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Directionality Theory and the Entropic Principle of Natural Selection

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Entropy 2014, 16, 5428-5522; doi:10.3390/e16105428 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Directionality Theory and the Entropic Principle of Natural Selection Lloyd A. Demetrius 1,2,* and Volker Matthias Gundlach 3 1 Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA 2 Max-Planck-Institute for Molecular Genetics, Berlin 14195, Germany 3 Fachbereich MNI, THM University of Applied Science, Wiesenstr. 14, Gießen 35390, Germany; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +1-617-495-1954; Fax: +1-617-495-2419. Received: 30 January 2013; in revised form: 13 August 2014 / Accepted: 15 September 2014 / Published: 20 October 2014 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 evolutionary 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–the 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) demographic, where the units are individuals parameterized by age, and their age-specific fecundity and mortality; (b) metabolic, where the units are metabolites, and the transitions are the biochemical reactions that convert substrates to products; (c) social, where the units are social groups, and the forces are the cooperative and competitive interactions between the individual groups. Entropy 2014, 16 5429 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 thermodynamic 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. Keywords: Malthusian parameter; evolutionary entropy; Gibbs-Boltzmann entropy; metabolic rate; origin of life 1. Introduction 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 morphological, physiological and behavioral features that characterize this adaptation are not immutable states. These features evolve: They undergo directional and adaptive change as one population type replaces another over evolutionary time. 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? Darwin’s answer to this problem was articulated in the Origin of Species [1]. The model of adaptation and evolution he proposed is based on three tenets, [2]: 1. (Variation) Individuals in a population differ in terms of their morphology, behavior and physiology. 2. (Heredity) There exists a positive correlation between the physiology and behavior of ancestors and their descendants. 3. (Selection) The resources necessary for life vary in terms of their abundance and diversity. Individuals with different characteristics vary in their ability to acquire and convert these resources into net-offspring production. These tenets entail that changes in the composition of populations are a consequence of variation in heritable differences, and selection acting on this variation. Evolutionary change is however limited by the existing modification. Continued evolution over the long term requires mutation, the constant generation of new heritable alternative forms. The concatenation of these two processes–mutation and Entropy 2014, 16 5430 natural selection will result, as Darwin argued, in changes within populations (microevolution), and concomitantly, in changes between populations (macroevolution). Microevolution and macroevolution thus involve different mechanisms, and unfold over different time scales. Microevolution pertains to changes in the composition of populations due to mutation and natural selection. This process occurs on a time scale of generations, and is the mechanism which underpins the diversity of populations, adaptive changes and geographic variation. Macroevolution refers to changes in the composition of lineages due to speciation and extinction. This process unfolds on a geological time scale and is the mechanism which underlies directional trends in morphological and morphometric properties of species over large episodes of geological time. A central element in Darwin’s argument is that all macroevolutionary processes have their origin in evolutionary change within populations, and hence are the result of natural selection acting on genotypic and phenotypic variation. This proposition, which has now been supported by comparative molecular studies of genotypic variation within and between species, indicates that evolutionary processes on both a ecological and geological time scales can be analyzed in terms of processes which occur at the individual level, Mayr [3,4]. The relation between the dynamics which drive microevolution and the patterns observed at the macroevolutionary level was clearly recognized by the pioneers in theoretical genetics, Fisher, Haldane and Wright. These authors recognized that the Darwinian dynamic involves two complementary events: 1. a cooperative process–the interaction within the organism of related alleles and the transmission of these allelic types to the offspring, 2. a competitive process–the interaction within the population of related phenotypes and the selection of a phenotypic trait according to its capacity to appropriate resources and invest these resources into offspring production. The efforts of these pioneers to develop a mathematical model of Darwin’s theory focused initially on forging a synthesis of Mendel’s laws of particulate inheritance–the basic premise of the cooperative event–with various hypotheses regarding the dynamics of the competitive process. The problem which the analysis of competition generated can be formulated in the following terms: what class of demographic parameters characterize Darwinian fitness, that is the capacity of a type to appropriate resources and invest these resources into offspring production? The appropriation of resources and its reinvestment into offspring production can be factored into two actions, [5]. (a) A resource-metabolic process: The acquisition of resources from the external environment and its conversion into reproduction and survivorship. (b) A metabolic-demographic process: The transformation of the metabolic energy of the organism into demographic currency. When the metabolic-demographic process is the dominant event, then the outcome of competition will be determined by the rate at which the organism transforms the abundant resources into net-offspring production. However, when the resource-metabolic process is the limiting factor, then the outcome of competition will be determined by the rate at which the organism acquires the exiguous resources and converts these resources into demographic currency. Entropy 2014, 16 5431 Classical studies of the evolutionary process, Fisher [6], implicitly assumed that the resource abundance is large, effectively infinite. This entails that the metabolic-demographic process was the determining agent of natural selection. This perspective was the basis for the proposition that Darwinian fitness is characterized by the rate at which the population transforms the metabolic energy into net-offspring production, a quantity now called the Malthusian parameter, in honor of Thomas Malthus’ contribution to population dynamics [7]. Malthusian selection, the term we will use to describe the process of selection which involves the population growth rate, or one its surrogates, the net-reproductive rate, as the measure of Darwinian fitness, rapidly emerged as the dominant paradigm in evolutionary studies. The Malthusian
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