Integral projection models perform better for small demographic data sets than matrix population models: a case study of two perennial herbs

1. Matrix population models are widely used to describe population dynamics, conduct population viability analyses and derive management recommendations for plant populations. For endangered or invasive species, management decisions are often based on small demographic data sets. Hence, there is a need for population models which accurately assess population performance from such small data sets.
2. We used demographic data on two perennial herbs with different life histories to compare the accuracy and precision of the traditional matrix population model and the recently developed integral projection model (IPM) in relation to the amount of data.
3. For large data sets both matrix models and IPMs produced identical estimates of population growth rate (λ). However, for small data sets containing fewer than 300 individuals, IPMs often produced smaller bias and variance for λ than matrix models despite different matrix structures and sampling techniques used to construct the matrix population models.
4. Synthesis and applications . Our results suggest that the smaller bias and variance of λ estimates make IPMs preferable to matrix population models for small demographic data sets with a few hundred individuals. These results are likely to be applicable to a wide range of herbaceous, perennial plant species where demographic fate can be modelled as a function of a continuous state variable such as size. We recommend the use of IPMs to assess population performance and management strategies particularly for endangered or invasive perennial herbs where little demographic data are available.     

Estimating species trees using multiple-allele DNA sequence data

Several techniques, such as concatenation and consensus methods, are available for combining data from multiple loci to produce a single statement of phylogenetic relationships. However, when multiple alleles are sampled from individual species, it becomes more challenging to estimate relationships at the level of species, either because concatenation becomes inappropriate due to conflicts among individual gene trees, or because the species from which multiple alleles have been sampled may not form monophyletic groups in the estimated tree. We propose a Bayesian hierarchical model to reconstruct species trees from multiple-allele, multilocus sequence data, building on a recently proposed method for estimating species trees from single allele multilocus data. A two-step Markov Chain Monte Carlo (MCMC) algorithm is adopted to estimate the posterior distribution of the species tree. The model is applied to estimate the posterior distribution of species trees for two multiple-allele datasets--yeast (Saccharomyces) and birds (Manacus-manakins). The estimates of the species trees using our method are consistent with those inferred from other methods and genetic markers, but in contrast to other species tree methods, it provides credible regions for the species tree. The Bayesian approach described here provides a powerful framework for statistical testing and integration of population genetics and phylogenetics.     

ESTIMATING DIVERSIFICATION RATES: HOW USEFUL ARE DIVERGENCE TIMES?

The dynamics of species diversification rates are a key component of macroevolutionary patterns. Although not absolutely necessary, the use of divergence times inferred from sequence data has led to development of more powerful methods for inferring diversification rates. However, it is unclear what impact uncertainty in age estimates have on diversification rate inferences. Here, we quantify these effects using both Bayesian and frequentist methodology. Through simulation, we demonstrate that adding sequence data results in more precise estimates of internal node ages, but a reasonable approximation of these node ages is often sufficient to approach the theoretical minimum variance in speciation rate estimates. We also find that even crude estimates of divergence times increase the power of tests of diversification rate differences between sister clades. Finally, because Bayesian and frequentist methods provided similar assessments of error, novel Bayesian approaches may provide a useful framework for tests of diversification rates in more complex contexts than are addressed here.     

An integrated modeling approach to estimating Gunnison sage‐grouse population dynamics: combining index and demographic data

Evaluation of population dynamics for rare and declining species is often limited to data that are sparse and/or of poor quality. Frequently, the best data available for rare bird species are based on large‐scale, population count data. These data are commonly based on sampling methods that lack consistent sampling effort, do not account for detectability, and are complicated by observer bias. For some species, short‐term studies of demographic rates have been conducted as well, but the data from such studies are typically analyzed separately. To utilize the strengths and minimize the weaknesses of these two data types, we developed a novel Bayesian integrated model that links population count data and population demographic data through population growth rate (λ) for Gunnison sage‐grouse (Centrocercus minimus). The long‐term population index data available for Gunnison sage‐grouse are annual (years 1953–2012) male lek counts. An intensive demographic study was also conducted from years 2005 to 2010. We were able to reduce the variability in expected population growth rates across time, while correcting for potential small sample size bias in the demographic data. We found the population of Gunnison sage‐grouse to be variable and slightly declining over the past 16 years.     

The use of approximate Bayesian computation in conservation genetics and its application in a case study on yellow-eyed penguins

The inference of demographic parameters from genetic data has become an integral part of conservation studies. A group of Bayesian methods developed originally in population genetics, known as approximate Bayesian computation (ABC), has been shown to be particularly useful for the estimation of such parameters. These methods do not need to evaluate likelihood functions analytically and can therefore be used even while assuming complex models. In this paper we describe the ABC approach and identify specific parts of its algorithm that are being the subject of intensive studies in order to further expand its usability. Furthermore, we discuss applications of this Bayesian algorithm in conservation studies, providing insights on the potentialities of these tools. Finally, we present a case study in which we use a simple Isolation-Migration model to estimate a number of demographic parameters of two populations of yellow-eyed penguins (Megadyptes antipodes) in New Zealand. The resulting estimates confirm our current understanding of M. antipodes dynamic, demographic history and provide new insights into the expansion this species has undergone during the last centuries.     

Historical isolation and hydrodynamically constrained gene flow in declining populations of the South-African abalone, Haliotis midae

Over the past two decades, the South African abalone (Haliotis midae), has been under serious threat mainly due to overexploitation. To assure successful management and conservation of wild stocks, the consideration of species-specific evolutionary and population dynamic aspects is critical. In this study, eight microsatellites and 12 single nucleotide polymorphic loci (SNPs) were applied to determine genetic structure in nine populations sampled throughout the species?? natural distribution range. It spans along three biogeographical regions of the South African coastline: temperate in the West coast, warm temperate in the South coast and subtropical in the East coast. Data analysis applying frequentist and Bayesian-based clustering methods indicated weak genetic differentiation between populations of the West, South and East coast. Spatial Bayesian inference further revealed clinal variation along a longitudinal gradient and a transitional zone in the South coast. Coalescent analysis of long-term migration showed restricted interchange among the sampling locations of the South coast while estimates of effective population size were comparable between coastal regions. Furthermore demographic analysis of microsatellite data suggested population expansion, probably reflecting range expansion that occurred following glacial retreat during the Pleistocene. Overall, population structure analysis suggested contemporary (hydrographical conditions) as well as historical (Pleistocene contraction of habitat) restrictions to gene flow. This study provides the foundation for the establishment of an integrated management policy for preserving the natural diversity and adaptive potential of H. midae.     

Bayesian inference of recent migration rates using multilocus genotypes

A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.     

Apparent survival of tropical birds in a wet,premontane forest in Costa Rica

Despite the importance of tropical birds in the development of life history theory, we lack information about demographic rates and drivers of population dynamics for most species. We used a 7‐year (2007–2013) capture‐mark‐recapture dataset from an exceptionally wet premontane forest at mid‐elevation in Costa Rica to estimate apparent survival for seven species of tropical passerines. For four of these species, we provide the first published demographic parameters. Recapture probabilities ranged from 0.21 to 0.53, and annual estimates of apparent survival varied from 0.23 to 1.00. We also assessed the consequences of inter‐annual variation in rainfall on demographic rates. Our results are consistent with inter‐annual rainfall increasing estimates of apparent survival for two species and decreasing estimates for three species. For the three species where we could compare our estimates of apparent survival to estimates from drier regions, our estimates were not consistently higher or lower than those published previously. The temporal and spatial variability in demographic rates we document within and among species highlights the difficulties of generalizing life history characteristics across broad biogeographic gradients. Most importantly, this work emphasizes the context‐specific role of precipitation in shaping tropical avian demographic rates and underscores the need for mechanistic studies of environmental drivers of tropical life histories.     

Can Establishment Success Be Determined through Demographic Parameters? A Case Study on Five Introduced Bird Species

The dominant criterion to determine when an introduced species is established relies on the maintenance of a self-sustaining population in the area of introduction, i.e. on the viability of the population from a demographic perspective. There is however a paucity of demographic studies on introduced species, and establishment success is thus generally determined by expert opinion without undertaking population viability analyses (PVAs). By means of an intensive five year capture-recapture monitoring program (involving >12,000 marked individuals) we studied the demography of five introduced passerine bird species in southern Spain which are established and have undergone a fast expansion over the last decades. We obtained useful estimates of demographic parameters (survival and reproduction) for one colonial species (Ploceus melanocephalus), confirming the long-term viability of its local population through PVAs. However, extremely low recapture rates prevented the estimation of survival parameters and population growth rates for widely distributed species with low local densities (Estrilda troglodytes and Amandava amandava) but also for highly abundant yet non-colonial species (Estrilda astrild and Euplectes afer). Therefore, determining the establishment success of introduced passerine species by demographic criteria alone may often be troublesome even when devoting much effort to field-work. Alternative quantitative methodologies such as the analysis of spatio-temporal species distributions complemented with expert opinion deserve thus their role in the assessment of establishment success of introduced species when estimates of demographic parameters are difficult to obtain, as is generally the case for non-colonial, highly mobile passerines.     

Elevated substitution rate estimates from ancient DNA: model violation and bias of Bayesian methods

The increasing ability to extract and sequence DNA from noncontemporaneous tissue offers biologists the opportunity to analyse ancient DNA (aDNA) together with modern DNA (mDNA) to address the taxonomy of extinct species, evolutionary origins, historical phylogeography and biogeography. Perhaps more exciting are recent developments in coalescence-based Bayesian inference that offer the potential to use temporal information from aDNA and mDNA for the estimation of substitution rates and divergence dates as an alternative to fossil and geological calibration. This comes at a time of growing interest in the possibility of time dependency for molecular rate estimates. In this study, we provide a critical assessment of Bayesian Markov chain Monte Carlo (MCMC) analysis for the estimation of substitution rate using simulated samples of aDNA and mDNA. We conclude that the current models and priors employed in Bayesian MCMC analysis of heterochronous mtDNA are susceptible to an upward bias in the estimation of substitution rates because of model misspecification when the data come from populations with less than simple demographic histories, including sudden short-lived population bottlenecks or pronounced population structure. However, when model misspecification is only mild, then the 95% highest posterior density intervals provide adequate frequentist coverage of the true rates.     

Demographic consequences of changing body size in a terrestrial salamander

Changes in climate can alter individual body size, and the resulting shifts in reproduction and survival are expected to impact population dynamics and viability. However, appropriate methods to account for size‐dependent demographic changes are needed, especially in understudied yet threatened groups such as amphibians. We investigated individual‐ and population‐level demographic effects of changes in body size for a terrestrial salamander using capture–mark–recapture data. For our analysis, we implemented an integral projection model parameterized with capture–recapture likelihood estimates from a Bayesian framework. Our study combines survival and growth data from a single dataset to quantify the influence of size on survival while including different sources of uncertainty around these parameters, demonstrating how selective forces can be studied in populations with limited data and incomplete recaptures. We found a strong dependency of the population growth rate on changes in individual size, mediated by potential changes in selection on mean body size and on maximum body size. Our approach of simultaneous parameter estimation can be extended across taxa to identify eco‐evolutionary mechanisms acting on size‐specific vital rates, and thus shaping population dynamics and viability.     

Inferring past demographic changes from contemporary genetic data: A simulation‐based evaluation of the ABC methods implemented in diyabc

Inferring the demographic history of species and their populations is crucial to understand their contemporary distribution, abundance and adaptations. The high computational overhead of likelihood‐based inference approaches severely restricts their applicability to large data sets or complex models. In response to these restrictions, approximate Bayesian computation (ABC) methods have been developed to infer the demographic past of populations and species. Here, we present the results of an evaluation of the ABC‐based approach implemented in the popular software package diyabc using simulated data sets (mitochondrial DNA sequences, microsatellite genotypes and single nucleotide polymorphisms). We simulated population genetic data under five different simple, single‐population models to assess the model recovery rates as well as the bias and error of the parameter estimates. The ability of diyabc to recover the correct model was relatively low (0.49): 0.6 for the simplest models and 0.3 for the more complex models. The recovery rate improved significantly when reducing the number of candidate models from five to three (from 0.57 to 0.71). Among the parameters of interest, the effective population size was estimated at a higher accuracy compared to the timing of events. Increased amounts of genetic data did not significantly improve the accuracy of the parameter estimates. Some gains in accuracy and decreases in error were observed for scaled parameters (e.g., N_eμ) compared to unscaled parameters (e.g., N_e and μ). We concluded that diyabc ‐based assessments are not suited to capture a detailed demographic history, but might be efficient at capturing simple, major demographic changes.     

Increasing reproducibility,robustness, and generalizability of biomarker selection from meta-analysis using Bayesian methodology

A major limitation of gene expression biomarker studies is that they are not reproducible as they simply do not generalize to larger, real-world, heterogeneous populations. Frequentist multi-cohort gene expression meta-analysis has been frequently used as a solution to this problem to identify biomarkers that are truly differentially expressed. However, the frequentist meta-analysis framework has its limitations–it needs at least 4–5 datasets with hundreds of samples, is prone to confounding from outliers and relies on multiple-hypothesis corrected p-values. To address these shortcomings, we have created a Bayesian meta-analysis framework for the analysis of gene expression data. Using real-world data from three different diseases, we show that the Bayesian method is more robust to outliers, creates more informative estimates of between-study heterogeneity, reduces the number of false positive and false negative biomarkers and selects more generalizable biomarkers with less data. We have compared the Bayesian framework to a previously published frequentist framework and have developed a publicly available R package for use.     

Methods for Estimating Population Density in Data-Limited Areas: Evaluating Regression and Tree-Based Models in Peru

Obtaining accurate small area estimates of population is essential for policy and health planning but is often difficult in countries with limited data. In lieu of available population data, small area estimate models draw information from previous time periods or from similar areas. This study focuses on model-based methods for estimating population when no direct samples are available in the area of interest. To explore the efficacy of tree-based models for estimating population density, we compare six different model structures including Random Forest and Bayesian Additive Regression Trees. Results demonstrate that without information from prior time periods, non-parametric tree-based models produced more accurate predictions than did conventional regression methods. Improving estimates of population density in non-sampled areas is important for regions with incomplete census data and has implications for economic, health and development policies.     

Comparing survival among species with imperfect detection using multilevel analysis of mark—recapture data: a case study on bats

For comparative demography studies, 2 prerequisites are usually needed: 1) using typical parameter values for species, 2) correctly accounting for the uncertainty in the species specific estimates. However, although within‐species variability may be essential, it is typically not considered in analytical procedures, resulting in parameter estimates that may not be representative of the species. Further, data are analysed in 2 steps, first separately for each species, then estimates are compared among species. Accounting for the uncertainty in the species specific estimates is then difficult. Here we propose the application of multilevel Bayesian models on mark—recapture (MR) data for comparative studies on survival probabilities that solves these problems. Our models account for within‐species variability in space and time in the form of random effects. Models reflecting different biological predictions related to the species’ ecology and life‐history traits may further be contrasted. To illustrate our approach, we used long‐term data from 5 temperate tree‐roosting bat species and compared their survival probabilities. Results suggest that species foraging in open space, high reproductive output and short longevity records have lower survival than species foraging at short distances, with low reproductive output and high longevity records. Multilevel models provided relatively precise estimates, away from the edges of the parameter space, even for species with low encounter rates and short study duration. This is particularly valuable for less studied taxa such as bats for which available data are often more sparse. Our approach can be easily extended to include additional groups or levels of interest and effects at the individual level (e.g. sex or age). Different hypotheses regarding differences or similarities in parameters among species can be tested through the application of different models. Overall, it offers a flexible tool to ecologists, and population and evolutionary biologists for comparative studies, explicitly accounting for multilevel structures often encountered in MR data.     

Bayesian inference of fine-scale recombination rates using population genomic data

Recently, several statistical methods for estimating fine-scale recombination rates using population samples have been developed. However, currently available methods that can be applied to large-scale data are limited to approximated likelihoods. Here, we developed a full-likelihood Markov chain Monte Carlo method for estimating recombination rate under a Bayesian framework. Genealogies underlying a sampling of chromosomes are effectively modelled by using marginal individual single nucleotide polymorphism genealogies related through an ancestral recombination graph. The method is compared with two existing composite-likelihood methods using simulated data.Simulation studies show that our method performs well for different simulation scenarios. The method is applied to two human population genetic variation datasets that have been studied by sperm typing. Our results are consistent with the estimates from sperm crossover analysis.     

Inferring population decline and expansion from microsatellite data: a simulation-based evaluation of the Msvar method

Reconstructing the demographic history of populations is a central issue in evolutionary biology. Using likelihood-based methods coupled with Monte Carlo simulations, it is now possible to reconstruct past changes in population size from genetic data. Using simulated data sets under various demographic scenarios, we evaluate the statistical performance of Msvar, a full-likelihood Bayesian method that infers past demographic change from microsatellite data. Our simulation tests show that Msvar is very efficient at detecting population declines and expansions, provided the event is neither too weak nor too recent. We further show that Msvar outperforms two moment-based methods (the M-ratio test and Bottleneck) for detecting population size changes, whatever the time and the severity of the event. The same trend emerges from a compilation of empirical studies. The latest version of Msvar provides estimates of the current and the ancestral population size and the time since the population started changing in size. We show that, in the absence of prior knowledge, Msvar provides little information on the mutation rate, which results in biased estimates and/or wide credibility intervals for each of the demographic parameters. However, scaling the population size parameters with the mutation rate and scaling the time with current population size, as coalescent theory requires, significantly improves the quality of the estimates for contraction but not for expansion scenarios. Finally, our results suggest that Msvar is robust to moderate departures from a strict stepwise mutation model.     

Application of photographic capture–recapture modelling to estimate demographic parameters for male Asian elephants

In addition to the threats of habitat loss and degradation, adult males of the Asian elephant Elephas maximus also face greater threats from ivory poaching and conflict with humans. To understand the impact of these threats, conservationists need robust estimates of abundance and vital rates specifically for the adult male segment of elephant populations. By integrating the identification of individual male elephants in a population from distinct morphology and natural markings, with modern capture–recapture (CR) sampling designs, it is possible to estimate various demographic parameters that are otherwise difficult to obtain from this long-lived and wide-ranging megaherbivore. In this study, we developed systematic individual identification protocols and integrated them into CR sampling designs to obtain capture histories and thereby estimate the abundance of adult bull elephants in a globally important population in southern India. We validated these estimates against those obtained from an independent method combining line-transect density estimates with age–sex composition data for elephants. The sampled population was open to gains and losses between sampling occasions. The abundance of adult males in the 176 km² study area was (SÊ ) = 134(14.20) and they comprised 14% (±1%) of the total elephant population. Time-specific abundance estimates for each sampling occasion showed a distinct increase in adult male numbers over the sampling period, explained by seasonal patterns of local migration. CR-based estimates for adult male abundance closely matched estimates from distance-based methods. Thus, while providing abundance data of comparable rigour and precision, photographic CR methods permit estimation of demographic parameters for the Asian elephant that are both urgently needed and difficult to obtain.     

QUANTIFYING THE PLEISTOCENE HISTORY OF THE OAK GALL PARASITOID CECIDOSTIBA FUNGOSA USING TWENTY INTRON LOCI

The longitudinal spread of temperate organisms into refugial populations in Southern Europe is generally assumed to predate the last interglacial. However, few studies have attempted to quantify this process in nonmodel organisms using explicit models and multilocus data. We used sequence data for 20 intron‐spanning loci (12 kb per individual) to resolve the history of refugial populations of a widespread western Palaearctic oak gall parasitoid Cecidostiba fungosa (Pteromalidae). Using maximum likelihood and Bayesian methods we assess alternative population tree topologies and estimate divergence times and ancestral population sizes under a model of divergence between three refugia (Middle East, Balkans and Iberia). Both methods support an “Out of the East” history for C. fungosa, matching the pattern previously inferred for their gallwasp hosts. However, coalescent‐based estimates of the ages of population divides are much more recent (coinciding with the Eemian interglacial) than nodal ages of single gene trees for C. fungosa and other species. We also find that increasing the sample size from one haploid sequence per refugial population to three only marginally improves parameter estimates. Our results suggest that there is significant information in the minimal samples currently analyzable with maximum likelihood methods, and that similar methods could be applied to multiple species to test alternative models of assemblage evolution.