A different model to explain delayed germination

Goal: To provide an alternative to the usual bet-hedging explanation for delayed germination, one that takes account of known facts about germination in stable, fine-grained environments. Context: Small patches with local environmental conditions (microhabitats) such that seedlings can establish themselves are customarily called safe sites. Key Assumptions: We focus on a single species. Its safe sites become available randomly. Seeds that germinate outside safe sites all die as seedlings. All seeds are equal, i.e. their probability of dying over the year and probabilities to germinate when the right season is there do not depend on their age or any other aspect of their individual history. Moreover, we make the standard assumption of ESS theory that the population is genetically homogeneous but for the occasional mutant 'testing the ESS'. There is a trade-off between the germination probability in safe sites and the probability not to germinate outside safe sites. For germination strategies close to the ESS, the environment does not fluctuate. Procedure: Start with a simple population model, in which the yearly seed survival and the fraction of the area covered by safe sites are fixed quantities. For this model, derive an optimization principle that finds the Evolutionarily Steady Strategy vector consisting of the probabilities to germinate in safe sites and elsewhere. Using this optimization principle, analyse the effect of various trade-offs using Levins' fitness set technique. Analyse how the results extend to ESSs for general life histories and community dynamics subject only to the key assumptions. Conclusion: Seeds in safe sites should not all germinate on the first opportunity if the relationship between the probability to germinate in safe sites and the probability to germinate elsewhere is accelerating and has a sufficiently steep slope at the highest germination probabilities.