Last modified: 2014-06-09

#### Abstract

Population cycles are usually explained as a combination of deterministic mechanisms, such as predation, that drive density-dependent dynamics and stochastic forces that disrupt the neat patterns that would otherwise result. It is often convenient to apply the signal vs. noise dichotomy in this context, where a deterministic signal is blurred by stochastic noise. In some particularly fascinating situations, however, this dichotomy is unhelpful because the “signal” is inextricable from the “noise”: stochasticity itself plays a role in shaping the overall pattern in the dynamics. In this way, stochasticity has a *qualitative* effect on the dynamics, such that the population fluctuations look quite different from what should result from the underlying deterministic factors alone. This creates quite a challenge: when we see patterns in ecological data, how can we tell if they were generated by mostly deterministic factors (with stochasticity simply adding some jitter) or if stochasticity played a key role in shaping the patterns themselves? This question is important, because the answer determines whether stochasticity should be included explicitly in hypotheses for the observed patterns. By studying models that can show both of these outcomes and comparing their assumptions and behaviors, I begin to dissect what allows stochasticity to have a qualitative effect and become part of the “signal”. This study suggests that developing a more nuanced understanding of how stochasticity and nonlinearity interact in ecological systems will likely be more fruitful than viewing stochastic perturbations as “noise” to be filtered out.