Fitting stochastic predator-prey models using both population density and kill rate data

No sensitivity to functional forms in the Rosenzweig-MacArthur model with strong environmental stochasticity

The classic Rosenzweig-MacArthur predator-prey model has been shown to exhibit, like other coupled nonlinear ordinary differential equations (ODEs) from ecology, worrying sensitivity to model structure. This sensitivity manifests as markedly different community dynamics arising from saturating functional responses with nearly identical shapes but different mathematical expressions. Using a stochastic differential equation (SDE) version of the Rosenzweig-MacArthur model with the three functional responses considered by Fussmann & Blasius (2005), I show that such sensitivity seems to be solely a property of ODEs or stochastic systems with weak noise. SDEs with strong environmental noise have by contrast very similar fluctuations patterns, irrespective of the mathematical formula used. Although eigenvalues of linearized predator-prey models have been used as an argument for structural sensitivity, they can also be an argument against structural sensitivity. While the sign of the eigenvalues' real part is sensitive to model structure, its magnitude and the presence of imaginary parts are not, which suggests noise-driven oscillations for a broad range of carrying capacities. I then discuss multiple other ways to evaluate structural sensitivity in a stochastic setting, for predator-prey or other ecological systems.

Integrated Population Models: Achieving Their Potential

Precise and accurate estimates of abundance and demographic rates are primary quantities of interest within wildlife conservation and management. Such quantities provide insight into population trends over time and the associated underlying ecological drivers of the systems. This information is fundamental in managing ecosystems, assessing species conservation status and developing and implementing effective conservation policy. Observational monitoring data are typically collected on wildlife populations using an array of different survey protocols, dependent on the primary questions of interest. For each of these survey designs, a range of advanced statistical techniques have been developed which are typically well understood. However, often multiple types of data may exist for the same population under study. Analyzing each data set separately implicitly discards the common information contained in the other data sets. An alternative approach that aims to optimize the shared information contained within multiple data sets is to use a “model-based data integration” approach, or more commonly referred to as an “integrated model.” This integrated modeling approach simultaneously analyzes all the available data within a single, and robust, statistical framework. This paper provides a statistical overview of ecological integrated models, with a focus on integrated population models (IPMs) which include abundance and demographic rates as quantities of interest. Four main challenges within this area are discussed, namely model specification, computational aspects, model assessment and forecasting. This should encourage researchers to explore further and develop new practical tools to ensure that full utility can be made of IPMs for future studies.

Incorporating nonlinearity with generalized functional responses to simulate multiple predator effects

Predicting the combined effects of predators on shared prey has long been a focus of community ecology, yet quantitative predictions often fail. Failure to account for nonlinearity is one reason for this. Moreover, prey depletion in multiple predator effects (MPE) studies generates biased predictions in applications of common experimental and quantitative frameworks. Here, we explore additional sources of bias stemming from nonlinearities in prey predation risk. We show that in order to avoid bias, predictions about the combined effects of independent predators must account for nonlinear size-dependent risk for prey as well as changes in prey risk driven by nonlinear predator functional responses and depletion. Historical failure to account for biases introduced by well-known nonlinear processes that affect predation risk suggest that we may need to reevaluate the general conclusions that have been drawn about the ubiquity of emergent MPEs over the past three decades.

Functional Responses Shape Node and Network Level Properties of a Simplified Boreal Food Web

Ecological communities are fundamentally connected through a network of trophic interactions that are often complex and difficult to model. Substantial variation exists in the nature and magnitude of these interactions across various predators and prey and through time. However, the empirical data needed to characterize these relationships are difficult to obtain in natural systems, even for relatively simple food webs. Consequently, prey-dependent relationships and specifically the hyperbolic form (Holling’s Type II), in which prey consumption increases with prey density but ultimately becomes saturated or limited by the time spent handling prey, are most widely used albeit often without knowledge of their appropriateness. Here, we investigate the sensitivity of a simplified food web model for a natural, boreal system in the Kluane region of the Yukon, Canada to the type of functional response used. Intensive study of this community has permitted best-fit functional response relationships to be determined, which comprise linear (type I), hyperbolic (type II), sigmoidal (type III), prey- and ratio-dependent relationships, and inverse relationships where kill rates of alternate prey are driven by densities of the focal prey. We compare node- and network-level properties for a food web where interaction strengths are estimated using best-fit functional responses to one where interaction strengths are estimated exclusively using prey-dependent hyperbolic functional responses. We show that hyperbolic functional responses alone fail to capture important ecological interactions such as prey switching, surplus killing and caching, and predator interference, that in turn affect estimates of cumulative kill rates, vulnerability of prey, generality of predators, and connectance. Exclusive use of hyperbolic functional responses also affected trends observed in these metrics over time and underestimated annual variation in several metrics, which is important given that interaction strengths are typically estimated over relatively short time periods. Our findings highlight the need for more comprehensive research aimed at characterizing functional response relationships when modeling predator-prey interactions and food web structure and function, as we work toward a mechanistic understanding linking food web structure and community dynamics in natural systems.