Optimal investment across different aspects of anti-predator defences

We present a simple model of investment across a suite of different anti-predatory defences. Defences can incur an initial construction cost and and/or may be costly each time they are utilised. Our aim is to use a simple, but general, mathematical model to explore when prey that face a single predatory threat where each attack is of the same nature should invest only in a single defence, and when they should spread their investment across more than one defence. This should help to explain the observed variety of defences that a single prey individual may employ during repeated attacks of a similar nature or even at different stages during one attack. Previous verbal reasoning suggested that prey should specialise in investment in defences that can be utilised early in the predation sequence. Our quantitative model predicts that (depending of the relatively properties of different defences), there may be concentrated investment in early acting, or in late-acting defences, or a spread of investment across both defence types. This variety of predictions is in agreement with the variation in defences shown by natural organisms subjected to repeated predatory attack.