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Human activity alters natural habitats for many species. Understanding variation in animals' behavioural responses to these changing environments is critical. We show how signal detection theory can be used within a wider framework of state-dependent modelling to predict behavioural responses to a major environmental change: novel, exotic species. We allow thresholds for action to be a function of reserves, and demonstrate how optimal thresholds can be calculated. We term this framework ‘state-dependent detection theory’ (SDDT). We focus on behavioural and fitness outcomes when animals continue to use formerly adaptive thresholds following environmental change. In a simple example, we show that exposure to novel animals whichappear dangerous—but are actually safe—(e.g. ecotourists) can have catastrophic consequences for ‘prey’ (organisms that respond as if the new organisms are predators), significantly increasing mortality even when the novel species is not predatory. SDDT also reveals that the effect on reproduction can be greater than the effect on lifespan. We investigate factors that influence the effect of novel organisms, and address the potential for behavioural adjustments (via evolution or learning) to recover otherwise reduced fitness. Although effects of environmental change are often difficult to predict, we suggest that SDDT provides a useful route ahead.

Predicting behavioural responses to novel organisms: state-dependent detection theory