Some Mathematical Consideration on Two-mode Searching II

Along the lines of a previous paper, making use of an intuitive model, we consider mathematically the relation between the efficiency of searcher's two-mode searching behaviour and the target's patchy distribution, and discuss the strategic adaptability of two-mode searching. In this paper, the model is constructed by a time-discrete stochastic process on S1, that is, on a circle. Also in the present model, if the patch size becomes sufficiently small, a two-mode searching behaviour is strategically adaptable for the searcher. This result obviously indicates thast the target's distribution may be adopted as its evolutionary strategy asgainst the searcher, like a relation between a patchy distribuited prey and its predator.