Modelling plankton ecosystems and the Library of Lotka

Predicting how change will impact ecosystems requires the development of complex models. The complexity of ecosystem models often defies the power of analytical mathematical techniques so they are commonly solved using computers. A problem with this approach is the difficulty in assessing the credibility of model simulation results.We apply ecological axioms to the construction of complex model ecologies. The axioms ensure realistic ecological properties and internal consistency of a broad class of models that encompass many theoretical and applied models. A key new analytical result for our dynamical systems in ecospace is that extinctions can be studied without knowledge of either interior equilibrium points or their stability. By looking only at boundary extinction points we can immediately comment on the extinction behaviour without solving for any of the dynamics. This is a striking simplification, and even holds when the dynamics are chaotic.We demonstrate the approach by constructing three plankton ecosystem models that we designed to have specific properties and show that the effect of change on plankton blooms and/or extinctions depends on the properties of the model chosen for the simulation.

► We apply ecological axioms to plankton models to ensure consistent normal ecologies. ► Consistent normal ecologies have analytic expressions for competition eigenvalues. ► We show important properties of complex models depend on choices of functional forms. ► Predictions of ecosystem response to climate change depend on properties of the model. ► The Library of Lotka metaphor synthesises the challenges facing ecosystem modelling.