Complex Population Dynamics

• William W. Murdoch
• Peter Turchin

Abstract

Population cycles and other complex population dynamics occur in a wide range of taxa and environments, including temperate and tropical forest insects, marine and freshwater fish and invertebrates, and boreal mammals. Population cycles show enormous variation in amplitude (from less than one to five orders of magnitude), period (from a single generation to 30-50 generations), and the strength of periodicity (ranging from noisy pseudoperiodic or apparently chaotic oscillations to an almost perfect periodicity). In addition, cycles may involve not only the total population abundance, but also other aspects of dynamics, e.g. oscillations in age structure and complex spatio-temporal behaviors, such as synchronous oscillations or periodic traveling waves.

There are many potential explanations for oscillatory population dynamics (in the general sense), with some focusing on intrinsic factors, but most often invoking some aspect of consumer-resource interactions (we briefly review some theoretical and empirical mechanisms by which population cycles can arise in Section 11). The theoretical literature on population cycles is enormous, but there has been no attempt to systematize it and to relate various postulated mechanisms to the oscillatory patterns observed in real populations.

Our long-term goal is to bring order to what is known theoretically and empirically about population cycles. More specifically, we propose to:

1. define and classify the range of mechanisms that can induce oscillatory population behavior in theoretical models;
2. establish correspondences between theoretical mechanisms that could drive cycles and quantitative descriptors of oscillatory population dynamics (these will be defined in Section 111. 1);
3. apply a combination of modeling and statistical techniques to a number of data sets (Section IV) in an attempt to determine which of the possible theoretical mechanisms may be responsible for population oscillations in each particular case.
4. attempt to develop general statements about mechanisms that are responsible for cycles in nature, and the conditions under which different mechanisms may operate and different types of oscillatory dynamics may arise.

Previous investigations of population oscillations have utilized primarily two distinct approaches: potential mechanisms have been investigated with mathematical models, while data patterns have been investigated with phenomenological time-series analyses (cycles have also been investigated experimentally, but this approach is not part of our proposal because it falls outside of the scope of the research supported by the Center). We propose to bring together individuals representing both approaches to collaborate on a program in which theoretical model development and statistical analyses of data will be tightly linked. We hope to gain strong synergistic advantages from such a collaboration.