(Houston 1982, YNP 1997). For a population to be regulated by density-dependent factors, some combination of the following processes must operate. As population density increases, mortality and emigration rates increase and the rate of reproduction decreases. Increases in mortality can result from depletion of food supplies because individuals find it increasingly difficult to obtain adequate nutrition. Diseases, whose transmission is facilitated by high population densities, and predators also can increase mortality (Sinclair 1989, Royama 1992, Begon et al. 1996). Rates of reproduction may decrease because females cannot obtain enough food to support high rates of pregnancy and because offspring may be born at lower weights and less appropriate times than when food supplies are good. These rates may change gradually with population density, or there may be thresholds at which major changes occur (Fowler 1987; McCullough 1990, 1992).

The combination of these processes tends to cause population densities to decline when they are high and to increase when they are low. However, this does not guarantee that population densities will stabilize or reach some equilibrium because changes in rainfall, snow accumulation, fires, and other abiotic events may cause large fluctuations in the capacity of the landscape to support the population (Soether et al. 1997). In other words, because the environmental conditions in the landscape may vary considerably, the magnitude of variation in the density of a population by itself cannot be used to assess the importance of density-dependent factors in regulating the size of a population. Most populations of larger herbivores are subject to a combination of stochastic and density-dependent processes that lead to large variation in rates of juvenile survival and subsequent changes in population growth rates (McCullough 1990, Sinclair and Arcese 1995, Soether 1997, Gaillard et al. 1998).

The conceptual basis of density-dependent population regulation is simple, and there are many examples of ungulate populations in which fecundity declines or mortality increases as population density increases. However, no single statistical method identifying density dependence has emerged, despite vigorous discussion (Strong 1986, Pollard et al 1987, Turchin 1990, Dennis and Taper 1994, Soether 1997, White and Bartmann 1997, Shenk et al. 1998, Bjornstad et al. 1999). Many unharvested ungulates are regulated, at some point, by density dependence (McCullough 1979, Sinclair 1979, Fowler 1981, Gaillard et al. 1998), but populations are always subject to a multitude of factors and it can be difficult to distinguish the effects of density from those of other influences. The best evidence for density dependence comes from direct measures of changes in population processes such as mortality, fecundity, and migration (Shenk et al. 1998).



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