Direct versus Delayed Density Dependent Mortality and Population Cycles

Density-dependent mortality does not always act in an instantaneous fashion; rather, it has the potential to operate with a time lag. For example, suppose a prey species' population is growing strongly and has a specialist predator (i.e., a predator that depends on only one or two species for the majority of its diet). But if the prey species is growing faster than the predator population can eat, then the predator will not be able to effectively control the population. However, if the predator is able to convert this abundant energy source into more offspring the following year, more predators will exist on the landscape and, therefore, will be better able to control the prey population. In such a case, the density-dependent mortality response became delayed by 1 year. Hence, populations have the possibility to be limited by both direct density-dependent mortality (fairly instantaneous) versus delayed density-dependent mortality (exhibits a time lag).

Cyclic population fluctuations have been well documented in bird, mammal, and insect species in northern latitudes, of which, probably the most famous being the characteristic 10-year cycle observed in snow shoe hares. Interestingly, population cycles generally are known to collapse in more southern latitudes. These cyclic dynamics have been of particular interest to population ecologists because they suggest strong biotic interactions including the influences of both direct and delayed density-dependent mortality. Using time-series analysis of populations, direct and delayed density dependence can be estimated and distinct combinations ofboth factors will promote characteristic cycle lengths (Figure 5):

where p is the cycle period length, is the strength of direct density dependence, and is the strength of delayed density dependence. Although many hypotheses exist to explain cycles, a common explanation for the dissipation of cycles in southern latitudes is that there is a switch from specialist predators whose dynamics are

Figure 5 Distinct combinations of estimated direct and delayed density dependence from time-series analysis have the potential to illicit recognizable cycle lengths (values next to curves in graph). Note more negative values of direct and delayed density dependence indicate stronger effects. Characteristic 10-year cycles exist with a combination of strong delayed density dependence and weak direct density dependence. Populations exhibiting no cycles are a product of weak delayed density dependence.

tightly coupled to those of their prey, to generalist predators whose dynamics are not coupled. This explanation is supported by evidence that generalist predators are more common in southern latitudes than in northern latitudes. The switch from specialist to generalist predators is thought to cause a weakening of delayed density dependence to a strengthening of direct density dependence and cycle collapse.

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