4
Predator-Prey Interactions

The goal of predator control efforts in Alaska is primarily to increase prey populations for human harvest. Each control effort can be viewed as an experiment whose outcome can be predicted based on ecological theory of predator-prey interactions. It might seem obvious that if predator numbers are reduced, prey numbers would increase and that everything is self-evident without any additional theory. But predator-prey interactions are too complex to assume that fewer wolves automatically means increased prey in a way that wildlife managers feel is beneficial. In particular, if prey are limited by habitat, then predator control may do little good. Also, the cost and political feasibility of predator control depend on how extensively it must enforced in order to achieve enhanced prey numbers. A policy of predator control would be especially attractive if it allowed for some new equilibrium at which prey and predator populations are both enhanced, because both are valued. Therefore, this chapter begins with an overview of predator-prey theory, which provides the context for the committee's analyses of the results of past wolf and bear control efforts. The chapter concludes with an assessment of the current status of knowledge that can and should be used to determine whether a wolf and/or bear control effort might work in ways that reduce cost and increase political approval.

THEORY OF PREDATOR-PREY INTERACTIONS

Predator-prey theory is one of the oldest and richest branches of theoretical ecology. Its models predict a wide array of results, depending on characteristics of predators, prey, and the environment in which they interact. This section



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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management 4 Predator-Prey Interactions The goal of predator control efforts in Alaska is primarily to increase prey populations for human harvest. Each control effort can be viewed as an experiment whose outcome can be predicted based on ecological theory of predator-prey interactions. It might seem obvious that if predator numbers are reduced, prey numbers would increase and that everything is self-evident without any additional theory. But predator-prey interactions are too complex to assume that fewer wolves automatically means increased prey in a way that wildlife managers feel is beneficial. In particular, if prey are limited by habitat, then predator control may do little good. Also, the cost and political feasibility of predator control depend on how extensively it must enforced in order to achieve enhanced prey numbers. A policy of predator control would be especially attractive if it allowed for some new equilibrium at which prey and predator populations are both enhanced, because both are valued. Therefore, this chapter begins with an overview of predator-prey theory, which provides the context for the committee's analyses of the results of past wolf and bear control efforts. The chapter concludes with an assessment of the current status of knowledge that can and should be used to determine whether a wolf and/or bear control effort might work in ways that reduce cost and increase political approval. THEORY OF PREDATOR-PREY INTERACTIONS Predator-prey theory is one of the oldest and richest branches of theoretical ecology. Its models predict a wide array of results, depending on characteristics of predators, prey, and the environment in which they interact. This section

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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management reviews aspects of the theory that are most pertinent to questions about predator control, particularly in Alaska, and discusses their implications for predator management and control in Alaska. Major theoretical results are presented in italics and are followed by a brief discussion of their implications for management. Oscillations and Stable Levels Predator and prey populations can either oscillate wildly or persist at relatively stable levels (May 1981). Theoretical models show that persistence of predators and prey at relatively stable levels (or equilibria) is likely only when prey populations are resource-limited and the prey have a refuge where they are safe from predation. Although the issue of population stability might seem like a topic of theoretical more than immediate practical concern, whether or not a predator-prey system is naturally prone to large fluctuations matters a great deal. In particular, if Alaskan caribou or moose populations naturally fluctuate wildly, the desires of hunters for stable prey populations and reliable harvests year after year might be contrary to natural population dynamics and an inordinate amount of human intervention might be required to achieve stable harvest levels. Removal of Predators from A Plant-Herbivore-Predator Interaction System The removal of predators from a plant-herbivore-predator interaction system can either stabilize or destabilize herbivore population dynamics (May 1991). Predator control is in effect a predator-removal experiment. In addition to the direct results of such a manipulation (fewer wolves or bears), dramatic alterations in the character of prey population dynamics can be triggered. Models indicate that predator removal can destabilize or stabilize herbivore population dynamics or have no effect whatever. The result depends subtly on the rate at which the environmental carrying capacity for the herbivores changes relative to the rate at which predator populations change (Crawley 1983). If vegetation changes rapidly and predators exert their effects during substantial vegetation changes, the presence of predators typically stabilizes prey populations. In other words, long-lived (relative to the speed at which plant resources available to herbivores change) and starvation-tolerant or generalist predators can stabilize numbers of their prey. If wolves in Alaska act in this manner, even though the removal of wolves might yield more prey over the short run, substantial reductions in wolves could increase rather than decrease fluctuations in moose and caribou numbers over a long time span.

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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management Alternative Stable States Two alternative stable states can exist in predator-prey systems: a lower equilibrium corresponding to very low prey and predator populations, and a higher equilibrium corresponding to high predator and prey populations (with the prey close to their carrying capacity). This idea received much attention in the 1970s from mathematical biologists, many of whom were inspired by so-called catastrophe theory (Walters and others 1975; Ludwig and others 1978). According to this theory, each equilibrium state ''attracts" neighboring population trajectories, so that a shift from one equilibrium to the other can be abrupt, and can occur simply if densities of predators or prey are temporarily altered, without the need for sustained management. The "predator pit" alluded to by wildlife biologists is a verbal version of these models in which it is assumed there is a low density equilibrium for these systems separated from a high density, relatively stable equilibrium. Prey populations are in the "predator pit" when their yearly losses to predation are greater than their yearly population gains (Seip 1995). Prey populations in the predator pit will decline to the lower equilibrium. The key requirement for 2 different equilibria is a functional response on the part of the predators such that the per capita risk of being taken by a predator actually increases with increasing prey density in the neighborhood of the lower equilibrium but decreases in the neighborhood of the higher equilibrium. The existence of two alternative, relatively stable states would provide a strong argument for predator control because the elimination or reduction of predators for a brief time period could kick the system into the higher equilibrium—that is, an equilibrium with more predators and more prey. In this context, equilibrium does not mean constant predator and prey densities, but that densities tend to return to the vicinity of the equilibrium if they are caused to deviate substantially from it. Using Regression Analysis to Estimate Growth Rates If a simple regression analysis is used to ask what controls prey populations in a predator-prey system, the factor that explains the greatest proportion of the variance in prey population growth rates depends largely on where "noise" enters the system, and not on what actually controls the dynamics (Boyce and Anderson 1997). Simulations of predator-prey dynamics with environmental variation entered in different places (for example, in herbivore carrying capacity or in the feeding rate of wolves) have shown that regression analyses of annual increments in wolf and ungulate populations can be very misleading. The pattern of random environmental variation might dictate the outcome of the regressions much more than do the actual linkages between predators and prey. That result is disturbing if one is going to rely on simple regressions and correlations to test hypotheses about

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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management "what controls caribou or moose populations." In particular, the fact that calf:cow ratios or that moose and caribou numbers are negatively correlated with numbers of wolves, does not mean that wolves are the primary determinant of and regulating force in moose and caribou populations. In other words, "correlation does not prove causation." Unfortunately, the limitations of correlative evidence are often forgotten during discussions of population dynamics. Those limitations are especially severe when one examines highly complex interactions involving vegetation, herbivores, and carnivores. This does not mean that regression models are uninformative—rather, it means that the best way of fitting data is to fit data that describe dynamics through time, not data that are slices of static patterns (see appendix C for a specific example developed by the committee). INTEGRATING THEORY AND DATA Models of predator-prey interactions make it clear that possible outcomes of predator control experiments are highly varied and are likely to depend on the particular conditions under which control was carried out. Therefore, long-term management could be improved if a more solid understanding of wolf-caribou or wolf-moose interactions were available. For instance, a definitive demonstration of the existence or absence of alternative stable states would be a key piece of information. More generally, the type of vegetation and how it changes through time determine the impact of predators on herbivorous prey. Calculating simple correlations between hypothetical driving variables constitutes a weak form of analysis. In a dynamic system such as this, more is gained by fitting population dynamic models to the data as opposed to simply seeing what is correlated with what (see appendix C). The practical implications of predator-prey theory are that: Correlative studies have limited abilities to determine causal relationships. The interactions between prey and their plant resources need to be understood. The task of identifying which "model" describes a particular situation is technically challenging. Because of the above challenges, analysis of predator control in Alaska is a major scientific task. Moreover, it is a task that can gain only limited guidance from scientific studies elsewhere, inasmuch as these same technical challenges have thwarted resource management throughout the world. In short, a real understanding of predator management and its consequences in Alaska will require state-of-the-art science carried out in Alaska. In the end, however, perfect understanding is unattainable and we must learn to live with and base our actions on incomplete knowledge and imperfect predictive abilities.

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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management From a management perspective, three important questions are (1) can predators maintain ungulate populations at densities well below carrying capacity, (2) if so, how long can predators keep ungulate population densities low, (3) if prey populations increase to the environmental carrying capacity, how long will they remain there after predator control ceases? To determine whether predators can depress ungulate populations, factors affecting recruitment (birth and immigration) and loss (death and emigration) must be evaluated. Each of these, in turn, depends on environmental factors such as characteristics and distribution of forage plants, weather, parasitism, disease, the availability of mates, and predation by wolves, bears, and humans. Those factors can interact with the density of the population in such a way that birth rates might decrease but predation rates may increase as population density increases. The number of prey killed by predators depends on the number of predators and the number of prey killed by each predator; both of these factors are related to the abundance of prey. The change in the density of predators in relation to prey density is called the numerical response. The change in the number of prey killed by an individual predator in relation to prey density is called the functional response. Although functional and numerical responses of predators are often linear over restricted ranges of prey density, they are strongly nonlinear when one considers a wide range of prey densities. Refugia from predators or other anti-predator behavior often reduce both the numerical and functional response of predators at very low prey densities. Both responses, however, usually increase rapidly with moderate but increasing prey densities, but the functional response levels off at higher prey densities due to satiation while the numerical response might level off at high prey densities due to the social structure of the predators. The product of the numerical and functional response equals the predation rate, and it generally increases with increasing prey density. When this happens, prey populations are likely to grow rapidly at very low population densities but their growth rates should slow down at higher population densities. However, under some conditions, the responses of predators are greatest at moderate prey densities and decline thereafter. If such a pattern exists, predators can prevent prey populations from increasing when they are at low densities, but if prey are able to increase to higher densities, their densities can increase beyond the point where predators exert effective control. The result is a system with relatively stable low and high prey densities, separated by intermediate densities at which the predation rate is too low to prevent the prey from increasing to a higher equilibrium; that is, where predation is relatively unimportant (figure 4.1). The rationale often given to justify wolf control is that if humans reduce the numbers of wolves, a low-density moose or caribou population might be released from its low equilibrium and allowed to stabilize at a higher-density equilibrium (Gasaway and others 1992). Haber (1977) has suggested the existence of a low equilibrium predator pit at 0.02–0.20 moose/km2

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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management FIGURE 4.1 Multiple equilibria. Multiple equilibria can exist for predators and their prey predator-caused mortality increases with increasing prey density up to some point, and then decreases. and an upper equilibrium at 0.4 moose/km 2. However, there is little evidence of stable high-density equilibria in nature (Messier 1994; Seip 1995). Van Ballenberghe (1987) reviewed the literature and concluded that 2-predator/single prey systems are more likely to be stable at low densities than are 1-predator/one prey systems. Thus, although wolf predation alone could limit the size or growth of a prey population (Ballard and others 1987; Larsen and others 1989; Peterson and others 1984a,b), the presence of a second predator, such as brown bears, can favor a low-density equilibrium (Messier and Crête 1985). Mortality during summer often removes 50% of annual calf production in ungulates; much of this predation is by bears, but its effects on population dynamics are not clear, because increased summer survival might be compensated for by decreased winter survival. Most researchers do not follow calves through the winter, even though population growth rate is more sensitive to mortality in older animals (Linnell and others 1995). Thus, in combination, wolves and bears can drive prey populations to low population densities. However, from a management perspective, the more important question is whether wolf predation can maintain prey populations at low densities for long periods (Sinclair 1989). Existing evidence on the point is inconclusive. For example, Messier (1994) reviewed the literature and concluded that wolf predation can be density-dependent at low moose densities (not more than 0.65 moose/km 2) but is often inversely density dependent at higher moose densities. If this were generally true, predators could depress prey populations for extended periods and control should allow a prey population to increase to, and remain for some time at, a higher density determined by food availability (Walters and others 1981), rather than by predation (Messier 1994;

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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management Sinclair 1989). But Boutin (1992) reviewed the same literature and concluded that the evidence that predation is a major limiting factor in most moose populations is not convincing. Differences in interpretation are possible because the supporting data are sparse. Not enough is known about the patterns of numerical and functional responses of wolves and the capacity of moose to sustain losses at different densities and environmental conditions. The cost of predator control programs would be reduced and their political acceptability would be increased if prey populations remained at high densities for a long time after predator control ceased and predator population densities rebounded to their pre-control levels. Factors that could result in persistent high prey densities include territorial behavior and intraspecific strife, which might set an upper limit on wolf numbers (Messier 1994). Alternatively, wolves that normally prey on moose might switch to caribou when they are particularly abundant, but fail to return to their earlier levels of predation on moose when caribou decrease in numbers (Dale and others 1994; Gasaway and others 1992). In his study on the numerical and functional responses of wolves in the Yukon, Hayes (1995) found that substantial changes in caribou distribution, or snowshoe hare abundance had little effect on wolf predation on moose. Before wolf-bear-prey interactions can be fully understood, more studies on functional and numerical responses of wolf populations to various combinations of prey (caribou, sheep, beavers, and snowshoe hares), of the behavior of bear populations, of the nutritional condition of the adult prey killed by wolves, and of the conditions under which wolves cause substantial calf mortality in prey will be needed (Messier 1994). However, it is already clear that no single pattern dominates those interactions. Variations in weather, habitat conditions, and behavior of predators and prey guarantee that outcomes will be varied, difficult to predict, and difficult to interpret. REFERENCES Ballard WB, JS Whitman, and CL Gardner. 1987. Ecology of an exploited wolf population in south-central Alaska. Wildl Monogr 98:1–54. Boutin S. 1992. Predation and moose population dynamics: a critique. J Wildl Manage 56:116–127. Boyce MS and RM Anderson. 1997. Evaluating the role of carnivores in the greater Yellowstone ecosystem. In Carnivores in ecosystems. Yale University Press, New Haven. Crawley MJ. 1983. Herbivory, the dynamics of animal-plant interactions. Studies in Ecology, v. 10, University of California Press, Berkeley, CA. Dale BW, LG Adams, and RT Bowyer. 1994. Functional response of wolves preying on barren-ground caribou in a multiple prey ecosystem. J Anim Ecol 63:64–652. Gasaway WC, RD Boertje, DV Grangaard, DG Kellyhouse, RO Stephenson, and DG Larsen. 1992. The role of predation in limiting moose at low densities in Alaska and Yukon and implications for conservation. Wildl Monogr 120:1–59. Haber GC. 1977. Socio-ecological dynamics of wolves and prey in a subarctic system. Ph.D. thesis, University of British Columbia, Vancouver.

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Wolves, Bears, and their Prey in Alaska: Biological and Social Challenges in Wildlife Management Hayes RD. 1995. Numerical and functional response of wolves, and regulation of moose in the Yukon. M.Sc. thesis, Simon Fraser University, Burnaby, British Columbia. Larson DG, DA Gauthier, RL Markel, and RD Hayes. 1989. Limiting factors on moose population growth in the southwest Yukon. Yukon Fish and Wildl Br Rep. Whitehouse. 105 Pp. Linnell JDC, R Aanes, and R Andersen. 1995. Who killed Bambi? The role of predation in the neonatal mortality of temporal ungulates. Wildl Biol 1:209 –223. Ludwig D, DD Jones, and CS Holling. 1978. Qualitative analysis of insect outbreak systems the spruce budworm and forest. J Anim Ecol 47:315–332. Messier F and C Crête. 1985. Moose-wolf dynamics and the regulation of moose populations. Oecologia 65:503–512. Messier F. 1994. Ungulate population models with predation: a case study with the North American moose. Ecol 75:478–488. Peterson RO, JD Woolington, and TN Bailey. 1984a. Wolves on the Kenai Peninsula, Alaska. Wildl Monogr 88:1–52. Peterson RO, RE Page, and KM Dodge. 1984b. Wolves, moose, and the allometry of population cycles. Science. 224:1350–1352. Seip DR. 1995. Introduction to wolf-prey interactions. In LN Carbyn, SH Fritts, and DR Seip, Eds. Ecology and conservation of wolves in a changing world. Canadian Circumpolar Inst, Univ Alberta, Edmonton, 1995. Sinclair ARE. 1989. Population regulation in animals. In JM Cherrett, Ed. Ecological concepts: the contribution of ecology to an understanding of the natural world. Blackwell Scientific Publications, Oxford. Van Ballenberghe V. 1987. Effects of predation on moose numbers: a review of recent North American studies. Viltrevy (Swedish Wildlife Research) Supplement 1:431–460. Walters CJ, R Hilborn, and R Peterman. 1975. Computer simulation of barren-ground caribou dynamics. Ecol Modelling. 1:303 –315. Walters CJ, M Stocker, and GC Haber. 1981. Simulation and optimization models for a wolf-ungulate system. Pp. 317-337 in CW Fowler and TD Smith, Eds. Dynamics of large mammal populations. John Wiley and Sons, NY.