Path probability selection in nature and path integral.

Understanding of any biological evolutions, such as speciation, adaptation behavior and biodiversity pattern, is based on a fundamental concept of fitness, in which natural selection implies the improvement and progress of fitness in either direct/indirect benefit or genetic transmission to the next generation. However, this basic idea of biological evolution, which is mathematically described by Price equation or its relations, has not fully considered feedback effects from the environment or other generations. They lost the global dynamics of the evolutions consequently. Drawing on the idea of modern physics, we introduce the path integral by iterating the Price equation step by step to characterize the evolutionary path in which the stationary fitness is replaced by the path probability. The evolutionary selection therefore will depend on path probability instead of fitness advantage. In such a framework of the evolutionary path, the intermediate process of evolution is not always pointing to the fitness-maximizing equilibrium and multiple evolutionary paths could thus coexist without fitness advantage discrimination. This mechanism could potentially explain fitness evolutionary strategies with the diversified fitness (e.g., coexistence of altruism and selfishness) and thus species diversity.