Single Species Population Dynamics

Abstract

In this chapter we move up to the level of the population. The models we consider here attempt to explain and predict patterns of change over time in population density, the number of individuals per unit area or volume. Population dynamics has always been a core topic in theoretical ecology. One of the original-and still strong-motivations for developing mathematical models is to understand the cause of cycles in particular populations, such as those shown in Figure 3.1. Is the famous lynx cycle the result of the trophic link between lynx and hare, or is it a cycle driven by the interaction between hares and their food resources with the lnyx just "along for the ride" as their food source waxes and wanes? We could imagine experimental approaches to this question, but their practicality is serious issue, and even when such experiments have been attempted their interpretation is not always clear (Turchin 2003). Models are therefore play two important roles: they identify classes of population interactions that could lead to the observed type of dynamics, and they may be able to identify unique predictions of each competing hypothesis that can be tested using observational data. We are also interested in understanding patterns in cross-species comparisons-how do macroscopic properties such as the cycle period depend on properties of the individual organisms? For example, Figure 3.2 shows that when the period of population cycles is scaled relative to the individual maturation time (the time between birth and sexual maturity), some scaled periods are not observed (the INT category), and there is a clear difference in scaled period between specialists and generalists (a specialist feeds almost exclusively on just one species, a generalist feeds on many species). At the end of a long road that we are now starting, we will understand how this pattern was predicted a priori using models that account for individual growth and development, and their interactions with competition for resources. Population modeling is also important for species management: managing fisheries for the highest possible sustainable yield, developing recovery plans for species threatened by extinction, or trying to contain or prevent the spread of invasive species. For these questions, we are often interested in how a population , or set of interacting populations, responds to a change in system parameters. For example: how 65