Scaling up the predator functional response in heterogeneous environment: When Holling type III can emerge?

Considerations When Applying the Consumer Functional Response Measured Under Artificial Conditions

Since its creation, considerable effort has been given to improving the utility of the consumer functional response. To date, the majority of efforts have focused on improving mathematical formulation in order to include additional ecological processes and constraints, or have focused on improving the statistical analysis of the functional response to enhance rigor and to more accurately match experimental designs used to measure the functional response. In contrast, relatively little attention has been given to improving the interpretation of functional response empirical results, or to clarifying the implementation and extrapolation of empirical measurements to more realistic field conditions. In this paper I explore three concepts related to the interpretation and extrapolation of empirically measured functional responses. First, I highlight the need for a mechanistic understanding when interpreting foraging patterns and highlight pitfalls that can occur when we lack understanding between the shape of the functional response curve and the mechanisms that give rise to that shape. Second, I discuss differences between experimental and real-world field conditions that must be considered when trying to extrapolate measured functional responses to more natural conditions. Third, I examine the importance of the time scale of empirical measurements, and the need to consider tradeoffs that alter or limit foraging decisions under natural conditions. Clearly accounting for these three conceptual areas when measuring functional responses and when interpreting and attempting to extrapolate empirically measured functional responses will lead to more accurate estimates of consumer impacts under natural field conditions, and will improve the utility of the functional response as a heuristic tool in ecology.

Nonlocal grazing in patterned ecosystems

Many ecosystems exhibit gapped, labyrinthine, striped or spotted patterns. Important examples are vegetation patterns in drylands: these patterns are viewed as precursors of a catastrophic transition to a degraded state. A possible source of degradation is overgrazing, but many current spatially extended models include grazing in a local linear way. In this article nonlocal grazing responses are derived, taking into account (1) how many consumers there are (demographic response) (2) where they are (aggregative response) and (3) how much they forage (functional response). Different assumptions lead to different grazing responses, the type of grazing has a large influence on how ecosystems adapt to changing environmental conditions. In dryland simulations the different types of grazing are shown to alter the desertification process driven by decreasing rainfall. A sufficiently strong aggregative response leads to the suppression of vegetation patterns, nuancing their role as generic early warning signals.

Space race functional responses

We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis-Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka-Volterra predator-prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats.

Defining and detecting structural sensitivity in biological models: developing a new framework

When we construct mathematical models to represent biological systems, there is always uncertainty with regards to the model specification--whether with respect to the parameters or to the formulation of model functions. Sometimes choosing two different functions with close shapes in a model can result in substantially different model predictions: a phenomenon known in the literature as structural sensitivity, which is a significant obstacle to improving the predictive power of biological models. In this paper, we revisit the general definition of structural sensitivity, compare several more specific definitions and discuss their usefulness for the construction and analysis of biological models. Then we propose a general approach to reveal structural sensitivity with regards to certain system properties, which considers infinite-dimensional neighbourhoods of the model functions: a far more powerful technique than the conventional approach of varying parameters for a fixed functional form. In particular, we suggest a rigorous method to unearth sensitivity with respect to the local stability of systems' equilibrium points. We present a method for specifying the neighbourhood of a general unknown function with [Formula: see text] inflection points in terms of a finite number of local function properties, and provide a rigorous proof of its completeness. Using this powerful result, we implement our method to explore sensitivity in several well-known multicomponent ecological models and demonstrate the existence of structural sensitivity in these models. Finally, we argue that structural sensitivity is an important intrinsic property of biological models, and a direct consequence of the complexity of the underlying real systems.