Dynamics of coexistence of asexual and sexual reproduction in adaptive landscape

Background: The dynamics for species, especially rare species, with mixed type reproduction is instructive and meaningful for predicting the extinction of them. Though the extinction time is still a difficult problem for sexual or asexual populations. Adaptive landscape introduced by Wright, a powerful concept in systems biology can describe the evolution of organisms. To our knowledge, the dynamical of inhomogenous reproductive organisms have not investigated by a simple model globally. Methods: We describe how a Wright-Fisher process maps to the dynamics of a population with mixed type. We analytically construct adaptive landscape from the general diffusion equation. It shows that the construction is dynamical and the adaptive landscape is independent of the existence and normalization of the stationary distribution. Results: We first give a global model describing the evolution of an inhomogenous reproductive population by adaptive landscape. We visualize the dynamical behavior by adaptive landscape. Finite and infinite potential occur in the process. These results suggest a possible way to investigate the complex reproductive process in an inhomogeneous reproductive population.