Density-dependence produces spurious relationships among demographic parameters in a harvested species.

Harvest of wild organisms is an important component of human culture, economy, and recreation, but can also put species at risk of extinction. Decisions that guide successful management actions therefore rely on the ability of researchers to link changes in demographic processes to the anthropogenic actions or environmental changes that underlie variation in demographic parameters. Ecologists often use population models or maximum sustained yield curves to estimate the impacts of harvest on wildlife and fish populations. Applications of these models usually focus exclusively on the impact of harvest and often fail to consider adequately other potential, often collinear, mechanistic drivers of the observed relationships between harvest and demographic rates. In this study, we used an integrated population model and long-term data (1973-2016) to examine the relationships among hunting and natural mortality, the number of hunters, habitat conditions, and population size of blue-winged teal Spatula discors, an abundant North American dabbling duck with a relatively fast-paced life history strategy. Over the last two and a half decades of the study, teal abundance tripled, hunting mortality probability increased slightly ( < 0.02 ), and natural mortality probability increased substantially ( > 0.1 ) at greater population densities. We demonstrate strong density-dependent effects on natural mortality and fecundity as population density increased, indicative of compensatory harvest mortality and compensatory natality. Critically, an analysis that only assessed the relationship between survival and hunting mortality would spuriously indicate depensatory mortality due to multicollinearity between abundance, natural mortality and hunting mortality. Our findings demonstrate that models that only consider the direct effect of hunting on survival or natural mortality can fail to accurately assess the mechanistic impact of hunting on population dynamics due to multicollinearity among demographic drivers. This multicollinearity limits inference and may have strong impacts on applied management actions globally.

A hierarchical model for jointly assessing ecological and anthropogenic impacts on animal demography.

The management of sustainable harvest of animal populations is of great ecological and conservation importance. Development of formal quantitative tools to estimate and mitigate the impacts of harvest on animal populations has positively impacted conservation efforts. The vast majority of existing harvest models, however, do not simultaneously estimate ecological and harvest impacts on demographic parameters and population trends. Given that the impacts of ecological drivers are often equal to or greater than the effects of harvest, and can covary with harvest, this disconnect has the potential to lead to flawed inference. In this study, we used Bayesian hierarchical models and a 43-year capture-mark-recovery dataset from 404,241 female mallards Anas platyrhynchos released in the North American midcontinent to estimate mallard demographic parameters. Furthermore, we model the dynamics of waterfowl hunters and habitat, and the direct and indirect effects of anthropogenic and ecological processes on mallard demographic parameters. We demonstrate that density dependence, habitat conditions and harvest can simultaneously impact demographic parameters of female mallards, and discuss implications for existing and future harvest management models. Our results demonstrate the importance of controlling for multicollinearity among demographic drivers in harvest management models, and provide evidence for multiple mechanisms that lead to partial compensation of mallard harvest. We provide a novel model structure to assess these relationships that may allow for improved inference and prediction in future iterations of harvest management models across taxa.

Long-term research and hierarchical models reveal consistent fitness costs of being the last egg in a clutch.

Maintenance of phenotypic heterogeneity in the face of strong selection is an important component of evolutionary ecology, as are the consequences of such heterogeneity. Organisms may experience diminishing returns of increased reproductive allocation as clutch or litter size increases, affecting current and residual reproductive success. Given existing uncertainty regarding trade-offs between the quantity and quality of offspring, we sought to examine the potential for diminishing returns on increased reproductive allocation in a long-lived species of goose, with a particular emphasis on the effect of position in the laying sequence on offspring quality. To better understand the effects of maternal allocation on offspring survival and growth, we estimated the effects of egg size, timing of breeding, inter- and intra-annual variation, and position in the laying sequence on gosling survival and growth rates of black brant Branta bernicla nigricans breeding in western Alaska from 1987 to 2007. We found that gosling growth rates and survival decreased with position in the laying sequence, regardless of clutch size. Mean egg volume of the clutch a gosling originated from had a positive effect on gosling survival (ß = 0.095, 95% CRI: 0.024, 0.165) and gosling growth rates (ß = 0.626, 95% CRI: 0.469, 0.738). Gosling survival (ß = -0.146, 95% CRI: -0.214, -0.079) and growth rates (ß = -1.286, 95% CRI: -1.435, -1.132) were negatively related to hatching date. These findings indicate substantial heterogeneity in offspring quality associated with their position in the laying sequence. They also potentially suggest a trade-off mechanism for females whose total reproductive investment is governed by pre-breeding state.

Monitoring dynamic spatio-temporal ecological processes optimally.

Population dynamics vary in space and time. Survey designs that ignore these dynamics may be inefficient and fail to capture essential spatio-temporal variability of a process. Alternatively, dynamic survey designs explicitly incorporate knowledge of ecological processes, the associated uncertainty in those processes, and can be optimized with respect to monitoring objectives. We describe a cohesive framework for monitoring a spreading population that explicitly links animal movement models with survey design and monitoring objectives. We apply the framework to develop an optimal survey design for sea otters in Glacier Bay. Sea otters were first detected in Glacier Bay in 1988 and have since increased in both abundance and distribution; abundance estimates increased from 5 otters to >5,000 otters, and they have spread faster than 2.7 km/yr. By explicitly linking animal movement models and survey design, we are able to reduce uncertainty associated with forecasting occupancy, abundance, and distribution compared to other potential random designs. The framework we describe is general, and we outline steps to applying it to novel systems and taxa.

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.

The basis function approach for modeling autocorrelation in ecological data.

Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many seemingly disparate statistical methods used to account for autocorrelation can be expressed as regression models that include basis functions. Basis functions also enable ecologists to modify a wide range of existing ecological models in order to account for autocorrelation, which can improve inference and predictive accuracy. Furthermore, understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of collinearity, and analyzing large data sets. We present important concepts and properties related to basis functions and illustrate several tools and techniques ecologists can use when modeling autocorrelation in ecological data.

Combining statistical inference and decisions in ecology.

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods, including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem.

Rayleigh step-selection functions and connections to continuous-time mechanistic movement models.

BACKGROUND: The process known as ecological diffusion emerges from a first principles view of animal movement, but ecological diffusion and other partial differential equation models can be difficult to fit to data. Step-selection functions (SSFs), on the other hand, have emerged as powerful practical tools for ecologists studying the movement and habitat selection of animals. METHODS: SSFs typically involve comparing resources between a set of used and available points at each step in a sequence of observed positions. We use change of variables to show that ecological diffusion implies certain distributions for available steps that are more flexible than others commonly used. We then demonstrate advantages of these distributions with SSF models fit to data collected for a mountain lion in Colorado, USA. RESULTS: We show that connections between ecological diffusion and SSFs imply a Rayleigh step-length distribution and uniform turning angle distribution, which can accommodate data collected at irregular time intervals. The results of fitting an SSF model with these distributions compared to a set of commonly used distributions revealed how precision and inference can vary between the two approaches. CONCLUSIONS: Our new continuous-time step-length distribution can be integrated into various forms of SSFs, making them applicable to data sets with irregular time intervals between successive animal locations.

Long-term trends and drought: Spatiotemporal variation in juvenile sex ratios of North American ducks.

Sex ratios affect population dynamics and individual fitness, and changing sex ratios can be indicative of shifts in sex-specific survival at different life stages. While climate and landscape changes alter sex ratios of wild bird populations, long-term, landscape scale assessments of sex ratios are rare. Further, little work has been done to understand changes in sex ratios in avian communities. In this manuscript, we analyze long-term (1961-2015) data on five species of ducks across five broad climatic regions of the United States to estimate the effects of drought and long-term trends on the proportion of juvenile females captured at banding. As waterfowl have a 1:1 sex ratio at hatch, we interpret changes in sex ratios of captured juveniles as changes in sex-specific survival rates during early life. Seven of 12 species-region pairs exhibited evidence for long-term trends in the proportion of juvenile females at banding. The proportion of juvenile females at banding increased for duck populations in the western United States and typically declined for duck populations in the eastern United States. We only observed evidence for an effect of drought in two of the 12 species-region pairs, where the proportion of females declined during drought. As changes to North American landscapes and climate continue and intensify, we expect continued changes in sex-specific juvenile survival rates. More broadly, we encourage further research examining the mechanisms underlying long-term trends in juvenile sex ratios in avian communities.

Estimating survival and adoption rates of dependent juveniles.

Population growth and fitness are typically most sensitive to adult survival in long-lived species, but variation in recruitment often explains most of the variation in fitness, as past selection has canalized adult survival. Estimating juvenile survival until age of independence has proven challenging, because marking individuals in this age class may directly affect survival. For Greater Sage-grouse, uniquely marking juveniles in the first days of life likely results in adverse effects to survival, detection of juveniles is not perfect, and females adopt juveniles from other parents. These challenges are encountered by researchers studying avian and mammalian species with similar life histories, yet methods do not exist that explicitly estimate all these components of the recruitment process. We propose a novel data collection method and demographic model to simultaneously estimate rates of detection, survival, and adoption of juvenile individuals. Using multiple cameras to film the beginning of juvenile activity on specific days, we obtained counts of juveniles associated with marked females. Increases of juveniles to broods provided information that enabled us to estimate rates of adoption that can be applied at the population level. Losses from broods informed apparent survival. These losses could be attributed to death, or they could be chicks that were adopted by other females. We found evidence that apparent survival of juveniles was influenced by localized weather patterns when chicks were young. Similarly, we found that young chicks were more susceptible to the adverse effect of attending females being flushed by an observer. Both of these patterns diminished quickly as chicks aged. We provide the first-ever estimates of interval-specific adoption rates. Our results suggest that researchers should be cautious when designing studies to estimate juvenile survival. More importantly, they provide insight into adoption, a behavior that has been known to exist for decades.

Recursive Bayesian computation facilitates adaptive optimal design in ecological studies.

Optimal design procedures provide a framework to leverage the learning generated by ecological models to flexibly and efficiently deploy future monitoring efforts. At the same time, Bayesian hierarchical models have become widespread in ecology and offer a rich set of tools for ecological learning and inference. However, coupling these methods with an optimal design framework can become computationally intractable. Recursive Bayesian computation offers a way to substantially reduce this computational burden, making optimal design accessible for modern Bayesian ecological models. We demonstrate the application of so-called prior-proposal recursive Bayes to optimal design using a simulated data binary regression and the real-world example of monitoring and modeling sea otters in Glacier Bay, Alaska. These examples highlight the computational gains offered by recursive Bayesian methods and the tighter fusion of monitoring and science that those computational gains enable.

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.

Individual heterogeneity in fitness in a long-lived herbivore.

Heterogeneity in the intrinsic quality and nutritional condition of individuals affects reproductive success and consequently fitness. Black brant (Branta bernicla nigricans) are long-lived, migratory, specialist herbivores. Long migratory pathways and short summer breeding seasons constrain the time and energy available for reproduction, thus magnifying life-history trade-offs. These constraints, combined with long lifespans and trade-offs between current and future reproductive value, provide a model system to examine the role of individual heterogeneity in driving life-history strategies and individual heterogeneity in fitness. We used hierarchical Bayesian models to examine reproductive trade-offs, modeling the relationships between within-year measures of reproductive energy allocation and among-year demographic rates of individual females breeding on the Yukon-Kuskokwim Delta, Alaska, using capture-recapture and reproductive data from 1988 to 2014. We generally found that annual survival tended to be buffered against variation in reproductive investment, while breeding probability varied considerably over the range of clutch size-laying date combinations. We provide evidence for relationships between breeding probability and clutch size, breeding probability and nest initiation date, and an interaction between clutch size and initiation date. Average lifetime clutch size also had a weak positive relationship with apparent survival probability. Our results support the use of demographic buffering strategies for black brant. These results also indirectly suggest associations among environmental conditions during growth, fitness, and energy allocation, highlighting the effects of early growth conditions on individual heterogeneity, and subsequently, lifetime reproductive investment.

Diffusion modeling reveals effects of multiple release sites and human activity on a recolonizing apex predator.

BACKGROUND: Reintroducing predators is a promising conservation tool to help remedy human-caused ecosystem changes. However, the growth and spread of a reintroduced population is a spatiotemporal process that is driven by a suite of factors, such as habitat change, human activity, and prey availability. Sea otters (Enhydra lutris) are apex predators of nearshore marine ecosystems that had declined nearly to extinction across much of their range by the early 20th century. In Southeast Alaska, which is comprised of a diverse matrix of nearshore habitat and managed areas, reintroduction of 413 individuals in the late 1960s initiated the growth and spread of a population that now exceeds 25,000. METHODS: Periodic aerial surveys in the region provide a time series of spatially-explicit data to investigate factors influencing this successful and ongoing recovery. We integrated an ecological diffusion model that accounted for spatially-variable motility and density-dependent population growth, as well as multiple population epicenters, into a Bayesian hierarchical framework to help understand the factors influencing the success of this recovery. RESULTS: Our results indicated that sea otters exhibited higher residence time as well as greater equilibrium abundance in Glacier Bay, a protected area, and in areas where there is limited or no commercial fishing. Asymptotic spread rates suggested sea otters colonized Southeast Alaska at rates of 1-8 km/yr with lower rates occurring in areas correlated with higher residence time, which primarily included areas near shore and closed to commercial fishing. Further, we found that the intrinsic growth rate of sea otters may be higher than previous estimates suggested. CONCLUSIONS: This study shows how predator recolonization can occur from multiple population epicenters. Additionally, our results suggest spatial heterogeneity in the physical environment as well as human activity and management can influence recolonization processes, both in terms of movement (or motility) and density dependence.

Estimating correlations among demographic parameters in population models.

Estimating correlations among demographic parameters is critical to understanding population dynamics and life-history evolution, where correlations among parameters can inform our understanding of life-history trade-offs, result in effective applied conservation actions, and shed light on evolutionary ecology. The most common approaches rely on the multivariate normal distribution, and its conjugate inverse Wishart prior distribution. However, the inverse Wishart prior for the covariance matrix of multivariate normal distributions has a strong influence on posterior distributions. As an alternative to the inverse Wishart distribution, we individually parameterize the covariance matrix of a multivariate normal distribution to accurately estimate variances (σ 2) of, and process correlations (ρ) between, demographic parameters. We evaluate this approach using simulated capture-mark-recapture data. We then use this method to examine process correlations between adult and juvenile survival of black brent geese marked on the Yukon-Kuskokwim River Delta, Alaska (1988-2014). Our parameterization consistently outperformed the conjugate inverse Wishart prior for simulated data, where the means of posterior distributions estimated using an inverse Wishart prior were substantially different from the values used to simulate the data. Brent adult and juvenile annual apparent survival rates were strongly positively correlated (ρ = 0.563, 95% CRI 0.181-0.823), suggesting that habitat conditions have significant effects on both adult and juvenile survival. We provide robust simulation tools, and our methods can readily be expanded for use in other capture-recapture or capture-recovery frameworks. Further, our work reveals limits on the utility of these approaches when study duration or sample sizes are small.