Animal Behavior as a Strategy Optimizer: Evolution of Resource Assessment Strategies and Optimal Emigration Thresholds

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Abstract
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 strategies in relation to particular circumstances. Where there is resource sharing and systems are ideal free, there is generally no pure strategy which is likely to be evolutionarily stable, and the result will generally be mixed strategies for emigration threshold. For patches offering decreasing returns with investment, the ESS is generally for all individuals to stay until a certain threshold (I1crit). Individuals should then begin to depart at a rate which ensures that the value of staying equal that of leaving. For instance, where nmax competitors all arrive together and resource input gradually decreases, the stable mixed strategy has departure rates ordered so that (1/n) (dG/dI) remains constant as SLmax/nmax until the last individual leaves (Incrit). This emigration range (I1crit-Incrit) and the departure rate can be defined for several situations; there is strong evidence that such strategies exist in natural populations. These models are, however, deterministic; individuals depart as discrete events. This circumstance, especially when the group size is low, can cause certain imbalances which may rely on further mixed strategies (for willingness to leave at a certain group size) for their stability/ This effect may have a general application to the problem of emigration from shared resources.

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