Predation effects on mean time to extinction under demographic stochasticity

Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with each other, forming more or less complex networks of interactions. Models to assess extinction risk often lack explicit incorporation of these interspecific interactions. We study a birth and death process in which the death rate includes an effect from predation. This predation rate is included via a general nonlinear expression for the functional response of predation to prey density. We investigate the effects of the foraging parameters (e.g. attack rate and handling time) on the mean time to extinction. Mean time to extinction varies by orders of magnitude when we alter the foraging parameters, even when we exclude the effects of these parameters on the equilibrium population size. In particular we observe an exponential dependence of the mean time to extinction on handling time. These findings clearly show that accounting for the nature of interspecific interactions is likely to be critically important when estimating extinction risk.Comment: 11 pages, 4 figures; Typos removed. For further discussion about the paper go to http://purl.org/net/extinctio

The conflict interaction between two complex systems. Cyclic migration

We construct and study a discrete time model describing the conflict interaction between two complex systems with non-trivial internal structures. The external conflict interaction is based on the model of alternative interaction between a pair of non-annihilating opponents. The internal conflict dynamics is similar to the one of a predator-prey model. We show that the typical trajectory of the complex system converges to an asymptotic attractive cycle. We propose an interpretation of our model in terms of migration processes

Community-driven dispersal in an individual-based predator-prey model

We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefined tolerance threshold. The spatiotemporal dynamics of the model is described in terms of this threshold. We compare this dynamics with the one obtained through density-independent dispersal and find marked differences. In the community-driven scenario, the spatial correlations in the population density do not vary in a linear fashion as we increase the tolerance threshold. Instead we find the system to cross different dynamical regimes as the threshold is raised. Spatial patterns evolve from disordered, to scale-free complex patterns, to finally becoming well-organized domains. This model therefore predicts that natural populations, the dispersal strategies of which are likely to be influenced by their local environment, might be subject to complex spatiotemporal dynamics.Comment: 43 pages, 7 figures, vocabulary modifications, discussion expanded, references added, Ecological Complexity accepte

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research