# Evolutionarily stable consumer home range size in relation to resource demography and consumer spatial organization

## Abstract

There is a large variation in home range size within species, yet few models relate that variation to demographic and life-history traits. We derive an approximate deterministic population dynamics model keeping track of spatial structure, via spatial moment equations, from an individual-based spatial consumer-resource model; where space-use of consumers resembles that of central place foragers. Using invasion analyses, we investigate how the evolutionarily stable home range size of the consumer depends on a number of ecological and behavioral traits of both the resource and the consumer. We show that any trait variation leading to a decreased overall resource production or an increased spatial segregation between consumer and resource acts to increase consumer home range size. In this way, we extend theoretical predictions on optimal territory size to a larger range of ecological scenarios where home ranges overlap and population dynamics feedbacks are possible. Consideration of spatial traits such as dispersal distances also generates new results: (1) consumer home range size decreases with increased resource dispersal distance, and (2) when consumer agonistic behavior is weak, more philopatric consumers have larger home ranges. Finally, our results emphasize the role of the spatial correlation between consumer and resource distributions in determining home range size, and suggest resource dispersion is less important.

## Keywords

Home range Territory Foraging Spatial segregation Resource dispersion Adaptive dynamics## Notes

### Acknowledgements

Part of this research was supported by the Natural Environment Research Council (UK) Blue Skies Fellowship NE/D009367/1 to DJM, and FB was supported by a Ph.D. grant from the French Ministry of Research/Univ. Paris 6, and BiodivAgriM research program. We thank Alexandre Villers, Vincent Bretagnolle, Stephen Cornell, and John Fryxell for comments and suggestions on earlier versions of the manuscript, as well as two referees for very constructive criticism.

## Supplementary material

## References

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