Integrated population models: Model assumptions and inference

The Internet of Animals: what it is, what it could be

One of the biggest trends in ecology over the past decade has been the creation of standardized databases. Recently, this has included live data, formal linkages between disparate databases, and automated analytics, a synergy that we recognize as the Internet of Animals (IoA). Early IoA systems relate animal locations to remote-sensing data to predict species distributions and detect disease outbreaks, and use live data to inform management of endangered species. However, meeting the future potential of the IoA concept will require solving challenges of taxonomy, data security, and data sharing. By linking data sets, integrating live data, and automating workflows, the IoA has the potential to enable discoveries and predictions relevant to human societies and the conservation of animals.

Assessing Ecosystem State Space Models: Identifiability and Estimation

Hierarchical probability models are being used more often than non-hierarchical deterministic process models in environmental prediction and forecasting, and Bayesian approaches to fitting such models are becoming increasingly popular. In particular, models describing ecosystem dynamics with multiple states that are autoregressive at each step in time can be treated as statistical state space models (SSMs). In this paper, we examine this subset of ecosystem models, embed a process-based ecosystem model into an SSM, and give closed form Gibbs sampling updates for latent states and process precision parameters when process and observation errors are normally distributed. Here, we use simulated data from an example model (DALECev) and study the effects changing the temporal resolution of observations on the states (observation data gaps), the temporal resolution of the state process (model time step), and the level of aggregation of observations on fluxes (measurements of transfer rates on the state process). We show that parameter estimates become unreliable as temporal gaps between observed state data increase. To improve parameter estimates, we introduce a method of tuning the time resolution of the latent states while still using higher-frequency driver information and show that this helps to improve estimates. Further, we show that data cloning is a suitable method for assessing parameter identifiability in this class of models. Overall, our study helps inform the application of state space models to ecological forecasting applications where (1) data are not available for all states and transfers at the operational time step for the ecosystem model and (2) process uncertainty estimation is desired.

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).

A niche for null models in adaptive resource management

As global systems rapidly change, our collective ability to predict future ecological dynamics will become increasingly important for successful natural resource management. By merging stakeholder objectives with system uncertainty, and by adapting actions to changing systems and knowledge, adaptive resource management (ARM) provides a rigorous platform for making sound decisions in a changing world. Critically, however, applications of ARM could be improved by employing benchmarks (i.e., points of reference) for determining when learning is occurring through the cycle of monitoring, modeling, and decision-making steps in ARM. Many applications of ARM use multiple model-based hypotheses to identify and reduce systematic uncertainty over time, but generally lack benchmarks for gauging discovery of scientific evidence and learning. This creates the danger of thinking that directional changes in model weights or rankings are indicative of evidence for hypotheses, when possibly all competing models are inadequate. There is thus a somewhat obvious, but yet to be filled niche for including benchmarks for learning in ARM. We contend that carefully designed "ecological null models," which are structured to produce an expected ecological pattern in the absence of a hypothesized mechanism, can serve as suitable benchmarks. Using a classic case study of mallard harvest management that is often used to demonstrate the successes of ARM for learning about ecological mechanisms, we show that simple ecological null models, such as population persistence (Nt +1 = Nt ), provide more robust near-term forecasts of population abundance than the currently used mechanistic models. More broadly, ecological null models can be used as benchmarks for learning in ARM that trigger the need for discarding model parameterizations and developing new ones when prevailing models underperform the ecological null model. Identifying mechanistic models that surpass these benchmarks will improve learning through ARM and help decision-makers keep pace with a rapidly changing world.

Variation in Demography and Life-History Strategies Across the Range of a Declining Mountain Bird Species

Species- and population-specific responses to their environment may depend to a large extent on the spatial variation in life-history traits and in demographic processes of local population dynamics. Yet, those parameters and their variability remain largely unknown for many cold-adapted species, which are exposed to particularly rapid rates of environmental change. Here, we compared the demographic traits and dynamics for an emblematic bird species of European mountain ecosystems, the ring ouzel (Turdus torquatus). Using integrated population models fitted in a Bayesian framework, we estimated the survival probability, productivity and immigration of two populations from the Western European Alps, in France (over 11 years) and Switzerland (over 6 years). Juvenile apparent survival was lower and immigration rate higher in the Swiss compared to the French population, with the temporal variation in population growth rate driven by different demographic processes. Yet, when compared to populations in the northwestern part of the range, in Scotland, these two Alpine populations both showed a much lower productivity and higher adult survival, indicating a slower life-history strategy. Our results suggest that demographic characteristics can substantially vary across the discontinuous range of this passerine species, essentially due to contrasted, possibly locally evolved life-history strategies. This study therefore raises the question of whether flexibility in life-history traits is widespread among boreo-alpine species and if it might provide adaptive potential for coping with current environmental change.

Partial and complete dependency among data sets has minimal consequence on estimates from integrated population models

Integrated population models (IPMs) are widely used to combine disparate data sets in joint analysis to better understand population dynamics and provide guidance for conservation activities. An often-cited assumption of IPMs is independence among component data sets within the combined likelihood. Dependency among data sets should lead to underestimation of variance and bias because individuals contribute data to more than one data set. In practice, studied individuals often occur in multiple data sets in IPMs (i.e., overlap), which is one way for the independence assumption to be violated. Such cases have the potential to dissuade practitioners and limit application of IPMs to solve emerging ecological problems. We assessed precision and bias of demographic rates estimated from IPMs using a complete gradient (0-100%) of overlap among data sets, wide ranges in demographic rates (e.g., survival 0.1-0.8) and sample sizes (100-1,200 individuals) and variable data sources. We compared results from our simulations with those from IPMs constructed using empirical data on tree swallows (Tachycineta bicolor) where data sets either had complete overlap or included different individuals. Contrary to previous investigators, we found no substantive bias or uncertainty in any demographic rate from IPMs derived from data sets with complete overlap. While variability in demographic rates was greater at low sample sizes (i.e., low capture, recapture, and survey probabilities), there were negligible differences in the posterior mean or root mean square error of demographic rates among IPMs with strong dependence vs. complete independence among data sets. Our simulations suggest IPMs can be designed using only capture-recapture data or harvest and capture-recovery data where population estimates are obtained from the same data as survival and productivity data. While we encourage researchers to carefully consider the modeling approach best suited for their data sets, our results suggest that dependence among data sets does not generally compromise IPM estimates. Thus, violation of the independence assumption should not dissuade researchers from the application of IPMs in ecological research.

A modelling framework for integrating reproduction, survival and count data when projecting the fates of threatened populations

A key goal of ecological research is to obtain reliable estimates of population demographic rates, abundance and trends. However, a common challenge when studying wildlife populations is imperfect detection or breeding observation, which results in unknown survival status and reproductive output for some individuals. It is important to account for undetected individuals in population models because they contribute to population abundance and dynamics, and can have implications for population management. Promisingly, recent methodological advances provide us with the tools to integrate data from multiple independent sources to gain insights into the unobserved component of populations. We use data from five reintroduced populations of a threatened New Zealand bird, the hihi (Notiomystis cincta), to develop an integrated population modelling framework that allows missing values for survival status, sex and reproductive output to be modelled. Our approach combines parallel matrices of encounter and reproduction histories from marked individuals, as well as counts of unmarked recruits detected at the start of each breeding season. Integrating these multiple data types enabled us to simultaneously model survival and reproduction of detected individuals, undetected individuals and unknown (never detected) individuals to derive parameter estimates and projections based on all available data, thereby improving our understanding of population dynamics and enabling full propagation of uncertainty. The methods presented will be especially useful for management programmes for populations that are intensively monitored but where individuals are still imperfectly detected, as will be the case for most threatened wild populations.

Reconstructing population dynamics of a threatened marine mammal using multiple data sets

Models of marine mammal population dynamics have been used extensively to predict abundance. A less common application of these models is to reconstruct historical population dynamics, filling in gaps in observation data by integrating information from multiple sources. We developed an integrated population model for the Florida manatee (Trichechus manatus latirostris) to reconstruct its population dynamics in the southwest region of the state over the past 20 years. Our model improved precision of key parameter estimates and permitted inference on poorly known parameters. Population growth was slow (averaging 1.02; 95% credible interval 1.01-1.03) but not steady, and an unusual mortality event in 2013 led to an estimated net loss of 332 (217-466) manatees. Our analyses showed that precise estimates of abundance could be derived from estimates of vital rates and a few input estimates of abundance, which may mean costly surveys to estimate abundance don't need to be conducted as frequently. Our study also shows that retrospective analyses can be useful to: (1) model the transient dynamics of age distribution; (2) assess and communicate the conservation status of wild populations; and (3) improve our understanding of environmental effects on population dynamics and thus enhance our ability to forecast.

Reintroduced wolves and hunting limit the abundance of a subordinate apex predator in a multi-use landscape

Top-down effects of apex predators are modulated by human impacts on community composition and species abundances. Consequently, research supporting top-down effects of apex predators occurs almost entirely within protected areas rather than the multi-use landscapes dominating modern ecosystems. Here, we developed an integrated population model to disentangle the concurrent contributions of a reintroduced apex predator, the grey wolf, human hunting and prey abundances on vital rates and abundance of a subordinate apex predator, the puma. Increasing wolf numbers had strong negative effects on puma fecundity, and subadult and adult survival. Puma survival was also influenced by density dependence. Overall, puma dynamics in our multi-use landscape were more strongly influenced by top-down forces exhibited by a reintroduced apex predator, than by human hunting or bottom-up forces (prey abundance) subsidized by humans. Quantitatively, the average annual impact of human hunting on equilibrium puma abundance was equivalent to the effects of 20 wolves. Historically, wolves may have limited pumas across North America and dictated puma scarcity in systems lacking sufficient refugia to mitigate the effects of competition.

Why we should care about movements: Using spatially explicit integrated population models to assess habitat source-sink dynamics

Assessing the source–sink status of populations and habitats is of major importance for understanding population dynamics and for the management of natural populations. Sources produce a net surplus of individuals (per capita contribution to the metapopulation > 1) and will be the main contributors for self‐sustaining populations, whereas sinks produce a deficit (contribution < 1). However, making these types of assessments is generally hindered by the problem of separating mortality from permanent emigration, especially when survival probabilities as well as moved distances are habitat‐specific.

To address this long‐standing issue, we propose a spatial multi‐event integrated population model (IPM) that incorporates habitat‐specific dispersal distances of individuals. Using information about local movements, this IPM adjusts survival estimates for emigration outside the study area.

Analysing 24 years of data on a farmland passerine (the northern wheatear Oenanthe oenanthe), we assessed habitat‐specific contributions, and hence the source–sink status and temporal variation of two key breeding habitats, while accounting for habitat‐ and sex‐specific local dispersal distances of juveniles and adults. We then examined the sensitivity of the source–sink analysis by comparing results with and without accounting for these local movements.

Estimates of first‐year survival, and consequently habitat‐specific contributions, were higher when local movement data were included. The consequences from including movement data were sex specific, with contribution shifting from sink to likely source in one habitat for males, and previously noted habitat differences for females disappearing.

Assessing the source–sink status of habitats is extremely challenging. We show that our spatial IPM accounting for local movements can reduce biases in estimates of the contribution by different habitats, and thus reduce the overestimation of the occurrence of sink habitats. This approach allows combining all available data on demographic rates and movements, which will allow better assessment of source–sink dynamics and better informed conservation interventions.

Next-generation serology: integrating cross-sectional and capture-recapture approaches to infer disease dynamics

Two approaches have been classically used in disease ecology to estimate epidemiological parameters from field studies: cross-sectional sampling from unmarked individuals and longitudinal capture-recapture setups, which generally involve more limited numbers of marked individuals due to cost and logistical constraints. Although the benefits of longitudinal setups are increasingly acknowledged in the disease ecology community, cross-sectional data remain largely overrepresented in the literature, probably because of the inherent costs of longitudinal surveys. In this context, we used simulated data to compare the performances of cross-sectional and longitudinal designs to estimate the force of infection (i.e., the rate at which susceptible individuals become infected). Then, inspired from recent method developments in quantitative ecology, we explore the benefits of integrating both cross-sectional (seroprevalences) and longitudinal (individuals histories) data sets. In doing so, we investigate the effects of host species life history, antibody persistence, and degree of a priori knowledge and uncertainty on demographic and epidemiological parameters, as those are expected to affect in different ways the level of inference possible from the data. Our results highlight how those elements are important to consider in determining optimal sampling designs. In the case of long-lived species exposed to infectious agents resulting in persistent antibody responses, integrated designs are especially valuable as they benefit from the performances of longitudinal designs even with relatively small longitudinal sample sizes. As an illustration, we apply this approach to a combination of empirical and simulated data inspired from a case of bats exposed to a rabies virus. Overall, this work highlights that serology field studies could greatly benefit from the opportunity of integrating cross-sectional and longitudinal designs.