Individual-based chaos: Extensions of the discrete logistic model

• Seed production and juvenile recruitment are modeled mathematically in annual plants.
• Overcompensating density dependence in either process generates oscillations in population density.
• These oscillations are chaotic in iterative maps and appear to be chaotic in simulations.
• The oscillations are robust to demographic stochasticity for sufficiently large lattice sizes.
• Such robustness suggests the theoretical possibility that these oscillations might be observable empirically.

Simple models of density-dependent population growth such as the discrete logistic map provide powerful demonstrations of complex population dynamics. Yet it is unclear whether the dynamics observed in such idealized systems would be present, under realistic conditions, in the context of demographic stochasticity, which is well known to exist in finite natural populations. Here, using a set of simple, individual-based models (IBM's) and their population-level iterative map counterparts, we computationally investigate the contribution of demographic stochasticity to density-dependent population dynamics in a simple model of seed production and recruitment. Notably, for a sufficiently large lattice, even in the presence of demographic stochasticity, many of the qualitative features of these idealized maps – including bifurcations – are still present. Demographic stochasticity and the constraints imposed by a finite lattice size appear to produce mixed dynamics that are partially stochastic, yet qualitatively similar to the deterministic models. The mechanistic assumptions and lattice sizes required to generate these dynamics cast doubt on whether they might be observable in annual plant populations. Nevertheless, we cannot rule out the theoretical possibility that such dynamics might be observable in ecological communities having similar mechanistic properties.