Territory size and shape in fire ants: a model based on neighborhood interactions

Ecology, June, 1998 by Eldridge S. Adams

INTRODUCTION

Animals that defend foraging territories often show considerable intraspecific variation in territory area. Ecologists have long been interested in explaining this variation and in predicting how the sizes or shapes of territories differ among individuals (Covich 1976, Carpenter 1987). Within a population, variation in territory area contributes to the unequal division of limiting resources, which may in turn affect the dynamics or stability of animal numbers (e.g., Lomnicki 1988). Furthermore, the processes determining territory area may shed light on decision making by competing animals.

In many territorial species, territories are molded by boundary disputes among neighboring residents. Mosaics of contiguous territories have been observed in diverse animals (e.g., birds: Watson and Miller 1971, Woolfenden and Fitzpatrick 1984; fish: Kodric-Brown 1978, McNichol and Noakes 1981; mammals: Koford 1957, Kitchen 1974; insects: Mabelis 1979, Adams and Levings 1987). Numerous experiments have shown that neighbors restrict one another's territory areas by fighting and display (e.g., Watson 1967, Krebs 1971, Welsh 1975, Nursall 1977, Norman and Jones 1984, Adams 1990, Gordon 1992). One approach to modeling territory size is to predict the positions of boundaries formed by these neighborhood interactions.

Although many models of territory size have been proposed, there has been little effort to predict the geometric consequences of boundary conflicts. Various optimality models consider how the costs and benefits of territory defense change with the area or perimeter of the defended space (reviewed by Holldobler and Lumsden 1980, Schoener 1983, Davies and Houston 1984, Carpenter 1987). While these models successfully predict some aspects of territorial behavior, their application to territory mosaics is limited because most consider decision making by only a single resident (but see Tullock 1983, Maynard Smith 1982, Jones and Krummel 1985). When territories are contiguous, the size of any particular territory depends not only on the decisions of the resident, but also on actions of each of its neighbors, which may in turn be affected by the behavior of more remote residents. Therefore, to predict territory boundaries, it may be necessary to consider the simultaneous actions of groups of interacting residents.

An alternative to the standard optimality models is to apply geometric procedures that divide the habitat into cells. For example, territories have been approximated by Dirichlet tessellation, in which straight line segments are placed midway between neighbors (Hasegawa and Tanemura 1976, Tanemura and Hasegawa 1980, McCleery and Perrins 1985). The resulting cells, known as Thiessen or Voronoi polygons, among other names (Weaire and Rivier 1984), have also been used in plant ecology to provide indices of neighborhood competition (Czaran and Bartha 1992). Similar results are obtained by drawing circular territories and dividing equally the areas of overlap (Grant 1968, Maynard Smith 1974, Covich 1976, Stamps and Krishnan 1990). While this approach yields quantitative predictions of territory size and shape, the methods applied to date have been incomplete, usually assuming that the positions of boundary segments depend only on the distances to the two closest residents. Territory partitioning in ant populations has been represented by nonoverlapping circles or rectangles (Korzukhin and Porter 1994, Stoker et al. 1994); however, these models assume a strict size hierarchy such that any particular colony is unaffected by the presence of smaller colonies, regardless of the degree of size difference.

Territory boundary positions may also be predicted from the behavioral mechanisms underlying the movement and interaction of residents. The spatial consequences of such mechanisms have been modelled for wolf packs by the use of partial differential equations (Lewis and Murray 1993, White et al. 1996). These models predict the distribution of wolf density for isolated or interacting packs based on movement of the wolves relative to the den, and on the distribution of and reaction to scent marks. This approach is similar in intent to the one developed in this paper in that both consider the relationship between individual behaviors and the partitioning of space. However, the computer algorithm described below is easier to modify or extend, particularly when the behavior of a resident towards one of its neighbors depends upon the outcome of its interactions with other neighbors.

This paper describes a model that predicts the equilibrial positions of boundaries molded by interactions among a set of competing animals. I illustrate this approach by its application to the fire ant Solenopsis invicta Buren, in which colonies defend exclusive foraging territories (Wilson et al. 1971, Tschinkel et al. 1995). I then briefly discuss ways to extend and test the model for other organisms and ecological circumstances.

A TERRITORY MODEL based ON NEIGHBORHOOD INTERACTIONS