Fitness-based mobility enhances the maintenance of biodiversity in the spatial system of cyclic competition

In ecosystems, species are willing to stay longer when they are in good environments and, in this regard, explaining biodiversity and understanding the relative effect of species’ behavior is a fundamental issue in ecological sciences. Staying or moving stands for the movement of the population, and mobility has been accepted as one of the important mechanisms in systems of cyclic competition. In this paper, we investigate the biodiversity in the system of cyclic competition when an individual’s mobility is affected by environmental fitness. We found that fitness-based mobility, which is defined by the ratio of the difference between predator and prey among species, can lead to the slow behavior of species when local fitness is higher than the average fitness and enhance the biodiversity of species. The fitness-based mobility behavior is successful in reducing the extinction probability on the lattice network. However, when the average degree of the network increases, the extinction probability increases significantly. In addition, when we consider the same model on heterogeneous networks, the extinction probability is always 1 regardless of the sensitivity to the fitness. The finding indicates that the heterogeneous network destroys species coexistence. Through extensive numerical investigations, we provided solid evidence supporting the great importance of fitness-based mobility in maintaining biodiversity. We further highlighted the significant relationship among fitness, the fraction of empty sites, and the tunable parameter by investigating the correlation that the relationship is not influenced by mobility.