Bayesian State-space Framework Research Articles

Cascading effects of mass mortality events in Arctic marine communities.

Mass mortality events caused by pulse anthropogenic or environmental perturbations (e.g., extreme weather, toxic spills or epizootics) severely reduce the abundance of a population in a short time. The frequency and impact of these events are likely to increase across the globe. Studies on how such events may affect ecological communities of interacting species are scarce. By combining a multispecies Gompertz model with a Bayesian state-space framework, we quantify community-level effects of a mass mortality event in a single species. We present a case study on a community of fish and zooplankton in the Barents Sea to illustrate how a mass mortality event of different intensities affecting the lower trophic level (krill) may propagate to higher trophic levels (capelin and cod). This approach is especially valuable for assessing community-level effects of potential anthropogenic-driven mass mortality events, owing to the ability to account for uncertainty in the assessed impact due to uncertainty about the ecological dynamics. We hence quantify how the assessed impact of a mass mortality event depends on the degree of precaution considered. We suggest that this approach can be useful for assessing the possible detrimental outcomes of toxic spills, for example oil spills, in relatively simple communities such as often found in the Arctic, a region under increasing influence of human activities due to increased land and sea use.

Using a state-space population model to detect age-dependent species interactions

Models that incorporate species interactions and their effects on the dynamics of commercially important fish stocks are needed to better understand the importance of ecological interactions and to facilitate sustainable fisheries. We developed a dynamic age-structured population model for the Northeast Arctic stock of Atlantic haddock (Melanogrammus aeglefinus) based on scientific survey and commercial landings data. Our goal was to investigate climate effects and ecological interactions within the haddock food web. A Bayesian state-space framework was used to separate information from ecological noise and observation error. Our results indicate significant impacts of species interactions on haddock dynamics. Haddock survival was associated with biomass indices of cod (Gadus morhua) (negative effect) and capelin (Mallotus villosus) (positive effect). The latter may reflect lower predation by predators such as marine mammals at high capelin biomass. We further detect weak density dependence in the survival of young haddock and a convex relationship between haddock abundance and the scientific survey indices. Our findings highlight the importance of considering natural resources as part of an ecosystem with its diverse interactions both within and between species. This study shows that it is possible to detect ecological interactions with a population model based on noisy data.

A stochastic rank ordered logit model for rating multi-competitor games and sports

AbstractMany games and sports, including races, involve outcomes in which competitors are rank ordered. In some sports, competitors may play in multiple events over long periods of time, and it is natural to assume that their abilities change over time. We propose a Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games. Our approach assumes competitors’ performances follow independent extreme value distributions, with each competitor’s ability evolving over time as a Gaussian random walk. The model accounts for the possibility of ties, an occurrence that is not atypical in races in which some of the competitors may not finish and therefore tie for last place. Inference can be performed through Markov chain Monte Carlo (MCMC) simulation from the posterior distribution. We also develop a filtering algorithm that is an approximation to the full Bayesian computations. The approximate Bayesian filter can be used for updating competitor abilities on an ongoing basis. We demonstrate our approach to measuring abilities of 268 women from the results of women’s Alpine downhill skiing competitions recorded over the period 2002–2013.

Bayesian inference on the effect of density dependence and weather on a guanaco population from Chile.

Understanding the mechanisms that drive population dynamics is fundamental for management of wild populations. The guanaco (Lama guanicoe) is one of two wild camelid species in South America. We evaluated the effects of density dependence and weather variables on population regulation based on a time series of 36 years of population sampling of guanacos in Tierra del Fuego, Chile. The population density varied between 2.7 and 30.7 guanaco/km2, with an apparent monotonic growth during the first 25 years; however, in the last 10 years the population has shown large fluctuations, suggesting that it might have reached its carrying capacity. We used a Bayesian state-space framework and model selection to determine the effect of density and environmental variables on guanaco population dynamics. Our results show that the population is under density dependent regulation and that it is currently fluctuating around an average carrying capacity of 45,000 guanacos. We also found a significant positive effect of previous winter temperature while sheep density has a strong negative effect on the guanaco population growth. We conclude that there are significant density dependent processes and that climate as well as competition with domestic species have important effects determining the population size of guanacos, with important implications for management and conservation.

Separating Intrinsic and Environmental Contributions to Growth and Their Population Consequences

Among-individual heterogeneity in growth is a commonly observed phenomenon that has clear consequences for population and community dynamics yet has proved difficult to quantify in practice. In particular, observed among-individual variation in growth can be difficult to link to any given mechanism. Here, we develop a Bayesian state-space framework for modeling growth that bridges the complexity of bioenergetic models and the statistical simplicity of phenomenological growth models. The model allows for intrinsic individual variation in traits, a shared environment, process stochasticity, and measurement error. We apply the model to two populations of steelhead trout (Oncorhynchus mykiss) grown under common but temporally varying food conditions. Models allowing for individual variation match available data better than models that assume a single shared trait for all individuals. Estimated individual variation translated into a roughly twofold range in realized growth rates within populations. Comparisons between populations showed strong differences in trait means, trait variability, and responses to a shared environment. Together, individual- and population-level variation have substantial implications for variation in size and growth rates among and within populations. State-dependent life-history models predict that this variation can lead to differences in individual life-history expression, lifetime reproductive output, and population life-history diversity.

Combining a Bayesian nonparametric method with a hierarchical framework to estimate individual and temporal variation in growth

Growth modeling has long played an important role in ecology, conservation and management of many species. However, adopting a statistical framework that includes both temporal and individual variability in the growth dynamics has proven challenging. In this paper, we use a Bayesian state space framework (BSSF) to estimate parameters of a discrete time model from a mark-recapture data set of age-1 juvenile Atlantic salmon. We use a Gaussian process (GP) based approach to model variation in seasonal growth potential. In addition, we use auxiliary information on the food environment as prior knowledge of seasonal fluctuations in growth. Parameters for the GP prior and measurement error variances were fixed to speed convergence. Posterior estimates of model parameters were relatively insensitive to these choices. Our model captures the seasonal growth dynamics of juvenile Atlantic salmon as evidenced by close agreement between observed and predicted lengths (r2=0.98). In addition, the relatively narrow confidence intervals indicated significant learning in the parameters of interest. Finally, our model approach was able to accurately recover missing data points. Although this model was applied to a mark-recapture dataset of Atlantic salmon, the generality of the approach should make it applicable to a wide variety of size trajectory datasets, and thus, provides a useful tool to estimate individual and temporal variability in growth from datasets with repeated measurements.

Modelling the impact of hen harrier management measures on a red grouse population in the UK

Human‐wildlife conflict is one of the greatest barriers to effective conservation. The recovery of the hen harrier Circus cyaneus in the United Kingdom has been limited due to illegal persecution, a consequence of the raptors’ predation on the economically valuable game‐bird, the red grouse Lagopus lagopus scoticus. To improve management of the system it is necessary to understand the interactions between the two species in their broader community context. We therefore developed a multi‐species model in which the life history and interactions of each of the two bird species are described through linked process models. This model was fit to population data using a Bayesian state–space framework and used to investigate the effectiveness of a conflict–mitigation technique known as diversionary feeding, in which harrier nests are provided with food in an attempt to reduce consumption of grouse chicks. To explore the utility of diversionary feeding we specified four scenarios in which 1) harriers were absent from the system, 2) there was no diversionary feeding of harriers, 3) only a portion of the harrier nests were provided with diversionary food and 4) all nests were provided with diversionary food. The results from fitting the model under the different scenarios were used to determine the strength of harriers’ impact on grouse density, as well as the effectiveness of diversionary feeding. Given the lack of information on other grouse predators and only two years of data on supplementary feeding, our results need to be implanted with caution. However, we found theoretical support for the hen harriers’ suppression of grouse cycle amplitude and average density. Furthermore, our results suggest that on grouse estates where diversionary feeding is the only active management, diversionary feeding is only marginally successful and not sufficient to mitigate the consequences of hen harrier predation on red grouse chicks.

An Empirical Test of a Diffusion Model: Predicting Clouded Apollo Movements in a Novel Environment

Functional connectivity is a fundamental concept in conservation biology because it sets the level of migration and gene flow among local populations. However, functional connectivity is difficult to measure, largely because it is hard to acquire and analyze movement data from heterogeneous landscapes. Here we apply a Bayesian state-space framework to parameterize a diffusion-based movement model using capture-recapture data on the endangered clouded apollo butterfly. We test whether the model is able to disentangle the inherent movement behavior of the species from landscape structure and sampling artifacts, which is a necessity if the model is to be used to examine how movements depend on landscape structure. We show that this is the case by demonstrating that the model, parameterized with data from a reference landscape, correctly predicts movements in a structurally different landscape. In particular, the model helps to explain why a movement corridor that was constructed as a management measure failed to increase movement among local populations. We illustrate how the parameterized model can be used to derive biologically relevant measures of functional connectivity, thus linking movement data with models of spatial population dynamics.