Physiological ecology meets the ideal-free distribution: Predicting the distribution of size-structured fish populations across temperature gradients

We describe a habitat selection model that predicts the distribution of siz e-structured groups of fish in a habitat where food availability and water temperature vary spatially. This model is formed by combining a physiologic al model of fish growth with the logic of ideal free distribution (IFD) the ory. In this model we assume that individuals scramble compete for resource s, that relative competitive abilities of fish vary with body size, and tha t individuals select patches that maximize their growth rate. This model ov ercomes limitations in currently existing physiological and IFD-based model s of habitat selection. This is because existing physiological models do no t take into account the fact that the amount of food consumed by a fish in a patch will depend on the number of competitors there (something that IFD theory addresses), while traditional IFD models do not take into account th e fact that fish are likely to choose patches based on potential growth rat e rather than gross food intake (something that physiological models addres s). Our model takes advantage of the complementary strengths of these two a pproaches to overcome these weaknesses. Reassuringly, our model reproduces the predictions of its two constituent models under the simple conditions w here they apply. When there is no competition for resources it mimics the p hysiological model of habitat selection, and when there is competition but no temperature variation between patches it mimics either the simple IFD mo del or the IFD model for unequal competitors. However, when there are both competition and temperature differences between patches our model makes dif ferent predictions. It predicts that input-matching between the resource re newal rate and the number of fish (or competitive units) in a patch, the ha llmark of IFD models, will be the exception rather than the rule. It also m akes the novel prediction that temperature based size-segregation will be c ommon, and that the strength and direction of this segregation will depend on per capita resource renewal rates and the manner in which competitive we ight scales with body size. Size-segregation should become more pronounced as per capita resource abundance falls. A larger fish/cooler water pattern is predicted when competitive ability increases more slowly than maximum ra tion with body size, and a smaller fish/cooler water pattern is predicted w hen competitive ability increases more rapidly than maximum ration with bod y size.