Evolutionarily stable learning schedules and cumulative culture in discrete generation models.

Individual learning (e.g., trial-and-error) and social learning (e.g., imitation) are alternative ways of acquiring and expressing the appropriate phenotype in an environment. The optimal choice between using individual learning and/or social learning may be dictated by the life-stage or age of an organism. Of special interest is a learning schedule in which social learning precedes individual learning, because such a schedule is apparently a necessary condition for cumulative culture. Assuming two obligatory learning stages per discrete generation, we obtain the evolutionarily stable learning schedules for the three situations where the environment is constant, fluctuates between generations, or fluctuates within generations. During each learning stage, we assume that an organism may target the optimal phenotype in the current environment by individual learning, and/or the mature phenotype of the previous generation by oblique social learning. In the absence of exogenous costs to learning, the evolutionarily stable learning schedules are predicted to be either pure social learning followed by pure individual learning ("bang-bang" control) or pure individual learning at both stages ("flat" control). Moreover, we find for each situation that the evolutionarily stable learning schedule is also the one that optimizes the learned phenotype at equilibrium.

Von Neumann-Morgenstern Stable Sets in Matching Problems

The following properties of the core of a one well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (von Neumann-Morgenstern) stable sets in one-to-one matching problem only if it is a maximal set satisfying the following properties : (a) the core is a subset of the set; (b) the set is a lattice; (c) the set of unmatched agents is identical for any two matchings belonging to the set. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b) and (c). We also show that our main result does not extend from one-to-one matching problems to many-to-one matching problems.

Stable sets in one-seller assignment games

We consider von Neumann -- Morgenstern stable sets in assignment games with one seller and many buyers. We prove that a set of imputations is a stable set if and only if it is the graph of a certain type of continuous and monotone function. This characterization enables us to interpret the standards of behavior encompassed by the various stable sets as possible outcomes of well-known auction procedures when groups of buyers may form bidder rings. We also show that the union of all stable sets can be described as the union of convex polytopes all of whose vertices are marginal contribution payoff vectors. Consequently, each stable set is contained in the Weber set. The Shapley value, however, typically falls outside the union of all stable sets.

Communication, Coordination, and Efficiency in Evolutionary One-population Models

We analyze the role of commitment in pre-play communication for ensuring efficient evolutionarily stable outcomes in coordination games. All players are a priori identical as they are drawn from the same population. In games where efficient outcomes can be reached by players coordinating on the same action we find commitment to be necessary to enforce efficiency. In games where efficienct outcomes only result from play of different actions, communication without commitment is most effective although efficiency can no longer be guaranteed. Only when there are many messages then inefficient outcomes are negligible as their basins of attraction become very small.

Communication, coordination and efficiency in evolutionary one-population models

We analyze the role of commitment in pre-play communication for ensuringefficient evolutionarily stable outcomes in coordination games. All players are a priori identical as they are drawn from the same population. In games where efficient outcomes can be reached by players coordinating on the same action we find commitment to be necessary to enforce efficiency. In games where efficienct outcomes only result from play of different actions, communication without commitment is most effective although efficiency can no longer be guaranteed. Only when there are many messages then inefficient outcomes are negligible as their basins of attraction become very small.

Partitioning of reproduction in mother-daughter versus sibling associations : a test of optimal skew theory

A critical feature of cooperative animal societies is the reproductive skew, a shorthand term for the degree to which a dominant individual monopolizes overall reproduction in the group. Our theoretical analysis of the evolutionarily stable skew in matrifilial (i.e., mother-daughter) societies, in which relatednesses to offspring are asymmetrical, predicts that reproductive skews in such societies should tend to be greater than those of semisocial societies (i.e., societies composed of individuals of the same generation, such as siblings), in which relatednesses to offspring are symmetrical. Quantitative data on reproductive skews in semisocial and matrifilial associations within the same species for 17 eusocial Hymenoptera support this prediction. Likewise, a survey of reproductive partitioning within 20 vertebrate societies demonstrates that complete reproductive monopoly is more likely to occur in matrifilial than in semisocial societies, also as predicted by the optimal skew model.

On forward induction and evolutionary and strategic stability

We analyze which normal form solution concepts capture the notion offorward induction, as defined by van Damme (JET, 1989) in the classof generic two player normal form games preceded by an outsideoption. We find that none of the known strategic stability concepts(including Mertens stable sets and hyperstable sets) captures this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (Swinkels, JET, 1992) is always consistent with forward induction.

Adaptive diversity in heterogeneous environments for populations regulated by a mixture of soft and hard selection

The stable co-existence of two haploid genotypes or two species is studied in a spatially heterogeneous environment submitted to a mixture of soft selection (within-patch regulation) and hard selection (outside-patch regulation) and where two kinds of resource are available. This is analysed both at an ecological time-scale (short term) and at an evolutionary time-scale (long term). At an ecological scale, we show that co-existence is very unlikely if the two competitors are symmetrical specialists exploiting different resources. In this case, the most favourable conditions are met when the two resources are equally available, a situation that should favour generalists at an evolutionary scale. Alternatively, low within-patch density dependence (soft selection) enhances the co-existence between two slightly different specialists of the most available resource. This results from the opposing forces that are acting in hard and soft regulation modes. In the case of unbalanced accessibility to the two resources, hard selection favours the most specialized genotype, whereas soft selection strongly favours the less specialized one. Our results suggest that competition for different resources may be difficult to demonstrate in the wild even when it is a key factor in the maintenance of adaptive diversity. At an evolutionary scale, a monomorphic invasive evolutionarily stable strategy (ESS) always exists. When a linear trade-off exists between survival in one habitat versus that in another, this ESS lies between an absolute adjustment of survival to niche size (for mainly soft-regulated populations) and absolute survival (specialization) in a single niche (for mainly hard-regulated populations). This suggests that environments in agreement with the assumptions of such models should lead to an absence of adaptive variation in the long term.

Caste determination through mating in primitively eusocial societies.

Eusocial animal societies are typified by the presence of a helper (worker) caste which predominantly cares for young offspring in a social group while investing little in their own direct reproduction. A key question is what determines whether an individual becomes a worker or leaves to initiate her own reproduction. In some insects, caste is determined nutritionally during development. In others, and in vertebrate societies, adults are totipotent and the cues that determine caste are less well known. The mate limitation hypothesis (MLH) states that a female's mating status acts as a cue for caste determination: females that mate become reproductives, while those that fail to mate become workers. The MLH is consistent with empirical observations in sweat bees showing that over the course of the nesting season, there are increases in both the proportion of females that become reproductives and the frequency of males in the mating pool. We modelled a foundress's offspring sex-ratio strategy to investigate whether an increasingly male-biased operational sex-ratio over time is evolutionarily stable under the MLH. Our results indicate that such a pattern could occur if early workers were more valuable than late workers. This pattern was then more likely if male mortality was high, if worker mortality was low, if the value of a worker was high and if the period over which workers can help was short. Our results suggest that the MLH can be evolutionarily stable, but only under restrictive conditions. Manipulative experiments are now required to investigate whether mating determines caste in nature.

Dispersal and Inbreeding Avoidance.

Using a game-theoretical approach, we investigate the dispersal patterns expected if inbreeding avoidance were the only reason for dispersal. The evolutionary outcome is always complete philopatry by one sex. The rate of dispersal by the other sex depends on patch size and mating system, as well as inbreeding and dispersal costs. If such costs are sex independent, then two stable equilibria coexist (male or female philopatry), with symmetric domains of attraction. Which sex disperses is determined entirely by history, genetic drift, and gene flow. An asymmetry in costs makes one domain of attraction extend at the expense of the other. In such a case, the dispersing sex might also be, paradoxically, the one that incurs the higher dispersal costs. As asymmetry increases, one equilibrium eventually disappears, which may result in a sudden evolutionary shift in the identity of the dispersing sex. Our results underline the necessity to control for phylogenetic relationships (e.g., through the use of independent-comparisons methods) when investigating empirical trends in dispersal. Our model also makes quantitative predictions on the rate of dispersal by the dispersing sex and suggests that inbreeding avoidance may only rarely be the sole reason for dispersal.

A model for the evolution of reinforcement learning in fluctuating games

Many species are able to learn to associate behaviours with rewards as this gives fitness advantages in changing environments. Social interactions between population members may, however, require more cognitive abilities than simple trial-and-error learning, in particular the capacity to make accurate hypotheses about the material payoff consequences of alternative action combinations. It is unclear in this context whether natural selection necessarily favours individuals to use information about payoffs associated with nontried actions (hypothetical payoffs), as opposed to simple reinforcement of realized payoff. Here, we develop an evolutionary model in which individuals are genetically determined to use either trial-and-error learning or learning based on hypothetical reinforcements, and ask what is the evolutionarily stable learning rule under pairwise symmetric two-action stochastic repeated games played over the individual's lifetime. We analyse through stochastic approximation theory and simulations the learning dynamics on the behavioural timescale, and derive conditions where trial-and-error learning outcompetes hypothetical reinforcement learning on the evolutionary timescale. This occurs in particular under repeated cooperative interactions with the same partner. By contrast, we find that hypothetical reinforcement learners tend to be favoured under random interactions, but stable polymorphisms can also obtain where trial-and-error learners are maintained at a low frequency. We conclude that specific game structures can select for trial-and-error learning even in the absence of costs of cognition, which illustrates that cost-free increased cognition can be counterselected under social interactions.

Optimal latent period in a bacteriophage population model structured by infection-age

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. The time till lysis (or latent period) is assumed to have an arbitrary distribution. We have carried out an optimization procedure, and we have found that the latent period corresponding to maximal fitness (i.e. maximal growth rate of the bacteriophage population) is of fixed length. We also study the dependence of the optimal latent period on the amount of susceptible bacteria and the number of virions released by a single infection. Finally, the evolutionarily stable strategy of the latent period is also determined as a fixed period taking into account that super-infections are not considered

Conditional male dimorphism and alternative reproductive tactics in a Neotropical arachnid (Opiliones)

In arthropods, most cases of morphological dimorphism within males are the result of a conditional evolutionarily stable strategy (ESS) with status-dependent tactics. In conditionally male-dimorphic species, the status` distributions of male morphs often overlap, and the environmentally cued threshold model (ET) states that the degree of overlap depends on the genetic variation in the distribution of the switchpoints that determine which morph is expressed in each value of status. Here we describe male dimorphism and alternative mating behaviors in the harvestman Serracutisoma proximum. Majors express elongated second legs and use them in territorial fights; minors possess short second legs and do not fight, but rather sneak into majors` territories and copulate with egg-guarding females. The static allometry of second legs reveals that major phenotype expression depends on body size (status), and that the switchpoint underlying the dimorphism presents a large amount of genetic variation in the population, which probably results from weak selective pressure on this trait. With a mark-recapture study, we show that major phenotype expression does not result in survival costs, which is consistent with our hypothesis that there is weak selection on the switchpoint. Finally, we demonstrate that switchpoint is independent of status distribution. In conclusion, our data support the ET model prediction that the genetic correlation between status and switchpoint is low, allowing the status distribution to evolve or to fluctuate seasonally, without any effect on the position of the mean switchpoint.

Variation in habitat choice and delayed reproduction: Adaptive queuing strategies or individual quality differences?

In most species, some individuals delay reproduction or occupy inferior breeding positions. The queue hypothesis tries to explain both patterns by proposing that individuals strategically delay breeding (queue) to acquire better breeding or social positions. In 1995, Ens, Weissing, and Drent addressed evolutionarily stable queuing strategies in situations with habitat heterogeneity. However, their model did not consider the non - mutually exclusive individual quality hypothesis, which suggests that some individuals delay breeding or occupy inferior breeding positions because they are poor competitors. Here we extend their model with individual differences in competitive abilities, which are probably plentiful in nature. We show that including even the smallest competitive asymmetries will result in individuals using queuing strategies completely different from those in models that assume equal competitors. Subsequently, we investigate how well our models can explain settlement patterns in the wild, using a long-term study on oystercatchers. This long-lived shorebird exhibits strong variation in age of first reproduction and territory quality. We show that only models that include competitive asymmetries can explain why oystercatchers' settlement patterns depend on natal origin. We conclude that predictions from queuing models are very sensitive to assumptions about competitive asymmetries, while detecting such differences in the wild is often problematic.

The evolution of begging: Signaling and sibling competition

In many species, young solicit food from their parents, which respond by feeding them. Because of the difference in genetic make-up between parents and their offspring and the consequent conflict, this interaction is often studied as a paradigm for the evolution of communication. Existent theoretical models demonstrate that chick signaling and parent responding can be stable if solicitation is a costly signal. The marginal cost of producing stronger signals allows the system to converge to an equilibrium: young beg with intensity that reflects their need, and parents use this information to maximize their own inclusive fitness. However, we show that there is another equilibrium where chicks do not beg and parents’ provisioning effort is optimal with respect to the statistically probable distribution of chicks’ states. Expected fitness for parents and offspring at the nonsignaling equilibrium is higher than at the signaling equilibrium. Because nonsignaling is stable and it is likely to be the ancestral condition, we would like to know how natural systems evolved from nonsignaling to signaling. We suggest that begging may have evolved through direct sibling fighting before the establishment of a parental response, that is, that nonsignaling squabbling leads to signaling. In multiple-offspring broods, young following a condition-dependent strategy in the contest for resources provide information about their condition. Parents can use this information even though it is not an adaptation for communication, and evolution will lead the system to the signaling equilibrium. This interpretation implies that signaling evolved in multiple-offspring broods, but given that signaling is evolutionarily stable, it would also be favored in species which secondarily evolved single-chick broods.