A minimal model of the variability of marine ecosystems

In marine ecology, population abundance time series often reveal patterns, such as decadal pseudo-cycles, on scales that make them difficult to mathematically characterize by means of conventional models based on functional responses. We propose here a simple non-deterministic model based on three strong ecological constraints, without any use of functional responses or external factors: (i) mass balance constraints between flows and biomass, (ii) a satiation constraint relating inflows and biomass and (iii) an inertia principle restricting the variation of populations of a given species according to its lifespan. This model reproduces in a robust manner observed patterns of variability and can be used to question the relevance of other modelling approaches of ecosystem dynamics with regard to determinism, constraints and stochasticity. Referring to a non-deterministic model without any functional relationships and environmental or anthropogenic forcing can help in avoiding misleading advice based on the belief that we can explain the causes of observed patterns, which may simply result from basic structural constraints within which the ecosystem functions.