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Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

Banach algebras --- Genetic algebras --- Nonassociative algebras --- Markov processes --- Phytophthora infestans --- Stochastic processes --- Algebra --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Genetics --- Banach algebras. --- Genetic algebras. --- Nonassociative algebras. --- Markov processes. --- Stochastic processes. --- Algebra. --- Genetics. --- Random processes --- Botrytis fallax --- Botrytis infestanus --- Botrytis solani --- Peronospora fintelmannii --- Peronospora infestans --- Peronospora trifurcata --- Phytophthora thalictri --- Potato late blight agent --- Potato late blight fungus --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Algebras, Non-associative --- Algebras, Nonassociative --- Non-associative algebras --- Algebras, Genetic --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Mathematics. --- Nonassociative rings. --- Rings (Algebra). --- Probabilities. --- Biomathematics. --- General Algebraic Systems. --- Non-associative Rings and Algebras. --- Probability Theory and Stochastic Processes. --- Mathematical and Computational Biology. --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Biology --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Math --- Science --- Probabilities --- Phytophthora --- Algebra, Abstract --- Algebras, Linear --- Biomathematics --- Banach spaces --- Topological algebras --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions