Mutation-selection equilibrium in games with mixed strategies

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n×n payoff matrix. Players can use mixed strategies, which are given by the vector (p₁,…,p_n). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S_n. We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.     

The good, the bad and the discriminator--errors in direct and indirect reciprocity

This paper presents, in a series of simple diagrams, concise results about the replicator dynamics of direct and indirect reciprocity. We consider repeated interactions between donors and recipients, and analyse the relationship between three basic strategies for the donor: unconditional cooperation, all-out defection, and conditional cooperation. In other words, we investigate the competition of discriminating and indiscriminating altruists with defectors. Discriminators and defectors form a bistable community, and hence a population of discriminators cannot be invaded by defectors. But unconditional altruists can invade a discriminating population and 'soften it up' for a subsequent invasion by defectors. The resulting dynamics exhibits various forms of rock-paper-scissors cycles and depends in subtle ways on noise, in the form of errors in implementation. The probability for another round (in the case of direct reciprocity), and information about the co-player (in the case of indirect reciprocity), add further elements to the ecology of reciprocation.     

Cooperation enhanced by the ‘survival of the fittest’ rule in prisoner's dilemma games on complex networks

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection, whereby we introduce a model of strategy evolution taking place on evolving networks based on Darwinian ‘survival of the fittest’ rule. In the present work, players whose payoffs are below a certain threshold will be deleted and the same number of new nodes will be added to the network to maintain the constant system size. Furthermore, the networking effect is also studied via implementing simulations on four typical network structures. Numerical results show that cooperators can obtain the biggest boost if the elimination threshold is fine-tuned. Notably, this coevolutionary rule drives the initial networks to evolve into statistically stationary states with a broad-scale degree distribution. Our results may provide many more insights for understanding the coevolution of strategy and network topology under the mechanism of nature selection whereby superior individuals will prosper and inferior ones be eliminated.     

Game Dynamics with Learning and Evolution of Universal Grammar

We investigate a model of language evolution, based on population game dynamics with learning. First, we examine the case of two genetic variants of universal grammar (UG), the heart of the human language faculty, assuming each admits two possible grammars. The dynamics are driven by a communication game. We prove using dynamical systems techniques that if the payoff matrix obeys certain constraints, then the two UGs are stable against invasion by each other, that is, they are evolutionarily stable. Then, we prove a similar theorem for an arbitrary number of disjoint UGs. In both theorems, the constraints are independent of the learning process. Intuitively, if a mutation in UG results in grammars that are incompatible with the established languages, then the mutation will die out because mutants will be unable to communicate and therefore unable to realize any potential benefit of the mutation. An example for which these theorems do not apply shows that compatible mutations may or may not be able to invade, depending on the population's history and the learning process. These results suggest that the genetic history of language is constrained by the need for compatibility and that mutations in the language faculty may have died out or taken over due more to historical accident than to any straightforward notion of relative fitness. MSC 1991: 37N25 · 92D15 · 91F20     

Global analyses of evolutionary dynamics and exhaustive search for social norms that maintain cooperation by reputation

Reputation formation is a key to understanding indirect reciprocity. In particular, the way to assign reputation to each individual, namely a norm that describes who is good and who is bad, greatly affects the possibility of sustained cooperation in the population. Previously, we have exhaustively studied reputation dynamics that are able to maintain a high level of cooperation at the ESS. However, this analysis examined the stability of monomorphic population and did not investigate polymorphic population where several strategies coexist. Here, we study the evolutionary dynamics of multiple behavioral strategies by replicator dynamics. We exhaustively study all 16 possible norms under which the reputation of a player in the next round is determined by the action of the self and the reputation of the opponent. For each norm, we explore evolutionary dynamics of three strategies: unconditional cooperators, unconditional defectors, and conditional cooperators. We find that only three norms, simple-standing, Kandori, and shunning, can make conditional cooperation evolutionarily stable, hence, realize sustained cooperation. The other 13 norms, including scoring, ultimately lead to the invasion by defectors. Also, we study the model in which private reputation errors exist to a small extent. In this case, we find the stable coexistence of unconditional and conditional cooperators under the three norms.     

The effects of the evolution of stoichiometry-related traits on population dynamics in plankton communities

Both ecological stoichiometry and the evolution of traits for energetic interactions such as prey protection and predatory efficiency are considered to be important aspects affecting population dynamics. However, no attempt has been made to examine the effect of the evolution of traits relating to stoichiometry. This study first examined the effects of the evolution of nutrient utilization traits (i.e., the minimum nutrient content of prey, the maximum nutrient uptake affinity of prey and the nutrient contents of predators) on population dynamics in a plankton community. When the evolution of these traits was assumed, the range of the nutrient loading conditions where the system became unstable was smaller than when the evolution was not assumed, but the range of the conditions for zooplankton extinction became larger. Furthermore, when the trade-offs (i.e. genetic correlation between the traits) were assumed, the system rarely became extinct and the range of the nutrient loading conditions where the system became stable became larger through evolution. Stable dynamics were caused by increasing uptake affinity through evolution, and zooplankton extinction was caused by decreasing the minimum content of limiting nutrients. Thus, our results suggest that the evolution of traits relating to stoichiometry can affect the dynamics of the systems, and the outcomes the dynamics change greatly depend on which traits can evolve.     

Spatial seed and pollen games: dispersal,sex allocation,and the evolution of dioecy

The evolutionary forces shaping within‐ and across‐species variation in the investment in male and female sex function are still incompletely understood. Despite earlier suggestions that in plants the evolution or cosexuality vs. dioecy, as well as sex allocation among cosexuals, is affected by seed and pollen dispersal, no formal model has explicitly used dispersal distances to address this problem. Here, we present a game‐theory model as well as a simulation study that fills in this gap. Our model predicts that dioecy should evolve if seeds and pollen disperse widely and that sex allocation among cosexuals should be biased towards whichever sex function produces more widely dispersing units. Dispersal limitations stabilize cosexuality by reinforcing competition between spatially clumped dispersal units from the same source, leading to saturating fitness returns that render sexual specialization unprofitable. However, limited pollen dispersal can also increase the risk of selfing, thus potentially selecting for dioecy as an outbreeding mechanism. Finally, we refute a recent claim that cosexuals should always invest equally in both sex functions.     

杭州石荠ling不同地方种群分化及空间利用策略研究

从杭州石荠ling（Mosla hangchowensis)5个不同地方种群采集种子,在实验室萌发,幼苗移植以实验地,在营养生长末期时,研究了株高,冠幅,主茎长,最大分枝长,基茎粗,叶面积,一级分枝数,平均二级分枝数,主茎叶对数,根长和根幅等11个空间结构参数,分析不同种群的空利用策略和分化程度,结果发现,基本无基因交流的各地方种群产生了不同的适应方式,并在表型上有可见的差异,其中惠安种群以扩大冠幅占领较大的横向空间,种群分化程度最大,杭州种群以增加高度占领较大的纵向空间,分化程度次之,临海,天台和普陀种群分化程度较小,临海和天台种群水选下层种子萌发生长的植物个体比水选上层各形成植株个体大,但个体对空间的利用策略仍一致。     

The effects of mutations on motions of side-chains in protein L studied by 2H NMR dynamics and scalar couplings

Recently developed 2H spin relaxation experiments are applied to study the dynamics of methyl-containing side-chains in the B1 domain of protein L and in a pair of point mutants of the domain, F22L and A20V. X-ray and NMR studies of the three variants of protein L studied here establish that their structures are very similar, despite the fact that the F22L mutant is 3.2kcal/mol less stable. Measurements of methyl 2H spin relaxation rates, which probe dynamics on a picosecond-nanosecond time scale, and three-bond 3J(Cgamma-CO), 3J(Cgamma-N) and 3J(Calpha-Cdelta) scalar coupling constants, which are sensitive to motion spanning a wide range of time-scales, reveal changes in the magnitude of side-chain dynamics in response to mutation. Observed differences in the time-scale of motions between the variants have been related to changes in energetic barriers. Of interest, several of the residues with different motional properties across the variants are far from the site of mutation, suggesting the presence of long-range interactions within the protein that can be probed through studies of dynamics.     

Pyrethroids cypermethrin,deltamethrin and fenvalerate have different effects on in vitro maturation of pig oocytes at different stages of growth

Pesticides can significantly harm reproduction in animals and people. Pyrethroids are often used as insecticides, and their toxicity for mammals is considered to be low. However, cypermethrin, deltamethrin and fenvalerate – as potent specific inhibitors of protein phosphatase calcineurin – can influence the meiosis of mammalian oocytes. The objective of this study was to evaluate the effects of these pyrethroids on the in vitro maturation of pig oocytes at different levels of meiotic competence. Under the tested concentrations, cypermethrin, deltamethrin and fenvalerate neither had a significant effect on the viability of oocytes nor did they induce significant degeneration of oocytes. However, these pyrethroids significantly affected meiotic maturation. The effects depended on the stage of meiotic competence of the oocytes. Maturation of growing pig oocytes with partial meiotic competence was induced. On the other hand, in fully grown pig oocytes with full meiotic competence, maturation in vitro was delayed. The specificity of these effects was further supported by the same effect of non-pyrethroidal inhibitors of calcineurin – cyclosporin A or hymenistatin I – on the maturation of oocytes with different levels of meiotic competence. However, pyrethroids, which do not inhibit calcineurin – allethrin or permethrin – had no effect on pig oocyte maturation. We demonstrated a significant effect of pyrethroids on the maturation of mammalian oocytes under in vitro conditions. This indicates that exposure to these substances could affect the fertility of people or animals.     

Heavy metals have different effects on mycelial morphology of Achlya bisexualis as determined by fractal geometry

The morphological response, as measured by changes to mycelial area, radial extension and border fractal dimension, of the oomycete Achlya bisexualis to Cu, Co, Hg, Zn and Cd at concentrations of between 0.05 and 3 mM is described. All of the metals decreased mycelial area and radial extension. Border fractal dimension increased in the presence of Cu, Co and Hg with individual hyphae extending out beyond the mycelial margin. In the presence of 3 mM Hg these hyphae displayed spiral growth. Zn and Cd had no effect on border fractal dimension. We suggest that all of the metals slow growth and that Cu, Co and Hg may also disrupt the relationship between tip growth and branching at the edge of the mycelium.     

Runaway social games,genetic cycles driven by alternative male and female strategies,and the origin of morphs

Analysis of evolutionarily stable strategies (ESS) and decade-long field studies indicate that two color morphs of female side-blotched lizards exhibit density- and frequency-dependent strategies. Orange females are r-strategists: they lay large clutches of small progeny that are favored at low density. Conversely, yellow females are K-strategists: they lay small clutches of large progeny that are favored when carrying capacity is exceeded and the population crashes to low density. Interactions among three male morphs resembles a rock-paper-scissors (RPS) game. Fertilization success of males depends on frequency of neighboring morphs. Orange males usurp territory from blue neighbors and thereby mate with many females. However, orange males are vulnerable to cuckoldry by sneaky yellow males that mimic females. The yellow strategy is thwarted in turn by the mate-guarding strategy of blue. Sinervo and Lively (1996) developed a simple asexual model of the RPS game. Here, we model the dynamics of male and female morphs with one- and two-locus genetic models. Male and female games were considered in isolation and modeled as games that were genetically coupled by the same locus. Parameters for payoff matrices, which describe the force of frequency-dependent selection in ESS games, were estimated from free-ranging animals. Period of cycles in nature was 5 years for males and 2 years for females. Only the one locus model with three alleles (o, b, y) was capable of driving rapid cycles in male and female games. Furthermore, the o allele must be dominant to the y allele in females. Finally, the amplitude of male cycles was only reproduced in genetic models which allowed for irreversible plasticity of by genotypes, which is consistent with hormonally-induced changes that transform some males with yellow to dark blue. We also critique experimental designs that are necessary to detect density- and frequency-dependent selection in nature. Finally, runaway ESS games are discussed in the context of self-reinforcing genetic correlations that build and promote the formation of morphotypic variation.     

Influence of gene-linkage and recombination of evolutionary algorithms on the rate of evolution, genetic diversity and the response of evolving populations to disturbance

Both biological populations and fault tolerant evolvable hardware systems need to respond rapidly to changes in their dynamic environmental niche. Such changes can be caused by a disturbance event or fault occurring. Here I examine evolutionary algorithms, based on eukaryote sexual selection, which allow different levels of recombination of ‘genes’. The differences in recombination are based on ‘genes’ related to the optimisation process being either linked on a single ‘chromosome’ or being present on separate ‘chromosomes’. When genes are present on separate chromosomes the initial rate of evolution of a randomly generated population is faster than if the genes are linked on the same chromosome. However, when the optimisation problem is changed during the optimisation period, indicating a disturbance or fault occurring, the initial fitness of the linked population is higher and the rate of optimisation immediately after the disturbance is more rapid than for the non-linked populations. The genotypic and phenotypic diversity of the linked populations are also significantly higher immediately prior to the disturbance event. I propose this diversity provides the necessary variation to allow more rapid evolution following a disturbance. The results demonstrate the importance of population diversity in response to change, supporting theory from conservation biology.     

D- and L-isoprenaline have different effects on adrenoceptors in the systemic vasculature of the cod, Gadus morhua

The effects of D- and L-isoprenaline on systemic vascular adrenoceptors of the cod was studied using blood pressure recording from conscious cod in vivo and isolated coeliac artery strip preparations in vitro. Experiments with isolated artery preparations demonstrated that the D-, but not the L-isomer of isoprenaline acts as an alpha-adrenoceptor antagonist. A dose-dependent reduction of ventral and dorsal aortic blood pressures together with a dose-dependent increase in the heart rate could be produced by injection of L-isoprenaline. D-Isoprenaline, on the other hand, had no effect on the blood pressures or heart rate except in the highest dose injected. The results show an alpha-adrenoceptor blocking capacity of D-isoprenaline in the cod. The effect of L-isoprenaline on the blood pressure supports the idea that the hypotensive effect of DL-isoprenaline seen in previous studies of the cod may be attributed to an effect of the L-isomer on beta-adrenoceptors mediating vasodilation of the cod systemic vasculature.     

Diversification rates have no effect on the convergent evolution of foraging strategies in the most speciose genus of bats,Myotis*

Adaptive radiations are defined as rapid diversification with phenotypic innovation led by colonization to new environments. Notably, adaptive radiations can occur in parallel when habitats with similar selective pressures are accessible promoting convergent adaptions. Although convergent evolution appears to be a common process, it is unclear what are the main drivers leading the reappearance of morphologies or ecological roles. We explore this question in Myotis bats, the only Chiropteran genus with a worldwide distribution. Three foraging strategies—gleaning, trawling, and aerial netting—repeatedly evolved in several regions of the world, each linked to characteristic morphologies recognized as ecomorphs. Phylogenomic, morphometric, and comparative approaches were adopted to investigate convergence of such foraging strategies and skull morphology as well as factors that explain diversification rates. Genomic and morphometric data were analyzed from ～80% extant taxa. Results confirm that the ecomorphs evolved multiple times, with trawling evolving more often and foliage gleaning most recently. Skull morphology does not reflect common ancestry and evolves convergently with foraging strategy. Although diversification rates have been roughly constant across the genus, speciation rates are area‐dependent and higher in taxa with temperate distributions. Results suggest that in this species‐rich group of bats, first, stochastic processes have led divergence into multiple lineages. Then, natural selection in similar niches has promoted repeated adaptation of phenotypes and foraging strategies. Myotis bats are thus a remarkable case of ecomorphological convergence and an emerging model system for investigating the genomic basis of parallel adaptive radiation.     

Nitrate and phosphate availability and distribution have different effects on root system architecture of Arabidopsis

Plant root systems can respond to nutrient availability and distribution by changing the three-dimensional deployment of their roots: their root system architecture (RSA). We have compared RSA in homogeneous and heterogeneous nitrate and phosphate supply in Arabidopsis. Changes in nitrate and phosphate availability were found to have contrasting effects on primary root length and lateral root density, but similar effects on lateral root length. Relative to shoot dry weight (DW), primary root length decreased with increasing nitrate availability, while it increased with increasing phosphate supply. Lateral root density remained constant across a range of nitrate supplies, but decreased with increasing phosphate supply. In contrast, lateral root elongation was suppressed both by high nitrate and high phosphate supplies. Local supplies of high nitrate or phosphate in a patch also had different effects. Primary root growth was not affected by a high nitrate patch, but growth through a high phosphate patch reduced primary root growth after the root left the patch. A high nitrate patch induced an increase in lateral root density in the patch, whereas lateral root density was unaffected by a high phosphate patch. However, both phosphate- and nitrate-rich patches induced lateral root elongation in the patch and suppressed it outside the patch. This co-ordinated response of lateral roots also occurs in soil-grown plants exposed to a nutrient-rich patch. The auxin-resistant mutants axrl, axr4 and aux1 all showed the wild-type lateral root elongation responses to a nitrate-rich patch, suggesting that auxin is not required for this response.     

Boron and fish oil have different beneficial effects on strength and trabecular microarchitecture of bone

An experiment was performed to determine whether boron deprivation would adversely affect vertebra (trabecular) bone microarchitecture, and whether any adverse effect would be modified by dietary fatty acid composition. Female rats were fed diets containing 0.1 mg (9 μmol) boron/kg in a factorial arrangement with variables of supplemental boron at 0 (boron-deprived) or 3 (boron-adequate) mg (278 μmol)/kg and fat sources of 75 g safflower oil/kg or 65 g fish (menhaden) oil/kg plus 10 g linoleic acid/kg. After 6 weeks, six females per treatment were bred. Dams and pups continued on their respective diets through gestation, lactation, and after weaning. At age 21 weeks, the microarchitecture of the fourth lumbar vertebrae from 12 randomly selected pups from each treatment was determined by microcomputed tomography. Boron deprivation decreased bone volume fraction and increased trabecular separation and structural model index. Boron deprivation decreased trabecular thickness when the dietary oil was safflower. A three-point bending test for bone strength found that boron deprivation decreased the maximum force needed to break the femur. Feeding fish oil instead of safflower oil decreased connectivity density in vertebrae of boron-deficient but not in boron-adequate rats. Fish oil instead of safflower oil increased the maximum force to break and the bending moment of the femur, especially in rats fed adequate boron. The findings confirm that boron and fish oil are beneficial to cortical bone strength, and show that nutritional intakes of boron are beneficial for trabecular bone microarchitecture and influence the beneficial effects of fish oil on bone.     

The regulatory domains of CNA have different effects on the inhibition of CN activity by FK506 and CsA

Calcineurin (CN) is the common receptor for two immunophilin-immunosuppressant complexes, Cyp-CsA and FKBP-FK506. Calcineurin is composed of a catalytic subunit (CNA) and a regulatory subunit (CNB). CNA contains the catalytic domain and three regulatory domains: a CNB-binding domain (BBH, 350-370), a calmodulin- binding domain (CBD, 389-413), and an autoinhibitory domain (AID, 457-482). To investigate the effects of these three regulatory domains on the inhibition of CN by the two drugs we constructed three C-terminal deletion mutants: CNAabc (1-456), CNAab (1-388) and CNAa (1-347). Inhibition of CNA and its derivatives by the two drugs was examined and compared with inhibition by peptides (AID [457-482] and LCBD [389-456], CBD and the extension of the AID were included). Our results show that the BBH is critical for inhibition of CN by Cyp-CsA and FKBP-FK506. The LCBD has no effect and the AID reduces the inhibition of CN by two complexes. In addition, LCBD and AID as autoinhibitors may inhibit enzyme activity via different sites.     

ZFYVE26/SPASTIZIN and SPG11/SPATACSIN mutations in hereditary spastic paraplegia types AR-SPG15 and AR-SPG11 have different effects on autophagy and endocytosis

ZFYVE26/Spastizin and SPG11/Spatacsin encode 2 large proteins that are mutated in hereditary autosomal-recessive spastic paraplegia/paraparesis (HSP) type 15 (AR-SPG15) and type 11 (AR-SPG11), respectively. We previously have reported that AR-SPG15-related ZFYVE26 mutations lead to autophagy defects with accumulation of immature autophagosomes. ZFYVE26 and SPG11 were found to be part of a complex including the AP5 (adaptor related protein complex 5) and to have a critical role in autophagic lysosomal reformation with identification of autophagic and lysosomal defects in cells with both AR-SPG15- and AR-SPG11-related mutations. In spite of these similarities between the 2 proteins, here we report that ZFYVE26 and SPG11 are differently involved in autophagy and endocytosis. We found that both ZFYVE26 and SPG11 interact with RAB5A and RAB11, 2 proteins regulating endosome trafficking and maturation, but only ZFYVE26 mutations affected RAB protein interactions and activation. ZFYVE26 mutations lead to defects in the fusion between autophagosomes and endosomes, while SPG11 mutations do not affect this step and lead to a milder autophagy defect. We thus demonstrate that ZFYVE26 and SPG11 affect the same cellular physiological processes, albeit at different levels: both proteins have a role in autophagic lysosome reformation, but only ZFYVE26 acts at the intersection between endocytosis and autophagy, thus representing a key player in these 2 processes. Indeed expression of the constitutively active form of RAB5A in cells with AR-SPG15-related mutations partially rescues the autophagy defect. Finally the model we propose demonstrates that autophagy and the endolysosomal pathway are central processes in the pathogenesis of these complicated forms of hereditary spastic paraparesis.

Abbreviations: ALR, autophagic lysosome reformation; AP5, adaptor related protein complex 5; AR, autosomal-recessive; HSP, hereditary spastic paraplegia/paraparesis; ATG14, autophagy related 14; BafA, bafilomycin A₁; BECN1, beclin 1; EBSS, Earle balanced salt solution; EEA1, early endosome antigen 1; EGF, epidermal growth factor; EGFR, epidermal growth factor receptor; GDP, guanosine diphosphate; GFP, green fluorescent protein; GTP, guanosine triphosphate; HSP, hereditary spastic paraplegias; LBPA, lysobisphosphatidic acid; MAP1LC3B/LC3B, microtubule associated protein 1 light chain 3 beta; MVBs, multivesicular bodies; PIK3C3, phosphatidylinositol 3-kinase, catalytic subunit type 3; PIK3R4, phosphoinositide-3-kinase regulatory subunit 4; PtdIns3P, phosphatidylinositol-3-phosphate; RFP, red fluorescent protein; RUBCN, RUN and cysteine rich domain containing beclin 1 interacting protein; shRNA, short hairpin RNA; SQSTM1/p62, sequestosome 1; TCC: thin corpus callosum; TF, transferrin; UVRAG, UV radiation resistance associated.