On the interplay of speciation and dispersal: An evolutionary food web model in space

We introduce an evolutionary metacommunity of multitrophic food webs on several habitats coupled by migration. In contrast to previous studies that focus either on evolutionary or on spatial aspects, we include both and investigate the interplay between them. Locally, the species emerge, interact and go extinct according to the rules of the well-known evolutionary food web model proposed by Loeuille and Loreau in 2005. Additionally, species are able to migrate between the habitats. With random migration, we are able to reproduce common trends in diversity-dispersal relationships: Regional diversity decreases with increasing migration rates, whereas local diversity can increase in case of a low level of dispersal. Moreover, we find that the total biomasses in the different patches become similar even when species composition remains different. With adaptive migration, we observe species compositions that differ considerably between patches and contain species that are descendant from ancestors on both patches. This result indicates that the combination of spatial aspects and evolutionary processes affects the structure of food webs in different ways than each of them alone.Comment: under review at JT

Boolean versus continuous dynamics in modules with two feedback loops

We investigate the dynamical behavior of simple networks, namely loops with an additional internal regulating connection. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method and within a single framework, we study different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations or stable fixed points. These conditions depend only on general features such as the degree of cooperativity of the regulating interactions and the logical structure of the interactions. There are no simple rules for deciding when Boolean and continuous dynamics agree with each other, but we identify several relevant criteria