among study areas, with some populations declining and some increasing for both species. In addition, When the hierarchical study design is not accounted for, one would conclude stronger support for latitudinal gradient in trends than when using our approach that accounts for the nested design. In contrast to the model that does not account for nesting, the nested model did not include an effect of latitude in the 95% credible interval. These results shed light on the range‐level population status of these pond‐breeding amphibians, and our approach provides a framework that can be used to examine drivers of local and regional occurrence dynamics.     

Inferences about population dynamics from count data using multistate models: a comparison to capture–recapture approaches

Wildlife populations consist of individuals that contribute disproportionately to growth and viability. Understanding a population's spatial and temporal dynamics requires estimates of abundance and demographic rates that account for this heterogeneity. Estimating these quantities can be difficult, requiring years of intensive data collection. Often, this is accomplished through the capture and recapture of individual animals, which is generally only feasible at a limited number of locations. In contrast, N‐mixture models allow for the estimation of abundance, and spatial variation in abundance, from count data alone. We extend recently developed multistate, open population N‐mixture models, which can additionally estimate demographic rates based on an organism's life history characteristics. In our extension, we develop an approach to account for the case where not all individuals can be assigned to a state during sampling. Using only state‐specific count data, we show how our model can be used to estimate local population abundance, as well as density‐dependent recruitment rates and state‐specific survival. We apply our model to a population of black‐throated blue warblers (Setophaga caerulescens) that have been surveyed for 25 years on their breeding grounds at the Hubbard Brook Experimental Forest in New Hampshire, USA. The intensive data collection efforts allow us to compare our estimates to estimates derived from capture–recapture data. Our model performed well in estimating population abundance and density‐dependent rates of annual recruitment/immigration. Estimates of local carrying capacity and per capita recruitment of yearlings were consistent with those published in other studies. However, our model moderately underestimated annual survival probability of yearling and adult females and severely underestimates survival probabilities for both of these male stages. The most accurate and precise estimates will necessarily require some amount of intensive data collection efforts (such as capture–recapture). Integrated population models that combine data from both intensive and extensive sources are likely to be the most efficient approach for estimating demographic rates at large spatial and temporal scales.     

Distribution of the disease pathogen Batrachochytrium dendrobatidis in non‐epidemic amphibian communities of western Canada

Chytridiomycosis is an emerging infectious disease of amphibians caused by the waterborne pathogen Batrachochytrium dendrobatidis (Bd) and is responsible for the recent decline of species worldwide. Elucidating patterns in disease prevalence has proved challenging, as small‐scale studies to date have provided conflicting results. We present data on the prevalence of Bd (the proportion of individuals with Bd) collected from amphibians sampled throughout British Columbia. We had two different datasets: our original dataset includes 1129 individuals sampled in 103 sites representing 14 species. A second dataset has 839 individuals sampled in 19 sites representing 10 species. We use a Bayesian state‐space occupancy modelling approach to estimate the probability that an individual is Bd+ as a function of individual and site characteristics. Cross‐validation techniques and the original dataset were used to find the best model: this model includes species, life stage, and geographic location. Our results suggest that Bd prevalence is not strongly related to seasonality, latitude or site type. Within a species, Bd prevalence depended on life stage; the watershed in which a site occurs may also usefully predict prevalence. Overall observed infection prevalence was ～16%. Our best model accurately assigns Bd status to an individual ～ 42% of the time. Taking advantage of the Bayesian framework, we ran an analysis with the second dataset using estimates from the original model as prior values. We present posterior density distributions for those sites and species with narrow credible intervals, and show that sites tend to be either highly likely or highly unlikely to have individuals with Bd, while individuals of some stages of some species have an intermediate likelihood of being Bd‐positive. The Bayesian model using informed priors had increased accuracy rates in assigning Bd status to both individuals and groups of individuals.     

The demographic effects of functional traits: an integral projection model approach reveals population‐level consequences of reproduction‐defence trade‐offs

Quantitatively linking individual variation in functional traits to demography is a necessary step to advance our understanding of trait‐based ecological processes. We constructed a population model for Asclepias syriaca to identify how functional traits affect vital rates and population growth and whether trade‐offs in chemical defence and demography alter population growth. Plants with higher foliar cardenolides had lower fibre, cellulose and lignin levels, as well as decreased sexual and clonal reproduction. Average cardenolide concentrations had the strongest effect on population growth. In both the sexual and clonal pathway, the trade‐off between reproduction and defence affected population growth. We found that both increasing the mean of the distribution of individual plant values for cardenolides and herbivory decreased population growth. However, increasing the variance in both defence and herbivory increased population growth. Functional traits can impact population growth and quantifying individual‐level variation in traits should be included in assessments of population‐level processes.     

Bursty Communication Patterns Facilitate Spreading in a Threshold-Based Epidemic Dynamics

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.     

Continuous Covariates in Mark‐Recapture‐Recovery Analysis: A Comparison of Methods

Summary Time varying, individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured. We examine three methods to incorporate time varying, individual covariates of the survival probabilities into the analysis of data from mark‐recapture‐recovery experiments: deterministic imputation, a Bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history, and a conditional approach considering only the events for which the associated covariate data are completely observed (the trinomial model). After describing the three methods, we compare results from their application to the analysis of the effect of body mass on the survival of Soay sheep (Ovis aries) on the Isle of Hirta, Scotland. Simulations based on these results are then used to make further comparisons. We conclude that both the trinomial model and Bayesian imputation method perform best in different situations. If the capture and recovery probabilities are all high, then the trinomial model produces precise, unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate. In contrast, the Bayesian imputation method performs substantially better when capture and recovery probabilities are low, provided that the specified model of the covariate is a good approximation to the true data‐generating mechanism.     

On latent-variable model misspecification in structural measurement error models for binary response

Summary .  We consider structural measurement error models for a binary response. We show that likelihood-based estimators obtained from fitting structural measurement error models with pooled binary responses can be far more robust to covariate measurement error in the presence of latent-variable model misspecification than the corresponding estimators from individual responses. Furthermore, despite the loss in information, pooling can provide improved parameter estimators in terms of mean-squared error. Based on these and other findings, we create a new diagnostic method to detect latent-variable model misspecification in structural measurement error models with individual binary response. We use simulation and data from the Framingham Heart Study to illustrate our methods.     

Modeling growth and telomere dynamics in Saccharomyces cerevisiae

A general branching process is proposed to model a population of cells of the yeast Saccharomyces cerevisiae following loss of telomerase. Previously published experimental data indicate that a population of telomerase-deficient cells regain exponential growth after a period of slowing due to critical telomere shortening. The explanation for this phenomenon is that some cells engage telomerase-independent pathways to maintain telomeres that allow them to become “survivors.” Our model takes into account random variation in individual cell cycle times, telomere length, finite replicative lifespan of mother cells, and survivorship. We identify and estimate crucial parameters such as the probability of an individual cell becoming a survivor, and compare our model predictions to experimental data.     

Intracolonial conflict in the slave-making ant <Emphasis Type="Italic">Protomognathus americanus</Emphasis>: dominance hierarchies and individual reproductive success

Summary Social group viability results from a trade-off between cooperation and conflict, driven respectively by group and individual interests. Workers of the slave-making ants are known to have a high egg-laying potential, leading to a potential conflict over male production. Queenright and queenless nests of the slave-making ant Protomognathus americanus show a near-linear dominance hierarchy, and dominance rank is correlated with reproductive activity. Genetic and behavioural analysis revealed that the queen, when present in the nest, is behaviourally dominant and monopolises reproduction. In queenless nests, the haploid (male) brood is produced primarily by a single worker. We suggest the dominance hierarchy regulates male production, between the queen and her workers as well as among workers. Comparison of our results to another study allows us to place our data in an ecological context. This slave-making ant species appears to fit the concession model of reproductive skew: where resources (i.e. host nests) are poor, there is strong skew and where resources are richer reproduction is more egalitarian.Received 31 July 2003; revised 7 October 2003; accepted 9 October 2003.     

Bayesian analysis for nonlinear regression model under skewed errors,with application in growth curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew‐t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.     

EVOLUTION OF THE SOCIAL‐LEARNER‐EXPLORER STRATEGY IN AN ENVIRONMENTALLY HETEROGENEOUS TWO‐ISLAND MODEL

Social‐learner‐explorer (SE) is a learning strategy that combines accurate social learning with exploratory individual learning in that order. Arguably, it is one of the few plausible learning strategies that can support cumulative culture. We investigate numerically the factors that affect the evolution of SE in an environmentally heterogeneous two‐island model. Conditions favorable to the evolution of SE include a small exogenous cost of social learning, the occurrence of migration after social learning but before individual learning, the ability to adaptively modify the behavioral phenotype in the postmigration environment (asymmetrical individual learning), and a relatively high migration rate. The implications of our model for the evolution of SE in humans are discussed. Of particular interest is the prediction that behaviors affecting fitness would have to be socially learned in the natal environment and then subsequently modified by individual learning in the postmigration environment, suggesting a life‐cycle stage dependent reliance on the two types of learning.     

Extra-pair mate choice in the female great tit <Emphasis Type="Italic">Parus major</Emphasis>: good males or compatible males

The good genes hypothesis and the genetic compatibility hypothesis are the two main hypotheses that focus on the genetic benefit that a female can gain through her choice of a mate. We tested the two hypotheses on extra-pair mating in the great tit, Parus major. We found that female great tits choose males on the basis of breast stripe width, which is in accordance with the good genes hypothesis. Although females chose less related extra-pair males, the evidence for female choice for compatible males was overall weak. However, our data suggest a post-copulatory mechanism of inbreeding avoidance. The observed individual inbreeding coefficient, F, was similar for within-pair offspring (WPO) and extra-pair offspring (EPO). The observed individual F of WPO was lower than the expected individual F, whereas the observed F of EPO was similar to what was expected. These results highlight the importance of processes after copulation for the outcome of female mate choice. Our study shows that in a system with apparent pre-copulatory female choice for good genes, a post-copulatory mechanism may still promote the production of offspring that carry compatible genes.     

Nondetection sampling bias in marked presence‐only data

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