Mechanistic models calibrated using Bayesian inference – what is the tipping point of Antarctic shallow-water algae?

Abstract

In applied mathematics and statistics, ecology is a challenging discipline: data is noisy and scarce, but we wish to make confident predictions and conclusions. Some of the information we rely upon isn’t precisely “data”, but may be ecological understanding of physical mechanisms, and/or other forms of expert-elicited knowledge. Hence, carefully chosen mechanistic models (for getting the mechanisms right) together with Bayesian inference (for capturing the uncertainty rigorously) is a powerful combination for making defensible conclusions in ecology.

In this talk, I will present an example of simulating Antarctic shallow-water algae using a combination of population growth models (as ordinary differential equations) and Bayesian inference (implemented using Sequential Monte Carlo sampling). We first introduce a new class of population growth models that explicitly permits the equilibrium size of a population to depend on availability of resources. We show three examples of these models that are suitable (both in their structure and complexity) for simulating populations of Antarctic shallow-water algae. After calibrating the models to data from various Antarctic shallow-water sites, we demonstrate that these algae populations in nature are already at or beyond a tipping point – indicating that a reorganisation of these ecosystems towards algal domination is highly likely in the future.