Biodiv Sci ›› 2021, Vol. 29 ›› Issue (3): 409-418.

• Forum •

### Path-dependent speciation in the process of evolution

Minlan Li1,2, Chao Wang1,*(), Ruiwu Wang1,*()

1. 1. School of Ecology and Environment, Northwestern Polytechnical University, Xi’an 710072
2. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072
• Received:2020-07-11 Accepted:2021-01-04 Online:2021-03-20 Published:2021-01-13
• Contact: Chao Wang,Ruiwu Wang
• About author:First author contact:

#Co-first authors

Abstract:

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 respective discontinuities of two or more dimensional variables between populations are all greater than the difference of variables within the population, the individuals with corresponding variables belong to different species.
Conclusions: The path-dependent evolutionary mechanism in this model demonstrated that species can coexist with different probabilities when environmental pressures are limited. A new species, cryptic species, sympatric species may occur in a path-dependent evolution process. This model also showed that species survival in an ecosystem is not determined by its fitness directly, but dependent on the probability of its evolutionary path.