Human hunting mortality threshold rules for extinction in mammals (and fish)

Question: Are there general life-history rules for exploitation-caused extinction of mammal populations? Mathematical methods: A population of size N faced with the added mortality of human exploitation will deterministically go extinct if its per-capita birth rate can no longer match its per-capita mortality rate as N approaches zero. We develop exploitation-extinction theory for a mammal life history using R0 < 1 as N goes to zero, and combine the criterion with several facts about mammal life histories. Conclusions: Extinction results if the ratio of the instantaneous mortality rate caused by hunting (F) divided by the adult instantaneous mortality rate (M, for the unexploited population) exceeds a critical value (F/M > C). The C value is determined mostly by the level of recruitment compensation as N declines, and C is likely very similar for different sized mammals. We use existing mammal life-history data to estimate C (∼0.5). We then estimate the threshold of instantaneous mortality rate, F, as a function of adult body mass, W; it’s a −0.25 power allometry. Finally, we extend the model to fish. C is expected to vary a lot between fish species, mostly because fish are expected to have much larger recruitment compensation than mammals, the recruitment may correlate with body size, and immature fish are often not exploited. We show how to combine these to predict C.