Complexity and demographic stability in population models

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 to be far reaching generalizations of the tenets derived from classical studies of stability in an evolutionary context. These results thus provide a new conceptual framework for explaining patterns of variation in population numbers observed in natural populations.     

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.     

Directionality theory: an empirical study of an entropic principle in life-history evolution

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 when population size is large, and random variations in these attributes when population size is small. This paper assesses the validity of these predictions by employing a demographic dataset of 66 species of perennial plants. This empirical analysis is consistent with directionality theory and provides support for its significance as an explanatory and predictive model of life-history evolution.     

Directionality theory and the evolution of body size

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 response to the ecological constraints a population experiences, with trends in entropy as the population evolves under mutation and natural selection. (i) Stationary size or fluctuations 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 significance 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.     

Thermodynamic view on decision-making process: emotions as a potential power vector of realization of the choice

This research is devoted to possible mechanisms of decision-making in frames of thermodynamic principles. It is also shown that the decision-making system in reply to emotion includes vector component which seems to be often a necessary condition to transfer system from one state to another. The phases of decision-making system can be described as supposed to be nonequilibrium and irreversible to which thermodynamics laws are applied. The mathematical model of a decision choice, proceeding from principles of the nonlinear dynamics considering instability of movement and bifurcation is offered. The thermodynamic component of decision-making process on the basis of vector transfer of energy induced by emotion at the given time is surveyed. It is proposed a three-modular model of decision making based on principles of thermodynamics. Here it is suggested that at entropy impact due to effect of emotion, on the closed system—the human brain,—initially arises chaos, then after fluctuations of possible alternatives which were going on—reactions of brain zones in reply to external influence, an order is forming and there is choice of alternatives, according to primary entrance conditions and a state of the closed system. Entropy calculation of a choice expectation of negative and positive emotion shows judgment possibility of existence of “the law of emotion conservation” in accordance with several experimental data.     

A critique of directionality theory

Directionality theory suggests that demographic entropy, defined in a way analogous to thermodynamic entropy, is as important as the Malthusian parameter in determining life history evolution in an age-structured population. In particular, it suggests that entropy should increase in equilibrium species and decrease in opportunistic species. This theory has been applied to explain the evolution of body size and of senescence. It has been claimed recently that this theory has been validated by a simulation study, but it is argued here that this study reveals substantial flaws in directionality theory and that the Malthusian parameter rather than entropy is the appropriate tool in the study of life history evolution.     

Mortality plateaus and directionality theory

Recent large scale studies of senescence in animals and humans have revealed mortality rates that levelled off at advanced ages. These empirical findings are now known to be inconsistent with evolutionary theories of senescence based on the Malthusian parameter as a measure of fitness. 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 fitness. 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 fitness.     

Computational methods in synthetic biology

We discuss how a theoretical synthetic biology research programme may liberate empiricism in biological sciences beyond the unaided human brain. Because synthetic biological systems are relatively small and largely independent of evolutionary contexts, they can be represented with mathematical models strongly founded on first principles of molecular biology and laws of statistical thermodynamics. A universal mathematical formalism for describing synthetic constructs may then be plausibly used to explain in unambiguous, quantitative terms how biological phenotypic complexity emerges as a result of well-defined biomolecular interactions. SynBioSS, a publicly available software package, is described that implements this mathematical formalism.     

Darwinian fitness

The term Darwinian fitness refers to the capacity of a variant type to invade and displace the resident population in competition for available resources. Classical models of this dynamical process claim that competitive outcome is a deterministic event which is regulated by the population growth rate, called the Malthusian parameter. Recent analytic studies of the dynamics of competition in terms of diffusion processes show that growth rate predicts invasion success only in populations of infinite size. In populations of finite size, competitive outcome is a stochastic process--contingent on resource constraints--which is determined by the rate at which a population returns to its steady state condition after a random perturbation in the individual birth and death rates. This return rate, a measure of robustness or population stability, is analytically characterized by the demographic parameter, evolutionary entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn. This article appeals to computational and numerical methods to contrast the predictive power of the Malthusian and the entropic principles. The computational analysis rejects the Malthusian model and is consistent with of the entropic principle. These studies thus provide support for the general claim that entropy is the appropriate measure of Darwinian fitness and constitutes an evolutionary parameter with broad predictive and explanatory powers.     

Darwinian fitness, evolutionary entropy and directionality theory

Two recent articles provide computational and empirical validation of the following analytical fact: the outcome of competition between an invading genotype and that of a resident population is determined by the rate at which the population returns to its original size after a random perturbation. This phenomenon can be quantitatively described in terms of the demographic parameter termed "evolutionary entropy", a measure of the variability in the age at which individuals produce offspring and die. The two articles also validate certain predictions of directionality theory, an evolutionary model that integrates demography and ecology with population genetics. In particular, directionality theory predicts that in populations that spend the greater part of their life cycle in the stationary growth phase, evolution will result in an increase in entropy. These species will be described by a late age of sexual maturity, small progeny sets and a broad reproductive time-span. In populations that undergo large fluctuations in size, however, the evolutionary outcome will be different. When the average size is large, evolution will result in a decrease in entropy-these populations will be described by early age of sexual maturity, large numbers of offspring and narrow reproductive span but when the average size is small, the evolutionary outcome will be random and non-directional.     

A thermodynamic perspective on food webs: quantifying entropy production within detrital-based ecosystems

Because ecosystems fit so nicely the framework of a "dissipative system", a better integration of thermodynamic and ecological perspectives could benefit the quantitative analysis of ecosystems. One obstacle is that traditional food web models are solely based upon the principles of mass and energy conservation, while the theory of non-equilibrium thermodynamics principally focuses on the concept of entropy. To properly cast classical food web models within a thermodynamic framework, one requires a proper quantification of the entropy production that accompanies resource processing of the food web. Here we present such a procedure, which emphasizes a rigorous definition of thermodynamic concepts (e.g. thermodynamic gradient, disequilibrium distance, entropy production, physical environment) and their correct translation into ecological terms. Our analysis provides a generic way to assess the thermodynamic operation of a food web: all information on resource processing is condensed into a single resource processing constant. By varying this constant, one can investigate the range of possible food web behavior within a given fixed physical environment. To illustrate the concepts and methods, we apply our analysis to a very simple example ecosystem: the detrital-based food web of marine sediments. We examine whether entropy production maximization has any ecological relevance in terms of food web functioning.     

Directionality theory: a computational study of an entropic principle in evolutionary processes

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 evolutionary process.     

Single molecule thermodynamics in biological motors

Biological molecular machines use thermal activation energy to carry out various functions. The process of thermal activation has the stochastic nature of output events that can be described according to the laws of thermodynamics. Recently developed single molecule detection techniques have allowed each distinct enzymatic event of single biological machines to be characterized providing clues to the underlying thermodynamics. In this study, the thermodynamic properties in the stepping movement of a biological molecular motor have been examined. A single molecule detection technique was used to measure the stepping movements at various loads and temperatures and a range of thermodynamic parameters associated with the production of each forward and backward step including free energy, enthalpy, entropy and characteristic distance were obtained. The results show that an asymmetry in entropy is a primary factor that controls the direction in which the motor will step. The investigation on single molecule thermodynamics has the potential to reveal dynamic properties underlying the mechanisms of how biological molecular machines work.     

Thermodynamic stability of ecosystems

The stability of ecosystems during periods of stasis in their macro-evolutionary trajectory is studied from a non-equilibrium thermodynamic perspective. Individuals of the species are considered as units of entropy production and entropy exchange in an open thermodynamic system. Within the framework of the classical theory of irreversible thermodynamics, and under the condition of constant external constraints, such a system will naturally evolve toward a globally stable thermodynamic stationary state. It is thus suggested that the ecological steady state, or stasis, is a particular case of the thermodynamic stationary state, and that the evolution of community stability through natural selection is a manifestation of non-equilibrium thermodynamic directives. Furthermore, it is argued that punctuation of stasis leading to ecosystem succession, may be a manifestation of non-equilibrium "phase transitions" brought on by a change of external constraints through a thermodynamic critical point.     

Order without design

Experimental reality in molecular and cell biology, as revealed by advanced research technologies and methods, is manifestly inconsistent with the design perspective on the cell, thus creating an apparent paradox: where do order and reproducibility in living systems come from if not from design?I suggest that the very idea of biological design (whether evolutionary or intelligent) is a misconception rooted in the time-honored and thus understandably precious error of interpreting living systems/organizations in terms of classical mechanics and equilibrium thermodynamics. This error, introduced by the founders and perpetuated due to institutionalization of science, is responsible for the majority of inconsistencies, contradictions, and absurdities plaguing modern sciences, including one of the most startling paradoxes - although almost everyone agrees that any living organization is an open nonequilibrium system of continuous energy/matter flow, almost everyone interprets and models living systems/organizations in terms of classical mechanics, equilibrium thermodynamics, and engineering, i.e., in terms and concepts that are fundamentally incompatible with the physics of life.The reinterpretation of biomolecules, cells, organisms, ecosystems, and societies in terms of open nonequilibrium organizations of energy/matter flow suggests that, in the domain of life, order and reproducibility do not come from design. Instead, they are natural and inevitable outcomes of self-organizing activities of evolutionary successful, and thus persistent, organizations co-evolving on multiple spatiotemporal scales as biomolecules, cells, organisms, ecosystems, and societies. The process of self-organization on all scales is driven by economic competition, obeys empirical laws of nonequilibrium thermodynamics, and is facilitated and, thus, accelerated by memories of living experience persisting in the form of evolutionary successful living organizations and their constituents.     

The Critical Roles of Information and Nonequilibrium Thermodynamics in Evolution of Living Systems

Living cells are spatially bounded, low entropy systems that, although far from thermodynamic equilibrium, have persisted for billions of years. Schrödinger, Prigogine, and others explored the physical principles of living systems primarily in terms of the thermodynamics of order, energy, and entropy. This provided valuable insights, but not a comprehensive model. We propose the first principles of living systems must include: (1) Information dynamics, which permits conversion of energy to order through synthesis of specific and reproducible, structurally-ordered components; and (2) Nonequilibrium thermodynamics, which generate Darwinian forces that optimize the system. Living systems are fundamentally unstable because they exist far from thermodynamic equilibrium, but this apparently precarious state allows critical response that includes: (1) Feedback so that loss of order due to environmental perturbations generate information that initiates a corresponding response to restore baseline state. (2) Death due to a return to thermodynamic equilibrium to rapidly eliminate systems that cannot maintain order in local conditions. (3) Mitosis that rewards very successful systems, even when they attain order that is too high to be sustainable by environmental energy, by dividing so that each daughter cell has a much smaller energy requirement. Thus, nonequilibrium thermodynamics are ultimately responsible for Darwinian forces that optimize system dynamics, conferring robustness sufficient to allow continuous existence of living systems over billions of years.     

The generation of complexity in evolution: a thermodynamic and information-theoretical discussion.

It is argued that the evolutionary tendency toward complexity derives from the Second Law of thermodynamics and the set of physicochemical constraints provided by the biosphere. Complexity-generating processes provide the means by which thermodynamic information resulting from solar energy influxes can be dissipated. In particular, reductions in energetic information promote the growth of molecular size, and reductions in configurational information promote aperiodicity in molecular sequences. Natural selection converts the sequence entropy generated in these processes into molecular information.     

Popper, falsifiability, and evolutionary biology

First, a brief history is provided of Popper's views on the status of evolutionary biology as a science. The views of some prominent biologists are then canvassed on the matter of falsifiability and its relation to evolutionary biology. Following that, I argue that Popper's programme of falsifiability does indeed exclude evolutionary biology from within the circumference of genuine science, that Popper's programme is fundamentally incoherent, and that the correction of this incoherence results in a greatly expanded and much more realistic concept of what is empirical, resulting in the inclusion of evolutionary biology. Finally, this expanded concept of empirical is applied to two particular problems in evolutionary biology — viz., the species problem and the debate over the theory of punctuated equilibria — and it is argued that both of them are still mainly metaphysical.