Models are proposed which examine emigration thresholds from resource patches encountered within a given search strategy. With one patch type and no competition during utilization, there is a single optimal investment duration (Iopt) which depends on the gain accumulated during investment in the patch, G(I), and on the mean search cost between patches. Solutions for Iopt depend on the form of G(I); various models are considered which offer diminishing returns with investment. With variation in the value of the patch type encountered, the animal should leave a patch when dG/dI becomes equal to SLmax, the average gain rate for the overall search strategy when the investment in each patch is optimal. For some resources, Iopt may equal 0. Selection should here favor more and more efficient "resource assessment" strategies which ensure the most efficient monitoring of cues correlating with G(I). These are all pure stratengies in relation to particular circumstances. Where there is resource sharing and systems ...