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1.
Directionality theory: a computational study of an entropic principle in evolutionary processes 总被引:2,自引:0,他引:2
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. 相似文献
2.
Demetrius L 《Proceedings. Biological sciences / The Royal Society》2000,267(1460):2385-2391
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. 相似文献
3.
Stephens DW 《Journal of theoretical biology》2000,206(1):1-16
The science of thermodynamics is concerned with understanding the properties of inanimate matter in so far as they are determined by changes in temperature. The Second Law asserts that in irreversible processes there is a uni-directional increase in thermodynamic entropy, a measure of the degree of uncertainty in the thermal energy state of a randomly chosen particle in the aggregate. The science of evolution is concerned with understanding the properties of populations of living matter in so far as they are regulated by changes in generation time. Directionality theory, a mathematical model of the evolutionary process, establishes that in populations subject to bounded growth constraints, there is a uni-directional increase in evolutionary entropy, a measure of the degree of uncertainty in the age of the immediate ancestor of a randomly chosen newborn. This article reviews the mathematical basis of directionality theory and analyses the relation between directionality theory and statistical thermodynamics. We exploit an analytic relation between temperature, and generation time, to show that the directionality principle for evolutionary entropy is a non-equilibrium extension of the principle of a uni-directional increase of thermodynamic entropy. The analytic relation between these directionality principles is consistent with the hypothesis of the equivalence of fundamental laws as one moves up the hierarchy, from a molecular ensemble where the thermodynamic laws apply, to a population of replicating entities (molecules, cells, higher organisms), where evolutionary principles prevail. 相似文献
4.
Directionality theory: an empirical study of an entropic principle in life-history evolution 总被引:2,自引:0,他引:2
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. 相似文献
5.
Dietz K 《BioEssays : news and reviews in molecular, cellular and developmental biology》2005,27(11):1097-1101
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. 相似文献
6.
L Demetrius 《Proceedings of the Royal Society of London. Series B, Containing papers of a Biological character. Royal Society (Great Britain)》1985,225(1239):147-159
This paper presents a unified account of the properties of the measures, Malthusian parameter and entropy in predicting evolutionary change in populations of macromolecules, cells and individuals. The Malthusian parameter describes the intrinsic rate of increase of the population. The entropy describes the intrinsic variability in populations: it characterizes the variability in mutation and replication rates in populations of macromolecules; the rate of decay of synchrony in populations of cells; and the degree of iteroparity in populations of individuals. The Malthusian parameter determines ultimate population numbers: under constant environmental conditions, it is the rate of increase when equilibrium conditions are attained. Entropy determines population stability: the gain in the Malthusian parameter due to small fluctuations in the life-cycle variables is determined by entropy. These properties, which are valid for populations of macromolecules, cells and individuals, show that the Malthusian parameter and entropy act as complimentary fitness indices in understanding evolutionary change in populations. 相似文献
7.
Fangliang He 《Oikos》2010,119(4):578-582
There is considerable debate about the utility of statistical mechanics in predicting diversity patterns in terms of life history traits. Here, I reflect on this debate and show that a community is controlled by the balance of two opposite forces: the entropic part (the natural tendency of the system to be in the configuration with the highest possible entropy) and environmental, ecological and evolutionary constraints maintaining order (reducing entropy). The Boltzmann distribution law that can be derived from the maximum entropy formalism provides a fundamental model for linking species abundance to life history traits and environmental constraining factors. This model predicts a global pattern of diversity evenness along a latitudinal gradient. Although the Boltzmann distribution and the logistic regression models represent two fundamentally different approaches, the two models have an identical mathematical form. Their identical formalisms facilitate the interpretation of logistic regression models with statistical mechanics, and reveal several limitations of the maximum entropy formalism. I argued that although maximum entropy formalism is a promising tool for modeling species abundances and for linking microscopic quantities of individual life history traits to macroscopic patterns of diversity, it is necessary to revise the Boltzmann distribution law for successful prediction of species abundance. 相似文献
8.
The high rate of HIV-1 evolution contributes to immune escape, enables the virus to escape drug therapy, and may underlie the difficulty of producing an effective vaccine. Identifying constraints on HIV evolution is therefore of prime importance. To investigate this problem, we examined the relationships between sequence diversity, selection, and protein structure. We found that while there was an increase in sequence diversity over time, this variation had a tendency to be limited to specific structural regions. When individual sites were analyzed, there was, in contrast, substantial and widespread evolutionary constraint over gag and env. This constraint was present even in the highly variable envelope proteins. The evolutionary significance of an individual site is indicated by the change in selection pressure along the time course: increasing entropy indicates that the site is evolving predominantly in a more "clock"-like manner, low entropy values with no increase indicate a high degree of constraint, and high entropy values indicate a lack of constraint. Few sites display high degrees of turnover. Mapping these sites onto the three-dimensional protein structure, we found a significant difference between evolutionary rates for regions buried in the core of the protein and those on the surface. This constraint did not change over the time period analyzed and was not subtype dependent, as similar results were found for subtypes B and C. This link between sequence and structure not only demonstrates the limits of recent HIV-1 evolution but also highlights the origins of evolutionary constraint on viral change. 相似文献
9.
The HSSP (Homology-Derived Secondary Structure of Proteins) database provides multiple sequence alignments (MSAs) for proteins of known three-dimensional (3D) structure in the Protein Data Bank (PDB). The database also contains an estimate of the degree of evolutionary conservation at each amino acid position. This estimate, which is based on the relative entropy, correlates with the functional importance of the position; evolutionarily conserved positions (i.e., positions with limited variability and low entropy) are occasionally important to maintain the 3D structure and biological function(s) of the protein. We recently developed the Rate4Site algorithm for scoring amino acid conservation based on their calculated evolutionary rate. This algorithm takes into account the phylogenetic relationships between the homologs and the stochastic nature of the evolutionary process. Here we present the ConSurf-HSSP database of Rate4Site estimates of the evolutionary rates of the amino acid positions, calculated using HSSP's MSAs. The database provides precalculated evolutionary rates for nearly all of the PDB. These rates are projected, using a color code, onto the protein structure, and can be viewed online using the ConSurf server interface. To exemplify the database, we analyzed in detail the conservation pattern obtained for pyruvate kinase and compared the results with those observed using the relative entropy scores of the HSSP database. It is reassuring to know that the main functional region of the enzyme is detectable using both conservation scores. Interestingly, the ConSurf-HSSP calculations mapped additional functionally important regions, which are moderately conserved and were overlooked by the original HSSP estimate. The ConSurf-HSSP database is available online (http://consurf-hssp.tau.ac.il). 相似文献
10.
An application of the entropic theory of perception to evolutionary systems indicates that environmental entropy increases will exert pressures on an organism to adapt. We speculate that the instability caused by such environmental changes will also cause an increase in the mutation rate of organisms leading to an eventual increase in their complexity. Such complexity generation allows organisms to adapt to the more entropic environment. Although we conclude that increases in environmental entropy cause an organism to evolve into a more complex organism, increases in entropy may not be necessary for complexity generationper se. 相似文献
11.
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. 相似文献
12.
J. T. Trevors 《Antonie van Leeuwenhoek》2010,97(4):313-318
Biological generalizations about bacteriology are discussed to provide a broad perspective of what we know about bacteria.
Bacteriology (and possibly all biology) from an overall perspective can be researched and understood as observations and experimentations
on mass and energy, which are themselves the products of evolutionary change for about 3.5–3.9 billion years. All organisms
have mass, transform, store and use biochemical energy and obey the most fundamental of all laws-the laws of thermodynamics.
Bacteria can be viewed as semi-permeable, thermodynamically open systems of mass, controlled by relatively small amounts of
genetic instructions with lower entropy than their higher entropy, surrounding environments. Some fundamental properties describing
bacterial life are also presented. 相似文献
13.
Sabater B 《Bio Systems》2006,83(1):10-17
The physiology at limiting and stress conditions challenges the current view that the overall reaction of metabolic processes is always far from equilibrium and, therefore, that organisms are not committed to lower their rates of entropy production. Plausibly, critical steps of natural selection takes place at limiting conditions, near equilibrium, in the linear range response of entropy production, and consequently the trend to lower the rate of entropy production could be the fitness arrow of biological evolution. The evolutionary relevance of the Prigogine theorem is discussed in connection with the ergodic hypothesis of Boltzmann. The emergence of metabolic strategies to economise carbon/energy resources, of resource-waste systems like active transport and the irreversible increase in the complexity of organisms during evolution may be consequences of a more general trend of metabolic systems to lower the rates of entropy production. 相似文献
14.
15.
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.
16.
Markov models of evolution describe changes in the probability distribution of the trait values a population might exhibit. In consequence, they also describe how entropy and conditional entropy values evolve, and how the mutual information that characterizes the relation between an earlier and a later moment in a lineage’s history depends on how much time separates them. These models therefore provide an interesting perspective on questions that usually are considered in the foundations of physics—when and why does entropy increase and at what rates do changes in entropy take place? They also throw light on an important epistemological question: are there limits on what your observations of the present can tell you about the evolutionary past? 相似文献
17.
This article is concerned with the characterization and existence of evolutionarily stable strategies (ESS) in Games against Nature, a class of models described by finite size populations and absolute fitness measures. We address these problems in terms of a new formalism which revolves around the concept evolutionary entropy, a measure of the diversity of options associated with a strategy pure - strategies have zero entropy, mixed strategies positive entropy. We invoke this formalism to show that ESS are characterized by extremal states of entropy. We illustrate this characterization of ESS by an analysis of the evolution of the sex ratio and the evolution of seed size. 相似文献
18.
The entropy, which is central to the second law of thermodynamics, determines that the thermal energy always flows spontaneously from regions of higher temperature to regions of lower temperature. In the protein–solvent thermodynamic system, the entropy is defined as a measure of how evenly the thermal energy would distribute over the entire system (Liu et al., 2012). Such tendency to distribute energy as evenly as possible will reduce the state of order of the initial system, and hence, the entropy can be regarded as an expression of the disorder, or randomness of the system (Yang et al., 2012). For a protein–solvent system under a constant solvent condition, the origin of entropy is the thermal energy stored in atoms, which makes atoms jostle around and bump onto one another, thus leading to vibrations of the covalent bonds connecting two atoms (occurring on the fs timescale) and the rotational and translational motions of amino acid side chain groups (occurring on ps timescale) and water molecules. These motions break the noncovalent bonds around structural regions that are weakly constrained thereby triggering the competitive interactions among residues or between residues and water molecules leading ultimately to the loop motions (occurring on ns timescale) around the protein surface. The loop motions can further transmit either through the water network around the protein surface or via specific structural components (such as the hinge-bending regions) over the entire protein molecule leading to large concerted motions (occurring on μs to s timescales) that are most relevant to protein functions (Amadei, Linssen & Berendsen, 1993; Tao, Rao & Liu, 2010). Thus, the multiple hierarchies of the protein dynamics on distinct timescales (Henzler-Wildman & Kern, 2007) are a consequence of the cascade amplification of the microscopic motions of atoms and groups for which the entropy originating from atomic thermal energy is most fundamental. In the case of protein–ligand binding, the importance of the entropy is embodied in the following aspects. (i) The release of the water molecule kinetic energy (which is a process of the solvent entropy maximization) will cause Brownian motions of individual water molecules which result in strong Brownian bombardments to solute molecules causing molecule wanders/diffusions and subsequent accident contacts/collisions between proteins and ligands. (ii) Such collisions will inevitably cause water molecule displacement and, if the contact interfaces are properly complementary, the requirement to increase the solvent entropy would further displace the water network around the binding interfaces thus leading to the formation the initial protein-ligand complex. (iii) In the initial complex, the loose association of the two partners provide the opportunity for protein to increase conformational entropy, thus triggering the conformational adjustments through competitive interaction between protein residues and ligand, leading ultimately to the formation of tightly associated complex (Liu et al., 2012). In the protein folding process, the first stage, i.e. the rapid hydrophobic collapse (Agashe, Shastry & Udgaonkar, 1995; Dill, 1985), is in fact driven by the effect of the solvent entropy maximization. Specifically, the requirement to maintain as many as possible the dynamic hydrogen bonds among the water molecules will squeeze/sequestrate the hydrophobic amino acid side chains into the interior of the folding intermediates and expose the polar/charged side chains onto the intermediate surface. This will minimize the solvent accessible surface area of the folding intermediates and as thus maximize the entropy of the solvent. The resulting molten globule states (Ohgushi & Wada, 1983) may contain a few secondary structural components and native tertiary contacts, while many native contacts, or close residue–residue interactions present in the native state have not yet formed. However, the nature to increase the protein conformational entropy can trigger a further conformational adjustment process, i.e. the conformational entropy increase breaks the transient secondary or tertiary contacts and triggers the competitive interactions among protein residues and between residues and water. This process may repeat many rounds until the negative enthalpy change resulting from the noncovalent formations can overcompensate for protein conformational entropy loss. In summary, we consider that the tendency to maximize the entropy of the protein–solvent system, which originates from the atomic thermal energy, is the most fundamental driving factor for protein folding, binding, and dynamics, whereas the enthalpy reduction, an opposing factor that tends to make the system become ordered, can compensate for the effect of entropy loss to ultimately allow the system to reach equilibrium at the free energy minima, either global or local. 相似文献
19.
Abstract: Directed evolution of life through millions of years, such as increasing adult body size, is one of the most intriguing patterns displayed by fossil lineages. Processes and causes of such evolutionary trends are still poorly understood. Ammonoids (externally shelled marine cephalopods) are well known to have experienced repetitive morphological evolutionary trends of their adult size, shell geometry and ornamentation. This study analyses the evolutionary trends of the family Acrochordiceratidae Arthaber, 1911 from the Early to Middle Triassic (251–228 Ma). Exceptionally large and bed‐rock‐controlled collections of this ammonoid family were obtained from strata of Anisian age (Middle Triassic) in north‐west Nevada and north‐east British Columbia. They enable quantitative and statistical analyses of its morphological evolutionary trends. This study demonstrates that the monophyletic clade Acrochordiceratidae underwent the classical evolute to involute evolutionary trend (i.e. increasing coiling of the shell), an increase in its shell adult size (conch diameter) and an increase in the indentation of its shell suture shape. These evolutionary trends are statistically robust and seem more or less gradual. Furthermore, they are nonrandom with the sustained shift in the mean, the minimum and the maximum of studied shell characters. These results can be classically interpreted as being constrained by the persistence and common selection pressure on this mostly anagenetic lineage characterized by relatively moderate evolutionary rates. Increasing involution of ammonites is traditionally interpreted by increasing adaptation mostly in terms of improved hydrodynamics. However, this trend in ammonoid geometry can also be explained as a case of Cope’s rule (increasing adult body size) instead of functional explanation of coiling, because both shell diameter and shell involution are two possible paths for ammonoids to accommodate size increase. 相似文献
20.
Darwinian fitness and the intensity of natural selection: studies in sensitivity analysis 总被引:1,自引:0,他引:1
Darwinian fitness, the capacity of a variant type to establish itself in competition with the resident population, is determined by evolutionary entropy, a measure of the uncertainty in age of the mother of a randomly chosen newborn. This article shows that the intensity of natural selection, as measured by the sensitivity of entropy with respect to changes in the age-specific fecundity and mortality variables, is a convex function of age, decreasing at early and increasing at later ages. We exploit this result to provide quantitative evolutionary explanations of the large variation in survivorship curves observed in natural populations. Previous studies to explain variation in survivorship curves have been based on the proposition that Darwinian fitness is determined by the Malthusian parameter. Hence the intensity of natural selection will be determined by the sensitivity of the Malthusian parameter with respect to changes in the age-specific fecundity and mortality variables. This measure of the selection gradient is known to be a decreasing function of age, with implications which are inconsistent with empirical observations of survivorship curves in human and animal populations. The analysis described in this paper point to the mitigated import of sensitivity studies based on the Malthusian parameter. Our analysis provides theoretical and empirical support for the ecological and evolutionary significance of sensitivity analysis based on entropy, which is the appropriate measure of Darwinian fitness. 相似文献