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.