Adaptive diversity in heterogeneous environments for populations regulatedby a mixture of soft and hard selection

The stable co-existence of two haploid genotypes or two species is studied in a spatially heterogeneous environment submitted to a mixture of soft sel ection (within-patch regulation) and hard selection (outside-patch regulati on) and where two kinds of resource are available. This is analysed both at an ecological time-scale (short term) and at an evolutionary time-scale (l ong term). At an ecological scale, we show that co-existence is very unlike ly if the two competitors are symmetrical specialists exploiting different resources. In this case, the most favourable conditions are met when the tw o resources are equally available, a situation that should favour generalis ts at an evolutionary scale. Alternatively, low within-patch density depend ence (soft selection) enhances the co-existence between two slightly differ ent specialists of the most available resource. This results from the oppos ing forces that are acting in hard and soft regulation modes. In the case o f unbalanced accessibility to the two resources, hard selection favours the most specialized genotype, whereas soft selection strongly favours the les s specialized one. Our results suggest that competition for different resou rces may be difficult to demonstrate in the wild even when it is a key fact or in the maintenance of adaptive diversity. At an evolutionary scale, a mo nomorphic invasive evolutionarily stable strategy (ESS) always exists. When a linear trade-off exists between survival in one habitat versus that in a nother, this ESS lies between an absolute adjustment of survival to niche s ize (for mainly soft-regulated populations) and absolute survival (speciali zation) in a single niche (for mainly hard-regulated populations). This sug gests that environments in agreement with the assumptions of such models sh ould lead to an absence of adaptive variation in the long term.