Bayesian data analysis in population ecology: motivations, methods, and benefits

Demographic and evolutionary consequences of hunting of wild birds

Hunting has a long tradition in human evolutionary history and remains a common leisure activity or an important source of food. Herein, we first briefly review the literature on the demographic consequences of hunting and associated analytical methods. We then address the question of potential selective hunting and its possible genetic/evolutionary consequences. Birds have historically been popular models for demographic studies, and the huge amount of census and ringing data accumulated over the last century has paved the way for research about the demographic effects of harvesting. By contrast, the literature on the evolutionary consequences of harvesting is dominated by studies on mammals (especially ungulates) and fish. In these taxa, individuals selected for harvest often have particular traits such as large body size or extravagant secondary sexual characters (e.g. antlers, horns, etc.). Our review shows that targeting individuals according to such genetically heritable traits can exert strong selective pressures and alter the evolutionary trajectory of populations for these or correlated traits. Studies focusing on the evolutionary consequences of hunting in birds are extremely rare, likely because birds within populations appear much more similar, and do not display individual differences to the same extent as many mammals and fishes. Nevertheless, even without conscious choice by hunters, there remains the potential for selection through hunting in birds, for example by genetically inherited traits such as personality or pace-of-life. We emphasise that because so many bird species experience high hunting pressure, the possible selective effect of harvest in birds and its evolutionary consequences deserves far more attention, and that hunting may be one major driver of bird evolutionary trajectories that should be carefully considered in wildlife management schemes.

Hierarchical modelling of variance components makes analysis of resolvable incomplete block designs more efficient

The standard approach to variance component estimation in linear mixed models for alpha designs is the residual maximum likelihood (REML) method. One drawback of the REML method in the context of incomplete block designs is that the block variance may be estimated as zero, which can compromise the recovery of inter-block information and hence reduce the accuracy of treatment effects estimation. Due to the development of statistical and computational methods, there is an increasing interest in adopting hierarchical approaches to analysis. In order to increase the precision of the analysis of individual trials laid out as alpha designs, we here make a proposal to create an objectively informed prior distribution for variance components for replicates, blocks and plots, based on the results of previous (historical) trials. We propose different modelling approaches for the prior distributions and evaluate the effectiveness of the hierarchical approach compared to the REML method, which is classically used for analysing individual trials in two-stage approaches for multi-environment trials.

Effectiveness of hierarchical Bayesian models for citizen science data with missing values: A case study on the factors influencing beach litter in Shimane Prefecture, Japan

Citizen science can play an important role in addressing the issue of marine debris. However, citizen science data are often composed of inconsistent methods compared to data collected by experts. In this study, we applied beach cleanup data, collected in different survey years at different survey sites, to a hierarchical Bayesian model to elucidate the factors affecting the distribution of beach litter. The results showed the model accounting for differences between years had a smaller Watanabe-Akaike Information criterion than the model that did not account for it, indicating better accuracy of the model. The amount of beach litter was influenced by current velocity and bay openness, and these effects varied across years. The results indicate that citizen science data, which may contain missing values due to various constraints such as economic and human resources, can make an important contribution toward solving marine debris issues by flexible statistical analysis methods.

Spatial patterns in the contribution of biotic and abiotic factors to the population dynamics of three freshwater fish species

BACKGROUND

Population dynamics are driven by a number of biotic (e.g., density-dependence) and abiotic (e.g., climate) factors whose contribution can greatly vary across study systems (i.e., populations). Yet, the extent to which the contribution of these factors varies across populations and between species and whether spatial patterns can be identified has received little attention.

METHODS

Here, we used a long-term (1982-2011), broad scale (182 sites distributed across metropolitan France) dataset to study spatial patterns in the population's dynamics of three freshwater fish species presenting contrasted life-histories and patterns of elevation range shifts in recent decades. We used a hierarchical Bayesian approach together with an elasticity analysis to estimate the relative contribution of a set of biotic (e.g., strength of density dependence, recruitment rate) and abiotic (mean and variability of water temperature) factors affecting the site-specific dynamic of two different size classes (0⁺ and >0⁺ individuals) for the three species. We then tested whether the local contribution of each factor presented evidence for biogeographical patterns by confronting two non-mutually exclusive hypotheses: the "range-shift" hypothesis that predicts a gradient along elevation or latitude and the "abundant-center" hypothesis that predicts a gradient from the center to the edge of the species' distributional range.

RESULTS

Despite contrasted life-histories, the three species displayed similar large-scale patterns in population dynamics with a much stronger contribution of biotic factors over abiotic ones. Yet, the contribution of the different factors strongly varied within distributional ranges and followed distinct spatial patterns. Indeed, while abiotic factors mostly varied along elevation, biotic factors-which disproportionately contributed to population dynamics-varied along both elevation and latitude.

CONCLUSIONS

Overall while our results provide stronger support for the range-shift hypothesis, they also highlight the dual effect of distinct factors on spatial patterns in population dynamics and can explain the overall difficulty to find general evidence for geographic gradients in natural populations. We propose that considering the separate contribution of the factors affecting population dynamics could help better understand the drivers of abundance-distribution patterns.

Impact of barge movement on phytoplankton diversity in a river: A Bayesian risk estimation framework

The adverse effect of barge movement on the river's aquatic ecosystem is of global concern. The phytoplankton community, a bioindicator, is possibly the foremost victim of the barge movement. This study hypothesized phytoplankton diversity loss induced by barge movement in a large river. This article presents a novel risk assessment framework to evaluate the hypothesis-with a goal to uncoupling phytoplankton diversity loss due to barge movement over a spatiotemporal scale. For this purpose, a study was conducted in the Bhagirathi-Hooghly stretch of Inland National Waterway 1 of India. This study has proposed a new index of diversity loss and its inferential framework based on full Bayesian Generalized Linear Mixed Model. The results have diagnosed significant barge-induced impact on the phytoplankton diversity and identified ten most impacted species. The proposed framework has successfully disentangled barge-induced phytoplankton diversity loss from the biological process and predicted a substantive overall risk of phytoplankton loss of 31.44%. Besides, it has uncoupled spatiotemporal differential estimates, suggesting a risk of diversity loss in order of 'During vs After' (38.0%) > 'Before vs After' (30.7%) > 'Before vs During' (24%) barge movement in temporal scale and increasing diversity loss along downstream. Finally, the instant study has highlighted the utility of these results to facilitate better water framework directive for inland waterways.

Capturing the dynamics of small populations: A retrospective assessment using long-term data for an island reintroduction

The art of population modelling is to incorporate factors essential for capturing a population's dynamics while otherwise keeping the model as simple as possible. However, it is unclear how optimal model complexity should be assessed, and whether this optimal complexity has been affected by recent advances in modelling methodology. This issue is particularly relevant to small populations because they are subject to complex dynamics but inferences about those dynamics are often constrained by small sample sizes. We fitted Bayesian hierarchical models to long-term data on vital rates (survival and reproduction) for the toutouwai Petroica longipes population reintroduced to Tiritiri Matangi, a 220-ha New Zealand island, and quantified the performance of those models in terms of their likelihood of replicating the observed population dynamics. These dynamics consisted of overall growth from 33 (±0.3) to 160 (±6) birds from 1992-2018, including recoveries following five harvest events for further reintroductions to other sites. We initially included all factors found to affect vital rates, which included inbreeding, post-release effects (PRE), density-dependence, sex, age and random annual variation, then progressively removed these factors. We also compared performance of models where data analysis and simulations were done simultaneously to those produced with the traditional two-step approach, where vital rates are estimated first then fed into a separate simulation model. Parametric uncertainty and demographic stochasticity were incorporated in all projections. The essential factors for replicating the population's dynamics were density-dependence in juvenile survival and PRE, i.e. initial depression of survival and reproduction in translocated birds. Inclusion of other factors reduced the precision of projections, and therefore the likelihood of matching observed dynamics. However, this reduction was modest when the modelling was done in an integrated framework. In contrast, projections were much less precise when done with a two-step modelling approach, and the cost of additional parameters was much higher under the two-step approach. These results suggest that minimization of complexity may be less important than accounting for covariances in parameter estimates, which is facilitated by integrating data analysis and population projections using Bayesian methods.

Application of a Bayesian Statistical Framework for Planetary Protection as a Means of Verifying Low-Biomass, Zero-Inflated Test Data from Spacecraft

Planetary Protection is applicable for missions to biologically sensitive targets of interest in the solar system. For robotic missions landing on the Martian surface, Earth-based biological contamination must be reduced, controlled, and monitored to adhere to forward planetary protection requirements. To address the overall biological load limit and microbial density requirements per spacecraft each component is tracked based on its manufacturing pedigree and/or directly assessed using a direct sampling technique with either a swab or wipe. The tracking and reporting of requirements compliance has varied from mission to mission and reporting of numbers has consistently leaned towards the conservative worst-case scenario. With an increase in the number of missions and mission complexities, the need to establish a technically sound, statistical, and biological solution that provides a single point solution which addresses the distribution of spacecraft contamination becomes critical. Select components of the InSight mission, launched in 2018, have been used as a test case to evaluate the efficacy of applying Bayesian statistics to planetary protection data sets. Eight representative components covering the various bounding cases of high and low surface area, biological count, and sampling devices were analyzed as well as an assembly level case to evaluate the rollup of directly sampled and manufacturing pedigree components. A Bayesian approach was developed leveraging different priors from the zero-inflated data sets and compared to the heritage and existing NASA bioburden assessment approaches. In addition, several non-informative priors were evaluated for use in performing bioburden calculations. The results have demonstrated a viable framework to enable a Bayesian statistical approach to be further developed and utilized for planetary protection requirements assessment.

A Mathematical Modeling Approach to Uncover Factors Influencing the Spread of Campylobacter in a Flock of Broiler-Breeder Chickens

Despite continued efforts to improve biosecurity protocols, Campylobacter continues to be detected in the majority of commercial chicken flocks across Europe. Using an extensive data set of Campylobacter prevalence within a chicken breeder flock for over a year, multiple Bayesian models are presented to explore the dynamics of the spread of Campylobacter in response to seasonal variation, species-specificity, bird health, and total colonization prevalence. These models indicated that birds within the flock varied greatly in their response to bacterial challenge, and that this phenomenon had a large impact on the overall prevalence of different species of Campylobacter. Campylobacter jejuni appeared more frequently in the summer, while Campylobacter coli persisted for a longer duration, amplified by the most susceptible birds in the flock. Our study suggests that strains of Campylobacter that appear most frequently likely possess no demographic advantage, but are instead amplified due to the health of the birds that ingest it.

Ensuring identifiability in hierarchical mixed effects Bayesian models

Ecologists are increasingly familiar with Bayesian statistical modeling and its associated Markov chain Monte Carlo (MCMC) methodology to infer about or to discover interesting effects in data. The complexity of ecological data often suggests implementation of (statistical) models with a commensurately rich structure of effects, including crossed or nested (i.e., hierarchical or multi-level) structures of fixed and/or random effects. Yet, our experience suggests that most ecologists are not familiar with subtle but important problems that often arise with such models and with their implementation in popular software. Of foremost consideration for us is the notion of effect identifiability, which generally concerns how well data, models, or implementation approaches inform about, i.e., identify, quantities of interest. In this paper, we focus on implementation pitfalls that potentially misinform subsequent inference, despite otherwise informative data and models. We illustrate the aforementioned issues using random effects regressions on synthetic data. We show how to diagnose identifiability issues and how to remediate these issues with model reparameterization and computational and/or coding practices in popular software, with a focus on JAGS, OpenBUGS, and Stan. We also show how these solutions can be extended to more complex models involving multiple groups of nested, crossed, additive, or multiplicative effects, for models involving random and/or fixed effects. Finally, we provide example code (JAGS/OpenBUGS and Stan) that practitioners can modify and use for their own applications.

Of power and despair in cetacean conservation: estimation and detection of trend in abundance with noisy and short time-series

Many conservation instruments rely on detecting and estimating a population decline in a target species to take action. Trend estimation is difficult because of small sample size and relatively large uncertainty in abundance/density estimates of many wild populations of animals. Focusing on cetaceans, we performed a prospective analysis to estimate power, type-I, sign (type-S) and magnitude (type-M) error rates of detecting a decline in short time-series of abundance estimates with different signal-to-noise ratio. We contrasted results from both unregularized (classical) and regularized approaches. The latter allows to incorporate prior information when estimating a trend. Power to detect a statistically significant estimates was in general lower than 80%, except for large declines. The unregularized approach (status quo) had inflated type-I error rates and gave biased (either over- or under-) estimates of a trend. The regularized approach with a weakly-informative prior offered the best trade-off in terms of bias, statistical power, type-I, type-S and type-M error rates and confidence interval coverage. To facilitate timely conservation decisions, we recommend to use the regularized approach with a weakly-informative prior in the detection and estimation of trend with short and noisy time-series of abundance estimates.

Predicting reintroduction outcomes for highly vulnerable species that do not currently coexist with their key threats

Predicting reintroduction outcomes before populations are released is inherently challenging. It becomes even more difficult when the species being considered for reintroduction no longer coexists with the key threats limiting its distribution. However, data from other species facing the same threats can be used to make predictions under these circumstances. We used an integrated Bayesian modeling approach to predict growth of a reintroduced population at a range of predator densities when no data are available for the species in the presence of that predator. North Island Saddlebacks (Philesturnus rufusater) were extirpated from mainland New Zealand by exotic mammalian predators, particularly ship rats (black rats [Rattus rattus]) but are now being considered for reintroduction to sites with intensive predator control. We initially modeled data from previous saddleback reintroductions to predator-free sites to predict population growth at a new predator-free site while accounting for random variation in vital rates among sites. We then predicted population growth at different rat-tracking rates (an index of rat density) by incorporating a previously modeled relationship between rat-tracking and vital rates of another predator-sensitive species, the North Island Robin (Petroica longipes), and accounted for greater vulnerability of saddlebacks to rat predation based on information on historical declines of both species. The results allowed population growth to be predicted as a function of management effort while accounting for uncertainty, which means formal decision analysis could be used to decide whether to proceed with a reintroduction. Similar approaches could be applied to other situations where data on the species of interest are limited and provide an alternative to decision making based solely on expert judgment.

A comment on priors for Bayesian occupancy models

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are "uninformative" or "vague", such priors can easily be unintentionally highly informative. Here we report on how the specification of a "vague" normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts.

An efficient extension of N-mixture models for multi-species abundance estimation

In this study we propose an extension of the N-mixture family of models that targets an improvement of the statistical properties of rare species abundance estimators when sample sizes are low, yet typical for tropical studies. The proposed method harnesses information from other species in an ecological community to correct each species' estimator. We provide guidance to determine the sample size required to estimate accurately the abundance of rare tropical species when attempting to estimate the abundance of single species.We evaluate the proposed methods using an assumption of 50 m radius plots and perform simulations comprising a broad range of sample sizes, true abundances and detectability values and a complex data generating process. The extension of the N-mixture model is achieved by assuming that the detection probabilities are drawn at random from a beta distribution in a multi-species fashion. This hierarchical model avoids having to specify a single detection probability parameter per species in the targeted community. Parameter estimation is done via Maximum Likelihood.We compared our multi-species approach with previously proposed multi-species N-mixture models, which we show are biased when the true densities of species in the community are less than seven individuals per 100 hectares. The beta N-mixture model proposed here outperforms the traditional Multi-species N-mixture model by allowing the estimation of organisms at lower densities and controlling the bias in the estimation.We illustrate how our methodology can be used to suggest sample sizes required to estimate the abundance of organisms, when these are either rare, common or abundant. When the interest is full communities, we show how the multi-species approaches, and in particular our beta model and estimation methodology, can be used as a practical solution to estimate organism densities from rapid inventory datasets. The statistical inferences done with our model via Maximum Likelihood can also be used to group species in a community according to their detectabilities.

ednaoccupancy: An r package for multiscale occupancy modelling of environmental DNA data

In this article, we describe ednaoccupancy, an r package for fitting Bayesian, multiscale occupancy models. These models are appropriate for occupancy surveys that include three nested levels of sampling: primary sample units within a study area, secondary sample units collected from each primary unit and replicates of each secondary sample unit. This design is commonly used in occupancy surveys of environmental DNA (eDNA). ednaoccupancy allows users to specify and fit multiscale occupancy models with or without covariates, to estimate posterior summaries of occurrence and detection probabilities, and to compare different models using Bayesian model-selection criteria. We illustrate these features by analysing two published data sets: eDNA surveys of a fungal pathogen of amphibians and eDNA surveys of an endangered fish species.

A Bayesian estimation approach for the mortality in a stage-structured demographic model

Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be obtained using suitable mathematical models that describe the population dynamics based on individual life history responses to environmental conditions and resource availability. These responses are described by development, fecundity and survival rate functions, which can be estimated from laboratory experiments. If experimental data are not available, data on field population dynamics can be used for their estimation. This is the case of the extrinsic mortality term that appears in the mortality rate function due to biotic factors. We propose a Bayesian approach to estimate the probability density functions of the parameters in the extrinsic mortality rate function, starting from data on population abundance. The method investigates the time variability in the mortality parameters by comparing simulated and observed trajectories. The grape berry moth, a pest of great importance in European vineyards, has been considered as a case study. Simulated data have been considered to evaluate the convergence of the algorithm, while field data have been used to obtain estimates of the mortality for the grape berry moth.

An integrated data model to estimate spatiotemporal occupancy, abundance, and colonization dynamics

Ecological invasions and colonizations occur dynamically through space and time. Estimating the distribution and abundance of colonizing species is critical for efficient management or conservation. We describe a statistical framework for simultaneously estimating spatiotemporal occupancy and abundance dynamics of a colonizing species. Our method accounts for several issues that are common when modeling spatiotemporal ecological data including multiple levels of detection probability, multiple data sources, and computational limitations that occur when making fine-scale inference over a large spatiotemporal domain. We apply the model to estimate the colonization dynamics of sea otters (Enhydra lutris) in Glacier Bay, in southeastern Alaska.