Papers by Lloyd Demetrius
Proceedings of the Royal Society B: Biological Sciences, 2005
Understanding the relationship between ecological constraints and life-history properties constit... more Understanding the relationship between ecological constraints and life-history properties constitutes a central problem in evolutionary ecology. Directionality theory, a model of the evolutionary process based on demographic entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn, provides an analytical framework for addressing this problem. The theory predicts that in populations that spend the greater part of their evolutionary history in the stationary growth phase (equilibrium species), entropy will increase. Equilibrium species will be characterized by high iteroparity and strong demographic stability. In populations that spend the greater part of their evolutionary history in the exponential growth phase (opportunistic species), entropy will decrease when population size is large, and will undergo random variation when population size is small. Opportunistic species will be characterized by weak iteroparity and weak demographic stability whe...
arXiv (Cornell University), Apr 28, 2023
Self-organization is the autonomous assembly of a network of interacting components into a stable... more Self-organization is the autonomous assembly of a network of interacting components into a stable, organized pattern. This article shows that the process of selfassembly can be encoded in terms of evolutionary entropy, a statistical measure of the cooperativity of the interacting components. Evolutionary entropy describes the rate at which a network of metabolic components transduce an external energy source into mechanical energy and work. We invoke Directionality Theory, an analytic model of the collective behavior of a network of interacting components, to show that the spontaneous emergence of organization can be depicted as the outcome of a fluctuation-selection process, and articulated in terms of the following tenet. The Entropic Principle of Self-Organization: The equilibrium states of a self-assembly process are states which maximize evolutionary entropy, contingent on the production rate of the external energy source. The Entropic Principle of Self-Organization is a universal rule, which pertains to the self-assembly of processes in various disciplines: Physics-phase transitions; Chemistry-molecular assembly; Biology-protein folding and morphogenesis; Sociology-the emergence of institutions. The principle also elucidates the origin of cellular life;-the transition from inorganic matter to the emergence of protocells, capable of replication and metabolism.
Proceedings of The Royal Society B: Biological Sciences, Feb 21, 2006
Bulmer's critique of directionality theory (Bulmer 2006) can be distilled in terms of two claims.... more Bulmer's critique of directionality theory (Bulmer 2006) can be distilled in terms of two claims. (i) The characterization of equilibrium and opportunistic species in terms of bounded and unbounded growth constraints has little justification as an ecologically meaningful definition. (ii) The Malthusian parameter is the primary variable in the study of life-history evolution-natural selection maximizes the Malthusian parameter and drags the entropy along with it. This article contests and refutes these claims. Specifically, we provide an analytical argument and give empirical evidence to justify the characterization of equilibrium and opportunistic species in terms of certain bounds on the population growth rate. We also show that the standard model of life-history evolution, based on the Malthusian parameter as the measure of Darwinian fitness, is a limiting case (as population size tends to infinity) of directionality theory. Accordingly, it represents an approximation-whose validity increases with population size-of directionality theory. We therefore reaffirm the significance of directionality theory as an evolutionary model of life-history variation and claim that entropy rather than the Malthusian parameter is the appropriate measure of Darwinian fitness, and hence the fundamental concept in the study of life-history evolution.
EMBO Reports, Jul 1, 2005
arXiv (Cornell University), May 20, 2020
The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodyn... more The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy -a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the flow of energy in macroscopic bodies is described by the Second Law of Thermodynamics: In isolated systems, that is systems closed to the input of energy and matter, thermodynamic entropy increases. The dynamics of the lower level interactions in populations of replicating organisms is encoded by the parameter Evolutionary entropy, a statistical measure which describes the number and diversity of metabolic cycles in a population of replicating organisms. Directionality in the transformation of energy in populations of organisms is described by the Fundamental Theorem of Evolution: In systems open to the input of energy and matter, Evolutionary entropy increases, when the energy source is scarce and diverse, and decreases when the energy source is abundant and singular. This article shows that when ρ → 0, and N → ∞, where ρ is the production rate of the external energy source, and N denote the number of replicating units, evolutionary entropy, an organized state of energy; and thermodynamic entropy, a randomized state of energy, coincide. Accordingly, the Fundamental Theorem of Evolution, is a generalization of the Second Law of Thermodynamics.
Genetics, 1975
This paper studies the properties of a new class of demographic parameters for age-structured pop... more This paper studies the properties of a new class of demographic parameters for age-structured populations and analyzes the effect of natural selection on these parameters. Two new demographic variables are introduced: the entropy of a population and the reproductive potential. The entropy of a population measures the variability of the contribution of the different age classes to the stationary population. The reproductive potential measures the mean of the contribution of the different age classes to the Malthusian parameter. The Malthusian parameter is precisely the difference between the entropy and the reproductive potential. The effect of these demographic variables on changes in gene frequency is discussed. The concept of entropy of a genotype is introduced and it is shown that in a random mating population in Hardy-Weinberg equilibrium and under slow selection, the rate of change of entropy is equal to the genetic variance in entropy minus the covariance in entropy and reprod...
Journal of The Royal Society Interface, 2014
The amyloid cascade model for the origin of sporadic forms of Alzheimer's disease (AD) posits... more The amyloid cascade model for the origin of sporadic forms of Alzheimer's disease (AD) posits that the imbalance in the production and clearance of beta-amyloid is a necessary condition for the disease. A competing theory called the entropic selection hypothesis asserts that the primary cause of sporadic AD is age-induced mitochondrial dysregulation and the following cascade of events: (i) metabolic reprogramming—the upregulation of oxidative phosphorylation in compensation for insufficient energy production in neurons, (ii) natural selection—competition between intact and reprogrammed neurons for energy substrates and (iii) propagation—the spread of the disease due to the selective advantage of neurons with upregulated metabolism. Experimental studies to evaluate the predictions of the amyloid cascade model are being continually retuned to accommodate conflicts of the predictions with empirical data. Clinical trials of treatments for AD based on anti-amyloid therapy have been u...
Entropy, 2014
Darwinian fitness describes the capacity of an organism to appropriate resources from the environ... more 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.
The American Naturalist, 2015
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, a... more JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
Theoretical population biology, 2004
This article is concerned with relating the stability of a population, as defined by the rate of ... more This article is concerned with relating the stability of a population, as defined by the rate of decay of fluctuations induced by demographic stochasticity, with its heterogeneity in age-specific birth and death rates. We invoke the theory of large deviations to establish a fluctuation theorem: The demographic stability of a population is positively correlated with evolutionary entropy, a measure of the variability in the age of reproducing individuals in the population. This theorem is exploited to predict certain correlations between ecological constraints and evolutionary trends in demographic stability, namely, (i) bounded growth constraints--a uni-directional increase in stability, (ii) unbounded growth constraints (large population size)--a uni-directional decrease in stability, (iii) unbounded growth constraints (small population size)--random, non-directional change in stability. These principles relating ecological constraints with trends in demographic stability are shown ...
Frontiers in physiology, 2014
Epidemiological and biochemical studies show that the sporadic forms of Alzheimer's disease (... more Epidemiological and biochemical studies show that the sporadic forms of Alzheimer's disease (AD) are characterized by the following hallmarks: (a) An exponential increase with age; (b) Selective neuronal vulnerability; (c) Inverse cancer comorbidity. The present article appeals to these hallmarks to evaluate and contrast two competing models of AD: the amyloid hypothesis (a neuron-centric mechanism) and the Inverse Warburg hypothesis (a neuron-astrocytic mechanism). We show that these three hallmarks of AD conflict with the amyloid hypothesis, but are consistent with the Inverse Warburg hypothesis, a bioenergetic model which postulates that AD is the result of a cascade of three events-mitochondrial dysregulation, metabolic reprogramming (the Inverse Warburg effect), and natural selection. We also provide an explanation for the failures of the clinical trials based on amyloid immunization, and we propose a new class of therapeutic strategies consistent with the neuroenergetic se...
Theoretical Population Biology, 2013
Competition between individuals for resources which are limited and diverse in composition is the... more Competition between individuals for resources which are limited and diverse in composition is the ultimate driving force of evolution. Classical studies of this event contend that the outcome is a deterministic process predicted by the growth rate of the competing types-a tenet called the Malthusian selection principle. Recent studies of competition indicate that the dynamics of selection is a stochastic process, regulated by the population size, the abundance and diversity of the resource, and predicted by evolutionary entropy-a statistical parameter which characterizes the rate at which the population returns to the steady state condition after a random endogenous or exogenous perturbation. This tenet, which we will call the entropic selection principle entails the following relations: (a) When resources are constant, limited and diverse, variants with higher entropy will have a selective advantage and increase in frequency. (b) When resources undergo large variations in abundance and are singular, variants with lower entropy will have a selective advantage and increase in frequency. This article delineates the analytic, computational and empirical support for this tenet. We show moreover that the Malthusian selection principle, a cornerstone of classical evolutionary genetics, is the limit, as population size and resource abundance tends to infinity of the entropic selection principle. The Malthusian tenet is an approximation to the entropic selection principle-an approximation whose validity increases with increasing population size and increasing resource abundance. Evolutionary entropy is a generic concept that characterizes the interaction dynamics of metabolic entities at several levels of biological organization: cellular, organismic and ecological. Accordingly, the entropic selection principle represents a general rule for explaining the processes of adaptation and evolution at each of these levels.
Proceedings of the Royal Society B: Biological Sciences, 2001
Recent large scale studies of senescence in animals and humans have revealed mortality rates that... more Recent large scale studies of senescence in animals and humans have revealed mortality rates that levelled o¡ at advanced ages. These empirical ¢ndings are now known to be inconsistent with evolutionary theories of senescence based on the Malthusian parameter as a measure of ¢tness. This article analyses the incidence of mortality plateaus in terms of directionality theory, a new class of models based on evolutionary entropy as a measure of ¢tness. We show that the intensity of selection, in the context of directionality theory, is a convex function of age, and we invoke this property to predict that in populations evolving under bounded growth constraints, evolutionarily stable mortality patterns will be described by rates which abate with age at extreme ages. The explanatory power of directionality theory, in contrast with the limitations of the Malthusian model, accords with the claim that evolutionary entropy, rather than the Malthusian parameter, constitutes the operationally valid measure of Darwinian ¢tness.
Proceedings of the Royal Society of London. Series B: Biological Sciences, 2000
Directionality theory, a dynamic theory of evolution that integrates population genetics with dem... more Directionality theory, a dynamic theory of evolution that integrates population genetics with demography, is based on the concept of evolutionary entropy, a measure of the variability in the age of reproducing individuals in a population. The main tenets of the theory are three principles relating the resp onse to the ecological constraints a population experiences, with trends in entropy as the population evolves under mutation and natural selection. (i) Stationary size or £uctuations around a stationary size (bounded growth): a unidirectional increase in entropy; (ii) prolonged episodes of exponential growth (unbounded growth), large population size: a unidirectional decrease in entropy; and (iii) prolonged episodes of exponential growth (unbounded growth), small population size: random, non-directional change in entropy. We invoke these principles, together with an allometric relationship between entropy, and the morphometric variable body size, to provide evolutionary explanations of three empirical patterns pertaining to trends in body size, namely (i) Cope's rule, the tendency towards size increase within phyletic lineages; (ii) the island rule, which pertains to changes in body size that occur as species migrate from mainland populations to colonize island habitats; and (iii) Bergmann's rule, the tendency towards size increase with increasing latitude. The observation that these ecotypic patterns can be explained in terms of the directionality principles for entropy underscores the signi¢cance of evolutionary entropy as a unifying concept in forging a link between micro-evolution, the dynamics of gene frequency change, and macro-evolution, dynamic changes in morphometric variables.
Proceedings of the Royal Society B: Biological Sciences, 2005
Analytical studies of evolutionary processes based on the demographic parameter entropy—a measure... more Analytical studies of evolutionary processes based on the demographic parameter entropy—a measure of the uncertainty in the age of the mother of a randomly chosen newborn—show that evolutionary changes in entropy are contingent on environmental constraints and can be characterized in terms of three tenets: (i) a unidirectional increase in entropy for populations subject to bounded growth constraints; (ii) a unidirectional decrease in entropy for large populations subject to unbounded growth constraints; (iii) random, non-directional change in entropy for small populations subject to unbounded growth constraints. This article aims to assess the robustness of these analytical tenets by computer simulation. The results of the computational study are shown to be consistent with the analytical predictions. Computational analysis, together with complementary empirical studies of evolutionary changes in entropy underscore the universality of the entropic principle as a model of the evoluti...
Proceedings of the National Academy of Sciences, 1997
Directionality in populations of replicating organisms can be parametrized in terms of a statisti... more Directionality in populations of replicating organisms can be parametrized in terms of a statistical concept: evolutionary entropy. This parameter, a measure of the variability in the age of reproducing individuals in a population, is isometric with the macroscopic variable body size. Evolutionary trends in entropy due to mutation and natural selection fall into patterns modulated by ecological and demographic constraints, which are delineated as follows: ( i ) density-dependent conditions (a unidirectional increase in evolutionary entropy), and ( ii ) density-independent conditions, ( a ) slow exponential growth (an increase in entropy); ( b ) rapid exponential growth, low degree of iteroparity (a decrease in entropy); and ( c ) rapid exponential growth, high degree of iteroparity (random, nondirectional change in entropy). Directionality in aggregates of inanimate matter can be parametrized in terms of the statistical concept, thermodynamic entropy, a measure of disorder. Directio...
Proceedings of the National Academy of Sciences, 1977
The concepts of entropy and reproductive potential of a genotype were introduced in a previous pa... more The concepts of entropy and reproductive potential of a genotype were introduced in a previous paper [Demetrius, L. (1974) Proc. Natl. Acad. Sci. USA 71, 4645-4647] and an analoge of the fundamental theorem of natural selection was derived. This paper relates to entropy of a population with the rate of convergence of the population to the stable age distribution. I show that (i) at maximal entropy, no oscillatory components exist and the birth sequence is unaffected by perturbations in the stable age distribution; and (ii) at zero entropy, oscillatory components occur and increase as rapidly as the real exponential component in the birth sequence. These results have implications towards (i) the relation between population fitness and adaptedness, (ii) modes of selection and the evolution of reproductive strategies, and (iii) the evolution of senescence.
PLoS ONE, 2010
Background: Standard epidemiological theory claims that in structured populations competition bet... more Background: Standard epidemiological theory claims that in structured populations competition between multiple pathogen strains is a deterministic process which is mediated by the basic reproduction number (R 0) of the individual strains. A new theory based on analysis, simulation and empirical study challenges this predictor of success.
Physica A: Statistical Mechanics and its Applications, 2005
This article introduces the concept of network entropy as a characteristic measure of network top... more This article introduces the concept of network entropy as a characteristic measure of network topology. We provide computational and analytical support for the hypothesis that network entropy is a quantitative measure of robustness. We formulate an evolutionary model based on entropy as a selective criterion and show that (a) it predicts the direction of changes in network structure over evolutionary time and (b) it accounts for the high degree of robustness and the heterogenous connectivity distribution, which is often observed in biological and technological networks. Our model is based on Darwinian principles of evolution and preferentially selects networks according to a global fitness criterion, rather than local preferences in classical models of network growth. We predict that the evolutionarily stable states of evolved networks will be characterized by extremal values of network entropy.
Uploads
Papers by Lloyd Demetrius