## Effect of Mortality on Population Dynamics

Search for mortality processes that control population dynamics requires a clear definition of the term 'control' which has multiple meanings. Old debates on whether natural enemies of climate control population dynamics failed because of the lack of well-defined terms. The term 'control' implies a causation relationship between mortality process and the dynamics of population. Thus, a simple correlation between the mortality rate and pattern of population density through time is not a sufficient evidence of 'control'. The evidence on the effect of the mortality process on the population dynamics can be gathered either from intervention experiments, in which modification of the rate of mortality causes changes in the pattern of population dynamics, or from a computer simulation of such experiments assuming the model is enough realistic and was sufficiently validated. Numerous examples of intervention experiments are available in the area of pest control.

Regular application of pesticides in agriculture leads to the additional mortality of pest insects, which is followed by the decrease of their population density. Classical biological control is another example of additional mortality associated with imported natural enemies.

The effect ofadditional mortality on the average level of population density can be studied experimentally in some populations (e.g., in the lab or in a controlled agricultural ecosystem). However, these kinds of experiments are either not feasible or ethically prohibited for the majority of natural populations. Thus, we have to rely on mathematical models to evaluate the consequences of a new introduced mortality process. The same additional mortality (e.g., 50% per generation) may cause a dramatic decline in the average population density in one population and only a slight reduction in the density of another population due to density-dependent compensatory mechanisms. The sensitivity of the average log-transformed population density, log(M), to the ¿-value of introduced mortality, k, can be estimated using a simulation model. The inverse value of sensitivity was called M-stability:

qk which indicates the degree of resistance of the population to the change of its density due to added mortality.

Populations with a strong density-dependent mortality or reproduction have a high M-stability. Indeed, if the density of such population declines, then the rates of density-dependent mortality processes also decrease and compensate partially the introduced mortality. For example, if a population of pest insect has high mortality caused by specialized parasitoids, then it may by difficult to suppress with pesticides. Let us assume that the pesticide does not kill parasitoids because it is applied before their emergence. As the density of the host population starts to decline, the numbers of specialized parasitoids will decline because of the shortage of their hosts, which will cause a decrease in the rate of parasitism. This decrease in parasitism will compensate partially the mortality induced by pesticide. In other words, the pesticide application targeted at the pest affects indirectly the density of its natural enemies much stronger than the density of the target population. If the pesticide had a direct nontarget effect on parasitoids, the situation would be even worse because then the density of parasitoids would decline to a lower level. Populations without strong density-dependent mortality processes have little compensation to the introduced additional mortality and therefore their average density will decrease substantially (low M-stability). Additional mortality may cause extinction of local populations if they have an inverse density-dependent mortality (e.g., group effect) or reproduction (e.g., mating success). This happens if population density is reduced below the level that supports cooperation between individuals and/or sufficient mating rate. At this threshold population level, the M-stability equals zero.

M-stability does not necessarily imply local stability at the equilibrium state. The equilibrium can be unstable and the population system may follow a cyclic trajectory, but this population may have a strong M-stability if its average density does not change easily in response to additional mortality. Local stability can be lost if density dependence in mortality processes is delayed, whereas M-stability is supported even by delayed density-dependent processes.

The conception of M-stability can be applied to the effect of harvest mortality on the average fish stock. If a fish population has a high M-stability then harvesting is partially compensated by the decrease in natural mortality which is density dependent, and hence causes a relatively small reduction in the average population density. However, fish populations with low M-stability can be easily depleted due to harvesting. The difference in M-stability can partially explain observed changes in the species composition of fish populations. A myth that fish populations have a 'harvestable surplus', which can be harvested without any effect on the stock (it is believed that harvest deaths are substituting for the deaths that would occur naturally), has led to the global depletion of fish populations. Mathematical models show that additional mortality is compensated only partially by the decrease in natural mortality and hence always draw population density to a lower level. Analysis of M-stability can help to estimate what reduction ofharvest rates is needed to restore fish population levels. Another application of M-stability is the protection of endangered populations. Species with low M-stability have a high risk of extinction because they do not have strong compensatory density-dependent mortality processes. Large mammals belong to this category because they have low mortality and low fecundity; hence, the density-dependent component of mortality is weak. These species require most intensive conservation efforts.

See also: Classical and Augmentative Biological Control; Metapopulation Models; Parasitism; Predation; Stability.

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