Spatial Differences in Density Independent versus Density Dependent Mortality

Generally, populations are not ubiquitous but rather are spatially structured and have boundaries to their range. This spatial complexity has the potential to alter mortality processes. First, a metapopulation can be spatially structured into many subpopulations that are connected by migration. For example, we can alter eqn [1] to present a simple two-population model where local dynamics are

Population size (N)

Figure 4 If a species exhibits an Allee effect, then density-dependent mortality will curvilinearly increase in low population sizes (dotted line).

Population size (N)

Figure 4 If a species exhibits an Allee effect, then density-dependent mortality will curvilinearly increase in low population sizes (dotted line).

defined by the logistic model but migration (m) is density independent:

where 0 is the fraction of migrants dying during migration. However, in reality, not all subpopulations live in equal quality habitat and therefore migration may become density dependent. For example, some subpopulations can inhabit 'sources' where birth rates are higher than death rates (r > 0) and emigration is greater than immigration. Others inhabit 'sinks' where death rates are greater than birth rates (r < 0) and immigration is greater than emigration. Because of these dynamics, source populations have the potential to 'rescue' sink populations. However, it is to be noted that a sink population with a large immigrant pool has the potential to push the population higher toward carrying capacity and increase the observable density-dependent mortality than would have occurred in the absence of immigration.

Not only can subpopulations exhibit different levels of mortality at local scales due to metapopulation dynamics, but density-dependent and density-independent mortality can differ at landscape scales. The 'realized niche' concept predicts that a species range is determined by the observed resource use of species in the presence of biotic interactions (competition and predation). Additionally, the 'abundant center' hypothesis predicts that populations that are at the center of their range should have more robust populations (due to better availability of resources) than at the edge of their range. This can potentially lead to improved birth rates, lower mortality rates, and higher carrying capacity. Lastly, populations at the edge of their range tend to be much more variable than at the center and the relative importance of density-independent versus density-dependent processes will differ throughout a population's range causing the difference in population variability. These relationships illustrate two points. First, it is important to recognize density-dependent and density-independent processes simultaneously influencing populations. Consequently, we can alter eqn [1] to incorporate both processes:

where D represents the per capita rate of density-independent mortality. Second, the strength of these two processes has the potential to change across a species range. Due to limitations in the realized niche, small peripheral populations suffer greater amounts of density-independent mortality, thereby increasing the possibilities of local extinctions. Additionally, in populations that exhibit boom and bust life cycles (e.g., insects), the strength of winter density-dependent mortality is generally the same or greater in smaller peripheral populations than in larger central populations. This occurs because peripheral populations exhibit strong overcom-pensating reproduction (consider the populations are low on the logistic growth curve and are temporarily growing in a more exponential pattern); however, resource quality required for winter survival cannot support the large summer population through the winter, thereby causing the strong density-dependent mortality returning the population to a low level.


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.

Direct density dependence Strong 4-Weak

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