Territory Size and Shape in Fire Ants: A Model Based on Neighborhood Interactions

Many aggressive animals form territory mosaics marked by distinct boundaries. This paper describes an approach to modeling territory size and shape within mosaics based on boundary disputes among neighboring animals. The model assumes that each resident applies pressure against its neighbors, as a result of aggression and display, and that boundaries form curves along which the pressure exerted by adjacent residents is equal. To illustrate, I predicted territory boundaries for populations of the fire ant Solenopsis invicta using several alternative mathematical descriptions of territorial fighting. According to the most successful formula, the aggressive pressure applied at any point on the territory perimeter increases linearly with the biomass of the defending colony but decreases with territory area and with the square of the distance to the colony’s nest. An iterative algorithm predicts the size and location of boundary segments given the positions and sizes of colonies. By all measured criteria, this model produced more accurate predictions of territory areas and shapes than alternative models that omit the effects of resident size or the dependence of aggressive pressure on territory area. Modifications can incorporate nest relocations, strategic variation in the degree of aggressive pressure applied, habitat heterogeneity, and other biological details. However, even with simple assumptions, the model predicts much of the variation in the sizes and shapes of fire ant territories in natural conditions. This implies that territories are molded by a balance of aggression between neighbors and that each territory is affected by the actions of numerous residents.