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Potts J.R.,Center for Mathematical Biology | Lewis M.A.,Center for Mathematical Biology | Lewis M.A.,University of Alberta
Proceedings of the Royal Society B: Biological Sciences | Year: 2014

Territory formation is ubiquitous throughout the animal kingdom. At the individual level, various behaviours attempt to exclude conspecifics fromregions of space. At the population level, animals often segregate into distinct territorial areas. Consequently, it should be possible to derive territorial patterns from the underlying behavioural processes of animal movements and interactions. Such derivations are an important element in the development of an ecological theory that can predict the effects of changing conditions on territorial populations. Here, we review the approaches developed over the past 20 years or so, which go under the umbrella of 'mechanistic territorial models'. We detail the two main strands to this research: partial differential equations and individual-based approaches, showing what each has offered to our understanding of territoriality and how they can be unified. We explain how they are related to other approaches to studying territories and home ranges, and point towards possible future directions. © 2014 The Authors.

Krkosek M.,University of Otago | Connors B.M.,Salmon Coast Field Station | Connors B.M.,Simon Fraser University | Lewis M.A.,Center for Mathematical Biology | And 2 more authors.
American Naturalist | Year: 2012

Allee effects are thought to mediate the dynamics of population colonization, particularly for invasive species. However, Allee effects acting on parasites have rarely been considered in the analogous process of infectious disease establishment and spread. We studied the colonization of uninfected wild juvenile Pacific salmon populations by ectoparasitic salmon lice (Lepeophtheirus salmonis) over a 4-year period. In a data set of 68,376 fish, we observed 85 occurrences of precopular pair formation among 1,259 preadult female and 613 adult male lice. The probability of pair formation was dependent on the local abundance of lice, but this mate limitation is likely offset somewhat by mate-searching dispersal of males among host fish. A mathematical model of macroparasite population dynamics that incorporates the empirical results suggests a high likelihood of a demographic Allee effect, which can cause the colonizing parasite populations to die out. These results may provide the first empirical evidence for Allee effects in a macroparasite. Furthermore, the data give a rare detailed view of Allee effects in colonization dynamics and suggest that Allee effects may dampen the spread of parasites in a coastal marine ecosystem. © 2012 by The University of Chicago.

Schaerf T.M.,Center for Mathematical Biology | Schaerf T.M.,University of Sydney | Makinson J.C.,Center for Mathematical Biology | Myerscough M.R.,University of Sydney | Beekman M.,Center for Mathematical Biology
Journal of the Royal Society Interface | Year: 2013

Reproductive swarms of honeybees are faced with the problem of finding a good site to establish a new colony. We examined the potential effects of swarm size on the quality of nest-site choice through a combination of modelling and field experiments.We used an individual-based model to examine the effects of swarm size on decision accuracy under the assumption that the number of bees actively involved in the decision-making process (scouts) is an increasing function of swarm size. We found that the ability of a swarm to choose the best of two nest sites decreases as swarm size increases when there is some time-lag between discovering the sites, consistent with Janson and Beekman (Janson and Beekman 2007 Proceedings of European Conference on Complex Systems, pp. 204-211.). However, when simulated swarms were faced with a realistic problem of choosing between many nest sites discoverable at all times, larger swarms were more accurate in their decisions than smaller swarms owing to their ability to discover nest sites more rapidly. Our experimental fieldwork showed that large swarms invest a larger number of scouts into the decision-making process than smaller swarms. Preliminary analysis of waggle dances from experimental swarms also suggested that large swarms could indeed discover and advertise nest sites at a faster rate than small swarms. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

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