The 1^st principle of population dynamics describes the growth of a population of self-reproducing entities when the per-capita rate of growth, or the birth and death rates, remain constant. In nature, of course, this rarely happens and so our next job is to understand the forces that cause changes in R or G.

Individual organisms of the same species often aid each other in the struggle to survive and reproduce as, for instance, when they form into herds, packs, schools, flocks, and swarms that help them to obtain resources or avoid enemies. Remember the example of the aggressive mountain pine beetle that was able to cooperatively overwhelm vigorous trees by pheromone mediated mass attack. We call this intraspecific cooperation, meaning cooperation between members of the same species. Because aggregations of bark beetles and other cooperative species are able to form more readily when populations are dense, the benefits of intraspecific cooperation are likely to increase with population density. This gives rise to a +feedback process because the higher the density of the population, the greater are the benefits; i.e, more births and fewer deaths. This causes the per-capita rate of change of the population, R or G, to rise with population density. In other words, cooperation can lead to a positive relationship between the rate of population change and population density, as shown in the figure.

It is important to realize that cooperative interactions can create unstable thresholds above which the population grows and below which it declines (the point U in the figure). People involved in conservation issues often call the unstable equilibrium (U) an extinction threshold because once a population declines below this point it automatically continues to extinction. Forest pest managers, on the other hand, tend to think of U as an escape threshold because once a pest exceeds this density it explodes to very high densities and, as we will see later, can also spread over vast areas.

The student should realize that when the 2^nd principle is in effect, populations grow under the influence of two +feedback processes; i.e., both the 1^st and 2^nd principles are in fact operating simultaneously. Under these conditions populations can grow faster than exponentially, what is called hyper-exponential growth. The human population may be growing hyper-exponentially because cooperative endeavors (science) lead to technological advances that continue to reduce the per-capita death rate as the population grows. Cooperation between humans can also assist the growth of economic systems, a phenomenon known as the law of increasing returns. Here economic organizations can become more productive as they get larger because coalitions between individuals, departments, and such, help the organization to become more efficient.

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© 1998 Alan A. Berryman