Evolutionary matrix games and optimization theory

An evolutionarily stable strategy (ESS) is only required to be capable of resisting invasion by rare mutant strategies. In contrast, an absolute invader strategy (AIS) is a rare mutant strategy that can invade any established strategy. We show that the predictions of the outcome of evolution made by optimization models are compatible with those made by the classical expected payoff comparisons in matrix games. We also show that if a matrix game has an AIS that AIS is unique and is also an ESS. But an ESS need not be an AIS. In pure-strategy submodels, an AIS need not be unique. An AIS of a matrix game has global asymptotic stability property in the game dynamics which involve only pure strategies including the AIS.     

Global mutations and local mutations have very different effects on evolution, illustrated by mixed strategies of asymmetric binary games

We study the evolutionary effect of rare mutations causing global changes in traits. We consider asymmetric binary games between two players. The first player takes two alternative options with probability x and 1−x; and the second player takes options with probability y and 1−y. Due to natural selection and recurrent mutation, the population evolves to have broad distributions of x and y. We analyze three cases showing qualitatively different dynamics, exemplified by (1) vigilance-intrusion game, (2) asymmetric hawk-dove game and (3) cleaner-client game. We found that the evolutionary outcome is strongly dependent upon the distribution of mutants’ traits, more than the mutation rates. For example in the vigilance-intrusion game, the evolutionary dynamics show a perpetual stable oscillation if mutants are always close to the parent (local-mutation mode), whilst the population converges to a stable equilibrium distribution if mutants can be quite different from the parent (global-mutation mode), even for extremely low mutation rate. When common local mutations and rare global mutations occur simultaneously, the evolutionary outcome is controlled by the latter.     

Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new players are born from parents who played in the past. We consider two-player games with two strategies and a unique mixed evolutionarily stable strategy. We show that in the first type of dynamics, it is asymptotically stable for small time delays and becomes unstable for big ones when the population oscillates around its stationary state. In the second type of dynamics, however, evolutionarily stable strategy is asymptotically stable for any size of a time delay.     

Stability of the replicator equation for a single species with a multi-dimensional continuous trait space

The replicator equation model for the evolution of individual behaviors in a single species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional continuously stable strategy (CSS) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger neighborhood invader strategy (NIS) concept is needed if the supports are arbitrary.     

Evolution of learning capacities and learning levels

Humans strongly depend on individual and social learning, both of which are highly effective and accurate. I study the effects of environmental change on the evolution of the effectiveness and accuracy of individual and social learning (individual and social learning levels) and the number of pieces of information learned individually and socially (individual and social learning capacities) by analyzing a mathematical model. I show that individual learning capacity decreases and social learning capacity increases when the environment becomes more stable; both decrease when the environment becomes milder. I also show that individual learning capacity increases when individual learning level increases or social learning level decreases, while social learning capacity increases when individual or social learning level increases. The evolution of high learning levels can be triggered when the environment becomes severe, but a high social learning level can evolve only when a high individual learning level can simultaneously evolve with it.     

Solubility properties of alkaline phosphatase from matrix vesicles

Alkaline phosphatase has been extracted from matrix vesicles of a calcifying cartilage with 0.15 M KCl, 0.4 M guanidinium chloride and 0.05 M deoxycholate/50% butanol mixture. The catalytic properties of the three extracts have been compared. Although the highest amount of enzyme activity is extracted with the latter reagent (55%), some of it is also extracted with KCl (11%) and guanidinium (7%). By submitting isolated matrix vesicles to a short time sonication the distribution pattern of the alkaline phosphatase activity in the extracts is clearly modified, as the amount extracted with KCl increases from 14 to 50% and the portion extracted with deoxycholate decreases from 55 to 27% of the total enzyme activity of matrix vesicles. The enzymatic preparations were comparable on the basis of specific activities, affinity for the substrates (p-nitrophenylphosphate, ATP), thermostability, sensitivity to inhibitors and activators. By electrofocusing a value of pI = 4.15 was found for the alkaline phosphatase of matrix vesicles independently of the extraction medium. These results contradict the concept that alkaline phosphatase is exclusively an intrinsic membrane protein.     

Payoffs and strategies in territorial contests: ESS analyses of two ecotypes of the spiderAgelenopsis aperta

Summary Game-theoretic analyses were completed on the territorial contest behavior of two populations of a desert spider that exhibit markedly different levels of within-species competition. Numerical payoff matrices were constructed from field data collected on the behavior and demography of each population. Payoffs were expressed in terms of expected future egg production. Three behavior patterns that a spider might exhibit following assessment of its weight relative to that of its opponent and the value of the site were considered: withdraw, display, or escalate. The model predicts for the more harsh grassland habitat an evolutionarily stable strategy (ESS) that makes ownership decisive in settling contests between opponents with small weight differences, whereas it otherwise assigns victory to the heavier opponent. Whereas the empirical data collected for this grassland population closely approximates the predicted ESS, that for a population occupying a more favorable riparian habitat deviates significantly. The ESS prediction for this latter population is that an intruding spider will withdraw from a contest if it is similar in weight to the web-owner. Withdrawal is common in this population, but so are display and threat and these actions were not predicted. We hypothesize that gene flow from surrounding habitats is preventing the riparian population from completely adapting to its local environment.     

The dynamics of the proteome: strategies for measuring protein turnover on a proteome-wide scale.

Quantitative proteomics captures the steady-state amount of a protein in a cell but does not explain how a change in protein amount is manifest -- whether through a change in synthesis or a change in degradation. If we are to understand the changes in the proteome, we will need to define such processes. In this brief review, strategies for the determination of intracellular protein dynamics on a proteome-wide scale are discussed.     

Composition and DNA-binding properties of the nuclear matrix proteins from mammalian cell nuclei

A rapidly sedimenting DNA-protein complex was isolated from nuclear lysates in 2 M NaCl and characterized with regard to its polypeptide composition and the DNA-binding properties of the purified proteins. The complex consists of the nuclear matrix with attached DNA. Electrophoresis in SDS-polyacrylamide gels revealed two major and five minor polypeptide bands, mainly in the 60 to 75 kDa molecular weight region. The DNA-matrix complex dissociated into free DNA and proteins in the presence of 2 M NaCl and 5 M urea. The proteins could be purified by chromatography on hydroxyapatite and showed a strong tendency to reassociate at 0.15 M NaCl concentration in the absence of urea. DNA was bound to the reassociated proteins at 0.15 M NaCl concentration. Part of the DNA-protein complex was stable at 1 M NaCl concentration. The binding appeared to be random with regard to the DNA sequence.     

A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

Synthesis of novel ageladine A analogs showing more potent matrix metalloproteinase (MMP)-12 inhibitory activity than the natural product

By employing a previously established synthetic scheme, the synthesis described in the title was carried out in order to explore the substituent effects in the pyrrole ring of ageladine A on MMP-12 inhibitory activity. It became evident that a halogen atom (Br or Cl) at the 2-position and an additional bromine atom at the 4-position are highly effective for improving the inhibitory activity. These studies led us to discover three novel ageladine A analogs (4a, c, o) showing more potent MMP-12 inhibitory activity than the natural product.     

Inhibition of matrix metalloproteinase-2 by PARP inhibitors

Matrix metalloproteinase-2 (MMP-2), a ubiquitously expressed zinc-dependent endopeptidase, and poly(ADP-ribosyl) polymerase (PARP), a nuclear enzyme regulating DNA repair, are activated by nitroxidative stress associated with various pathologies. As MMP-2 plays a detrimental role in heart injuries resulting from enhanced nitroxidative stress, where PARP and MMP inhibitors are beneficial, we hypothesized that PARP inhibitors may affect MMP-2 activity. Using substrate degradation assays to determine MMP-2 activity we found that four PARP inhibitors (3-AB, PJ-34, 5-AIQ, and EB-47) inhibited 64 kDa MMP-2 in a concentration-dependent manner. The IC₅₀ values of PJ-34 and 5-AIQ were in the high micromolar range and comparable to those of known MMP-2 inhibitors doxycycline, minocycline or o-phenanthroline, whereas those for 3-AB and EB-47 were in the millimolar range. Co-incubation of PARP inhibitors with doxycycline showed an additive inhibition of MMP-2 that was significant for 3-AB alone. These data demonstrate that the protective effects of some PARP inhibitors may include inhibition of MMP-2 activity.     

Landscape dynamics and evolution of colonizer syndromes: interactions between reproductive effortand dispersal in a metapopulation

The evolutionary consequences of changes in landscape dynamics for the evolution of life history syndromes are studied using a metapopulation model. We consider in turn the long-term effects of a change in the local disturbance rate, in the maximal local population persistence, in habitat productivity, and in habitat fragmentation. We examine the consequences of selective interactions between dispersal and reproductive effort by comparing the outcome of joint evolution to a situation where the species has lost the potential to evolve either its reproductive effort or its dispersal rate. We relax the classical assumption that any occupied site in the metapopulation reaches its carrying capacity immediately after recolonization. Our main conclusions are the following: (1) genetic diversity modifies the range of landscape parameters for which the metapopulation is viable, but it alters very little the qualitative evolutionary trends observed for each trait within this range. Although they are both part of a competition/colonization axis, reproductive effort and dispersal are not substitutable traits: their evolution reflects more directly the change in the landscape dynamics, than a selective interaction among them. (2) no general syndrome of covariation between reproductive effort and dispersal can be predicted: the pattern of association between the two traits depends on the type of change in landscape dynamics and on the saturation level. We review empirical evidence on colonizer syndromes and suggest lines for further empirical work. This revised version was published online in July 2006 with corrections to the Cover Date.     

The evolution of conformist transmission in social learning when the environment changes periodically

Conformity is often observed in human social learning. Social learners preferentially imitate the majority or most common behavior in many situations, though the strength of conformity varies with the situation. Why has such a psychological tendency evolved? I investigate this problem by extending a standard model of social learning evolution with infinite environmental states (Feldman, M.W., Aoki, K., Kumm, J., 1996. Individual versus social learning: evolutionary analysis in a fluctuating environment. Anthropol. Sci. 104, 209-231) to include conformity bias. I mainly focus on the relationship between the strength of conformity bias that evolves and environmental stability, which is one of the most important factors in the evolution of social learning. Using the evolutionarily stable strategy (ESS) approach, I show that conformity always evolves when environmental stability and the cost of adopting a wrong behavior are small, though environmental stability and the cost of individual learning both negatively affect the strength of conformity.     

Subcellular fractionation of epiphyseal cartillage isolation of matrix vesicles and profiles of enzymes,phospholipids, calcium and phosphate

Epiphyseal cartilage was fractionated into subcellular components by non-enzymatic methods, and analyzed for activity of marker enzymes, for phospholipids, and for calcium and inorganic phosphate. Alkaline phosphatase, a marker enzyme for matrix vesicles and plasma membranes, was concentrated in the 100 000 × g (microsomal) pellet and, upon subsequent frationalism, in the low-density fractions from the sucrose gradient. Mitochondrial and endoplasmic reticular enzymes were localized primarily in the 20 000 × g pellet, lysosomal enzymes predominantly in the supernate from the microsomal pellet. Two phospholipids characteristic of matrix vesicles, sphingomyelin and phosphatidylserine, were enriched in the low-density sucrose fractions; however, unlike matrix vesicles, there was no depletion in phosphatidylcholine or increase in lysophospholipids. Ca and inorganic P were concentrated in the higher-density fractions, the amounts in the lower-density fractions being some- what lower than those seen in matrix vesicles. The alkaline phosphatase-rich, low-density fractions were thus not identical to matrix vesicles isolated by collagenase digestion, but rather appear to be composed primarily of plasma membranes. Enzyme profiles indicate they were relatively free of mitochondrial, endoplasmic reticular and lysosomal contaminants. The data further indicate that significant modification of the phospholipid, electrolyte, and possibly enzyme content of chondrocyte plasma membranes, must occur during blebbing and matrix vesicle formation.     

The evolution of anisogamy: the adaptive significance of damage, repair and mortality

Classic theory on the evolution of anisogamy focuses on the trade-off between gamete productivity and provisioning and mechanisms associated with post-zygotic survival. In this article, the role of mortality acting on both zygotes and gametes is explored as a factor influencing the evolution of different sized gametes. In particular, variable mortality through differential survival or metabolic damage is shown to affect the persistence of isogamy, the evolution of more than two sexes and the evolution of anisogamy. Evolutionary stable isogamous states are shown to be locally unstable and disruptive selection can induce the evolution of anisogamy. Analysis of both the isogamous and anisogamous ESS points reveals that the persistence of either of these conditions is not always assured. The implications of variable survival on the evolution of anisogamy are discussed.