Many organisms disperse by advection in media possessing a net unidirectional flow. The systems these organisms inhabit, exemplified by streams and rivers, are also characterized by a high degree of multi-scale spatial and temporal environmental variability. Most conceptual frameworks describing ecological organization in streams and rivers prominently feature both upstream-downstream linkages and variability that occurs across spatial and temporal scales. Recent modeling studies have explored how the spatial distribution of organisms result from multi-scale spatial variability in systems with dispersal by advection, but these have typically focused on equilibrium distributions while ignoring transient responses and temporal dynamics. In contrast, metrics for describing transient dynamics have been developed and applied to both non-spatial and spatially explicit systems, but in the spatially explicit case focus on symmetric rather than directionally-biased dispersal. We address this gap by studying the transient dynamics, following a spatially-extended perturbation, of models describing populations residing in advective media. Our analyses emphasize metrics that are independent of initial conditions – resilience, reactivity, and the amplification envelope – and relate them to the spatial scale of the population perturbation. This approach offers a powerful way of understanding the influence of spatial scale on the initial dynamics of a population following a spatially variable environmental perturbation, an important property in determining the ecological implications of transient dynamics in streams and rivers.
Results/Conclusions
We find that populations with advective dispersal may exhibit transient amplification of perturbations (i.e. have positive reactivity) even when their long term dynamics are stable. However, the degree and duration of transient amplification varies strongly with spatial scale, and in some cases only occurs in response to larger spatial scale perturbations. For single-population models we have examined, there is a relationship between transient dynamics and organism dispersal. Advective dispersal causes small scale perturbations to exhibit transient amplifications over behavioral time scales and decay quickly, whereas much larger scale perturbations decay at rates driven by births and deaths. Furthermore, organisms dispersing often during their lifetimes exhibit a peak amplification of perturbations that is small and occurs fast. This relationship holds less generally in a specialist consumer-resource model, likely due to the model’s tendency for internally generated spatial variation not observed in the single-species models. We conclude with empirical examples to argue that our efforts provide an important step towards understanding ecological dynamics in streams and other systems dominated by advective dispersal.
