Modelling biological invasions: chance, explanation, prediction

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Abstract
Biological invasions have their epidemic and endemic aspects: the former include ability to invade, competitive ability to succeed initially, and (if successful) rate and manner of spread; the latter, competitiveness to persist, and (if successful) level and pattern of persistence. There have been successes, at least in qualitative explanatory terms, in modelling all these aspects. For some, the stochastic element, which is intrinsic to populations of discrete individuals, is crucial. Other aspects, at least at the aggregate level, can usefully be analysed deterministically, with the stochastic element treated as an optional refinement. The lack of corresponding successes in prediction shows the quantitative weakness of simple models, which in their details are commonly more arbitrary than models in the physical sciences. Careful examination of the sensitivity of predictions to the detailed form of model components can reveal which of these need more accurate formulation, and any corresponding requirement for better data.

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