Revealing the ghost in the machine: Using spectral analysis to understand the influence of noise on population dynamics
- Institute of Integrative and Comparative Biology, University of Leeds, Leeds LS2 9JT, United Kingdom
To manage populations, whether of threatened, exploited, or pest species, or even of parasites or pathogens in hosts, we must be able to predict their population dynamics, and to do this, we need to understand the underlying processes. An important recent focus is the way that deterministic density-dependent processes interact with random influences (“noise”) to create novel patterns in the dynamics. Such noise typically has two sources. First, environmental noise is driven by changes in extrinsic processes (such as climate and resource availability). Second, demographic noise is the random way individuals progress through their life history and arises through the “discreteness of individuality”: an organism can be male or female, dead or alive, but the “vital rate” (sex ratio, survival, fecundity) may be noninteger. In large populations, demographic stochasticity can be ignored because it is averaged across a large number of individuals. So, at any point in time or space, the population will typically be very close to the average, but in small populations, the deviation between the population average and the realized value at any particular time may be considerable. The “strength” of demographic noise is inversely related to the square root of population size, and a general question that is asked by Reuman et al. (1) in this issue of PNAS is “how does demographic noise of different strengths affect dynamics?”
Why Does Noise Matter?
This is a key question because recent studies have repeatedly indicated that noise can be an important influence on population dynamics and can interact with deterministic density dependence to give rise to population dynamics that are not solely “deterministic dynamics with noise” but that may be qualitatively different (2, 3). This qualitative difference between deterministic and stochastic dynamics may arise from two main causes.
First, noise can cause dynamical systems to move between different nearby …
*E-mail: t.g.benton{at}leeds.ac.uk
