OOS 50-10
Where signal and noise collide: qualitative effects of stochasticity on population dynamics
Population dynamics result from a combination of deterministic mechanisms (e.g. competition, 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 patterns 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 qualitative role in shaping the patterns? The answer determines whether stochasticity should be included 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”.
Results/Conclusions
Intuitively, stochasticity is most likely to influence the qualitative dynamics when there are features in the deterministic part of a model that are associated with long transients. Nonetheless, it is extremely difficult to look at a model’s behavior and infer what role stochasticity played in generating the observed “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.