Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?

Density dependence in population growth rates is of immense importance to ecological theory and application, but is difficult to estimate. The Global Population Dynamics Database (GPDD), one of the largest collections of population time series available, has been extensively used to study cross-taxa patterns in density dependence. A major difficulty with assessing density dependence from time series is that uncertainty in population abundance estimates can cause strong bias in both tests and estimates of strength. We analyse 627 data sets in the GPDD using Gompertz population models and account for uncertainty via the Kalman filter. Results suggest that at least 45% of the time series display density dependence, but that it is weak and difficult to detect for a large fraction. When uncertainty is ignored, magnitude of and evidence for density dependence is strong, illustrating that uncertainty in abundance estimates qualitatively changes conclusions about density dependence drawn from the GPDD.     

Open removal models with temporary emigration and population dynamics to inform invasive animal management

Removal sampling data are the primary source of monitoring information for many populations (e.g., invasive species, fisheries). Population dynamics, temporary emigration, and imperfect detection are common sources of variation in monitoring data and are key parameters for informing management. We developed two open robust‐design removal models for simultaneously modeling population dynamics, temporary emigration, and imperfect detection: a random walk linear trend model (estimable without ancillary information), and a 2‐age class informed population model (InfoPM, closely related to integrated population models) that incorporated prior information for age‐structured vital rates and relative juvenile availability. We applied both models to multiyear, removal trapping time‐series of a large invasive lizard (Argentine black and white tegu, Salvator merianae) in three management areas of South Florida to evaluate the effectiveness of management programs. Although estimates of the two models were similar, the InfoPMs generally returned more precise estimates, partitioned dynamics into births, deaths, net migration, and provided a decision support tool to predict population dynamics under different effort scenarios while accounting for uncertainty. Trends in tegu superpopulation abundance estimates were increasing in two management areas despite generally high removal rates. However, tegu abundance appeared to decline in the Core management area, where trapping density was the highest and immigration the lowest. Finally, comparing abundance predictions of no‐removal scenarios to those estimated in each management area suggested significant population reductions due to management. These results suggest that local tegu population control via systematic trapping may be feasible with high enough trap density and limited immigration; and highlights the value of these trapping programs. We provided the first estimates of tegu abundance, capture probabilities, and population dynamics, which is critical for effective management. Furthermore, our models are applicable to a wide range of monitoring programs (e.g., carcass recovery or removal point‐counts).     

How few whales were there after whaling? Inference from contemporary mtDNA diversity

Reconstructing the history of exploited populations of whales requires fitting a trajectory through at least three points in time: (i) prior to exploitation, when abundance is assumed to be at the maximum allowed by environmental carrying capacity; (ii) the point of minimum abundance or 'bottleneck', usually near the time of protection or the abandonment of the hunt; and (iii) near the present, when protected populations are assumed to have undergone some recovery. As historical abundance is usually unknown, this trajectory must be extrapolated according to a population dynamic model using catch records, an assumed rate of increase and an estimate of current abundance, all of which have received considerable attention by the International Whaling Commission (IWC). Relatively little attention has been given to estimating minimum abundance (N(min)), although it is clear that genetic and demographic forces at this point are critical to the potential for recovery or extinction of a local population. We present a general analytical framework to improve estimates of N(min) using the number of mtDNA haplotypes (maternal lineages) surviving in a contemporary population of whales or other exploited species. We demonstrate the informative potential of this parameter as an a posteriori constraint on Bayesian logistic population dynamic models based on the IWC Comprehensive Assessment of the intensively exploited southern right whales (Eubalaena australis) and published surveys of mtDNA diversity for this species. Estimated historical trajectories from all demographic scenarios suggested a substantial loss of mtDNA haplotype richness as a result of 19th century commercial whaling and 20th century illegal whaling by the Soviet Union. However, the relatively high rates of population increase used by the IWC assessment predicted a bottleneck that was implausibly narrow (median, 67 mature females), given our corrected estimates of N(min). Further, high levels of remnant sequence diversity (theta) suggested that pre-exploitation abundance was larger than predicted by the logistic model given the catch record, which is known to be incomplete. Our results point to a need to better integrate evolutionary processes into population dynamic models to account for uncertainty in catch records, the influence of maternal fidelity on metapopulation dynamics, and the potential for inverse density dependence (an 'Allee effect') in severely depleted populations.     

Long-term population size of the North Atlantic humpback whale within the context of worldwide population structure

Once hunted to the brink of extinction, humpback whales (Megaptera novaeangliae) in the North Atlantic have recently been increasing in numbers. However, uncertain information on past abundance makes it difficult to assess the extent of the recovery in this species. While estimates of pre-exploitation abundance based upon catch data suggest the population might be approaching pre-whaling numbers, estimates based on mtDNA genetic diversity suggest they are still only a fraction of their past abundance levels. The difference between the two estimates could be accounted for by inaccuracies in the catch record, by uncertainties surrounding the genetic estimate, or by differences in the timescale to which the two estimates apply. Here we report an estimate of long-term population size based on nuclear gene diversity. We increase the reliability of our genetic estimate by increasing the number of loci, incorporating uncertainty in each parameter and increasing sampling across the geographic range. We report an estimate of long-term population size in the North Atlantic humpback of ~112,000 individuals (95 % CI 45,000–235,000). This value is 2–3 fold higher than estimates based upon catch data. This persistent difference between estimates parallels difficulties encountered by population models in explaining the historical crash of North Atlantic humpback whales. The remaining discrepancy between genetic and catch-record values, and the failure of population models, highlights a need for continued evaluation of whale population growth and shifts over time, and continued caution about changing the conservation status of this population.     

Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates

1. Development of population projections requires estimates of observation error, parameters characterizing expected dynamics such as the specific population growth rate and the form of density regulation, the influence of stochastic factors on population dynamics, and quantification of the uncertainty in the parameter estimates. 2. Here we construct a Population Prediction Interval (PPI) based on Bayesian state space modelling of future population growth of 28 reintroduced ibex populations in Switzerland that have been censused for up to 68 years. Our aim is to examine whether the interpopulation variation in the precision of the population projections is related to differences in the parameters characterizing the expected dynamics, in the effects of environmental stochasticity, in the magnitude of uncertainty in the population parameters, or in the observation error. 3. The error in the population censuses was small. The median coefficient of variation in the estimates across populations was 5.1%. 4. Significant density regulation was present in 53.6% of the populations, but was in general weak. 5. The width of the PPI calculated for a period of 5 years showed large variation among populations, and was explained by differences in the impact of environmental stochasticity on population dynamics. 6. In spite of the high accuracy in population estimates, the uncertainty in the parameter estimates was still large. This uncertainty affected the precision in the population predictions, but it decreased with increasing length of study period, mainly due to higher precision in the estimates of the environmental variance in the longer time-series. 7. These analyses reveal that predictions of future population fluctuations of weakly density-regulated populations such as the ibex often become uncertain. Credible population predictions require that this uncertainty is properly quantified.     

Pre-whaling genetic diversity and population ecology in eastern Pacific gray whales: insights from ancient DNA and stable isotopes

Commercial whaling decimated many whale populations, including the eastern Pacific gray whale, but little is known about how population dynamics or ecology differed prior to these removals. Of particular interest is the possibility of a large population decline prior to whaling, as such a decline could explain the ~5-fold difference between genetic estimates of prior abundance and estimates based on historical records. We analyzed genetic (mitochondrial control region) and isotopic information from modern and prehistoric gray whales using serial coalescent simulations and Bayesian skyline analyses to test for a pre-whaling decline and to examine prehistoric genetic diversity, population dynamics and ecology. Simulations demonstrate that significant genetic differences observed between ancient and modern samples could be caused by a large, recent population bottleneck, roughly concurrent with commercial whaling. Stable isotopes show minimal differences between modern and ancient gray whale foraging ecology. Using rejection-based Approximate Bayesian Computation, we estimate the size of the population bottleneck at its minimum abundance and the pre-bottleneck abundance. Our results agree with previous genetic studies suggesting the historical size of the eastern gray whale population was roughly three to five times its current size.     

Population Graphs: the graph theoretic shape of genetic structure

Patterns of intraspecific genetic variation result from interactions among both historical and contemporary evolutionary processes. Traditionally, population geneticists have used methods such as F-statistics, pairwise isolation by distance models, spatial autocorrelation and coalescent models to analyse this variation and to gain insight about causal evolutionary processes. Here we introduce a novel approach (Population Graphs) that focuses on the analysis of marker-based population genetic data within a graph theoretic framework. This method can be used to estimate traditional population genetic summary statistics, but its primary focus is on characterizing the complex topology resulting from historical and contemporary genetic interactions among populations. We introduce the application of Population Graphs by examining the range-wide population genetic structure of a Sonoran Desert cactus (Lophocereus schottii). With this data set, we evaluate hypotheses regarding historical vicariance, isolation by distance, population-level assignment and the importance of specific populations to species-wide genetic connectivity. We close by discussing the applicability of Population Graphs for addressing a wide range of population genetic and phylogeographical problems.     

Noninvasive Hair Sampling and Genetic Tagging of Co-Distributed Fishers and American Martens

ABSTRACT Estimation of abundance is important for assessing population responses to management actions. Accurate abundance estimates are particularly critical for monitoring temporal variation following reintroductions when the management goal is to attain population sizes capable of sustaining harvest. Numerous reintroductions have taken place in the Great Lakes region of North America, including efforts to restore extirpated fishers (Martes pennanti) and American martens (M. americana). We used a DNA-based noninvasive hair-snaring method based on one trap design and trapping -grid configuration, and evaluated capture—mark—recapture (CMR) analytical approaches to simultaneously estimate population size for co-distributed fishers and American martens in a 671-km² area of the Ottawa National Forest in the western Upper Peninsula of Michigan, USA. We included harvest as a final recapture period to increase probability of recapture and to evaluate potential violations of geographic closure assumptions. We used microsatellite markers to identify target species, eliminate congener species, and provide individual identity for estimation of abundance. Population estimates for fishers and martens on the study area ranged from 35 to 60 and 8 to 28, respectively. Estimators incorporating harvest data resulted in up to a 40% increase in abundance estimates relative to estimators without harvest. We considered population estimates not including harvest data the most appropriate for the study due to timing of sampling and environmental factors, but inclusion of harvested individuals was shown to be useful as a means to detect violations of the assumption of geographic closure. We suggest improvements on future CMR sampling designs for larger landscape scales of relevance to management through incorporation of habitat or historical harvest data. Noninvasive genetic methods that simultaneously estimate the numerical abundance of co-distributed species can greatly decrease assessment costs relative to traditional methods, and increase resulting demographic and ecological information.     

Measurement error in a random walk model with applications to population dynamics

Population abundances are rarely, if ever, known. Instead, they are estimated with some amount of uncertainty. The resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time. This article addresses some outstanding questions on the consequences of measurement error in one such dynamic model, the random walk with drift model, and proposes some new ways to correct for measurement error. We present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors, and we provide analytical results about the biases of estimators that ignore the measurement error. Our new estimators include both method of moments estimators and "pseudo"-estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model. We derive the asymptotic properties of our methods and existing methods, and we compare their finite-sample performance with a simulation experiment. We also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets.     

Accounting for uncertainty in dormant life stages in stochastic demographic models

Dormant life stages are often critical for population viability in stochastic environments, but accurate field data characterizing them are difficult to collect. Such limitations may translate into uncertainties in demographic parameters describing these stages, which then may propagate errors in the examination of population‐level responses to environmental variation. Expanding on current methods, we 1) apply data‐driven approaches to estimate parameter uncertainty in vital rates of dormant life stages and 2) test whether such estimates provide more robust inferences about population dynamics. We built integral projection models (IPMs) for a fire‐adapted, carnivorous plant species using a Bayesian framework to estimate uncertainty in parameters of three vital rates of dormant seeds – seed‐bank ingression, stasis and egression. We used stochastic population projections and elasticity analyses to quantify the relative sensitivity of the stochastic population growth rate (log λs) to changes in these vital rates at different fire return intervals. We then ran stochastic projections of log λs for 1000 posterior samples of the three seed‐bank vital rates and assessed how strongly their parameter uncertainty propagated into uncertainty in estimates of log λs and the probability of quasi‐extinction, P_q(t). Elasticity analyses indicated that changes in seed‐bank stasis and egression had large effects on log λs across fire return intervals. In turn, uncertainty in the estimates of these two vital rates explained > 50% of the variation in log λs estimates at several fire‐return intervals. Inferences about population viability became less certain as the time between fires widened, with estimates of P_q(t) potentially > 20% higher when considering parameter uncertainty. Our results suggest that, for species with dormant stages, where data is often limited, failing to account for parameter uncertainty in population models may result in incorrect interpretations of population viability.     

Using Lifetime Risk Estimates in Personal Genomic Profiles: Estimation of Uncertainty

Personal genome tests are now offered direct-to-consumer (DTC) via genetic variants identified by genome-wide association studies (GWAS) for common diseases. Tests report risk estimates (age-specific and lifetime) for various diseases based on genotypes at multiple loci. However, uncertainty surrounding such risk estimates has not been systematically investigated. With breast cancer as an example, we examined the combined effect of uncertainties in population incidence rates, genotype frequency, effect sizes, and models of joint effects among genetic variants on lifetime risk estimates. We performed simulations to estimate lifetime breast cancer risk for carriers and noncarriers of genetic variants. We derived population-based cancer incidence rates from Surveillance, Epidemiology, and End Results (SEER) Program and comparative international data. We used data for non-Hispanic white women from 2003 to 2005. We derived genotype frequencies and effect sizes from published GWAS and meta-analyses. For a single genetic variant in FGFR2 gene (rs2981582), combination of uncertainty in these parameters produced risk estimates where upper and lower 95% simulation intervals differed by more than 3-fold. Difference in population incidence rates was the largest contributor to variation in risk estimates. For a panel of five genetic variants, estimated lifetime risk of developing breast cancer before age 80 for a woman that carried all risk variants ranged from 6.1% to 21%, depending on assumptions of additive or multiplicative joint effects and breast cancer incidence rates. Epidemiologic parameters involved in computation of disease risk have substantial uncertainty, and cumulative uncertainty should be properly recognized. Reliance on point estimates alone could be seriously misleading.     

MAXIMUM NET PRODUCTIVITY LEVEL ESTIMATION FOR THE NORTHERN FUR SEAL (CALLORHINUS URSINUS) POPULATION OF ST. PAUL ISLAND, ALASKA

The goal of this study was to assess the maximum net productivity level for the northern fur seal ( Callorhinus ursinus ) population of St. Paul Island, Alaska. Definitive determination of this level is not possible due to uncertainty in life table parameters and density-dependent changes in those parameters. To account for such uncertainty, repetitive numerical simulations were used to generate frequency distributions of estimates for the maximum net productivity level and related population parameters. This approach systematically varied simulation input parameters, ran a separate simulation with each input parameter combination, and validated the simulations on the basis of comparison with historical observations. Results from validated simulations were compiled in frequency distributions to provide a measure of confidence for MNPL estimates. The distributions confirm that this population is probably well below its maximum net productivity level. Because they reflect the uncertainty in our understanding of northern fur seal population dynamics, these distributions are a more realistic basis for management than single point estimates.     

Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics

Aim The study and prediction of species–environment relationships is currently mainly based on species distribution models. These purely correlative models neglect spatial population dynamics and assume that species distributions are in equilibrium with their environment. This causes biased estimates of species niches and handicaps forecasts of range dynamics under environmental change. Here we aim to develop an approach that statistically estimates process‐based models of range dynamics from data on species distributions and permits a more comprehensive quantification of forecast uncertainties. Innovation We present an approach for the statistical estimation of process‐based dynamic range models (DRMs) that integrate Hutchinson's niche concept with spatial population dynamics. In a hierarchical Bayesian framework the environmental response of demographic rates, local population dynamics and dispersal are estimated conditional upon each other while accounting for various sources of uncertainty. The method thus: (1) jointly infers species niches and spatiotemporal population dynamics from occurrence and abundance data, and (2) provides fully probabilistic forecasts of future range dynamics under environmental change. In a simulation study, we investigate the performance of DRMs for a variety of scenarios that differ in both ecological dynamics and the data used for model estimation. Main conclusions Our results demonstrate the importance of considering dynamic aspects in the collection and analysis of biodiversity data. In combination with informative data, the presented framework has the potential to markedly improve the quantification of ecological niches, the process‐based understanding of range dynamics and the forecasting of species responses to environmental change. It thereby strengthens links between biogeography, population biology and theoretical and applied ecology.     

Abundance Estimation With a Transient Model Under the Robust Design

Abstract: A common situation in capture-mark-recapture (CMR) studies on birds and other organisms is to capture individuals not belonging to the studied population only present during the short time of the capture session. Presence of such transient individuals affects demographic parameter estimation from CMR data. Methods exist to reduce biases on survival estimates in the presence of transients and have been shown to be particularly efficient within the Robust Design framework (several secondary capture sessions within a short time interval during which the studied population can be assumed closed). We present a new model to estimate population size accounting for transients. We first used simulated data to show that the method reduces positive biases due to transients. In a second step, we applied the method to a real CMR dataset on a reed warbler (Acrocephalus scirpaceus) population. Population size estimates are reduced by up to 50% when correcting for the presence of transients. Many field studies on managed animal populations use capture-recapture methodology to obtain crucial parameters of the focal population demography. The resulting data sets are used either to estimate population size ignoring the presence of transients, or to estimate vital rates, accounting for transients but overlooking abundance estimation. Our method conciliates these 2 approaches.     

Re-Constructing Historical Adélie Penguin Abundance Estimates by Retrospectively Accounting for Detection Bias

Seabirds and other land-breeding marine predators are considered to be useful and practical indicators of the state of marine ecosystems because of their dependence on marine prey and the accessibility of their populations at breeding colonies. Historical counts of breeding populations of these higher-order marine predators are one of few data sources available for inferring past change in marine ecosystems. However, historical abundance estimates derived from these population counts may be subject to unrecognised bias and uncertainty because of variable attendance of birds at breeding colonies and variable timing of past population surveys. We retrospectively accounted for detection bias in historical abundance estimates of the colonial, land-breeding Adélie penguin through an analysis of 222 historical abundance estimates from 81 breeding sites in east Antarctica. The published abundance estimates were de-constructed to retrieve the raw count data and then re-constructed by applying contemporary adjustment factors obtained from remotely operating time-lapse cameras. The re-construction process incorporated spatial and temporal variation in phenology and attendance by using data from cameras deployed at multiple sites over multiple years and propagating this uncertainty through to the final revised abundance estimates. Our re-constructed abundance estimates were consistently higher and more uncertain than published estimates. The re-constructed estimates alter the conclusions reached for some sites in east Antarctica in recent assessments of long-term Adélie penguin population change. Our approach is applicable to abundance data for a wide range of colonial, land-breeding marine species including other penguin species, flying seabirds and marine mammals.     

Modeling vital rates improves estimation of population projection matrices

Population projection matrices are commonly used by ecologists and managers to analyze the dynamics of stage-structured populations. Building projection matrices from data requires estimating transition rates among stages, a task that often entails estimating many parameters with few data. Consequently, large sampling variability in the estimated transition rates increases the uncertainty in the estimated matrix and quantities derived from it, such as the population multiplication rate and sensitivities of matrix elements. Here, we propose a strategy to avoid overparameterized matrix models. This strategy involves fitting models to the vital rates that determine matrix elements, evaluating both these models and ones that estimate matrix elements individually with model selection via information criteria, and averaging competing models with multimodel averaging. We illustrate this idea with data from a population of Silene acaulis (Caryophyllaceae), and conduct a simulation to investigate the statistical properties of the matrices estimated in this way. The simulation shows that compared with estimating matrix elements individually, building population projection matrices by fitting and averaging models of vital-rate estimates can reduce the statistical error in the population projection matrix and quantities derived from it.     

A stage-based matrix population model of invasive lionfish with implications for control

The rapid invasion of lionfish into the Western North Atlantic and Caribbean will undoubtedly affect native reef fishes via processes such as trophic disruption and niche takeover, yet little is known about the dynamics of this invasion. We constructed a stage-based, matrix population model in which matrix elements were comprised of lower-level parameters. Lionfish vital rates were estimated from existing literature and from new field and laboratory studies. Sensitivity analysis of lower-level parameters revealed that population growth rate is most influenced by larval mortality; elasticity analysis of the matrix indicated strong influence of the adult and juvenile survival elements. Based on this model, approximately 27% of an invading adult lionfish population would have to be removed monthly for abundance to decrease. Hierarchical modeling indicated that this point estimate falls within a broad uncertainty interval which could result from imprecise estimates of life-history parameters. The model demonstrated that sustained removal efforts could be substantially more effective by targeting juveniles as well as adults.     

Abundance and residency dynamics of the Indo-Pacific humpback dolphin,Sousa chinensis,in the Dafengjiang River Estuary,China

Robust population size estimates are essential for informing population conservation status. Residency dynamics show population habitat use through time. Population size of Indo-Pacific humpback dolphins (Sousa chinensis) has been extensively investigated in Chinese waters, but their residency dynamics are rarely known. Mark-recapture analysis based on photo-identification records was applied to humpback dolphins in the Dafengjiang River Estuary habitat, one of the key habitats in the northern Beibu Gulf, China. Movement analyses based on lagged identification rate indicated the humpback dolphins spent, on average, 78.5 days inside and 46.9 days outside the survey area. Within the study area, the humpback dolphin abundance was 83 identifiable dolphins. A total of 353–430 humpback dolphins, estimated by POPAN modeling, were involved in this fluid habitat-use dynamic. Robust Design analysis showed strong seasonality in humpback dolphin abundance and emigration probability, implying a movement- and habitat-use pattern likely associated with spatiotemporal distribution of oceanographic characteristics and prey occurrences. Population surveys and conservation measures currently conducted in Chinese waters seldom consider seasonality in movements between habitat patches, which can be addressed by genetic analyses across habitats and cross-matching photo-identification records among neighboring habitats.     

Likelihood analysis of ongoing gene flow and historical association

Abstract.— We develop a Monte Carlo-based likelihood method for estimating migration rates and population divergence times from data at unlinked loci at which mutation rates are sufficiently low that, in the recent past, the effects of mutation can be ignored. The method is applicable to restriction fragment length polymorphisms (RFLPs) and single nucleotide polymorphisms (SNPs) sampled from a subdivided population. The method produces joint maximum-likelihood estimates of the migration rate and the time of population divergence, both scaled by population size, and provides a framework in which to test either for no ongoing gene flow or for population divergence in the distant past. We show the method performs well and provides reasonably accurate estimates of parameters even when the assumptions under which those estimates are obtained are not completely satisfied. Furthermore, we show that, provided that the number of polymorphic loci is sufficiently large, there is some power to distinguish between ongoing gene flow and historical association as causes of genetic similarity between pairs of populations.     

Population growth rates of reef sharks with and without fishing on the great barrier reef: robust estimation with multiple models

Overfishing of sharks is a global concern, with increasing numbers of species threatened by overfishing. For many sharks, both catch rates and underwater visual surveys have been criticized as indices of abundance. In this context, estimation of population trends using individual demographic rates provides an important alternative means of assessing population status. However, such estimates involve uncertainties that must be appropriately characterized to credibly and effectively inform conservation efforts and management. Incorporating uncertainties into population assessment is especially important when key demographic rates are obtained via indirect methods, as is often the case for mortality rates of marine organisms subject to fishing. Here, focusing on two reef shark species on the Great Barrier Reef, Australia, we estimated natural and total mortality rates using several indirect methods, and determined the population growth rates resulting from each. We used bootstrapping to quantify the uncertainty associated with each estimate, and to evaluate the extent of agreement between estimates. Multiple models produced highly concordant natural and total mortality rates, and associated population growth rates, once the uncertainties associated with the individual estimates were taken into account. Consensus estimates of natural and total population growth across multiple models support the hypothesis that these species are declining rapidly due to fishing, in contrast to conclusions previously drawn from catch rate trends. Moreover, quantitative projections of abundance differences on fished versus unfished reefs, based on the population growth rate estimates, are comparable to those found in previous studies using underwater visual surveys. These findings appear to justify management actions to substantially reduce the fishing mortality of reef sharks. They also highlight the potential utility of rigorously characterizing uncertainty, and applying multiple assessment methods, to obtain robust estimates of population trends in species threatened by overfishing.