Chaos does not drive lower synchrony for intrinsically-induced population fluctuations

Abstract

Amphibians naturally occur in metapopulations characterized by spatially separated breeding habitats connected by dispersing individuals. The rate at which individuals grow to maturity, size of the metapopulation, and movement behavior varies widely across amphibian species, and their compounding interactions play a large role in population dynamics and viability. When populations in a connected network exhibit cyclic behavior the level of synchrony between populations is important for assessing extinction risk. In addition, the qualitative behavior of fluctuations provides insight into the patterns of the population cycles and can be used to predict forward trajectories in time. Chaotic oscillations, characterized by aperiodic cycles and sensitivity to initial conditions, are known to amplify noise, thus lowering population synchrony; however, other oscillation types (invariant cycles, k-cycles) have not been explicitly explored in relation to synchrony. In this paper, we investigate the relationship between synchrony and oscillation type for a two-patch system of a species with 1, 2, and 3 life-history stages. Using dynamical systems analysis, we determine the mechanisms that induce the different oscillation types and relate them with dispersal rates and synchrony. We find that dispersal has a greater effect on population dynamics of a species with 1 life-history stage compared to the subtle changes in dynamics found for species with 2 and 3 life-history stages. For low levels of dispersal, oscillating populations are driven to equilibrium as synchrony increases. Under medium to high levels of dispersal, oscillations may be created from equilibrium with low levels of synchrony. In general, chaos does not have noticeably lower synchrony than other oscillation types but has synchrony levels comparable to the oscillation types surrounding chaos. In this study, we cover a broad range of dispersal probabilities and life histories intended for general amphibian systems. The variety of results found in our analysis emphasizes the importance of determining model parameters and life history assumptions when studying specific amphibian species to ensure that the resulting dynamics accurately reflect the system.