We proposed an aggregation model of two species aggregates of fitness and population to study the inter-action between the two species in their exchange-driven processes of the same species by introducing the monomer birthof fitness catalyzed by the population,where the fitness aggregates perform self-death process and the population aggre-gates perform self-birth process.The kinetic behaviors of the aggregate size distributions of the fitness and populationwere analyzed by the rate equation approach with their exchange rate kernel K_1(k,j) = K_1kj and K_2(k,j) = K_2kj,the fitness aggregate's self-death rate kernel J_1(k) = J_1k,population aggregate's self-birth rate kernel J_2(k) =J_2k andpopulation-catalyzed fitness birth rate kernel I(k,j) = Ikj^v.The kinetic behavior of the fitness was found dependingcrucially on the parameter v,which reflects the dependence of the population-catalyzed fitness birth rate on the size ofthe catalyst (population) aggregate.(i) In the v≤0 case,the effect of catalyzed-birth of fitness is rather weak and theexchange-driven aggregation and self-death of the fitness dominate the process,and the fitness aggregate size distributionα_k(t) does not have scale form.(ii) When v>0,the effect of the population-catalyzed birth of fitness gets strong enough,and the catalyzed-birth and self-death of the fitness aggregates,together with the self-birth of the population aggregatesdominate the evolution process of the fitness aggregates.The aggregate size distribution α_k (t) approaches a generalizedscaling form.
展开▼
