  Resilient ecological systems will be better able to maintain their structure
and function in the emerging Anthropocene. Estimating the resilience of
different systems will therefore provide valuable insight for conservation
decision-makers, and is a priority goal of resilience theory. Current
estimation methods rely on the accurate parameterisation of ecosystem models,
or the identification of important motifs in the structure of the ecological
system network. However, both of these methods face significant empirical and
theoretical challenges. In this paper, we adapt tools developed for the
analysis of biochemical regulatory networks to prove that a form of resilience
- robust perfect adaptation - is a property of particular ecological networks,
and to explain the specific process by which the ecosystem maintains its
resilience. We undertake an exhaustive search for robust perfect adaptation
across all possible three-species ecological networks, under a generalised
Lotka-Volterra framework. From over 20,000 possible network structures, we
identify 23 network structures that are capable of robust perfect adaptation.
The resilient properties of these networks provide important insights into the
potential mechanisms that could promote resilience in ecosystems, and suggest
new avenues for measuring and understanding the property of ecological
resilience in larger, more realistic socioecological networks.
