Path-dependent speciation in dynamic fitness landscapes

Species is a fundamental concept in evolutionary biology and biodiversity.However,existing species definitions are often influenced by artificial factors or are challenging in practical application,leading to confusion in species classification.Due to uncertain environmental changes and random genetic drift,the fitness expectations of a population may shift,causing species to evolve to a new evolutionary state based on their current instantaneous fitness within a dynamic fitness landscape.This contrasts with the classic static fitness landscape,where fitness expectations are constant.In a dynamic fitness landscape,speciation may exhibit path dependence,where the evolution of traits follows a probabilistic path,creating feedback that shapes evolutionary trajectories.The path-dependent evolutionary mechanism suggests that species survival within an ecosystem is not directly determined by their fitness but by the probability of their evolutionary pathways.This model also indicates that species can coexist with varying probabilities under limited environmental pressures.Consequently,new species,cryptic species,or sympatric species may emerge via path-dependent evolutionary processes.Within this framework,we developed a mathematical species concept,which may guide future species classification methodologies.

Analyzing the Interdependence Between Some Certain Gene Loci by Epistasis Measures in Fitness Landscapes of Schemata

GA hardness and interdependence between genes in the chromosome are important questions in the study of genetic algorithms(GA). Traditional methods, which are used to measure the interaction between genes, can only reflect the extent of epistasis between all genes in the chromosome. Therefore, the definition of the fitness landscape of schemata is proposed in this paper, and epistasis measures on this landscape of schemata are used to analyze the degree of interdependence between some certain gene loci in study. Some information between these sites can be reflected by some characters of the fitness landscape of schemata which are composed of these fixed sites. The stronger the interaction between these sites, the larger the variation of the fitness of schemata whose fixed sites correspond to those sites in study, and the more rugged the fitness landscape of these schemata. According to the degree of interaction between these given gene loci, building blocks of GA can be analyzed and determined, and further genetic operators and the structure of GA can be designed and adjusted to improve the performance of GA. At last, a lot of experiments including NK models are done, and results of empirical analysis show that this method is effective.

Error Thresholds in Single-Peak Gaussian Distributed Fitness Landscapes

Based on the Eigen and Crow-Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gausslan distributed random variables to incorporate the effects of the fluctuations of the fitness landscapes （noise of environments） and investigate the concentration distribution and error threshold of quasispecies by performing an ensemble average within this theoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for a sizable fluctuation, quite different from the previous deterministic models, our statistical results show that the transition from quasi-species to error catastrophe is not so sharp, indicating that the error threshold is located within a certain range and has a shift toward a larger value. Our results are qualitatively in agreement with the experimental data and provide a new implication for antiviral strategies.

Fitness Landscape Analysis for Optimum Multiuser Detection Problem

Optimum multiuser detection （OMD） for CDMA systems is an NP-complete combinatorial optimization problem. Fitness landscape has been proven to be very useful for understanding the behavior of combinatorial optimization algorithms and can help in predicting their performance. This paper analyzes the statistic properties of the fitness landscape of the OMD problem by performing autocorrelation analysis, fitness distance correlation test and epistasis measure. The analysis results explain why some random search algorithms are effective methods for OMD problem and give hints how to design more efficient randomized search heuristic algorithms for OMD.