The world’s ecosystems have been driven to the point of collapse by human activities. Conservation biologists often aim to reverse this decline by undertaking expensive interventions: eradicating invasive species, re-introducing native species that have been locally extirpated, or re-starting old fire regimes. In the past, while these sorts of interventions have delivered enormous benefits, they have sometimes triggered catastrophic outcomes. We need predictive models of these ecosystems to avoid costly mistakes.
From a mathematical perspective, an ecosystem can be modelled as a set of coupled nonlinear differential equations. The goal of conservation management is to undertake actions that will move the ecosystem from a degraded equilibrium point (e.g., where invasive species are present) to a new, recovered equilibrium. Management actions that move the ecosystem to another (potentially worse) degraded equilibrium must be avoided.
Because ecosystems contain dozens of species, and because their interactions are complex and nonlinear, this would be a difficult problem if we knew the form of the equations, and had accurate estimates of their parameters. Unfortunately, we are profoundly ignorant about both these factors, and have little or no data to help us resolve these uncertainties. How can conservation managers make defensible, effective decisions when they know so little about the ecosystem dynamics? How can the tools of mathematics help model such large, uncertain system models? This is a primary challenge of 21st century mathematical conservation ecology.