Abstract
Darwinian fitness describes the capacity of an organism to appropriate resources from the environment and to convert these resources into net-offspring production. Studies of competition between related types indicate that fitness is analytically described by entropy, a statistical measure which is positively correlated with population stability, and describes the number of accessible pathways of energy flow between the individuals in the population. Directionality theory is a mathematical model of the evolutionary process based on the concept evolutionary entropy as the measure of fitness. The theory predicts that the changes which occur as a population evolves from one non-equilibrium steady state to another are described by the following directionality principle–fundamental theorem of evolution: (a) an increase in evolutionary entropy when resource composition is diverse, and resource abundance constant; (b) a decrease in evolutionary entropy when resource composition is singular, and resource abundance variable. Evolutionary entropy characterizes the dynamics of energy flow between the individual elements in various classes of biological networks: (a) where the units are individuals parameterized by age, and their age-specific fecundity and mortality; where the units are metabolites, and the transitions are the biochemical reactions that convert substrates to products; (c) where the units are social groups, and the forces are the cooperative and competitive interactions between the individual groups. % This article reviews the analytical basis of the evolutionary entropic principle, and describes applications of directionality theory to the study of evolutionary dynamics in two biological systems; (i) social networks–the evolution of cooperation; (ii) metabolic networks–the evolution of body size. Statistical thermodynamics is a mathematical model of macroscopic behavior in inanimate matter based on entropy, a statistical measure which describes the number of ways the molecules that compose the a material aggregate can be arranged to attain the same total energy. This theory predicts an increase in thermodynamic entropy as the system evolves towards its equilibrium state. We will delineate the relation between directionality theory and statistical thermodynamics, and review the claim that the entropic principle for thermodynamic systems is the limit, as the resource production rate tends to zero, and population size tends to infinity, of the entropic principle for evolutionary systems.
Highlights
One of the remarkable features of the organic world is the large diversity of plants and animals that exist and the high degree of adaptation of these organisms to their natural environment
The question which emerges from this observation is: Can this directional change in the morphology and physiology of organisms be explained in terms of a dynamic model which takes into account the fact that biopopulations are composed of genetically unique individuals?
We will appeal to the depiction of thermodynamic and evolutionary entropy given by Equations (91) and (92) to show that the thermodynamic principle is the limit, as the resource production rate tends to zero and the population size tends to infinity, of the evolutionary entropic principle
Summary
One of the remarkable features of the organic world is the large diversity of plants and animals that exist and the high degree of adaptation of these organisms to their natural environment. This new class of models showed that the outcome of competition between related types is determined by the rate at which the population appropriates the exiguous resources This rate can be analytically described by the statistical parameter, evolutionary entropy. Competitive outcome, when limited resource constraint prevails, is decided by the rate at which an individual acquires energy from the environment and converts this energy into demographic currency This rate is precisely the macroscopic parameter, evolutionary entropy. These three modes of selection and the relations between them will be described in Sections 1.1 to 1.4 These sections provide a conceptual overview of the main tenets of directionality theory: We furnish a historical account of earlier efforts, due to Lotka and Fisher, to develop an analytic model of evolutionary dynamics within the framework of the statistical thermodynamics of Boltzmann.
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