The growth and disturbance of populations can result in strong, even catastrophic, fluctuations. Their causes can be environmental, or result from feedbacks involving spatial aggregations, species interactions, and ecosystem maturation. Coupled population-ecosystem dynamics and their role in explaining fluctuations of abundance and of ecosystem functions remain unresolved. Ecosystem engineers, such as mussels in marine coastal habitats, provide a good model system to address this problem. They show aggregation behavior leading to disturbance cycles, and drive strong biogeochemical changes involving accretion of (in)organic matter. We hypothesized that accretion impairs mechanical stability of mussel aggregates and facilitates disturbance and associated matter resuspension. This feedback could determine dynamical regimes and affect the local and regional provision of materials. Blue mussel (Mytilus spp.) aggregates were sampled to test the correlation between the quantity of sequestered materials and individual attachment strength. We used a deterministic mean-field ecosystem model based on susceptible-infected-recovered models to implement the interaction between aggregated population growth and disturbance, and materials fluxes and stocks for a single mussel bed. We performed stability analysis and numerical simulations to study the general effects of (i) positive and negative and (ii) linear vs. nonlinear population-ecosystem feedbacks on the non-equilibrium dynamics of population and ecosystem functions.
Results/Conclusions
Empirical results revealed a negative correlation between the depth of accumulated materials and the strength of mussel attachment. Simulations show that such a positive feedback of matter on disturbance can promote the emergence of strong pulse-relaxation fluctuations in mussel density and materials stocks. The qualitative properties of these dynamics are associated with rare catastrophic disturbance and resuspension events over temporal scales that are inversely related to their magnitude. One implication is that long-term mean statistics such as retention time and average fluxes could lead to false predictions on coupled population-ecosystem processes driving these systems. Generalized to both positive and negative population-ecosystem feedbacks, our results allow to predict the emergence of catastrophic shifts across system types. Ecosystem-based management still has to fully integrate spatial flows of organic and inorganic matter and strong fluctuations in their intensities as important drivers of ecosystems stability and function at the regional scale. By providing local predictions for the temporal dynamics of biotic and abiotic stocks and fluxes associated with ecosystem engineering, the theory provides a simple framework for this task.