Interactions between species and environments from incomplete information.

There are two contradictory aspects of the adaptive process in evolution. The first is that species must optimally increase their own fitness in a given environment. The second is that species must maintain their variation to be ready to respond to changing environments. In a strict sense, these two aspects might consider to be mutually exclusive. If species are optimally adapted, then the variation in the species that is suboptimal decreases and vice versa. To resolve this dilemma, species must find a balance between optimal adaptation and robust adaptation. Finding the balance between these processes requires both the local and global complete, static information. However, the balance between the processes must be dynamic. In this study, we propose a model that illustrates dynamic negotiation between the global and local information using lattice theory. The dynamic negotiation between these two levels results in an overestimate of fitness for each species. The overestimation of fitness in our model represents the multiplicity of fitness which is sometimes discussed as the exaptation. We show that species in our model demonstrate the power law of the lifespan distribution and 1/f fluctuation for the adaptive process. Our model allows for a balance between optimal adaptation and robust adaptation without any arbitrary parameters.