Interactions Between Density-Dependence and Dispersal

We take a well-known dynamic model of an isolated, unstructured population and modify this to include a factor that allows for a reduction in fitness due to declining population sizes, often termed an Allee effect. Analysis of the behaviour of this model is carried out on two fronts - determining the equilibrium values and examining the stability of these equilibria. Our results point to the stabilising effect on population dynamics of the Allee effect and an unexpected increase in stability with increased competition due to the interaction between competitive and Allee effects. Density-dependence is an important regulating factor in population dynamics that is commonly considered to reduce individual fitness at high densities. Recently, interest in mechanisms that reduce fitness at low population densities, a phenomenon known as the Allee effect, has grown. Here we study the effect of a wide range of population densities on different measures of fitness in the pea aphid, Acyrthosiphon pisum. By subjecting aphids to predation pressure, we find that fitness at very low population densities can be reduced. Comparisons of the data to different non-linear models of density-dependence suggest that aphids may in fact be subject to an Allee effect. We discuss some of the implications of this and possible mechanisms driving it. Lately, there has been a realisation that the assumption of density-independent dispersal is biologically unreasonable, due to the inherent complexity associated with dispersal, and therefore more effort is being invested in creating models that incorporate a more realistic, density-dependant type of dispersal. Another aspect of migration that there is still considerable scope for exploration is in models that consider the cost of dispersal. This will affect an individual's propensity to disperse from the natal patch in the first place, as well as affecting overall fecundity of a parent. Here, I have included a cost of dispersal in a model with density-dependent dispersal, based on both an upper critical density dispersal rule (to escape competitive pressures), and a lower critical density rule (to escape fitness loss from an Allee effect). I ask whether varying the nature of this cost will have any effect on the dynamics of the system, or have potential implications for the evolution of dispersal. Populations displaying cyclic fluctuations in their size over time have been of great interest to ecologists for the past three-quarters of a century. Here we present and examine a spatially structured model that simulates the population dynamics of Canada lynx (Lynx canadensis) and displays a time varying behaviour we term phase-shifting, where cycles in different population sub-units move in and out of phase with each other over time. We confirm that the phenomenon is more than different patches simply fluctuating at slightly different cycle period lengths; rather it is a new dynamical behaviour. We go on to demonstrate that this phenomenon can be found under a wide range of conditions, including some that were previously deemed unsuitable. The fundamental structure of the model is then altered in different ways, and we show that phase-shifting can still arise. Given the prevalence of this behaviour under a wide range of model conditions, it is perhaps surprising that little attention has been paid to it previously. The consequences of this type of dynamical behaviour are discussed, as well as discussing reasons why it may have been missed in previous time series analyses. Disagreement exists between the results of theoretical and empirical exploration into the effect of increasing community complexity on the stability of multi-species ecosystems. A recent return to interest in this area suggests previous results should be re-assessed, from both experimental studies and models, to understand where this discrepancy arises from. Here we propose various simple extensions to a standard multi-species community model that each increase the complexity of the system in a different way. We find that increasing the number of species in a community leads to a decrease in community persistence after the system is perturbed, and go on to show that increasing the dynamical diversity of the community members leads to an increase in stability through a reduction in extinction events, relative to the less complex form of the model. Our results suggest that different forms of complexity lead to different outcomes in the stability properties of the community. While aspects of this work agree with previous empirical findings that more complex communities are more robust to perturbation, we stress that the type of complexity included and the measure of stability used in community models must be properly defined, to allow objective comparisons to be made with previous and future work