PhD student, Pontifical Catholic University of Chile
Understanding population persistence from ecology and mathematics in dynamic landscapes
In a changing world is urgent to develop robust frameworks to understand how populations of animals can persist over space and time. Current approaches have been focused on ecological interactions between species, and independently on the role of animal movement in an ever changing landscape (given that this has strong effects on search of food, mates, and shelter). Here we developed a computational model incorporating these two key paradigms: how species compete for space and how they move and use this habitat with dynamic resources. Our results show that the strategy of searching of an animal can influence its persistence over time, and also it can determine the coexistence with other movement strategies. These results highlight the need to develop a more integrative framework to understand animal population persistence, beyond the traditional approaches used so far.
Abstract: The two main approaches in theoretical population ecology-the classical approach using differential equations and the approach using individual-based modeling-seem to be incompatible. Linked to these two approaches are two different timescales: population dynamics and behavior or physiology. Thus, the question of the relationship between classical and individual-based approaches is related to the question of the mutual relationship between processes on the population and the behavioral timescales. We present a simple protocol that allows the two different approaches to be reconciled by making explicit use of the fact that processes operating on two different timescales can be treated separately. Using an individual-based model of nomadic birds as an example, we extract the population growth rate by deactivating all demographic processes-in other words, the individuals behave but do not age, die, or reproduce. The growth rate closely matches the logistic growth rate for a wide range of parameters. The implications of this result and the conditions for applying the protocol to other individual-based models are discussed. Since in physics the technique of separating timescales is linked to some concepts of self-organization, we believe that the protocol will also help to develop concepts of self-organization in ecology.
Pub.: 25 Sep '08, Pinned: 29 Jun '17
Abstract: Organisms interact with each other mostly over local scales, so the local density experienced by an individual is of greater importance than the mean density in a population. This simple observation poses a tremendous challenge to theoretical ecology, and because nonlinear stochastic and spatial models cannot be solved exactly, much effort has been spent in seeking effective approximations. Several authors have observed that spatial population systems behave like deterministic nonspatial systems if dispersal averages the dynamics over a sufficiently large scale. We exploit this fact to develop an exact series expansion, which allows one to derive approximations of stochastic individual-based models without resorting to heuristic assumptions. Our approach makes it possible to calculate the corrections to mean-field models in the limit where the interaction range is large, and it provides insight into the performance of moment closure methods. With this approach, we demonstrate how the buildup of spatiotemporal correlations slows down the spread of an invasion, prolongs time lags associated with extinction debt, and leads to locally oscillating but globally stable coexistence of a host and a parasite.
Pub.: 17 Aug '06, Pinned: 29 Jun '17
Abstract: The international conference 'Models in population dynamics and ecology 2010: animal movement, dispersal and spatial ecology' took place at the University of Leicester, UK, on 1-3 September 2010, focusing on mathematical approaches to spatial population dynamics and emphasizing cross-scale issues. Exciting new developments in scaling up from individual level movement to descriptions of this movement at the macroscopic level highlighted the importance of mechanistic approaches, with different descriptions at the microscopic level leading to different ecological outcomes. At higher levels of organization, different macroscopic descriptions of movement also led to different properties at the ecosystem and larger scales. New developments from Levy flight descriptions to the incorporation of new methods from physics and elsewhere are revitalizing research in spatial ecology, which will both increase understanding of fundamental ecological processes and lead to tools for better management.
Pub.: 12 Nov '10, Pinned: 29 Jun '17