We study the computational power of systems where information is stored in independent strings and each computational step consists of exchanging information between randomly chosen pairs. The input for the system is environment which selects certain strings. To this end we introduce a population genetics model in which the operators of selection and inheritance are effectively computable (in polynomial time on probabilistic Turing machines). We show that such systems are as powerful as the usual models of parallel computations, namely they can simulate polynomial space computations in polynomially many steps. We also show that the model has the same power if the recombination rules for strings are very simple (context sensitive crossing over), which suggests that similar processes might be exploited by real organisms.