Continuously stable strategies as evolutionary branching points

Evolutionary branching points are a paradigmatic feature of adaptive dynamics, because they are potential starting points for adaptive diversification. The antithesis to evolutionary branching points are continuously stable strategies (CSS's), which are convergent stable and evolutionarily stable equilibrium points of the adaptive dynamics and hence are thought to represent endpoints of adaptive processes. However, this assessment is based on situations in which the invasion fitness function determining the adaptive dynamics have non-zero second derivatives at CSS. Here we show that the scope of evolutionary branching can increase if the invasion fitness function vanishes to higher than first order at CSS. Using classical models for frequency-dependent competition, we show that if the invasion fitness vanishes to higher orders, a CSS may be the starting point for evolutionary branching. Thus, when invasion fitness functions vanish to higher than first order at equilibrium points of the adaptive dynamics, evolutionary diversification can occur even after convergence to an evolutionarily stable strategy.     

How evolutionary biology challenges the classical theory of rational choice

A fundamental philosophical question that arises in connection with evolutionary theory is whether the fittest patterns of behavior are always the most rational. Are fitness and rationality fully compatible? When behavioral rationality is characterized formally as in classical decision theory, the question becomes mathematically meaningful and can be explored systematically by investigating whether the optimally fit behavior predicted by evolutionary process models is decision-theoretically coherent. Upon investigation, it appears that in nontrivial evolutionary models the expected behavior is not always in accord with the norms of the standard theory of decision as ordinarily applied. Many classically irrational acts, e.g. betting on the occurrence of one event in the knowledge that the probabilities favor another, can under certain circumstances constitute adaptive behavior. One interesting interpretation of this clash is that the criterion of rationality offered by classical decision theory is simply incorrect (or at least incomplete) as it stands, and that evolutionary theory should be called upon to provide a more generally applicable theory of rationality. Such a program, should it prove feasible, would amount to the logical reduction of the theory of rational choice to evolutionary theory.     

The Recognition Signal Hypothesis for the Adaptive Evolution of Religion

Recent research on the evolution of religion has focused on whether religion is an unselected by-product of evolutionary processes or if it is instead an adaptation by natural selection. Adaptive hypotheses for religion include direct fitness benefits from improved health and indirect fitness benefits mediated by costly signals and/or cultural group selection. Herein, I propose that religious denominations achieve indirect fitness gains for members through the use of ecologically arbitrary beliefs, rituals, and moral rules that function as recognition markers of cultural inheritance analogous to kin and species recognition of genetic inheritance in biology. This recognition signal hypotheses could act in concert with either costly signaling or cultural group selection to produce evolutionarily altruistic behaviors within denominations. Using a cultural phylogenetic analysis, I show that a large set of religious behaviors among extant Christian denominations supports the prediction of the recognition signal hypothesis that characters change more frequently near historical schisms. By incorporating demographic data into the model, I show that more-distinctive denominations, as measured through dissimilar characteristics, appear to be protected from intrusion by nonmembers in mixed-denomination households, and that they may be experiencing greater biological growth of their populations even in the present day.     

Recurrent cerebellar architecture solves the motor-error problem

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr-Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three-dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex.     

Mate choice and uncertainty in the decision process

The behavior of females in search of a mate determines the likelihood that a high quality male is encountered in the search process and alternative search strategies provide different fitness returns to searchers. Models of search behavior are typically formulated on an assumption that the quality of prospective mates is revealed to searchers without error, either directly or by inspection of a perfectly informative phenotypic character. But recent theoretical developments suggest that the relative performance of a search strategy may be sensitive to any uncertainty associated with the to-be-realized fitness benefit of mate choice decisions. Indeed, uncertainty in the decision process is inevitable whenever unobserved male attributes influence the fitness of searchers. In this paper, we derive solutions to the sequential search strategy and the fixed sample search strategy for the general situation in which observed and unobserved male attributes affect the fitness consequences of female mate choice decisions and we determine how the magnitude of various parameters that are influential in the standard models alter these more general solutions. The distribution of unobserved attributes amongst prospective mates determines the uncertainty of mate choice decisions-the reliability of an observed male character as a predictor of male quality-and the realized functional relationship between an observed male character and the fitness return to searchers. The uncertainty of mate choice decisions induced by unobserved male attributes has no influence on the generalized model solutions. Thus, the results of earlier studies of these search models that rely on the use of a perfectly informative male character apply even if an observed male trait does not reveal the quality of prospective mates with certainty. But the solutions are sensitive to any changes of the distribution of unobserved male attributes that alter the realized functional relationship between an observed character and the fitness return to searchers. For example, the standard sequential search model exhibits a reservation property--the acceptability of prospective mates is delimited by a unique threshold criterion--and the existence of this model property under generalized conditions depends critically on the association between the observed and unobserved male characters. In our formulations of the models we assumed that females use a single male character to evaluate the quality of prospective mates, but the model properties generalize to situations in which male quality is evaluated by a direct inspection of multiple male characters.     

Critical Social Learning: A Solution to Rogers's Paradox of Nonadaptive Culture

Alan Rogers (1988) presented a game theory model of the evolution of social learning, yielding the paradoxical conclusion that social learning does not increase the fitness of a population. We expand on this model, allowing for imperfections in individual and social learning as well as incorporating a "critical social learning" strategy that tries to solve an adaptive problem first by social learning, and then by individual learning if socially acquired behavior proves unsatisfactory. This strategy always proves superior to pure social learning and typically has higher fitness than pure individual learning, providing a solution to Rogers's paradox of nonadaptive culture. Critical social learning is an evolutionarily stable strategy (ESS) unless cultural transmission is highly unfaithful, the environment is highly variable, or social learning is much more costly than individual learning. We compare the model to empirical data on social learning and on spatial variation in primate cultures and list three requirements for adaptive culture.     

Symmetric competition as a general model for single-species adaptive dynamics

Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even though the derivation of the adaptive dynamics from a given invasion fitness function is general and model-independent, the derivation of the invasion fitness function itself requires specification of an underlying ecological model. Therefore, evolutionary insights gained from adaptive dynamics models are generally model-dependent. Logistic models for symmetric, frequency-dependent competition are widely used in this context. Such models have the property that the selection gradients derived from them are gradients of scalar functions, which reflects a certain gradient property of the corresponding invasion fitness function. We show that any adaptive dynamics model that is based on an invasion fitness functions with this gradient property can be transformed into a generalized symmetric competition model. This provides a precise delineation of the generality of results derived from competition models. Roughly speaking, to understand the adaptive dynamics of the class of models satisfying a certain gradient condition, one only needs a complete understanding of the adaptive dynamics of symmetric, frequency-dependent competition. We show how this result can be applied to number of basic issues in evolutionary theory.     

The adaptive value of parental responsiveness to nestling begging

Despite extensive theoretical and empirical research into offspring food solicitation behaviour as a model for parent-offspring conflict and communication, the adaptive value of parental responsiveness to begging has never been tested experimentally. Game theory models, as well as empirical studies, suggest that begging conveys information on offspring state, which implies that parental investment can be better translated to fitness by responding to begging when allocating resources rather than by ignoring it. However, this assumption and its underlying mechanisms have received little or no attention. Here we show by experiments with hand-raised house sparrow (Passer domesticus) nestlings that a 'responsive parent' will do better than a hypothetical 'non-responsive' mutant (that provides similar food amounts, but irrespective of begging). This is neither because food-deprived nestlings convert food to mass more efficiently, however, nor because responsiveness reduces costly begging. Rather, responsiveness to begging is adaptive because it reduces two opposing risks: one is wasting time when returning too soon to feed already satiated nestlings and the other is repeatedly overlooking some nestlings as a result of the stochastic nature of a random, non-responsive strategy. This study provides the first experimental evidence for the adaptive value of parental responsiveness to offspring begging.     

CONSPIRATORIAL WHISPERS AND CONSPICUOUS DISPLAYS: GAMES OF SIGNAL DETECTION

Recent models of signaling have assumed that the expenditure required to ensure detection of a display is negligible and have concentrated instead on the costs that may be necessary to maintain honesty. Such models predict that individuals who share the same interests are likely to communicate using “conspiratorial whispers,” signals that are cheap and inconspicuous. Here, I present a game-theoretical model of signal detection (in a noisy environment, in the presence of potential eavesdroppers), which demonstrates that the idea of conspiratorial whispers is far too simplistic. It is true that in “cooperative” signaling systems (where signalers attempt to elicit responses that are beneficial for receivers), signal cost is not required to maintain honesty. However, some level of expenditure is still needed to ensure that a signal is reliably detected. Moreover, there exists a conflict of interest between signalers and receivers over the division of this expenditure. To predict the stable level of display in such cases, one needs to know how this conflict of interest will be resolved. The model reveals that the outcome may range from a whisper to a conspicuous and costly (though still conspiratorial) display. The more closely related the receiver is to the signaler, the greater the level of signal exaggeration that is expected—the opposite prediction to that of honest signaling models.     

A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms

For structured populations in equilibrium with everybody born equal, ln(R (0)) is a useful fitness proxy for evolutionarily steady strategy (ESS) and most adaptive dynamics calculations, with R (0) the average lifetime number of offspring in the clonal and haploid cases, and half the average lifetime number of offspring fathered or mothered for Mendelian diploids. When individuals have variable birth states, as is, for example, the case in spatial models, R (0) is itself an eigenvalue, which usually cannot be expressed explicitly in the trait vectors under consideration. In that case, Q(Y| X):=-det (I-L(Y| X)) can often be used as fitness proxy, with L the next-generation matrix for a potential mutant characterized by the trait vector Y in the (constant) environment engendered by a resident characterized by X. If the trait space is connected, global uninvadability can be determined from it. Moreover, it can be used in all the usual local calculations like the determination of evolutionarily singular trait vectors and their local invadability and attractivity. We conclude with three extended case studies demonstrating the usefulness of Q: the calculation of ESSs under haplo-diploid genetics (I), of evolutionarily steady genetic dimorphisms (ESDs) with a priori proportionality of macro- and micro-gametic outputs (an assumption that is generally made but the fulfilment of which is a priori highly exceptional) (II), and of ESDs without such proportionality (III). These case studies should also have some interest in their own right for the spelled out calculation recipes and their underlying modelling methodology.     

Self-Improvement for Team-Players: The Effects of Individual Effort on Aggregated Group Information

By putting effort into behaviours like foraging or scanning for predators, an animal can improve the correctness of its personal information about the environment. For animals living in groups, the individual can gain further information if it is able to assess public information about the environment from other group members. Earlier work has shown that consensus group decisions based upon the public information available within the group are more likely to be correct than decisions based upon personal information alone, given that each individual in a group has a fixed probability of being correct. This study develops a model where group members are able to improve their personal likelihood of making a correct decision by conducting some level of (costly) effort. I demonstrate that there is an evolutionarily stable level of effort for all the individuals within the group, and the effort made by an individual should decrease with increasing group size. The relevance of these results to social decision making is discussed: in particular, these results are similar to standard theoretical predictions about the amount of vigilance shown by individuals decreasing with increasing group size. However, this model suggests that these results could come about where individuals are coordinating their effort within the group (unlike standard models, which assume that all individual effort is independent of the actions of others). This ties in with experimental findings where individuals have been shown to monitor the efforts of others.     

Neural control of behavioural choice in juvenile crayfish

Natural selection leads to behavioural choices that increase the animal''s fitness. The neuronal mechanisms underlying behavioural choice are still elusive and empirical evidence connecting neural circuit activation to adaptive behavioural output is sparse.We exposed foraging juvenile crayfish to approaching shadows of different velocities and found that slow-moving shadows predominantly activated a pair of giant interneurons, which mediate tail-flips that thrust the animals backwards and away from the approaching threat. Tail-flips also moved the animals farther away from an expected food source, and crayfish defaulted to freezing behaviour when faced with fast-approaching shadows. Under these conditions, tail-flipping, an ineffective and costly escape strategy was suppressed in favour of freezing, a more beneficial choice. The decision to freeze also dominated in the presence of a more desirable resource; however, the increased incentive was less effective in suppressing tail-flipping when paired with slow-moving visual stimuli that reliably evoked tail-flips in most animals. Together this suggests that crayfish make value-based decisions by weighing the costs and benefits of different behavioural options, and they select adaptive behavioural output based on the activation patterns of identifiable neural circuits.     

Suppression of social conflict and evolutionary transitions to cooperation

Evolutionary conflict arises at all levels of biological organization and presents a barrier to the evolution of cooperation. This barrier can be overcome by mechanisms that reduce the disparity between the fitness optima of subunits, sometimes called the "battleground" of conflict. An alternative, unstudied possibility is that effort invested in conflict is unprofitable. This possibility has received little attention because most existing models of social conflict assume that fitness depends on the ratio of players' conflict efforts, so that "peaceful" outcomes featuring zero conflict effort are evolutionarily unstable. Here I show that peaceful outcomes are stable where success depends on the difference rather than the ratio of efforts invested in conflict. These difference form models are particularly appropriate to model strategies of suppression or policing. The model suggests that incomplete information and asymmetries in strength can act to eliminate costly conflict within groups, even among unrelated individuals, and thereby facilitate the evolution of cooperation.     

Multiple patterns of parental care

Many animals show multiple patterns of parental care, where more than one of the four basic patterns (biparental care, uniparental care by males or females, or no care) is present within a single population during a single breeding season. We consider three reasons for the existence of multiple patterns of parental care: (1) mixed-strategy behaviours; (2) time-dependent behaviour with parents changing their care decision during the breeding season; and (3) quality differences between individuals leading to different care decisions being made depending on the qualities of both parents. The basic framework we use to investigate these is a two-stage game-theoretical model, and we highlight the importance of including feedback between the parental care decisions made by population members and the probability that a deserting individual will find a new mate. Including this feedback may introduce a nonlinear dependence of the fitness payoffs on the frequencies with which the pure strategies ('care' and 'desert') are played by each of the sexes. This can have important consequences for the existence of evolutionarily stable strategies (ESSs). For example, mixed-strategy ESSs may exist (an outcome forbidden if the feedback is not included) and, in one model, the feedback also prevents uniparental care by either sex from being evolutionarily stable. We also point out that decisions made by animals without dependent offspring can have important consequences for observed parental care behaviour. Copyright 1999 The Association for the Study of Animal Behaviour.     

A new mechanism for recurrent adaptive radiations

Models of adaptive radiation through intraspecific competition have attracted mounting attention. Here we show how extending such models in a simple manner, by including a quantitative trait under weak directional selection, naturally leads to rich macroevolutionary patterns involving recurrent adaptive radiations and extinctions. Extensive tests demonstrate the robustness of this finding to a wide range of variations in model assumptions. In particular, recurrent adaptive radiations and extinctions readily unfold both for asexual and for sexual populations. Since the mechanisms driving the investigated processes of endogenous diversification result from generic geometric features of the underlying fitness landscapes--frequency-dependent disruptive selection in one trait and weak directional selection in another--the reported phenomena can be expected to occur in a wide variety of eco-evolutionary settings.     

Efficacy and honesty in communication between relatives

Abstract The evolution of honest communication has recently become the focus of intense theoretical attention. However, strategic models dealing with honesty have largely ignored the implications of noise and perceptual error for signal evolution (just as models dealing with signal detection in the presence of noise ignore strategic issues). Here, I analyze an extended version of Maynard Smith's strategic model of signaling of need between relatives, the Philip Sidney game, that incorporates the possibility of perceptual error. I show that even in the presence of noise, there exists over a wide range of parameter values a unique, continuously stable signaling equilibrium, at which the signaler employs a costly display when needy but refrains from doing so when healthy. For a subset of this range, there also exists a second, lower cost signaling equilibrium that is not continuously stable. At the former equilibrium, predicted signal cost is inversely related to the coefficient of relatedness (r) between signaler and receiver. Cost is not, however, predicted to drop to zero even when r = 1 and there is no conflict of interest between the two (as is the case in errofree models), because it serves to enhance the efficacy of communication as well as to discourage deceit. Equilibrium signal cost is inversely related to the probability that the signaler is needy, and tends to increase with the level of noise. If noise becomes too great (i.e., if a detectable signal is too costly to produce), signaling is no longer stable; surprisingly, it is also unstable if the level of noise is too low (i.e., if a detectable signal is too cheap to produce).     

A theoretical model of the evolution of maternal effects under parent-offspring conflict

The evolution of maternal effects on offspring phenotype should depend on the extent of parent-offspring conflict and costs and constraints associated with maternal and offspring strategies. Here, we develop a model of maternal effects on offspring dispersal phenotype under parent-offspring conflict to evaluate such dependence. In the absence of evolutionary constraints and costs, offspring evolve dispersal rates from different patch types that reflect their own, rather than the maternal, optima. This result also holds true when offspring are unable to assess their own environment because the maternal phenotype provides an additional source of information. Consequently, maternal effects on offspring diapause, dispersal, and other traits that do not necessarily represent costly resource investment are more likely to maximize offspring than maternal fitness. However, when trait expression was costly, the evolutionarily stable dispersal rates tended to deviate from those under both maternal and offspring control. We use our results to (re)interpret some recent work on maternal effects and their adaptive value and provide suggestions for future work.     

The cost of dishonesty

The handicap principle states that stable biological signals must be honest and costly to produce. The cost of the signal should reflect the true quality of the signaller. Here, it is argued that honest signalling may be maintained although the used signals are not handicaps. A game theoretic model in the form of a game of signalling is presented: all the existing evolutionarily stable strategies (ESSs) are found. Honest and cheap signalling of male quality is shown to be evolutionarily stable if females divorce the mate if it turns out that he has cheated about his quality. However, for this ESS to apply, the cost of lost time must not be too great. The stability of the honest signalling is based on deceivers being prevented from spreading in the population because they suffer from a cost of divorce. Under some fairly strict conditions, a mixed polymorphism of dishonesty and honesty represents another possible ESS.     

Costs and Benefits of Chemical Defence in the Red Alga Bonnemaisonia hamifera

A number of studies have shown that the production of chemical defences is costly in terrestrial vascular plants. However, these studies do not necessarily reflect the costs of defence production in macroalgae, due to structural and functional differences between vascular plants and macroalgae. Using a specific culturing technique, we experimentally manipulated the defence production in the red alga Bonnemaisonia hamifera to examine if the defence is costly in terms of growth. Furthermore, we tested if the defence provides fitness benefits by reducing harmful bacterial colonisation of the alga. Costly defences should provide benefits to the producer in order to be maintained in natural populations, but such benefits through protection against harmful bacterial colonisation have rarely been documented in macroalgae. We found that algae with experimentally impaired defence production, but with an externally controlled epibacterial load, grew significantly better than algae with normal defence production. We also found that undefended algae exposed to a natural epibacterial load experienced a substantial reduction in growth and a 6-fold increase in cell bleaching, compared to controls. Thus, this study provides experimental evidence that chemical defence production in macroalgae is costly, but that the cost is outweighed by fitness benefits provided through protection against harmful bacterial colonisation.     

Optimization methods to solve adaptive management problems

Determining the best management actions is challenging when critical information is missing. However, urgency and limited resources require that decisions must be made despite this uncertainty. The best practice method for managing uncertain systems is adaptive management, or learning by doing. Adaptive management problems can be solved optimally using decision-theoretic methods; the challenge for these methods is to represent current and future knowledge using easy-to-optimize representations. Significant methodological advances have been made since the seminal adaptive management work was published in the 1980s, but despite recent advances, guidance for implementing these approaches has been piecemeal and study-specific. There is a need to collate and summarize new work. Here, we classify methods and update the literature with the latest optimal or near-optimal approaches for solving adaptive management problems. We review three mathematical concepts required to solve adaptive management problems: Markov decision processes, sufficient statistics, and Bayes’ theorem. We provide a decision tree to determine whether adaptive management is appropriate and then group adaptive management approaches based on whether they learn only from the past (passive) or anticipate future learning (active). We discuss the assumptions made when using existing models and provide solution algorithms for each approach. Finally, we propose new areas of development that could inspire future research. For a long time, limited by the efficiency of the solution methods, recent techniques to efficiently solve partially observable decision problems now allow us to solve more realistic adaptive management problems such as imperfect detection and non-stationarity in systems.