Fitness Beats Truth in the Evolution of Perception

Acta Biotheoretica - Does natural selection favor veridical percepts—those that accurately (if not exhaustively) depict objective reality? Perceptual and cognitive scientists standardly claim...     

Extrapolating Weak Selection in Evolutionary Games

In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in game outcomes translate into small fitness differences. Many results have been derived using weak selection approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results derived under weak selection are also qualitatively valid for intermediate and strong selection. By “qualitatively valid” we mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number of strategies . In particular, rank changes are almost certain for , which jeopardizes the predictive power of results derived for weak selection.     

Evolutionary dynamics of continuous strategy games on graphs and social networks under weak selection

Understanding the emergence of cooperation among selfish individuals has been a long-standing puzzle, which has been studied by a variety of game models. Most previous studies presumed that interactions between individuals are discrete, but it seems unrealistic in real systems. Recently, there are increasing interests in studying game models with a continuous strategy space. Existing research work on continuous strategy games mainly focuses on well-mixed populations. Especially, little theoretical work has been conducted on their evolutionary dynamics in a structured population. In the previous work (Zhong et al., BioSystems, 2012), we showed that under strong selection, continuous and discrete strategies have significantly different equilibrium and game dynamics in spatially structured populations. In this paper, we further study evolutionary dynamics of continuous strategy games under weak selection in structured populations. By using the fixation probability based stochastic dynamics, we derive exact conditions of natural selection favoring cooperation for the death–birth updating scheme. We also present a network gain decomposition of the game equilibrium, which might provide a new view of the network reciprocity in a quantitative way. Finally, we make a detailed comparison between games using discrete and continuous strategies. As compared to the former, we find that for the latter (i) the same selection conditions are derived for the general 2 × 2 game; especially, the rule b/c > k in a simplified Prisoner's Dilemma is valid as well; however, (ii) for a coordination game, interestingly, the risk-dominant strategy is disfavored. Numerical simulations have also been conducted to validate our results.     

Stochastic evolutionary dynamics of bimatrix games

Evolutionary game dynamics of two-player asymmetric games in finite populations is studied. We consider two roles in the game, roles α and β. α-players and β-players interact and gain payoffs. The game is described by a pair of matrices, which is called bimatrix. One's payoff in the game is interpreted as its fecundity, thus strategies are subject to natural selection. In addition, strategies can randomly mutate to others. We formulate a stochastic evolutionary game dynamics of bimatrix games as a frequency-dependent Moran process with mutation. We analytically derive the stationary distribution of strategies under weak selection. Our result provides a criterion for equilibrium selection in general bimatrix games.     

Mutation-selection equilibrium in games with multiple strategies

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n×n games in the limit of weak selection.     

Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game

Understanding the mechanisms that can lead to the evolution of cooperation through natural selection is a core problem in biology. Among the various attempts at constructing a theory of cooperation, game theory has played a central role. Here, we review models of cooperation that are based on two simple games: the Prisoner's Dilemma, and the Snowdrift game. Both games are two‐person games with two strategies, to cooperate and to defect, and both games are social dilemmas. In social dilemmas, cooperation is prone to exploitation by defectors, and the average payoff in populations at evolutionary equilibrium is lower than it would be in populations consisting of only cooperators. The difference between the games is that cooperation is not maintained in the Prisoner's Dilemma, but persists in the Snowdrift game at an intermediate frequency. As a consequence, insights gained from studying extensions of the two games differ substantially. We review the most salient results obtained from extensions such as iteration, spatial structure, continuously variable cooperative investments, and multi‐person interactions. Bridging the gap between theoretical and empirical research is one of the main challenges for future studies of cooperation, and we conclude by pointing out a number of promising natural systems in which the theory can be tested experimentally.     

Do the evolutionary origins of our moral beliefs undermine moral knowledge?

According to some recent arguments, (Joyce in The evolution of morality, MIT Press, Cambridge, 2006; Ruse and Wilson in Conceptual issues in evolutionary biology, MIT Press, Cambridge, 1995; Street in Philos Studies 127: 109–166, 2006) if our moral beliefs are products of natural selection, then we do not have moral knowledge. In defense of this inference, its proponents argue that natural selection is a process that fails to track moral facts. In this paper, I argue that our having moral knowledge is consistent with, (a) the hypothesis that our moral beliefs are products of natural selection, and (b) the claim (or a certain interpretation of the claim) that natural selection fails to track moral facts. I also argue that natural selection is a process that could track moral facts, albeit imperfectly. I do not argue that we do have moral knowledge. I argue instead that Darwinian considerations provide us with no reason to doubt that we do, and with some reasons to suppose that we might.     

Strategy selection in structured populations

Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix . We study a mutation and selection process. For weak selection strategy A is favored over B if and only if σa+b>c+σd. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games.     

Greek derivational structures: restrictions and constraints

This paper investigates the general principles governing the combination of a base with a particular suffix. Elaborating on the well-known conflict between base-driven and affix-driven selectional restrictions, we argue in favor of affix-driven selection. We claim that the various selectional restrictions imposed by the suffixes are inherent specifications, which characterize their entries at the lexical level; if suffixes are heads of derivational structures, these restrictions pass from heads to the derived items through percolation. Additionally, we propose that, beside selectional restrictions, the combinatorial behaviour of suffixes may be determined by a number of other lexically-specified properties such as the ‘unique suffix’ or ‘closing suffix’. Finally, we claim that derivational structures are also governed by language-independent or language-specific constraints, operating on input structures.     

Multi-species evolutionary dynamics

Dynamical attainability of an evolutionarily stable strategy (ESS) through the process of mutations and natural selection has mostly been addressed through the use of the continuously stable strategy (CSS) concept for species evolutionary games in which strategies are drawn from a continuum, and by the adaptive trait dynamics method. We address the issue of dynamical attainability of an ESS in coevolving species through the use of the concept of an ESNIS. It is shown that the definition of an ESNIS coalition for coevolving species is not in general equivalent to other definitions for CSS given in the literature. We show under some additional conditions that, in a dynamic system which involves the strategies of a dimorphic ESNIS coalition and at most two strategies that are not members of ESNIS coalition, the ESNIS coalition will emerge as the winner. In addition an ESNIS will be approached because of the invasion structure of strategies in its neighborhood. This proves that under the above conditions an ESNIS has a better chance of being attained than a strategy coalition which is a CSS. The theory developed is applied to a class of coevolutionary game models with Lotka–Volterra type interactions and we show that for such models, an ESS coalition will be dynamically attainable through mutations and natural selection if the ESS coalition is also an ESNIS coalition.Co-ordinating editor: Metz     

A theory for the evolutionary game

We present an evolutionary game theory. This theory differs in several respects from current theories related to Maynard Smith's pioneering work on evolutionary stable strategies (ESS). Most current work deals with two person matrix games. For these games the strategy set is finite. We consider evolutionary games which are defined over a continuous strategy set and which permit any number of players. Matrix games are included as a bilinear continuous game. However, under our definition, such games will not posses an ESS on the interior of the strategy set. We extend previous work on continuous games by developing an ESS definition which permits the ESS to be composed of a coalition of several strategies. This definition requires that the coalition must not only be stable with respect to perturbations in strategy frequencies which comprise the coalition, but the coalition must also satisfy the requirement that no mutant strategies can invade. Ecological processes are included in the model by explicitly considering population size and density dependent selection.     

Stochastic stability in three-player games

Animal behavior and evolution can often be described by game-theoretic models. Although in many situations the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only recently were evolutionarily stable strategies defined for multi-player games and their properties analyzed [Broom, M., Cannings, C., Vickers, G.T., 1997. Multi-player matrix games. Bull. Math. Biol. 59, 931–952]. Here we study the long-run behavior of stochastic dynamics of populations of randomly matched individuals playing symmetric three-player games. We analyze the stochastic stability of equilibria in games with multiple evolutionarily stable strategies. We also show that, in some games, a population may not evolve in the long run to an evolutionarily stable equilibrium.     

A rule is not a rule if it changes from case to case (a reply to Marshall's comment)

This is a reply to “Queller's rule ok: Comment on van Veelen ‘when inclusive fitness is right and when it can be wrong’ ” by James Marshall in the Journal of Theoretical Biology, in this issue.In order to circumvent the disagreement about the Price equation and focus on the issue of the predictive power of inclusive fitness for group selection models, I derive Queller's and Marshall's rule without the Price equation. Both rules however need a translation step in order to be able to link them to the group selection model in van Veelen (2009). Queller's rule applies to games with 2 players and 2 strategies, and is general. Marshall's rule on the other hand applies only to a small subset of 3-player games. His rule is correct, but for other, similarly small subsets we would get other rules. This implies that if we want a rule that applies to all symmetric games with 3 players and 2 strategies, it will have to use a vector of dimension 2 that represents population structure. More in general: for group selection models with groups of size n, a correct and general prediction will need to use a vector of dimension n−1 that represents population structure.     

Natural selection and the limitations of environmental resources

In this paper, I am clarifying and defending my argument (Nanay 2005) in favor of the claim that cumulative selection can explain adaptation provided that the environmental resources are limited. Further, elaborate on what this limitation of environmental resources means and why it is relevant for the explanatory power of natural selection.     

EVOLUTION OF GENETIC INTEGRATION BETWEEN DISPERSAL AND COLONIZATION ABILITY IN A BIRD

Discrete behavioral strategies comprise a suite of traits closely integrated in their expression with consistent natural selection for such coexpression leading to developmental and genetic integration of their components. However, behavioral traits are often also selected to respond rapidly to changing environments, which should both favor their context-dependent expression and inhibit evolution of genetic integration with other, less flexible traits. Here we use a multigeneration pedigree and long-term data on lifetime fitness to test whether behaviors comprising distinct dispersal strategies of western bluebirds—a species in which the propensity to disperse is functionally integrated with aggressive behavior—are genetically correlated. We further investigated whether selection favors flexibility in the expression of aggression in relation to current social context. We found a significant genetic correlation between aggression and dispersal that is concordant with consistent selection for coexpression of these behaviors. To a limited extent, individuals modified their aggression to match their mate; however, we found no fitness consequences on such adjustments. These results introduce a novel way of viewing behavioral strategies, where flexibility of behavior, while often aiding an organism's fit in its current environment, may be limited and thereby enable integration with less flexible traits.     

Why Darwin would have loved evolutionary game theory

Humans have marvelled at the fit of form and function, the way organisms'' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin''s arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so.     

Fourier Power Spectrum Characteristics of Face Photographs: Attractiveness Perception Depends on Low-Level Image Properties

We investigated whether low-level processed image properties that are shared by natural scenes and artworks – but not veridical face photographs – affect the perception of facial attractiveness and age. Specifically, we considered the slope of the radially averaged Fourier power spectrum in a log-log plot. This slope is a measure of the distribution of special frequency power in an image. Images of natural scenes and artworks possess – compared to face images – a relatively shallow slope (i.e., increased high spatial frequency power). Since aesthetic perception might be based on the efficient processing of images with natural scene statistics, we assumed that the perception of facial attractiveness might also be affected by these properties. We calculated Fourier slope and other beauty-associated measurements in face images and correlated them with ratings of attractiveness and age of the depicted persons (Study 1). We found that Fourier slope – in contrast to the other tested image properties – did not predict attractiveness ratings when we controlled for age. In Study 2A, we overlaid face images with random-phase patterns with different statistics. Patterns with a slope similar to those in natural scenes and artworks resulted in lower attractiveness and higher age ratings. In Studies 2B and 2C, we directly manipulated the Fourier slope of face images and found that images with shallower slopes were rated as more attractive. Additionally, attractiveness of unaltered faces was affected by the Fourier slope of a random-phase background (Study 3). Faces in front of backgrounds with statistics similar to natural scenes and faces were rated as more attractive. We conclude that facial attractiveness ratings are affected by specific image properties. An explanation might be the efficient coding hypothesis.     

Mating games: cultural evolution and sexual selection

In this paper, we argue that mating games, a concept that denotes cultural practices characterized by a competitive element and an ornamental character, are essential drivers behind the emergence and maintenance of human cultural practices. In order to substantiate this claim, we sketch out the essential role of the game’s players and audience, as well as the ways in which games can mature and turn into relatively stable cultural practices. After outlining the life phase of mating games – their emergence, rise, maturation, and possible eventual decline – we go on to argue that participation in these games (in each phase) does make sense from an adaptationist point of view. The strong version of our theory which proposes that all cultural practices are, or once were, mating games, allows us to derive a set of testable predictions for the fields of archaeology, economics, and psychology.     

Complexity,adaptive complexity and the Creative View of natural selection

In this paper, I respond to arguments proposed by Brunnander in this journal issue concerning my position regarding the Creative View of natural selection (Razeto-Barry & Frick, 2011). Brunnander argues that (i) the Creative View we defend does not serve to answer William Paley’s question because (ii) Paley’s question is “why there are complex things rather than simple ones” and (iii) natural selection cannot answer this question. Brunnander’s arguments for (iii) defend a Non-creative View of natural selection (sensu Razeto-Barry & Frick, 2011). Here I claim that Brunnander’s arguments for (iii) are mistaken and I also argue that even accepting (iii) we do not have to accept (i), given that statement (ii) is historically and conceptually flawed. Thus here I analyze Paley’s question from a historical point of view and from a contemporary perspective in a quest for the potential conceptual relevance of Paley’s question today. In this vein I argue that from a contemporary point of view statement (iii) may be correct but for different reasons than those adduced by Brunnander.     

Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.