Hyperbolic discounting underpins response curves of mammalian avoidance behaviour

As humans clear natural habitat, they are brought into increased conflict with wild animals. Some conflict is direct (e.g. elevated exposure of people to predators), some indirect (e.g. abandoning suitable habitat because of human activity). The magnitude of avoidance is expected to track frequency of human activity, but the type of response is an open question. We postulated that animals do not respond passively to increased disturbance nor does response follow a power law; instead, their ability to estimate magnitude leads to 'discounting' behaviour, as in classic time-to-reward economic models in which individuals discount larger value (or risk) in more distant time. We used a 10-year camera dataset from southern California to characterize response curves of seven mammal species. Bayesian regressions of two non-discounting models (exponential and inverse polynomial) and two discounting models (hyperbolic and harmonic) revealed that the latter better fit response curves. The Arps equation, from petroleum extraction modelling, was used to estimate a discount exponent, a taxon-specific 'sensitivity' to humans, yielding a general model across species. Although discounting can mean mammal activity recovers rapidly after disturbance, increased recreational pressure on reserves limits recovery potential, highlighting a need to strike a balance between animal conservation and human use.