Potential Functions and Molecular Evolution

Abstract

Selection and molecular evolution are often considered as processes on potential surfaces which are characterized as “fitness landscapes”. Two classes of potentials are particularly useful: “selection potential” for the selection process within a given population and “value landscapes” for evolutionary adaption. Among the various types of selection dynamics we distinguish rare and frequent mutation scenarios as well as different mechanisms for replication. The selection potential for independently replicating entities is a linear function of their concentrations. Evolutionary optimization leads to “corner equilibria” which represent pure states in the rare mutation scenario, or “quasispecies” if mutations occur frequently. The existence of a selection potential is a direct proof for the absence of complicated dynamics and dissipative structures. Dynamical systems for which no potential functions can be found are interesting in their turn because they may lead to oscillations and chaotic dynamics. Value landscapes provide direct insight into the course of evolutionary optimization. They are, however, very hard to determine even for the most simple examples which deal with “test-tube evolution”. We can discuss here only the results of a computer model which is thought to be representative also for real systems.