Dynamics of Species Diversity in Cyclic Competition by Environmental Factors and Methods for Prediction

Abstract

This thesis investigates how internal and external environmental factors influence species diversity and explores methods for its prediction, using the rock-paper-scissors game model, a non-hierarchical model. First, we examine how mutation rates and the competitive strengths of normal and mutant species affect their ecology. The mutation rate has a significant impact on the ecology of normal species. Specifically, an increase in mutation rate poses a greater challenge for normal species to survive, and similarly, the competitive strength of mutant species also adversely affects the ecology of normal species. This thesis reveals the correlation between mutation rate and interspecific competition rate from mutant to normal by identifying the “critical mutation rate”, which is a crucial threshold determining the survival or extinction of normal species. Furthermore, it examines the ecology of mutant species with respect to these two parameters and investigates whether parameter values exist that allow all six species to coexist. Second, we investigate how migration between two different environments affects the coexistence of the three species. When moving between two lattices with different mobilities, even if one lattice has a mobility greater than the critical mobility in an environment where survival is difficult, all three species coexist if the other lattice has a mobility less than the critical mobility. Furthermore, when migrating between two lattices with different densities, if the lattice is sufficiently dense compared to the other lattice, all species survive even in environments where the mobility is greater than the critical mobility. In other words, the movement between the two environments is shown to have a positive effect on survival. In this case, the resulting pattern is a plane wave, which differs from the spiral wave pattern. Lastly, since the existing RMF model is computationally time-consuming, we propose a method to predict dynamics efficiently while reducing computation time by utilizing CNN and Transformer models based on lattice information. While the DNN models’ accuracy is not optimal at the critical mobility level, where significant changes in extinction probability occur, they can still be leveraged statistically to predict critical mobility and extinction probability in a dramatically reduced time. These models demonstrate enhanced effectiveness with increasing lattice size. Furthermore, by estimating mobility using the number of actions over time, the probability of extinction can also be predicted. We examine the significance and limitations of these topics and explore future directions.