Allometric scaling of Lyapunov exponents in chaotic populations. Issue 3 (31st May 2020) - Anderson, David M.; Gillooly, James F.
Abstract: Chaos has been a central topic of research in ecology for decades, in part because of its implications for the predictability of population dynamics. Chaotic systems are characterized by low predictability at long timescales, as slight differences in initial conditions (e.g., the actual vs. the measured initial conditions) yield trajectories (e.g., the actual vs. the predicted trajectory) that diverge exponentially at a rate determined by the global Lyapunov Exponent (LE). The LE is therefore a critical descriptor of chaotic systems that sets the time horizon for predictability. Recent observations of chaos in populations or communities have shown that LEs vary by at least two orders of magnitude, yet the factors underlying this variability remain unclear. Here, we examine the drivers of heterogeneity in LEs among chaotic populations and communities. We show that LEs decline with increasing body size as a shallow power law (exponent −0.21), suggesting that LEs are inversely proportional to the populations' generation time (GT). However, this allometric scaling relationship holds only when considering the larger, slower growing populations in multispecies communities (the primary and secondary consumers), indicating that these populations constrain or determine LEs for the community. These results suggest that the rate at which the predictability of a chaotic time series declines over time generally reflects either the populations' GT, or that of a slower growing population in the community. Abstract : Recent observations of chaotic dynamics in natural and laboratory populations and communities have revealed substantial variability in Lyapunov exponents, which measure the rate at which nearby trajectories diverge. In this note, we use an allometric scaling approach to show that this variability largely reflects either the populations' generation time, or that of the slowest growing population(s) in the community.