AICME II abstracts Individual-Based Spatial Simulations of Ecological Systems

Ideal Free Distribution theory when competitors disagree over resource distributions Keith Farnsworth1 and Stefano Focardi

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The classic model for competitive habitat selection is the ideal free distribution, which put most generally states that if fitness is a monotonically increasing function of resources and a monotonically decreasing function of competitor density, and if individuals locate to maximise their fitness, then in equilibrium, all equivalent individuals will obtain an equal fitness. The assumption that individuals are all equal has been relaxed, first in terms of competitive ability (Sutherland and Parker 1992) and second in terms of post-acquisitional efficiency (Ruxton et al. 2001). Competitors may also differ in relation to the fitness gain conferred by different resources available, leading to each type of individual seeing a different resource map over which to play the competitive location game. The work presented here uses an individual based model to explore this third possibility and in particular, its ability to explain the well known phenomenon of sexual segregation among ungulate species. Previous explanations of sexual segregation in ungulates establish no more than a prerequisite for habitat segregation because they do not include a model of competitive habitat selection. We show here that the difference between male and female ungulate habitat preferences is usually insufficient to explain the observed segregation. We go on to show that when individual-level competition is accounted for, given sex differences in resource-fitness functions, then levels of segregation match field observations. Competitors of type A or B choose from among N habitat patches each offering resources X and Y in different amounts (both absolute and rela-

Individual-Based Spatial Simulations of Ecological Systems AICME II abstracts

tive). Type A individuals value these resources as X¿Y and type B value them as Y=X (many alternative arrangements are possible and generalisation to M resource types is within the scope of this method). Three functions describe the system: Fitness = f(X,Y) and Fitness=g(A,B) encapsulate the different objectives and competitive abilities of individuals, and R=r(R,t) defines the resource renewal rate (where R=X or Y). This idea is applicable to a wide range of problems in both ecology and economics. Whilst relatively simple to calculate by individual-based simulation, the analysis of systems where fitness-resource functions differ among competitors is very challenging, so we are looking for ways to aid its progress using the simulation results.

References [1] Sutherland, W. J. Parker, G. A. (1992). The relationship between continuous input and interference models of ideal free distributions with unequal competitors. Animal Behaviour 44:345-355 [2] Ruxton, G. D., Humphries, S., Farnsworth, K. D. (2001). Noncompetitive phenotypic differences can have a strong effect on ideal free distributions. Journal of Animal Ecology. 70:25-32.

1 School of Biology and Biochemistry, Queens University Belfast, 97 Lisburn Road, Belfast BT97BL, Northern Ireland, U.K. (e-mail: [email protected] ). 2 Istituto Nazionale per la Fauna Selvatica, via Ca Fornacetta 9, 40064 Ozzano dellEmilia, Italia (e-mail: [email protected] ).

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