Multilevel selection in a gradient

In this study we consider a population subdivided in groups. Each group is connected to two neighboring groups by means of migration channels. The migration channels are used with different probability, according to a gradient that gives a preferential direction of colonization. Within groups we have a fast population dynamics modeled with a Moran process. Between groups we have a process of colonization selection at low migration rate, based on the propagule model. We consider resident and invading individuals, with the invading individuals having a relative fitness r. Groups composed only of invaders will also have a relative group fitness R. We show that, independently of the value of r, a strong gradient reduces the advantage of groups with large fitness and thus works against group selection.