Evolution of cooperation in a multidimensional phenotype space

Extinction scenarios in evolutionary processes: A Multinomial Wright-Fisher approach

“…We believe that with a proper adjustment, the result also holds for a variation of the model with N depending on time [65,68,88] (this is, for instance, well known for branching processes with immigration). This theorem can also be extended to the paintbox models [20] and to a class of Cannings models in phenotypic spaces with weak and fast decaying dependency between phenotypes [98].…”

“…We believe that Theorem 4.6 can be extended to a broad class of stochastic population models with mean-field vector-field Γ promoting cooperation between the particles (cells/microorganisms in applications). Among specific biological mechanisms promoting forms of cooperation are: public goods [3,38,40,99,107,147], relative nonlinearity of competition [4,36,69], population-level randomness [40,41,98], and diversification of cells into distinct ecological niches [66,126]. Public goods models are of a special interest for us because of a possibility of an application to to the study of a gene-microbial-metabolite ecological network in the human gut [34].…”

“…4. An interesting instance of the Wright-Fisher model with an replicator update rule was introduced in [98]. This is a mathematical model for cooperation in a phenotypic space, and is endowed with a reach additional structure representing phenotypic traits of the cells in addition to the usual division into two main categories/types, namely cooperators and defectors.…”

“…This is a mathematical model for cooperation in a phenotypic space, and is endowed with a reach additional structure representing phenotypic traits of the cells in addition to the usual division into two main categories/types, namely cooperators and defectors. In the exact model considered in [98], the phenotypic space is modelled as a Euclidean space Z d . However, a variation with finite population (for instance, restricting the phenotypic space to a cube in Z d ) can be studied in a similar manner.…”

Strong Migration Limit for Games in Structured Populations: Applications to Dominance Hierarchy and Set Structure

“…This means that the payoffs depend only on the strategies used by the interacting individuals (Hamilton [17,18], Trivers [19], Frank [20], Nowak and Sigmund [21,22], Nowak [23], Traulsen and Nowak [24], Kroumi and Lessard [25]). Even in this case, interactions can form a complex system as in the set-structured population introduced in Tarnita et al [26]: every individual of the population belongs to exactly K sets among M sets, and a cooperator cooperates only with individuals that belong to at least L of the K sets, and defects otherwise.…”