Modeling Evolution Of Heterogeneous Populations
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Modeling Evolution of Heterogeneous Populations
Modeling Evolution of Heterogeneous Populations: Theory and Applications describes, develops and provides applications of a method that allows incorporating population heterogeneity into systems of ordinary and discrete differential equations without significantly increasing system dimensionality. The method additionally allows making use of results of bifurcation analysis performed on simplified homogeneous systems, thereby building on the existing body of tools and knowledge and expanding applicability and predictive power of many mathematical models. - Introduces Hidden Keystone Variable (HKV) method, which allows modeling evolution of heterogenous populations, while reducing multi-dimensional selection systems to low-dimensional systems of differential equations - Demonstrates that replicator dynamics is governed by the principle of maximal relative entropy that can be derived from the dynamics of selection systems instead of being postulated - Discusses mechanisms behind models of both Darwinian and non-Darwinian selection - Provides examples of applications to various fields, including cancer growth, global demography, population extinction, tragedy of the commons and resource sustainability, among others - Helps inform differences in underlying mechanisms of population growth from experimental observations, taking one from experiment to theory and back
Probabilistic Models of Population Evolution
This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications. Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, stochastic partial differential equations, and probabilistic models in evolutionary biology and population genetics. He obtained his PhD in 1975 at University of Paris-Sud.
Genome Chaos
Genome Chaos: Rethinking Genetics, Evolution, and Molecular Medicine transports readers from Mendelian Genetics to 4D-genomics, building a case for genes and genomes as distinct biological entities, and positing that the genome, rather than individual genes, defines system inheritance and represents a clear unit of selection for macro-evolution. In authoring this thought-provoking text, Dr. Heng invigorates fresh discussions in genome theory and helps readers reevaluate their current understanding of human genetics, evolution, and new pathways for advancing molecular and precision medicine. - Bridges basic research and clinical application and provides a foundation for re-examining the results of large-scale omics studies and advancing molecular medicine - Gathers the most pressing questions in genomic and cytogenomic research - Offers alternative explanations to timely puzzles in the field - Contains eight evidence-based chapters that discuss 4d-genomics, genes and genomes as distinct biological entities, genome chaos and macro-cellular evolution, evolutionary cytogenetics and cancer, chromosomal coding and fuzzy inheritance, and more