Optimal Territory Size Research Articles

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

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.

The effect of food abundance on territory size and population density of juvenile steelhead trout (Oncorhynchus mykiss).

Optimal territory size models predict a decrease in territory size with increasing food abundance. However, most of these models may not be applicable to juvenile salmonids in streams, because they defend contiguous territories at high densities. The optimal size of a contiguous territory is predicted to (1) be independent of food abundance when food is rare and (2) decrease only when food abundance is high enough to induce a reduction in territory size below the contiguous optimum. To test these predictions, we raised equal densities of juvenile steelhead trout in outdoor stream channels over a 32-fold range of food abundance in the absence of emigration for 25 days. Increasing competition for scarce food resulted in increasing mortality, higher willingness to emigrate, higher variance in body mass, lower growth, lower population density and lower biomass. The size of territories decreased with increasing local population density, and increased with increasing body size. However, territory size did not change with food abundance, a result consistent with the prediction of a contiguous territory size model. On average, total salmonid biomass increased 5.7 times in response to the 32-fold increase in food abundance. Our data provide strong support for an earlier quantitative relationship between the abundance of stream salmonids and their food.

Density dependence, territoriality, and divisibility of resources: from optimality models to population processes.

Species differ enormously in their territorial systems. Some species defend only small areas surrounded by undefended space, while others defend large contiguous territories. Using an optimization approach, we show that this variation can be explained from the density of two types of resources: divisible and nondivisible. We assume that benefits of territories are monotonously related to the defended amount of divisible resources (hereafter called food). In contrast, no benefits are obtained without a nondivisible resource (hereafter called nest site) in the territory, while more than one nest site does not further increase the benefits. The optimal territory size depends on the relative abundance of these resources. With a low density of nest sites, the optimal territory size is small and includes only the nest site. If the density of nest sites is relatively large, the optimal territory size is high, and territories are contiguous. Competition for these different resources yields contrasting patterns of how populations are regulated. If there is mainly competition for nest sites, we expect density-dependent exclusion through territoriality and no density-dependent reproduction. When competition is mainly for food, we expect density-dependent reproduction because optimal territory size will be compressed at higher densities, resulting in lower reproductive success. These predicted patterns indeed are observed in some well-studied passerine species for which both the territorial system and the occurrence of density dependence is known.

Manipulating territory size via vegetation structure: optimal size of area guarded by the convict cichlid (Pisces, Cichlidae)

To test the predictions of optimal territory size models, we attempted to manipulate the size of area that a dominant convict cichlid fish (Archocentrus nigrofasciatus) would defend around a food patch by placing simulated vegetation at three different distances from the edge of the patch (0, 11, and 22 cm). As expected, the size of area defended against four smaller intruders increased as the vegetation was moved farther from the patch. Consistent with optimal territory size models, both the costs of defence, measured as chase radius and chase rate, and the benefits of defence, measured as the amount of food eaten by the defender, increased with the distance of the vegetation from the patch. Growth rates of the defenders, however, did not differ among the treatments, perhaps because the benefits of monopolizing food were balanced by the costs of defending a larger area. Our data support the hypothesis that the size of a guarded area around an ephemeral resource patch affects both the costs and benefits of defence.

Approaches to the Study of Territory Size and Shape

▪ Abstract Intraspecific variation in territory size and shape can have strong effects on population structure and dynamics. The traditional theoretical approach to the study of territory size is based on optimality models that analyze decisions of focal residents as responses to the costs and benefits of defense. These models have stimulated numerous empirical studies showing that territory holders adjust their behavior according to rates of intrusion and availability of food. However, models of optimal territory size are applicable only in limited circumstances because they focus on unilateral decisions rather than on interactions. Furthermore, observational and experimental studies often find that territory sizes are insensitive to food supply. Recently, greater emphasis has been placed on two alternative approaches. The first concerns interactions among contiguous neighbors and how these affect use of space. In these models territory size and shape are determined by the balance of pressure exerted at boundaries or arise as the results of local rules of movement and interaction. The second alternative approach views territory size as the outcome of interactions between established residents and potential settlers attempting to acquire territories. By considering the simultaneous actions of multiple competitors, these models allow quantitative prediction of the effects of territory defense on population density and spatial patterns as well as responses to environmental change.

OPTIMAL TERRITORY SIZE IN THE CONVICT CICHLID

Abstract Models of optimal territory size are usually tested only by demonstrating that territory size is inversely related to food abundance or intruder number. The most fundamental predictions of the models, however, have rarely been tested: i.e. the fitness of the defender is a function of territory size and the optimal territory is one of intermediate size. We tested these predictions by measuring the growth rate of large convict cichlids (Archocentrus nigrofasciatus, formerly Cichlasoma nigrofasciatum) while defending food patches against smaller intruders over a 10-day period. Food patches differed in area by more than two orders of magnitude. We manipulated food abundance so that it increased with patch size in a decelerating way. As assumed, the realized benefits of defence (weight of food eaten by the defender) and the costs of defence (chase rate and chase radius) both increased in a decelerating way with increasing patch area. As predicted, the growth rate of the defender first increased and then decreased with increasing patch size. The initial increase in defender growth rate with increasing patch size was related to an increase in food eaten, but the decrease in growth rate for fish defending the largest patches was related to the costs of defence. Fish defending large patches had a low growth efficiency, apparently because of the social stress caused by intruders in their territories. Taken together, these results support the assumptions and predictions of optimal territory size models.

Territoriality and time budgets in beavers during sequential settlement

Beavers (Castor fiber) were sequentially released into a previously unoccupied area. The settlement of the animals approximated an ideal despotic distribution: they successively settled in rich habitat and then in poor habitat, and then became floaters. This pattern is regarded as evidence that territorial behavior limited density. The early arrivals showed a seasonal difference in territory size (small in winter, large in late spring and summer), which was expected from optimal territory size theory but which was not found in later arrivals. In the first 2 years, the beavers were swimming very large distances (up to 20.0 km per night), and were apparently undergoing a long-term decline in body condition. Body temperature decreased during swimming, especially in winter (daily amplitude 2.04 °C). Each year, winter territories were about the size (7.9 ± 0.9 (SE) km, including 3.0 ± 0.4 km of wooded banks) that beavers could patrol daily without losing body condition. The number of territories established at any one time during the 5 years of study was only half the carrying capacity calculated on the basis of the current length of wooded banks within territories, in accordance with the prediction for sequential settlement in linear habitats. However, extensive no-man's-land was not present between territories, but early arrivals claimed larger territories than later ones. Social and thermoregulatory factors seem to play an important role in determining the costs of territory defense, and hence territory size. Overexploitation of the beaver's main food source, willow (Salix spp.), seems unlikely in this productive habitat.

Time Budgets and Territory Size: Some Simultaneous Optimization Models for Energy Maximizers

A set of optimization models in two variables of choice, territory size and time spent patrolling for intruders, is presented for energy maximizers. Models vary in the curvilinearity of the relationship between territory circumference and both intrusion rate and cost of expelling a single intruder. Models are analyzed both with and without constraints; constraints are on processing rate and on the time spent patrolling, feeding and actively defending. The models all include the concept of “intruder equilibrium,” an equilibrial density of intruders in a territory resulting from a balance between intrusion rate and expulsion by the defender. This equilibrial density can be considered a measure of territorial exclusiveness. The two-variable models predict effects on territory size and patrol time of variation in food density, intrusion rate, costs of expelling a single intruder in energy and time, food-consumption rate of an intruder, area of detection while patrolling, total time available for territorial and feeding activities, time to eat a unit of food energy, energy cost of patrol per time, and processing-rate capacity. With increasing intruder rate, optimal territory size usually decreases, whereas optimal patrol time behaves much more irregularly. With increasing food density, optimal patrol time usually decreases, whereas optimal territory size behaves irregularly. In particular, when intrusion rate and expulsion costs accelerate sufficiently with increasing territory size and no constraints exist, the higher the food density the smaller the optimal territory size. When food density is large enough for a constraint to be effective, the opposite relation can hold and will always hold for a processing constraint. When a particular parameter changes, optimal territory size and optimal patrol time may covary or one may increase while the other decreases, depending on the parameter and model. A new set of one-variable models is suggested by the two-variable models; models optimizing patrol time while holding territory size constant could correspond to a tightly packed system of territories initially determined by settlement patterns. A unified onevariable analysis suggests that how food density affects territory size when patrol time is constant depends upon whether a constraint is operating: Provided that invasion rate does not vary with density of intruders on the territory, time minimizers and constrained energy maximizers decrease territory size with increasing food density; unconstrained energy maximizers do the opposite. The addition of a second optimization variable to a one-variable model can change qualitative predictions about variation in particular parameters ( e.g. , food density) and can increase the number of parameters predicted to affect optimal territory size and patrol time.

Feeding Territoriality in Aquatic Insects: Cost-Benefit Models and Experimental Tests

Two points are evident from a review of the literature describing feeding territoriality in aquatic insects. First, feeding territoriality is much more common in this group than was previously recognized. Second, most of the examples involve species that have small foraging areas and harvest rapidly renewing resources, such as filterable particles and attached microalgae. To interpret these patterns, I discuss how the net benefits of territorial defense vary as a function of several components of food availability. I present the results of recent laboratory and field experiments testing cost-benefit models that predict patterns of territory size and defense frequency. Feeding-territory size in grazing caddisfly larvae increases with the resident's body size and is inversely related to food abundance, which agrees with the predictions of several models of optimal territory size. Two kinds of stream insects that rely on food items delivered by water currents ( i.e. , surface-feeding water striders and filter-feeding larval black flies) respond to increases in food abundance by reducing their allocation of time to territorial defense.In black flies, complex interactions between competitor density and food abundance also influence the amount of time spent defending a territory. I consider several connections between territorial behavior and interspecific competition. The distribution and abundance of both territorial species and their competitors may depend in part upon how the costs and benefits of feeding territoriality vary along resource abundance gradients. The tendency of some territorial grazers to settle preferentially near conspecifics may occur because animals living in groups exclude interspecific competitors more efficiently than isolated individuals, which suggests some simple tests of optimal group size models. I conclude by summarizing the strengths and weaknesses of these study systems, both as a source of new and broader theories of feeding territoriality, and as a testing ground for those theories. An important strength of these consumer-resource systems is the ability to conduct realistic experimental studies examining the causes and consequences of territoriality. One important weakness is the lack of information on the time-energy budgets of these insects. The acquisition of such information deserves a high priority, since it will permit more rigorous tests of cost-benefit models that evaluate the adaptive significance of territorial behavior.

Social Spacing in Small Mammals: Patterns of Individual Variation

The pattern of social spacing in small mammals differs from that observed in many other vertebrates. Small mammals frequently have non-exclusive territories and tolerate a large amount of overlap with other conspecifics. The determinant factors of home range or territory size in small mammals are not known for most species. We carried out a study of the determinant factors of home range size in a model small mammal, the eastern chipmunk, Tamias striatus. The population was studied for five years. The effect of experimental perturbations on food supply and population density offered strong evidence that the mean home range size in the population was determined by resource abundance. Changes in population density had little or no measurable effect. We noted that even when mean home range size decreased significantly in response to an increase in available food, a great deal of variability in individual home range sizes remained. We hypothesized that this pattern of variation among individuals was also resource related; large home ranges would be located in areas of low resource density and small home ranges would be located in areas of high resource density. Our data to date do not offer support for this hypothesis; however our research has shown that the data needed to convincingly reject the null hypothesis are very complex. We discuss the evidence required to study patterns of individual variation, and how models of optimal territory size may be useful. Research that examines patterns of individual variation are few in number, yet studies of individual variation will ultimately provide the best insights on the dynamics of evolutionary ecology.

A simple model of optimal territory size for drift-feeding fish

A simple model of optimal feeding-territory size is developed for drift-feeding fish by modifying Hixon's (M. A. Hixon. 1980. Am. Nat. 115: 510–530) model for energy maximizers. Our model predicts that territory size should vary directly with food density when the fish is subject to time constraints, and directly with intruder pressure when the fish is subject to processing constraints. These unique predictions arise because any food not immediately eaten is carried downstream out of the territory. Our model also predicts that territory size should vary inversely with intruder pressure when the fish is subject to time constraints, and inversely with food density when the fish is subject to processing constraints. The qualitative predictions of the model are not affected by changes in the shape of the cost or benefit curves, unlike other simple models. A review of studies of salmonid territory size indicates that most are inadequate tests of the model because (i) food was not presented in a natural manner, (ii) ration levels were not controlled at levels that were clearly above or below a maximum daily ration, and (iii) the confounding effects of intruder pressure were not controlled. Future experiments will have to incorporate these factors to distinguish between the competing predictions posed by this and previous models.

Simple Models of Optimal Feeding-Territory Size: A Reconciliation

How optimal territory size changes with changes in food density and intruder pressure is in theory complex. Qualitative predictions (table 1) may change depending upon the goal of the territory holder (time minimization, energy maximization), the possible constraints on energy maximization (time availability, processing capability), and if and how food density and intruder pressure covary. Predictions for the amounts of time spent feeding and defending (tables 2, 3) are similarly variable. Often, the qualitative effect of environmental changes will be indeterminate without detailed specification of the functions describing territorial costs and benefits.

Food Density and Territory Size: An Alternative Model and a Test on the Reef Fish Eupomacentrus leucostictus

Food maximizers are animals that can use all the food they can obtain, thereby increasing fitness. Such animals, when territorial, should not necessarily be expected to contract their territories when or where food is more abundant. The optimal territory is not simply the smallest territory that fulfills the immediate metabolic needs of the territory holder. Instead, the optimal territory size is that at which the per-area benefit of increased food most greatly exceeds the per-area (or per-perimeter) costs of travel time, territorial defense, and increased exposure to predators. A mathematical exploration of this principle indicates that when or where food is more abundant, insectivorous birds should contract their territories, female lizards and harvester ants may contract or expand their territories, and female fish should expand their territories. In contrast to female fish, the biology of male fish indicates that they are not food maximizers and therefore should not expand their territories when or where food is more abundant. Territories of 22 individuals of the West Indian reef fish Eupomacentrus leucostictus were mapped before and after artificial augmentation of food abundance. The two sexes responded differently to the food augmentation. As predicted, all of the seven females tested expanded their territories; only one of 15 males expanded its territory. Empirical data from other food-maximizer animals are also consistent with the food-maximizer model.

An energy-based model of optimal feeding-territory size

An energy-based model of feeding territoriality is described. The model predicts an optimal territory size where the territory holder's net energy intake is maximized, on a daily or seasonal time scale. Simulated effects on optimal territory size of animal size, food availability, and competitor density are in general agreement with observed relationships in a wide variety of animals. When salmonid data are used to estimate the model parameter values, predicted territory sizes are similar to those actually observed. When emigration is allowed, the model predicts that territoriality, through individual selection alone, can regulate population size, but that this regulation breaks down when initial densities exceed some threshold value. Sensitivity analysis shows optimal territory size to be most affected by those parameters influencing food intake and energy expenditure. Some alternative criteria for optimization are also discussed. An animal maximizing net foraging efficiency has a smaller territory than one maximizing net energy, but the effects of animal size, food availability, and competitor density on territory size are the same in either case.