The question of whether an ecosystem should become more or less stable with added complexity has been a source of debate in ecology for decades. Complexity is typically measured as a function of diversity and community connectedness.

 

Early theoretical investigations addressed this question in a particular way - by proposing a general deterministic system, linearised about a hypothetical steady state. The stability of this system could then be characterized in a very concrete mathematical manner - as whether the hypothetical steady state was stable. In this formalism, the stability of an ecosystem then essentially becomes a function of the structure of species interactions at the fixed point. It is frequently found, theoretically at least, that more 'complex' ecosystems are less stable.

 

This observation however runs counter to our observations that decreasing diversity typically decreases ecosystems stability. In part, this is simply because the above-mentioned mathematical measure of stability does not capture what we intuitively mean by stability. The stability of an ecosystem could instead be characterized by its variability (the size of population fluctuations), its susceptibility to invasions, and its structural robustness (characterized by the number of secondary extinctions following the loss of a single species). Indeed these are standard measures often used to empirically characterize ecosystem stability.

 

It is clear that in any real ecosystem these latter measures can be fundamentally stochastic. I am planning to use the techniques from my background in statistical physics to address these questions analytically.