North-Holland, Amsterdam.Įlliott, C., Stuart, A., 1993. 4: Studies in Mathematics and its Applications. The Finite Element Method for Elliptic Problems. The Mathematical Theory of Finite Element Methods. On a uniformly accurate finite difference approximation of a singularly perturbed reaction–diffusion problem using grid equidistribution. Implicit–explicit methods for time-dependent partial differential equations. Mutual interference between predators can give rise to Turing spatial patterns. Users can download, edit, and run the codes from, to investigate the key dynamical properties of spatially extended predator–prey interactions.Īlonso, D., Bartumeus, F., Catalan, J., 2002. We also present the results of numerical experiments in one and two space dimensions and illustrate the simplicity of the numerical methods with short programs M ATLAB. For example, due to the structure of the resulting linear systems, standard direct, and iterative solvers are guaranteed to converge. Furthermore, there are implementational advantages of the methods. This is particularly important for the spatially extended systems that are studied in this paper as they display a wide spectrum of ecologically relevant behavior, including chaos. This is advantageous as it is well-known that the dynamics of approximations of differential equations (DEs) can differ significantly from that of the underlying DEs themselves. The algorithms are stable and convergent provided the time step is below a (non-restrictive) critical value. We suspect that microbe-microbe killing results in predation far more often than has previously been appreciated.We present two finite-difference algorithms for studying the dynamics of spatially extended predator–prey interactions with the Holling type II functional response and logistic growth of the prey. The authors add, "We find it fascinating that a relatively small change in just one ecological factor can determine who kills and eats whom in microbial predation. This study and follow-up research could aid understanding of both natural ecology and practical applications, such as optimizing the use of some microbes to control others. xanthus could determine which would be predator and which prey when the two species met later, highlighting the importance of considering historical context when evaluating present predator- prey relationships. They also note that in this study, the temperature at which P. The researchers say their findings suggest that many forms of microbe-microbe killing not traditionally associated with predation-the consumption of a killed organism by its killer-may in fact result in it. xanthus, the production of which appears to be influenced by temperature. They homed in on a non-protein substance released by P. The researchers conducted further experiments to better understand the mechanism by which growth at chillier temperatures may have reversed the predator-prey roles. fluorescens killing and obtaining nutrients from M. fluorescens was grown at 22 degrees Celsius, the predator-prey relationship switched, with P. xanthus acted as the predator and extensively killed P. fluorescens was grown in a dish at 32 degrees Celsius and then exposed to M. Building on that knowledge, Vasse and colleagues conducted several laboratory experiments to test how temperature might influence the predator-prey relationship between the bacterial species Myxococcus xanthus and Pseudomonas fluorescens.
Some bacteria prey on others, and ecological context can influence predation efficiency. However, there are few other known examples of such switching in response to non-biological ecological changes. In addition, predator-prey relationships can sometimes switch, as is the case for two crustacean species that mutually prey on each other, where a change in surrounding salinity reverses which species dominates. For instance, similarity or contrast between background color and coloration of a prey species can influence how easily it is detected by predators. Prior research has shown that ecological context can influence predator-prey relationships.