Search for a command to run...
Aim: Almost all the research in biology relies on a species concept as the basis for biodiversity. However, all of the existing species definitions are imprinted with artificial factors or difficult to observe in practical applications, which brings negative impacts on the species classification. Here, we introduce an "evolutionary path" using a path integral to provide a rule for species classification. We aim to show the speciation process and define the species concept with a mathematical form. Methods: In this species definition, we assumed that uncertain environmental changes and random drift in the population might simultaneously lead to a change in the fitness expectation. Therefore, a constant fitness expectation for any biological characteristic might not be reliable when considering how characteristics vary through time and space. We introduce the concept of "evolutionary path" which is formed by repeating a short-time transfer process. In this process, a species evolves to different states at different probabilities over time based on the instantaneous fitness landscape at any current moment. In this framework, evolution moves in the direction of increased fitness on the varying fitness landscape, and speciation will be of path dependence on the varying fitness landscape. Different individuals with the same or different biological characteristics (e.g. phenotype, genotype, etc.) will interact with another one at random, similar to the process of gambling among them. In a simulation, under the framework of evolutionary game theory, species differentiation will be similar to the evolution of the peaks on a mountain. Every peak after differentiation may represent a species, a cryptic species, or a sympatric species. The picture of species peaks within a mountain is determined by the relationship between the distance and the width of two adjacent peaks and by the dimensionality that characteristics differentiation satisfied. Results: We found a more practicable concept to define species, i.e, based on statistical analysis applicable for multiple types of traits like genetics, morphological characteristics, or ecological process between two populations. Once the 410 Biodiversity Science 2021, 29 (3): 409-418 https://www.biodiversity-science.net