The effect of costly information in diet choice

We distinguish three cases which consider the effect of information on animal behaviour: static information, obligate information and facultative information. Static information deals with the case in which the animal does not acquire additional information; it starts with enough information to discriminate options. Obligate information deals with the case in which the animal acquires information at no additional cost. Facultative information is when the animal may choose to pay a cost in order to acquire information. We illustrate the differences among these three situations by analysing the optimal diet problem subject to the different information regimes. Compared to the case with static information, obligate recognition time narrows the range of prey densities over which an optimal forager feeds selectively, and facultative recognition time reduces it further still. The three models yield qualitatively different predictions regarding how the optimal diet varies with relative abundances of alternative resources. In the space of resource densities, the line separating the optimal behaviours of selectivity and opportunism is straight for both the perfect and obligate information cases. In the case of facultative recognition time this line or isoleg is part of a quadratic curve. This non-linearity yields two completely new predictions: a less profitable resource may be lost from the diet after becoming more abundant and the poor resource may be included in the diet as a result of the rich resource becoming more common.