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Abstract

The term population viscosity refers to limited dispersal, which increases the genetic relatedness of neighbors. This effect both supports the evolution of altruism by focusing the altruists' gifts on relatives of the altruist, and also limits the extent to which altruism may emerge by exposing clusters of altruists to stiffer local competition. Previous analyses have emphasized the way in which these two effects can cancel, limiting the viability of altruism. These papers were based on models in which total population density was held fixed. We present here a class of models in which population density is permitted to fluctuate, so that patches of altruists are supported at a higher density than patches of non-altruists. Under these conditions, population viscosity can support the selection of both weak and strong altruism.

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... A similar issue exists with respect to the evolution of altruism, since partner choice/control mechanisms, such as voluntary reciprocal altruism (Axelrod, 1981), may be restricted to higher animals or may appear during later evolutionary stages. Spatial structure has been recognized as a general mechanism promoting the transition to altruism (Débarre et al., 2012;Van Baalen, 2007, 2008;Mitteldorf and Wilson, 2000). Spatial structure generally stems from local dispersal, which triggers the formation of clusters dominated by altruistic individuals, while individuals with similar phenotypes are positively assorted in space (Pepper, 2007;Wilson and Dugatkin, 1997). ...
... Spatial structure generally stems from local dispersal, which triggers the formation of clusters dominated by altruistic individuals, while individuals with similar phenotypes are positively assorted in space (Pepper, 2007;Wilson and Dugatkin, 1997). The balance between individual-level selection favouring cheaters and cluster-level selection favouring altruists ultimately determines the evolutionary outcome (Mitteldorf and Wilson, 2000;Van Baalen and Rand, 1998). Moreover, the coevolution of cooperation and dispersal can allow the emergence of altruism, with spatial clusters of altruistic individuals promoting the persistence and spread of altruistic phenotypes (Hochberg et al., 2008;Koella, 2000;Le Galliard et al., 2005;Mullon et al., 2018;Purcell et al., 2012). ...
... The interplay between three levels of organization The mechanism by which parasitic symbionts and hosts can invade mutualistic clusters is a two-species version of the tragedy of the commons (Feeny et al., 1990;Garrett, 1968;Hardin, 1998), which can be bypassed by local dispersal in the case of altruism (Mitteldorf and Wilson, 2000) as well as in the present case. Indeed, there is no transition to mutualism when dispersal is primarily global ( > 0.55), mutualists and parasites coexist for mixed dispersal strategy (0.55 > > 0.1), and mutualists almost outcompete parasites when dispersal is mainly local ( < 0.1, details not shown). ...
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Les domaines de l’écologie et l’évolution sont constitués de systèmes complexes – organismes, espèces, communautés – qui se prêtent mal à une approche réductionniste. Ces systèmes ont des propriétés émergentes qui dépassent la somme des propriétés de leurs parties. Leur étude demande alors de s’intéresser aux interactions entre les parties et le tout de ces systèmes. Par exemple, l’étude d’une métacommunauté ne peut pas se limiter à l’étude stricte du tout (la métacommunauté) ou l’étude stricte des parties (les communautés composant la métacommunauté). La compréhension de cet système complexe demande de considérer le tout, les parties, et les interactions entre eux. De plus, ces interactions peuvent être multidirectionnelles, elles ne sont pas exclusivement des parties vers le tout, la causalité réciproque est possible, le tout influençant alors les parties. Dans cette thèse nous explorons à travers trois systèmes biologiques distincts comment les interactions entre le tout et les parties définissent ces systèmes. La thèse est donc constitué de trois chapitres. Dans le premier nous explorons un modèle de métacommunauté simulant l’invasion de la pyrale du buis, un insecte herbivore invasif en Europe, et étudions les interactions entre les échelles spatiales locale et globale. Ce modèle écologique de dynamique des populations est calibré à partir de mesures empiriques sur le terrain et à travers une manipulation en mésocosme. Notre modèle reproduit l’instabilité des dynamiques locales. En effet, localement l’insecte s’éteint irrémédiablement à cause de sa sur-exploitation de sa ressource (le buis). Cependant, notre modèle montre que les interactions entre les communautés, grâce à la dispersion de l’insecte, peut mener à la persistance du système à l’échelle de la métacommunauté. De plus, nous montrons que la structure de la métacommunauté émerge des interactions entre les dynamiques locales. Le deuxième chapitre explore dans quelle mesure une interaction mutualiste entre un hôte et un symbionte peut émerger à partir d’une interaction parasitique en coévoluant avec la dispersion. Nous développons un modèle éco-évolutif individu-centré dans un espace spatialisé en 2D et considérons comme condition initiale une population d’hôtes en interaction avec une population de symbiontes parasitiques. Nous montrons que grâce à l’évolution d’une dispersion locale une structure spatiale peut émerger de la dynamique du système hôte-symbionte. L’émergence de cette structure spatiale induit la formation de plusieurs niveaux d’organisation en interactions entre eux : le niveau de l’individu, le niveau du regroupement spatial, et le niveau du paysage. Tandis que le niveau de l’individu favorise l’évolution du parasitisme, les deux niveaux supérieurs du regroupement spatial et de l’ensemble du paysage favorise l’évolution du mutualisme. Nous montrons que selon la force de la structure spatiale, modulée par l’intensité de la compétition à l’échelle du paysage, la transition du parasitisme vers le mutualisme peut se produire. Enfin, le dernier chapitre s’intéresse à l’évolution d’une stratégie d’acquisition de ressource chez des consommateurs dans un modèle éco-évolutif consommateurs-ressources. La littérature montre que la capacité des consommateurs à moduler activement leur manière de consommer les différentes ressources est un processus important dans le fonctionnement des écosystèmes, notamment leur stabilité. Cependant, ces résultats sont obtenus à partir de modèles de communautés fixes ce qui prive l’étude de certaines interactions potentielles entre le niveau de l’individu et celui de la communauté. À partir de notre modèle d’émergence de communautés nous montrons que la stratégie d’acquisition des ressources des consommateurs a un effet sur des propriétés de la communauté, notamment sa biomasse, sa productivité, sa diversité et sa stabilité. De plus, la structure de l’ensemble de la communauté module l’évolution des stratégies des consommateurs.
... A similar issue exists with respect to the evolution of altruism, since partner choice/control mechanisms, such as voluntary reciprocal altruism [Axelrod, 1981], may be restricted to higher animals or may appear during later evolutionary stages. Spatial structure has been recognized as a general mechanism promoting the transition to altruism [Mitteldorf and Wilson, 2000, Lion and Baalen, 2007, Débarre et al., 2012. Spatial structure generally stems from local dispersal, which triggers the formation of clusters dominated by altruistic individuals, while individuals with similar phenotypes are positively assorted in space Dugatkin, 1997, Pepper, 2007]. ...
... Spatial structure generally stems from local dispersal, which triggers the formation of clusters dominated by altruistic individuals, while individuals with similar phenotypes are positively assorted in space Dugatkin, 1997, Pepper, 2007]. The balance between individual-level selection favouring cheaters and cluster-level selection favouring altruists ultimately determines the evolutionary outcome Rand, 1998, Mitteldorf andWilson, 2000]. Moreover, the coevolution of cooperation and dispersal can allow the emergence of altruism, with spatial clusters of altruistic individuals promoting the persistence and spread of altruistic phenotypes [Koella, 2000, Le Galliard et al., 2005, Hochberg et al., 2008, Purcell et al., 2012, Mullon et al., 2018. ...
... The interplay between three levels of organization The mechanism by which parasitic symbionts and hosts can invade mutualistic clusters is a two-species version of the tragedy of the commons [Garrett, 1968, Feeny et al., 1990, Hardin, 1998], which can be bypassed by local dispersal in the case of altruism [Mitteldorf and Wilson, 2000] as well as in the present case. Indeed, there is no transition to mutualism when dispersal is primarily global (ε > 0.55), mutualists and parasites coexist for mixed dispersal strategy (0.55 > ε > 0.1), and mutualists almost outcompete parasites when dispersal is mainly local (ε < 0.1, details not shown). ...
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The evolution of mutualism between hosts and initially parasitic symbionts represents a major transition in evolution. Although vertical transmission of symbionts during host reproduction and partner control both favour the stability of mutualism, these mechanisms require specifically evolved features that may be absent during the transition. Therefore, the first steps of the transition from parasitism to mutualism are not fully understood. Spatial structure might be the key to this transition. We explore this hypothesis using a spatially explicit agent-based model. We demonstrate that, starting from a parasitic system with global dispersal, the coevolution between mutualistic effort and local dispersal of hosts and symbionts leads to a stable coexistence between parasites and mutualists. The local dispersal evolution mimics vertical transmission and triggers the formation of mutualistic clusters, counteracting the individual selection level of parasites that maintain global dispersal. However, the transition also requires competition between hosts in order to occur. Indeed, the transition occurs when mutualistic symbionts increase the density of hosts, which strengthens competition between hosts and disfavours parasitic host/symbiont pairs: mutualists create ecological conditions that allow their own spread. Therefore, the transition to mutualism may come from an eco-evolutionary feedback loop involving spatially structured population dynamics.
... Further progress in the field considered births and deaths: The second step of the dynamics, the one that allows a change of the strategy, is now interpreted as a death of a player followed by a birth. The new ecologic perspective allowed to assess the importance of new relevant issues, such as the fluctuation of the population density [17][18][19][20], the movement of agents [21][22][23][24][25], the spatial distribution of neighbors and their number [26,27], among others. Recent works also consider networks of interactions [7,12,[28][29][30][31][32], focus on the critical properties of the system [33][34][35], include other novel dynamic rules [36][37][38][39][40][41][42], analyze the formation of patterns [13,[43][44][45][46][47], and evaluate the effect on the population growing as external pressure rises [48]. ...
... Since births occur among neighboring sites, correlations are expected to be important, in general. Hence, we reconsider system (13)- (17), and try to express the three node moments as a function of the one and two node mean values. Although different approaches are possible (see for instance [80]), we explore here the so-called pair approximation. ...
... x i x j x j x k x j = x i x j , in general. For simplicity, we consider homogeneous situations for which system (13)- (17), within the pair approximation of Eq. (46), becomes ...
Article
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We study the evolution of cooperation as a birth-death process in spatially extended populations. The benefit from the altruistic behavior of a cooperator is implemented by decreasing the death rate of its direct neighbors. The cost of cooperation is the increase of a cooperator's death rate proportional to the number of its neighbors. When cooperation has higher cost than benefit, cooperators disappear. Then, the dynamics reduces to the contact process with defectors as the single-particle type. Increasing the benefit-cost ratio above 1, the extinction transition of the contact process splits into a set of nonequilibrium transitions between four regimes when increasing the baseline death rate p as a control parameter: (i) defection only, (ii) coexistence, (iii) cooperation only, (iv) extinction. We investigate the transitions between these regimes. As the main result, we find that full cooperation is established at the extinction transition as long as benefit is strictly larger than cost. Qualitatively identical phase diagrams are obtained for populations on square lattices and in pair approximation. Spatial correlations with nearest neighbors only are thus sufficient for sustained cooperation.
... In a recent study, Le Galliard et al. (2003) presented the analysis of a model accounting for population viscosity (limited dispersal of offspring at birth) combined with adult mobility, overlapping generations, and fluctuations in local population size caused by local interactions and demographic stochasticity. In that model, the costs of local competition do not completely negate the benefits of kin cooperation, a finding echoed by other recent theoretical analyses (Mitteldorf and Wilson 2000;Irwin and Taylor 2001). That study also highlighted the critical influence individual mobility exerts on the evolution of altruism: high altruism could evolve only in species with low mobility, whereas the evolutionary trajectory of highly mobile species was halted in a state of "quasi selfishness." ...
... The dynamical nature of local aggregation and contention in our model results from the stochastic nature of the demographic process and especially from the site opening process generated by individual mortality. The numerical model of Mitteldorf and Wilson (2000) also showed that population elasticity, that is, variable local density, can facilitate the evolution of altruism, even when generations do not overlap. In Nakamaru et al.'s (1997Nakamaru et al.'s ( , 1998 models, the availability of empty space was also a critical feature for the spread of cooperation. ...
... The adaptive increase of altruism would reduce the death rate and hence the rate of site opening: as a consequence, the selective pressure of local competition against altruism would be enhanced. Such a negative effect on the evolution of altruism might be offset, however, would some form of environmental stochasticity drive site opening, insensitive to the evolutionary change of altruism (Mitteldorf and Wilson 2000). ...
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Social behavior involves “staying and helping,” two individual attributes that vary considerably among organisms. Investigating the ultimate causes of such variation, this study integrates previously separate lines of research by analyzing the joint evolution of altruism and mobility. We unfold the network of selective pressures and derive how these depend on physiological costs, eco‐evolutionary feedbacks, and a complex interaction between the evolving traits. Our analysis highlights habitat saturation, both around individuals (local aggregation) and around unoccupied space (local contention), as the key mediator of altruism and mobility evolution. Once altruism and mobility are allowed to evolve jointly, three general insights emerge. First, the cost of mobility affects the origin of altruism, determining whether and how quickly selfishness is overcome. Second, the cost of altruism determines which of two qualitatively different routes to sociality are taken: an evolutionary reduction of mobility, resulting in higher habitat saturation, is either preceded or followed by the adaptive rise of altruism. Third, contrary to conventional expectations, a positive correlation between evolutionarily stable levels of altruism and mobility can arise; this is expected when comparing populations that evolved under different constraints on mobility or that differ in other life‐history traits.
... Novel insights will rely on models (conceptual or mathematical) that manage to resolve this tension, combining the potential for individual-level fitness benefits of flammability with the collective nature of fire spread within large groups of plants. Flammability differs markedly from other evolutionary systems in this sense, because group behaviours evolve most readily in small groups, when a high local density of cooperators or participants results in a local payoff for the individuals involved (and some nonparticipating neighbours) [35,36]. As such, the existing literature on evolution of cooperation, for example, offers few hints beyond the suggestion that evolving group behaviours in large groups is a real challenge. ...
... However, the fact that fire-prone and fire-suppressing landscapes were alternative stable states also demonstrates that flammability could not spontaneously spread within a fire-suppressing landscape to make it fire prone. This was true despite two key assumptions that are often invoked to explain the de novo evolution of group behaviours: (a) that dispersal is local, resulting in small patches of participants that are closely related or otherwise share participation traits [35,36], and (b) that payoffs are at least partly individually owned [61]. This case differs in one critical way: because fire can only percolate above some critical, non-trivial density of flammable individuals in the larger landscape, individuals only receive payoffs from participating when a large proportion of the individuals in the landscape also participate. ...
Article
Whether plants can evolve to promote flammability is controversial. Ecologically, fire only spreads in landscapes when many plants are flammable, but collective behaviours among large groups are difficult to evolve at the individual level. Here, we formulate a model that examines how flammability can spread from rarity, combining individual-level costs and payoffs of flammability with landscape-level fire spread, sufficiently generic to analogize flammability among grasses, Mediterranean systems, and others. We found that fire-prone and fire-suppressing landscapes, composed of flammable and non-flammable plants, respectively, were alternatively stable in some environments, and flammability therefore only increased from rarity in environments when fire-proneness was the only stable state. Thus, fire-vegetation feedbacks alone probably did not drive the evolution and spread of flammability. However, evolution of flammability did promote fire-proneness in temporally and spatially heterogeneous environments: when flammable plants already occupied some substantial fraction of a fire-prone landscape, a positive feedback with fire could maintain flammability in a decreasingly favourable environment, and fire feedbacks could expand the distribution of flammability traits from fire-prone into fire-suppressing areas in a heterogeneous landscape. Thus, fire feedbacks could potentially have promoted the widespread invasion and persistence of flammability traits to their current widespread prominence.
... The selection in our model was based on several realistic and general assumptions concerning the host's population structure and pathogen properties. We considered viscous animal populations [140,159,160], where limited dispersal makes infectious contact between relatives more likely [155]. The kin-specific bias of pathogen transmission might also be shaped by social and family structures, which should be considered in future simulations. ...
Article
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Aging is an evolutionary paradox. Several hypotheses have been proposed to explain it, but none fully explains all the biochemical and ecologic data accumulated over decades of research. We suggest that senescence is a primitive immune strategy which acts to protect an individual's kin from chronic infections. Older organisms are exposed to pathogens for a longer period of time and have a higher likelihood of acquiring infectious diseases. Accordingly, the parasitic load in aged individuals is higher than in younger ones. Given that the probability of pathogen transmission is higher within the kin, the inclusive fitness cost of infection might exceed the benefit of living longer. In this case, programmed lifespan termination might be an evolutionarily stable strategy. Here, we discuss the classical evolutionary hypotheses of aging and compare them with the pathogen control hypothesis, discuss the consistency of these hypotheses with existing empirical data, and present a revised conceptual framework to understand the evolution of aging.
... Yet, these authors ignore that multilevel selection (i.e., individual and group selection combined) has received broad support (e.g., Gilpin 1975;Wilson 1983;Sober & Wilson 1998;Gould 2002;Okasha 2006;Bijma et al. 2007;Godfrey-Smith 2009;Borrello 2010;Calcott & Sterelny 2011;Nowak & Highfield 2011;Wilson EO 2012;van Vliet & Doebeli 2019;Hertler et al. 2020;Cameron et al. 2021;Henriques et al. 2021). Hemelrijk (2002), for example, wrote: "The assumption that evolution occurs through a single evolutionary process is no longer tenable (e.g., see Plotkin & Odling-Smee 1981), and multiple-level selection theories have slowly become more accepted (e.g., Hogeweg 1994;Mitteldorf & Wilson 2000). Multiple-level selection processes may include some, or all, of the following factors: the multi-level character of biological systems and natural selection operating on them (Lewontin 1970;Hogeweg 1994;Sober & Wilson 1998), self-organization and its consequences for evolution (Boerlijst & Hogeweg 1991), and nonlinear genotypephenotype mappings (Kauffman 1993;Huynen & Hogeweg 1994;Kauffman 1995)." ...
... It is only that the benefit of altruism must preferentially accrue to other altruists and that the kin of an altruistic individual are often more likely to be altruists themselves. 2 Theoretical models have been used to demonstrated how the advantage that altruism gains from limited dispersal is exactly offset by the impact of kin competition (Taylor 1992). However, simulations (Mitteldorf & Wilson 2000) and empirical studies (Boots et al. 2021) have since shown that there are conditions under which population viscosity can support altruism. amplification of the coefficient of relatedness ( ). ...
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Background Kin and multilevel selection provide explanations for the existence of altruism based on traits or processes that enhance the inclusive fitness of an altruist individual. Kin selection is often based on individual-level traits, such as the ability to recognize other altruists, whereas multilevel selection requires a metapopulation structure and dispersal process. These theories are unified by the general principle that altruism can be fixed by positive selection provided the benefit of altruism is preferentially conferred to other altruists. Here we take a different explanatory approach based on the recently proposed concept of an “ecological scaffold”. We demonstrate that ecological conditions consisting of a patchy nutrient supply that generates a metapopulation structure, episodic mixing of groups, and severe nutrient limitation, can support or “scaffold” the evolution of altruism in a population of microbes by amplifying drift. This contrasts with recent papers in which the ecological scaffold was based on selective processes, and therefore demonstrates the power of the scaffolding even in the absence of selection. Results Using computer simulations motivated by a simple theoretical model, we show that, although an altruistic mutant can be fixed within a single population of non-altruists by drift when nutrients are severely limited, the resulting altruistic population remains vulnerable to non-altruistic mutants. We then show how the imposition of the “ecological scaffold” onto a population of non-altruists alters the balance between selection and drift in a way that supports the fixation and subsequent persistence of altruism despite the possibility of invasion by non-altruists. Conclusions The fixation of an altruistic mutant by drift is possible when supported by ecological conditions that impose a metapopulation structure, episodic mixing of groups, and severe nutrient limitation. This is significant because it offers an alternative explanation for the evolution of altruism based on drift rather than selection. Given the ubiquity of low-nutrient “oligotrophic” environments in which microbes exist (e.g., the open ocean, deep subsurface soils, or under the polar ice caps) our results suggest that altruistic and cooperative behaviors may be highly prevalent among microbial populations.
... If not only social interactions but also competitive interactions take place locally ("soft" selection [30,31]), altruists in assorted groups or domains tend to compete with other altruists, in which case the benefits of altruism may be largely or fully canceled by the concomitant increased competition. This local Malthusian trap is alleviated somewhat if the local carrying capacity increases with the proportion of altruists ("elastic" selection), which allows clusters of altruists to become net population sources [32]. Importantly, it can also be avoided if competitive interactions reach beyond the social group or neighborhood, so that altruists in assorted clusters can support each other at the expense of others [24,26,29,33]. ...
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Theories on the evolutionary origins of altruistic behavior have a long history and have become a canonical part of the theory of evolution. Nevertheless, the mechanisms that allow altruism to appear and persist are still incompletely understood. It is well known, however, that the spatial structure of populations is an important determinant. In both theoretical and experimental studies, much attention has been devoted to populations that are subdivided into discrete groups. Such studies typically imposed the structure and dynamics of the groups by hand. Here, we instead present a simple individual-based model in which altruistic organisms spontaneously self-organize into spatially separated colonies that themselves reproduce by binary fission and hence behave as Darwinian entities in their own right. Using software to automatically track the rise and fall of colonies, we are able to apply formal theory on multilevel selection and thus quantify the within- and among-group dynamics. This reveals that individual colonies inevitably succumb to defectors in a within-colony “tragedy of the commons”. Even so, altruism persists in the population because more altruistic colonies reproduce more frequently and drive less altruistic ones to extinction. Evidently, the colonies promote the selection of altruism but in turn depend on altruism for their existence; the selection of altruism hence involves a kind of evolutionary bootstrapping. The emergence of the colonies also depends crucially on the length scales of motility, altruism, and competition. This reconfirms the general relevance of these scales for social evolution, but also stresses that their impact can only be understood fully in the light of the emergent eco-evolutionary spatial patterns. The results also suggest that emergent spatial population patterns can function as a starting point for transitions of individuality.
... The mechanism by which parasitic symbionts and hosts can invade mutualistic clusters is a two-species version of the tragedy of the commons (Feeny et al., 1990;Hardin, 1968Hardin, , 1998. In the case of altruism, the tragedy of the commons can be bypassed by local dispersal which triggers the formation of cooperative clusters (Eldakar et al., 2010;Le Galliard, Ferriére, et al., 2003;Mitteldorf and Wilson, 2000), as in the present case. The evolution of altruism results from the conflict between two levels of selection, the organismic-level favouring cheaters and the group-level favoring altruism (Simon et al., 2013;Van Baalen and Rand, 1998;Wilson and Sober, 1989). ...
Article
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The evolution of mutualism between hosts and initially parasitic symbionts represents a major transition in evolution. Although vertical transmission of symbionts during host reproduction and partner control both favour the stability of mutualism, these mechanisms require specifically evolved features that may be absent in the first place. Therefore, the first steps of the transition from parasitism to mutualism may suffer from the cost of mutualism at the organismic level. We hypothesize that spatial structure can lead to the formation of higher selection levels favouring mutualism. This resembles the evolution of altruism, with the additional requirement that the offspring of mutualistic hosts and symbionts must co-occur often enough. Using a spatially explicit agent-based model we demonstrate that, starting from a parasitic system with global dispersal, the joint evolution of mutualistic effort and local dispersal of hosts and symbionts leads to a stable coexistence between parasites and mutualists. The evolution of local dispersal mimics vertical transmission and triggers the formation of mutualistic clusters, counteracting the organismic selection level of parasites that maintain global dispersal. The transition occurs when mutualistic symbionts increase the density of hosts, which strengthens competition between hosts and disfavours hosts inhabiting areas dominated by parasitic symbionts: mutualists construct the ecological conditions that allow their own spread. Therefore, the transition to mutualism may come from an eco-evolutionary feedback loop involving spatially structured population dynamics.
... Taylor's analysis [6] has motivated the development of an array of models which attempt to decouple the opposing effects of relatedness and kin competition by relaxing different assumptions made in his original model, and thereby shifting the relative scaling of competition and cooperation between kin. For example, population viscosity can be shown to promote altruism: when groups are able to expand in size [28] or into empty sites [29,30]; when traits may vary stochastically [31]; when individuals disperse in kin groups (i.e. 'budding dispersal'), maintaining high within-group relatedness while reducing competition in the natal patch [14]; when there are sex differences in dispersal rate [13]; and when dispersal rates are allowed to differ between altruists and cheats, giving rise to a scenario wherein altruists disperse at a lower rate than cheats [32] (see Cooper et al. [33] for further examples). ...
Article
A basic mechanism of kin selection is population viscosity, whereby individuals do not move far from their place of birth and hence tend to be surrounded by relatives. In such circumstances, even indiscriminate altruism among neighbours will often involve interactions between kin, which has a promoting effect on the evolution of altruism. This has the potential to explain altruistic behaviour across the whole tree of life, including in taxa for which recognition of kin is implausible. However, population viscosity may also intensify resource competition among kin, which has an inhibitory effect on altruism. Indeed, in the simplest scenario, in which individuals disperse with a fixed probability, these two effects have been shown to exactly cancel such that there is no net impact of viscosity on altruism. Here, we show that if individuals are able to disperse conditionally upon local density, they are favoured to do so, with more altruistic neighbourhoods exhibiting a higher rate of dispersal and concomitant relaxation of kin competition. Comparing across different populations or species, this leads to a negative correlation between overall levels of dispersal and altruism. We demonstrate both analytically and using individual-based simulations that population viscosity promotes the evolution of altruism under density-dependent dispersal.
... her local neighborhood, a cooperator's neighbor is more likely to be a cooperator than a defector's neighbor, i.e., P C|C > P C|D , because local dispersal induces positive spatial assortment (6,7,12,37). In particular, it is known that P C|C = P C | D + 1/(d − 1) in a sufficiently large random regular network, where d is the node degree (13). ...
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How do networks of social interaction govern the emergence and stability of prosocial behavior? Theoretical studies of this question typically assume unconditional behavior, meaning that an individual either cooperates with all opponents or defects against all opponents-an assumption that produces a pessimistic outlook for the evolution of cooperation, especially in highly connected populations. Although these models may be appropriate for simple organisms, humans have sophisticated cognitive abilities that allow them to distinguish between opponents and social contexts, so they can condition their behavior on the identity of opponents. Here, we study the evolution of cooperation when behavior is conditioned by social context, but behaviors can spill over between contexts. Our mathematical analysis shows that contextualized behavior rescues cooperation across a broad range of population structures, even when the number of social contexts is small. Increasing the number of social contexts further promotes cooperation by orders of magnitude.
... Population structure need not be constant. Changes in population viscosity can allow for the evolution of different types of cooperation [104]. The coevolution of population structure and cooperation has been proposed and subsequently demonstrated in mathematical models of Snowdrift and Prisoner's Dilemma games [105,106], with biofilms being a proposed example of this [107,108], as elaborated on in Box 3. HGT within groups can act as a mechanism to change population structure by increasing similarity between individuals in a population, which in turn increases between-group differences and accelerates group selection. ...
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Cooperation exists across all scales of biological organization, from genetic elements to complex human societies. Bacteria cooperate by secreting molecules that benefit all individuals in the population (i.e., public goods). Genes associated with cooperation can spread among strains through horizontal gene transfer (HGT). We discuss recent findings on how HGT mediated by mobile genetic elements promotes bacterial cooperation, how cooperation in turn can facilitate more frequent HGT, and how the act of HGT itself may be considered as a form of cooperation. We propose that HGT is an important enforcement mechanism in bacterial populations, thus creating a positive feedback loop that further maintains cooperation. To enforce cooperation, HGT serves as a homogenizing force by transferring the cooperative trait, effectively eliminating cheaters.
... Under these conditions, prosocial behavior will increase the likelihood that an individual's genetic information transmits to future generations, either through their offspring, or the offspring of other members of the group. Mitteldorf and Wilson (2000) showed that fluctuations in population density could temporarily increase the benefits of local cooperation, promoting the evolution of prosocial behavior. ...
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The primary goal of this article is to explain the crucial role of emotions in the moral behavior of social mammals. Morality can be understood as a natural system of reciprocal demands in which wolves are engaged from birth, and where the emotional bonds between members of the pack play a key role. Empirical evidence suggests that the relationship between emotions and social instincts allows wolves to exhibit morally qualified social behaviors, as evidenced by the complex social systems within wolf packs. The article draws connections between cognitive research on emotions and psychobiological systems to contemporary studies in wolf ethology. It provides empirical support to the philosophical hypothesis that emotions arise in response to a range of socially significant events. Thus, we aim to review the nature of the inherent emotional demands of morality and their relationship with the natural traits that allowed wolves to develop a complex social life. Therefore, the article presents the required elements for the emergence of inherent morality in mammals with a complex social life, which seems to be a strong argument in favor of a theory that provides an evolutionary basis for morality.
... Spatial game models assume individuals are more likely to interact with their neighbors than with distant ones. The spatial game dynamics has attracted increasing interest from different aspects and a considerable amount of research has been devoted (Nowak and May 1992;Lindgren and Nordahl 1994;Killingback and Doebeli 1996;Nakamaru et al. 1997Nakamaru et al. , 1998Szabó and Tőke 1998;van Baalen and Rand 1998;Brauchli et al. 1999;Mitteldorf and Wilson 2000;Nowak and Sigmund 2000;Hauert 2002;Le Galliard et al. 2003;Doebeli and Hauert 2005;Roca et al. 2009;Tarnita et al. 2009a;Nowak et al. 2010a, b). The main result is that spatial structure enables cooperators to form clusters and thereby reduces exploitation by defectors. ...
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A game-theoretical model is constructed to capture the effect of imitation on the evolution of cooperation. This imitation describes the case where successful individuals are more likely to be imitated by newcomers who will employ their strategies and social networks. Two classical repeated strategies ‘always defect (ALLD)’ and ‘tit-for-tat (TFT)’ are adopted. Mathematical analyses are mainly conducted by the method of coalescence theory. Under the assumption of a large population size and weak selection, the results show that the evolution of cooperation is promoted in this dynamic network. As we observed that the critical benefit-to-cost ratio is smaller compared to that in well-mixed populations. The critical benefit-to-cost ratio approaches a specific value which depends on three parameters, the repeated rounds of the game, the effective strategy mutation rate, and the effective link mutation rate. Specifically, for a very high value of the effective link mutation rate, the critical benefit-to-cost ratio approaches 1. Remarkably, for a low value of the effective link mutation rate, by letting the effective strategy mutation is nearly equal to zero, the critical benefit-to-cost ratio approaches \(1+\frac{1}{m-1}\) for the resulting highly connected networks, which allows TFT to be evolutionary stable. It illustrates that dominance of TFTs is associated with more connected networks. This research can enrich the theory of the coevolution of game strategy and network structure with dynamic imitation.
... Although we do not yet understand its basis, the evolution of kinrecognition and cooperative responses would be readily explicable via well-established effects on inclusive fitness (Hamilton, 1964;Mitteldorf & Wilson, 2000). Indeed, given their reproductive systems, we might expect kin cooperation to be especially strong among land plants. ...
Article
Plants were traditionally seen as rather passive actors in their environment, interacting with each other only in so far as they competed for the same resources. In the last 30 years, this view has been spectacularly overturned, with a wealth of evidence showing that plants actively detect and respond to their neighbours. Moreover, there is evidence that these responses depend on the identity of the neighbour, and that plants may cooperate with their kin, displaying social behaviour as complex as that observed in animals. These plant–plant interactions play a vital role in shaping natural ecosystems, and are also very important in determining agricultural productivity. However, in terms of mechanistic understanding, we have only just begun to scratch the surface, and many aspects of plant–plant interactions remain poorly understood. In this review, we aim to provide an overview of the field of plant–plant interactions, covering the communal interactions of plants with their neighbours as well as the social behaviour of plants towards their kin, and the consequences of these interactions. We particularly focus on the mechanisms that underpin neighbour detection and response, highlighting both progress and gaps in our understanding of these fascinating but previously overlooked interactions.
... A further approach based on a joint investment argument (Roberts and Sherratt, 1998) assumes that cooperative action is seen as a joint investment which triggers the continuation of cooperative action in order to avoid loss of the joint investment. Further theoretical approaches consider particular circumstances, such as the network structure of interactions or spatial location of individuals (Mitteldorf and Wilson, 2000;Rand and Nowak, 2013). Cooperation theory generally relies on the use of game theory tools for the conceptualization of situations that offer the opportunity of cooperation. ...
... A large and growing body of research 13,14,16,[19][20][21][22][23][24][25][26][27][28][29][30]32,[74][75][76][77][78][79][80][81][82][83][84][85][86] has shown that spatial structure can promote the evolution of cooperative or prosocial behaviours. Our work, while affirming this principle, reveals it to be more complicated than it may seem. ...
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Prosocial behaviours are encountered in the donation game, the prisoner’s dilemma, relaxed social dilemmas and public goods games. Many studies assume that the population structure is homogeneous, meaning that all individuals have the same number of interaction partners or that the social good is of one particular type. Here, we explore general evolutionary dynamics for arbitrary spatial structures and social goods. We find that heterogeneous networks, in which some individuals have many more interaction partners than others, can enhance the evolution of prosocial behaviours. However, they often accumulate most of the benefits in the hands of a few highly connected individuals, while many others receive low or negative payoff. Surprisingly, selection can favour producers of social goods even if the total costs exceed the total benefits. In summary, heterogeneous structures have the ability to strongly promote the emergence of prosocial behaviours, but they also create the possibility of generating large inequality. Prosocial behaviours are ubiquitous in nature. These building blocks of cooperative societies can come in many forms, depending on how the underlying social good is produced and distributed. In this study, the authors show that heterogeneous populations can strongly promote the evolution of prosocial behaviours. However, this efficient evolution reveals a thorny side of prosocial behaviours: they generate the possibility of widespread wealth inequality, even to the point of being a detriment to the poorest in the population. The authors provide a general framework that can be used to understand when this harmful prosociality will emerge in a population. These findings suggest that institutional interventions are often essential for maintaining equitable outcomes in heterogeneous societies.
... Hamilton's findings by introducing the counteracting effects of increased competition between 501 neighboring kin (Murray and Gerrard 1984;Wilson et al. 1992). More recent theoretical models 502 have recognized that even when accounting for these kin competition costs, in all but a few closed 503 systems (e. g. fig wasps), cooperation and dispersal should coevolve in a positive feedback: 504 cooperative social systems favor limited dispersal, and the population viscosity resulting from 505 limited dispersal makes cooperation more advantageous (Hochberg et al. 2008;Le Galliard et al. 506 2005;Mitteldorf and Wilson 2000;Platt and Bever 2009). A major empirical challenge for studies 507 of social evolution has been to test these models of the predicted relationship between social 508 systems and population structure. ...
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Relatively little is known about the processes shaping population structure in cooperatively breeding insect species, despite the long-hypothesized importance of population structure in shaping patterns of cooperative breeding. Polistes paper wasps are primitively eusocial insects, with a cooperative breeding system in which females often found nests in cooperative associations. Prior mark-recapture studies of Polistes have documented extreme female philopatry, although genetic studies frequently fail to detect the strong population structure expected for highly philopatric species. Together these findings have led to lack of consensus on the degree of dispersal and population structure in these species. This study assessed population structure of female P. fuscatus wasps at three scales: within a single site, throughout Central New York, and across the Northeastern USA. Patterns of spatial genetic clustering and isolation by distance were observed in nuclear and mitochondrial genomes at the continental scale. Remarkably, population structure was evident even at fine spatial scales within a single collection site. However, P. fuscatus had low levels of genetic differentiation across long distances. These results suggest that P. fuscatus wasps may employ multiple dispersal strategies, including extreme natal philopatry as well as longer distance dispersal. We observed greater genetic differentiation in mitochondrial genes than in the nuclear genome, indicative of increased dispersal distances in males. Our findings support the hypothesis that limited female dispersal contributes towards population structure in paper wasps.
... We note that our results mirror findings from evolutionary biology that across-individual genetic diversity can produce group-wide benefits [39]. We suspect that SVO agents can be leveraged in simulo to study open questions concerning the emergence and adaptiveness of human altruism [9,34]. ...
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Recent research on reinforcement learning in pure-conflict and pure-common interest games has emphasized the importance of population heterogeneity. In contrast, studies of reinforcement learning in mixed-motive games have primarily leveraged homogeneous approaches. Given the defining characteristic of mixed-motive games--the imperfect correlation of incentives between group members--we study the effect of population heterogeneity on mixed-motive reinforcement learning. We draw on interdependence theory from social psychology and imbue reinforcement learning agents with Social Value Orientation (SVO), a flexible formalization of preferences over group outcome distributions. We subsequently explore the effects of diversity in SVO on populations of reinforcement learning agents in two mixed-motive Markov games. We demonstrate that heterogeneity in SVO generates meaningful and complex behavioral variation among agents similar to that suggested by interdependence theory. Empirical results in these mixed-motive dilemmas suggest agents trained in heterogeneous populations develop particularly generalized, high-performing policies relative to those trained in homogeneous populations.
... Kümmerli et al. (2009) present an in depth look at the current landscape of research into limited dispersal. They acknowledges a great deal of interest from a great many authors on this very mechanism (Pollock, 1983;Grafen, 1984;Murray et al., 1984;Goodnight, 1992;Kelly, 1992;Nowak et al., 1992;Queller, 1992;Taylor, 1992a;Taylor, 1992b;Wilson et al., 1992;Kelly, 1994;Nowak et al., 1994;Queller et al., 1989;Frank, 1998;Van Baalen et al., 1998;Mitteldorf et al., 2000;Griffin et al., 2002;West et al., 2002;Hauert et al., 2004;Rousset, 2013;Gardner et al., 2006;Killingback et al., 2006;Lehmann et al., 2006;Ohtsuki et al., 2006;Traulsen et al., 2006) Dispersal rates and other characteristics vary greatly in nature with some organisms being motile throughout their lives, while others are adapted to move or be moved at precise, limited phases of their life cycles. Whatever the case, dispersing is a remarkable if costly behavior that does provides a number of benefits. ...
Thesis
Our relation to our kin shapes much of our social world. It's no surprise then, that how we recognize and react to our own kin has been a widely investigated topic. In particular, when tackling direct kin recognition, facial similarity has emerged as a putative cue of relatedness. In this thesis, I investigate whether or not the same can be said for third party kin recognition. Split between two lines of research, we explore individuals' predictions of nepotistic and mating behavior} in third party scenarios using facial stimuli. These two domains provide the backbone of our research. Categorization must serve action. So, what would strengthen the notion of a presence of third-party kin recognition in humans? Facial similarity \emph{must have} a context-dependent effect on participants predictions, susceptible to valence changes in scenarios and switches from the prosocial and mate choice domains. This is precisely what we set out to do with our two lines of research. Though our literature review revealed that when context is starved participants seem to be able to detect similarity and seemingly connect it to relatedness. Our nepotism and mating series of experiments, by re-inserting context, offers us a different conclusion altogether. Within scenarios in which valence is modified and our participants analysis is bounded by predictions made by kin selection, their choices do no reflect a connection between similarity and relatedness.
... Relatives thus interact more often than 2 random individuals. Compared with the well-mixed setting, population "viscosity" is known to promote cooperation (10) [although when the population density is fixed, local competition can cancel the cooperation-promoting effect of viscosity (11,12)]. Past decades have seen an intensive investigation of the evolution of cooperation in graph-structured populations (6)(7)(8)(9). ...
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Significance Evolving populations are constantly subjected to changing environmental conditions. The environment can determine how the expression of traits affects the individuals possessing them. Just as important, however, is the fact that the expression of traits can also alter the environment. We model this phenomenon by introducing game transitions into classical models of evolutionary dynamics. Interacting individuals receive payoffs from the games that they play, and these games can change based on past actions. We find that game transitions can significantly reduce the critical benefit-to-cost threshold for cooperation to evolve in social dilemmas. This result improves our understanding of when cooperators can thrive in nature, even when classical results predict a high critical threshold.
... Whether this competition between kin completely inhibits or merely reduces the selection for altruism has been shown to be heavily dependent on the assumptions of the model. For example, Wilson et al. [47] used an agent-based model, where females interact with neighbouring females on a grid and their offspring disperse locally, showed that local population regulation negated the benefits from altruism; Taylor [41,42] used an inclusive fitness approach to show the same result as Wilson et al. [47]; Gardner & West [10] find that budding (groups of individuals dispersing together) enables selection for altruism as it reduces local competition and increases the degree of kinship; Mittledorf & Wilson [33] find that allowing for elastic population densities, where patches of altruists are supported at higher densities than patches of non-altruists, can support the selection for altruism. ...
Preprint
We use a two-sex partial differential equation (PDE) model based on the Grandmother Hypothesis. We build on an earlier model by Kim et al. [27] by allowing for evolution in both longevity and age at last birth, and also assuming that post-fertile females support only their daughters' fertility. Similarly to Kim et al. [27], we find that only two locally stable equilibria exist: one corresponding to great ape-like longevities and the other corresponding to hunter-gatherer longevities. Our results show that grandmothering enables the transition between these two equilibria, without extending the end of fertility. Moreover, sensitivity analyses of the model show that male competition, arising from a skew in the mating sex ratio towards males, plays a significant role in determining whether the transition from great ape-like longevities to higher longevities is possible and the equilibrium value of the average adult lifespan. Whereas grandmothering effects have a significant impact on the equilibrium value of the average age at last birth and enable the transition to higher longevities, they have an insignificant impact on the equilibrium value of the average adult lifespan.
... The effect of certain "mass" variables on giving behavior has been highlighted in previous studies such as Brechet and Lambrecht (2006) ;Brandt, Hauert, and Sigmund (2006); and De Silva et al. (2009). Variables such as population size, population density, and the size of the labor force have been identified as contributing to the level of official aid (Mourão, 2012) or giving/altruism (Boone, 1996;Mitteldorf & Wilson, 2000;Moyo, 2009;Smith, 2003). These authors clarified how more dense locations (with respect to either the population or the size of the labor force) interact with each individual's propensity for giving and the different forms of giving selected. ...
Article
This research attempts to provide responses to the question “Does unemployment make people less likely to give?” by developing a theoretical model based on consumer choice and labor supply and using data from the World Giving Index, collected for 153 countries from 2010 to 2015. The results from panel data and from ordered probit estimations revealed that countries with higher unemployment rates (especially male and female youth unemployment) are associated with values related to a less generous profile on the part of respondents. Our results were obtained while controlling for a convenient set of variables, and the estimated coefficients generated an extension of this discussion toward the models of welfare states and the giving practices worldwide.
... Further progress in the field considered births and deaths: The second step of the dynamics, the one that allows a change of the strategy, is now interpreted as a death of a player followed by a birth. The new ecologic perspective allowed to assess the importance of new relevant issues, such as the fluctuation of the population density [17][18][19][20], the movement of agents [21][22][23][24][25], the spatial distribution of neighbours and their number [26,27], among others. Recent works also consider networks of interactions [7,12,[28][29][30][31][32], focus on the critical properties of the system [33][34][35], include other novel dynamic rules [36][37][38][39][40][41][42], analyze the formation of patterns [13,[43][44][45][46][47], and evaluate the effect on the population growing as external pressure rises [48]. ...
Preprint
We study the evolution of cooperation as a birth-death process in spatially extended populations. The benefit from the altruistic behavior of a cooperator is implemented by decreasing the death rate of its direct neighbours. The cost of cooperation is the increase of a cooperator's death rate proportional to the number of its neighbors. For any benefit-cost ratio above 1, the stable stationary concentrations of agents pass through four regimes as the baseline death rate $p$ increases: (i) defection only, (ii) coexistence, (iii) cooperation only, (iv) extinction. We investigate the transitions between these regimes. Qualitatively identical phase diagrams are obtained for populations on square lattices and in pair approximation. Spatial correlations with nearest neighbours only are thus sufficient for sustained cooperation.
... Thus, there appears to be an opportunity for the operation of group or multi-level selection [23,24]. A general requirement for group selection to be important is that intergroup differences be large compared with differences within groups [25,26]. In this context, Cowen [27] documented large differences in vital rates among different populations of sheephead. ...
Article
Sequential hermaphroditism, where males change to females (protandry) or the reverse (protogyny), is widespread in animals and plants, and can be an evolutionarily stable strategy (ESS) if fecundity rises faster with age in the second sex. Sequential hermaphrodites also generally have sex ratios skewed towards the initial sex, and standard theory based on fixed sexes indicates that this should reduce effective population size (Ne) and increase the deleterious effects of genetic drift. We show that despite having skewed sex ratios, populations that change sex at the ESS age do not have reduced Ne compared with fixed-sex populations with an even sex ratio. This implies that the ability of individuals to operate as both male and female allows the population to avoid some evolutionary constraints imposed by fixed sexes. Furthermore, Ne would be maximized if sex change occurred at a different (generally earlier) age than is selected for at the individual level, which suggests a potential conflict between individual and group selection. We also develop a novel method to quantify the strength of selection for sex reversal. © 2018 The Author(s) Published by the Royal Society. All rights reserved.
... Trying to address this issue led to the consideration of distributing the information encoded by the sequences in a mutualistic community of replicators known as the hypercycle model [9] in order to relax the error rate. However, the large amplitude of the oscillations of the stationary state of the hypercycle model could lead to its extinction upon stochastic perturbation which, together with the susceptibility of the hypercycle model to the invasion of selfish molecules, make it difficult for the community of replicators to emerge without a form of population viscosity [10]. Viscosity could have been provided by limited spatial dispersal over a substrate like clay [11,12] or as a limiting case, the compartmentalization of the sequences in a protocell acquiring a multi-level selection [13,14] structure when a the vesicle survival is coupled to its sequence content. ...
Article
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Protocell multilevel selection models have been proposed to study the evolutionary dynamics of vesicles encapsulating a set of replicating, competing and mutating sequences. The frequency of the different sequence types determines protocell survival through a fitness function. One of the defining features of these models is the genetic load generated when the protocell divides and its sequences are assorted between the offspring vesicles. However, these stochastic assortment effects disappear when the redundancy of each sequence type is sufficiently high. The fitness dependence of the vesicle with its sequence content is usually defined without considering a realistic account on how the lower level dynamics would specify the protocell fitness. Here, we present a protocell model with a fitness function determined by the output flux of a simple metabolic network with the aim of understanding how the evolution of both kinetic and topological features of metabolism would have been constrained by the particularities of the protocell evolutionary dynamics. In our model, the sequences inside the vesicle are both the carriers of information and Michaelis-Menten catalysts exhibiting saturation. We found that the saturation of the catalysts controlling the metabolic fluxes, achievable by modifying the kinetic or stoichiometric parameters, provides a mechanism to ameliorate the assortment load by increasing the redundancy of the catalytic sequences required to achieve the maximum flux. Regarding the network architecture, we conclude that combinations of parallel network motifs and bimolecular catalysts are a robust way to increase the complexity of the metabolism enclosed by the protocell.
... We found no effect of pairwise relatedness on the decision to nurse with one partner over another, as we had expected. Females may have been less inclined to fine-tune their discrimination [35,36,66,67] given that the females in their home area were on average genetically similar to them. This would mean that investment into another female's offspring during communal nursing could be compensated by the indirect fitness benefits gained. ...
Article
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Background Communal nursing in house mice is an example of cooperation where females pool litters in the same nest and indiscriminately nurse own and other offspring despite potential exploitation. The direct fitness benefits associated with communal nursing shown in laboratory studies suggest it to be a selected component of female house mice reproductive behaviour. However, past studies on communal nursing in free-living populations have debated whether it is a consequence of sharing the same nest or an active choice. Here using data from a long-term study of free-living, wild house mice we investigated individual nursing decisions and determined what factors influenced a female’s decision to nurse communally. Results Females chose to nurse solitarily more often than expected by chance, but the likelihood of nursing solitarily decreased when females had more partners available. While finding no influence of pairwise relatedness on partner choice, we observed that females shared their social environment with genetically similar individuals, suggesting a female’s home area consisted of related females, possibly facilitating the evolution of cooperation. Within such a home area females were more likely to nest communally when the general relatedness of her available options was relatively high. Females formed communal nests with females that were familiar through previous associations and had young pups of usually less than 5 days old. Conclusions Our findings suggest that communal nursing was not a by-product of sharing the same nesting sites, but females choose communal nursing partners from a group of genetically similar females, and ultimately the decision may then depend on the pool of options available. Social partner choice proved to be an integrated part of cooperation among females, and might allow females to reduce the conflict over number of offspring in a communal nest and milk investment towards own and other offspring. We suggest that social partner choice may be a general mechanism to stabilize costly cooperation. Electronic supplementary material The online version of this article (10.1186/s12983-018-0251-3) contains supplementary material, which is available to authorized users.
... Critically, proximity and recognition can enable cooperation even if individuals are not closely related, as long as they each share cooperative traits that they can pass on either genetically or culturally (Hamilton, 1964;McElreath and Boyd, 2007;Gintis, 2014). One road to this sort of assortment is limited dispersal, in which offspring live their lives near the location they were born (Koella, 2000;Mitteldorf and Wilson, 2000;Kummerli et al., 2009;. Another way to stabilize cooperation is to make it costly to do otherwise. ...
Article
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I discuss the function of social identity signaling in facilitating cooperative group formation, and how the nature of that function changes with the structure of social organization. I propose that signals of social identity facilitate assortment for successful coordination in large-scale societies, and that the multidimensional, context-dependent nature of social identity is crucial for successful coordination when individuals have to cooperate in different contexts. Furthermore, the structure of social identity is tied to the structure of society, so that as societies grow larger and more interconnected, the landscape of social identities grows more heterogeneous. This discussion bears directly on the need to articulate the dynamics of emergent, ephemeral groups as a major factor in human cultural evolution.
... Finally, ecological conditions such as spatial population structure may affect parent-offspring conflict. For example, dispersal involves the tendency of offspring to separate from locations where they originated (Mitteldorf and Wilson 2000). When there is limited dispersal, the spatial population structure is referred to as viscous. ...
... One of the great difficulties of Darwinian theory, recognized by Darwin himself, was the problem of altruism [35]; in particular, exploited cooperators are worse off than defectors. Hence, according to the basic principles of Darwinian selection, intuitively it seems almost certain that cooperation should go extinct. ...
Article
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We study a model for switching strategies in the Prisoner's Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model with each player following one strategy (cooperate or defect) at a time with all of its neighbors. We improve on the existing pair approximation (PA) model for this system by using approximate master equations (AMEs). We explore the parameter space demonstrating the accuracy of the approximation as compared with simulations. We study two variations of this partner-switching model to investigate the evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two variants.
... Ecologists and evolutionary biologists have long recognized that social interactions influence population structure by locally altering reproductive rates [122][123][124] , and theoretical and experimental work has demonstrated that the same principle applies for microorganisms (BOX 2). For example, public good secretion together with restricted movement and nutrient limitation within a biofilm can lead to patches of a single genotype 44,68,125 . ...
Article
Bacteria often live within matrix-embedded communities, termed biofilms, which are now understood to be a major mode of microbial life. The study of biofilms has revealed their vast complexity both in terms of resident species composition and phenotypic diversity. Despite this complexity, theoretical and experimental work in the past decade has identified common principles for understanding microbial biofilms. In this Review, we discuss how the spatial arrangement of genotypes within a community influences the cooperative and competitive cell-cell interactions that define biofilm form and function. Furthermore, we argue that a perspective rooted in ecology and evolution is fundamental to progress in microbiology.
Chapter
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Action selection is the task of doing the right thing at the right time. It requires the assessment of available alternatives, executing those most appropriate, and resolving conflicts among competing goals and possibilities. Using advanced computational modelling, this book explores cutting-edge research into action selection in nature from a wide range of disciplines, from neuroscience to behavioural ecology, and even political science. It delivers new insights into both detailed and systems-level attributes of natural intelligence and demonstrates advances in methodological practice. Contributions from leading researchers cover issues including whether biological action selection is optimal, neural substrates for action selection in the vertebrate brain, perceptual selection in decision making, and interactions between group and individual action selection. This first integrated review of action selection in nature contains a balance of review and original research material, consolidating current knowledge into a valuable reference for researchers while illustrating potential paths for future studies.
Chapter
Humans live in large and extensive societies and spend much of their time interacting socially. Likewise, most other animals also interact socially. Social behaviour is of constant fascination to biologists and psychologists of many disciplines, from behavioural ecology to comparative biology and sociobiology. The two major approaches used to study social behaviour involve either the mechanism of behaviour - where it has come from and how it has evolved, or the function of the behaviour studied. With guest articles from leaders in the field, theoretical foundations along with recent advances are presented to give a truly multidisciplinary overview of social behaviour, for advanced undergraduate and graduate students. Topics include aggression, communication, group living, sexual behaviour and co-operative breeding. With examples ranging from bacteria to social mammals and humans, a variety of research tools are used, including candidate gene approaches, quantitative genetics, neuro-endocrine studies, cost-benefit and phylogenetic analyses and evolutionary game theory.
Chapter
Action selection is the task of doing the right thing at the right time. It requires the assessment of available alternatives, executing those most appropriate, and resolving conflicts among competing goals and possibilities. Using advanced computational modelling, this book explores cutting-edge research into action selection in nature from a wide range of disciplines, from neuroscience to behavioural ecology, and even political science. It delivers new insights into both detailed and systems-level attributes of natural intelligence and demonstrates advances in methodological practice. Contributions from leading researchers cover issues including whether biological action selection is optimal, neural substrates for action selection in the vertebrate brain, perceptual selection in decision making, and interactions between group and individual action selection. This first integrated review of action selection in nature contains a balance of review and original research material, consolidating current knowledge into a valuable reference for researchers while illustrating potential paths for future studies.
Article
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The evolution of cooperation has gained more attention after Smith introduced game theory in the study of evolutionary biology. Subsequent works have extensively explained this phenomenon, consistently showing the importance of spatial structure for the evolution of cooperation. Here we analyze the effect of stochasticity on the evolution of cooperation in group-structured populations. We find a simple formula for the fixation probability of cooperators and show that cooperation can be favored by selection if a condition similar to Hamilton's rule is satisfied, which is also valid for strong selection and high migration. In fact, cooperation can be favored even in the absence of population viscosity and in the limit of an infinite number of finite-size groups. We discuss the importance of stochastic fluctuations in helping cooperation. We argue that this may be a general principle because fluctuations favoring the cooperators are often much more impactful than those favoring the defectors.
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Public Goods Games (PGGs) are n-person games with dependence of individual fitness benefits on the collective investment by the players. We have studied a simple PGG scenario played out by cooperating (C) and defecting (D) agents, applying the highly nonlinear threshold benefit function in an individual-based lattice model. A semi-analytical approximation of the lattice model has been developed and shown to describe the dynamics fairly well in the vicinity of the steady state. Besides the expected outcomes (i.e., the negative effect on cooperator persistence of higher cooperation costs and/or more intensive mixing of the population) we have found a surprising, counter-intuitive effect of the strength of selection on the steady state of the model. The effect is different at low and high cooperation costs, and it shows up only in the lattice model, suggesting that stochastic effects and higher order spatial correlations due to the emergent spatial clustering of cooperators (not taken into account in the semi-analytical approximation) must be responsible for the unexpected results for which we propose an intuitive explanation, present a tentative demonstration, and shortly discuss their biological relevance.
Chapter
The previous chapter depicted a rising chorus of consensus starting in the 1970s. Sober and Wilson describe how group selection was buried in the 1960s and 1970s and treated with utter contempt. It was so reviled that it was not forgotten, but recalled as an example of how not to think. Even in the 1980s, as Sober and Wilson recount, an unidentified, distinguished biologist once advised a younger colleague that there are three things that one does not defend in biology: group selection, phlogiston theory, and Lamarckian evolution. Indeed, discussion of group selection, at certain points in the history of evolutionary biology, evoked criticism and even ostracism, as illustrated by the following reflection shared by the still skeptical professor Detlef Fetchenhauer (2009):
Article
The outcome of sexual conflict can depend on the social environment, as males respond to changes in the inclusive fitness payoffs of harmfulness and harm females less when they compete with familiar relatives. Theoretical models also predict that if limited male dispersal predictably enhances local relatedness while maintaining global competition, kin selection can produce evolutionary divergences in male harmfulness among populations. Experimental tests of these predictions, however, are rare. We assessed rates of dispersal in female and male seed beetles Callosobruchus maculatus, a model species for studies of sexual conflict, in an experimental setting. Females dispersed significantly more often than males, but dispersing males travelled just as far as dispersing females. Next, we used experimental evolution to test whether limiting dispersal allowed the action of kin selection to affect divergence in male harmfulness and female resistance. Populations of C. maculatus were evolved for 20 and 25 generations under one of three dispersal regimens: completely free dispersal, limited dispersal, and no dispersal. There was no divergence among treatments in female reproductive tract scarring, ejaculate size, mating behaviour, fitness of experimental females mated to stock males, or fitness of stock females mated to experimental males. We suggest that this is likely due to insufficient strength of kin selection rather than a lack of genetic variation or time for selection. Limited dispersal alone is therefore not sufficient for kin selection to reduce male harmfulness in this species, consistent with general predictions that limited dispersal will only allow kin selection if local relatedness is independent of the intensity of competition among kin.
Article
Previous work with the spatial iterated prisoner's dilemma has shown that the ability to respond to a partner's defection by simply “walking away” allows so-called walk away cooperators to outcompete defectors as well as cooperators that do not respond to defection. These findings are important because they suggest a relatively simple route by which cooperation can evolve. But it remains to be seen just how robust the walk away strategy is to ecologically important variables such as population density, strategic error, and offspring dispersal. The results of our simulation experiments show that the evolutionary success of walk away cooperators decreases with decreasing population density and/or with increasing error. This relationship is best explained by the ways in which population density and error jointly affect the opportunity cost of walking away. This opportunity cost also explains why naive cooperators regularly outcompete walk away cooperators in pair-wise competition, something not observed in previous studies. Our results further show that local offspring dispersal can inhibit the evolution of cooperation by negating the protection low population density affords the most vulnerable cooperators. Our research identifies socio-ecological conditions in which forgiveness trumps flight in the spatial iterated prisoner's dilemma.
Article
Organisms that exploit different environments may experience a stochastic delay in adjusting their fitness when they switch habitats. We study two such organisms whose fitness is determined by the species composition of the local environment, as they interact through a public good. We show that a delay in the fitness adjustment can lead to the coexistence of the two species in a metapopulation, although the faster-growing species always wins in well-mixed competition experiments. Coexistence is favored over wide parameter ranges and is independent of spatial clustering. It arises when species are heterogeneous in their fitness and can keep each other balanced.
Article
How does delayed fitnesses adaptation after local habitat changes affect survival of species metapopulation? We study this question in a two-species model system, where the species composition of a local patch determines the reference fitness of all its individuals. When individuals move, this local species composition changes. As the local environment on the patch might adapt slowly to this change, we assume that individuals in turn adapt their fitness with a stochastic delay. We show that the combination of delay and spatial substructure can yield significantly different phase diagrams for the survival of these species with respect to models with immediate response. We investigate this exemplarily for the case where the two species interact via an exoproduct: thus, our population consists of a slow-growing producer species and a fast-growing dominant species. We provide a conceptual understanding of the role of delay by presenting analytic results in the well-mixed and low-mobility limit. By studying intermediate mobilities numerically, we ensure that our results are robust, and may be relevant to different ecological situations as well as microbial metapopulation experiments.
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With any theoretical model, the modeler must decide what kinds of detail to include and which simplifying assumptions to make. It could be assumed that models that include more detail are better, or more correct. However, no model is a perfect description of reality and the relative advantage of different levels of detail depends on the model's empirical purpose. We consider the specific case of how relatedness is modeled in the field of social evolution. Different types of model either leave relatedness as an independent parameter (open models), or include detail for how demography and life cycle determine relatedness (closed models). We exploit the social evolution literature, especially work on the evolution of cooperation, to analyze how useful these different approaches have been in explaining the natural world. We find that each approach has been successful in different areas of research, and that more demographic detail is not always the most empirically useful strategy.
Thesis
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The flexibility in grouping patterns which characterize species with high fission-fusion dynamics, presumably allows individuals to adjust their socio-spatial context according to variability in their ecological context. However, knowledge on how individual movement decisions relate to ecological variation and give rise to the observed grouping patterns is still scant. In this thesis I investigated the influence of social life on animal space-use and its relationship with the ability of animal groups to cope with environmental change. I explored the problem for species organized in groups which constantly change their size, composition and cohesion, known as species with high fission-fusion dynamics. In particular, I present an analysis directed to understand the relationship between space-use and social structure in a group of free-living spider monkeys (Ateles geoffroyi). I examined the socio-spatial patterns of adult individuals from the group, to evaluate changes from fruit-scarce to fruit-abundant periods in the size of the areas used, the size of monkey aggregations (subgroups) and in the occurrence of two types of association measures: spatial (based on the overlap of the areas used) and spatio-temporal (based on the co-occurrence of individuals in the same subgroup). Results indicated a more concentrated use of space, increased individual gregariousness and higher spatio-temporal association rates in the fruit-abundant seasons, as is compatible with an increase in passive associations. Nevertheless, results also suggested active associations in all the periods analyzed, which may influence individual space-use decisions, particularly for females. Altogether, the socio-spatial patterns of the spider monkeys seem to reflect temporal changes in both the ecological and social contexts experienced by individuals.
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Multiple scales in metapopulations can give rise to paradoxical behaviour: in a conceptual model for a public goods game, the species associated with a fitness cost due to the public good production can be stabilised in the well-mixed limit due to the mere existence of these scales. The scales in this model involve a length scale corresponding to separate patches, coupled by mobility, and separate time scales for reproduction and interaction with a local environment. Contrary to the well-mixed high mobility limit, we find that for low mobilities, the interaction rate progressively stabilises this species due to stochastic effects, and that the formation of spatial patterns is not crucial for this stabilisation.
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Natural selection is often regarded as a result of severe competition. Defect seems beneficial for a single individual in many cases.However, cooperation is observed in many levels of biological systems ranging from single cells to animals, including human society. We have yet known that in unstructured populations, evolution favors defectors over cooperators. On the other hand, there have been much interest on evolutionary games^1,2^ on structured population and on graphs^3-16^. Structures of biological systems and societies of animals can be taken as networks. They discover that network structures determine results of the games. Together with the recent interest of complex networks^17,18^, many researchers investigate real network structures. Recently even economists study firms' transactions structure^19^. Seminal work^11^ derives the condition of favoring cooperation for evolutionary games on networks, that is, benefit divided by cost, b/c , exceeds average degree, ( k ). Although this condition has been believed so far^20^, we find the condition is b/c ( k~nm~ ) instead. k~nm~ is the mean nearest neighbor degree. Our condition enables us to compare how network structure enhances cooperation across different kinds of networks. Regular network favors most, scale free network least. On ideal scale free networks, cooperation is unfeasible. We could say that ( k ) is the degree of itself, while k~nm~ is that of others. One of the most interesting points in network theory is that results depend not only on itself but also on others. In evolutionary games on network, we find the same characteristic.
Chapter
Evidence indicates that cognitive ability, brain size and life span co-evolved during primate evolution. It is not difficult to conceive how prolongation of the initial phases of the life span - gestation, infancy and adolescence and young adulthood - contributed to this co-evolution. Prolonged gestation would have provided larger brains at birth, whereas prolonged infancy, adolescence and young adulthood would have extended brain neuroplasticity to allow experience and learning to modify brain structure in individuals (genotypes) faced with new cognitive and social stresses, making them more competitive and reproductively successful. Natural selection in primates also involved genetically related kinships. Through cooperation within kinships, older genotypes who were most cognitively and socially competitive because of their larger brains could contribute to the success of their kin, indirectly extending their own genes in the general population. In some cases, a new longer-lived, more cognitively-capable, larger-brained primate species appeared.
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I was asked to explain why and how a Dutchman got to be a professor teaching animal behaviour in a French university. Someone must have thought that my story could provide some guidance for aspiring ethologists and behavioural ecologists. I am not so sure that my career path is one that should be followed, but perhaps someone can learn from my mistakes. I think I can now afford to write about them without much of a negative effect on my career. Not that I have bothered much about my ‘career’, but that is perhaps the core of my problem. I have never been good at preparing myself for the future, so after treading the mills of the Dutch educational system I found myself regularly confronted with steps in life that I should have prepared, if not better, then at least earlier. And so I ended up in a ‘cul de sac’. But let me start from the beginning. I can't tell you what kind of ‘—ist’ I am exactly at this point – primatologist, behavioural ecologist or evolutionary psychologist – but I went to the university to become an ethologist. The reason was simple: I liked animals a lot, and notably the furry ones. I definitely preferred seeing them alive, healthy and doing their own thing. I understood from books by the likes of Tinbergen, Lorenz, Wickler and Eibl-Eibesfeldt that ethologists did professionally what I liked to do anyway: watch animals behave.
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A viscous population (Hamilton, 1964) is one in which the movement of organisms from their place of birth is relatively slow. This viscosity has two important effects: one is that local interactions tend to be among relatives, and the other is that competition for resources tends to be among relatives. The first effect tends to promote and the second to oppose the evolution of altruistic behaviour. In a simulation model of Wilsonet al. (1992) these two factors appear to exactly balance one another, thus opposing the evolution of local altruistic behaviour. Here I show, with an inclusive fitness model, that the same result holds in a patchstructured population.
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MUCH attention has been given to the Prisoners' Dilemma as a metaphor for the problems surrounding the evolution of coopera-tive behaviour1-6. This work has dealt with the relative merits of various strategies (such as tit-for-tat) when players who recognize each other meet repeatedly, and more recently with ensembles of strategies and with the effects of occasional errors. Here we neglect all strategical niceties or memories of past encounters, considering only two simple kinds of players: those who always cooperate and those who always defect. We explore the consequences of placing these players in a two-dimensional spatial array: in each round, every individual 'plays the game' with the immediate neighbours; after this, each site is occupied either by its original owner or by one of the neighbours, depending on who scores the highest total in that round; and so to the next round of the game. This simple, and purely deterministic, spatial version of the Prisoners' Dilemma, with no memories among players and no strategical elaboration, can generate chaotically changing spatial patterns, in which cooperators and defectors both persist indefinitely (in fluctuating proportions about predictable long-term averages). If the starting configurations are sufficiently symmetrical, these ever-changing sequences of spatial patterns-dynamic fractals-can be extraordinarily beautiful, and have interesting mathematical properties. There are potential implications for the dynamics of a wide variety of spatially extended systems in physics and biology.
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Recent theoretical studies have indicated that the evolution of cooperation can be severely constrained by the spatial scales over which density regulation acts. If density regulation occurs on a local scale within a group, variation in productivity among groups is suppressed and the among-group component of selection is eliminated. Here, I present the results from a simple model that shows that there is more scope for the evolution of cooperation under density regulation than previously thought. This statement, however, is conditioned upon the fact that the traits under selection are themselves involved in the density-regulating process. Furthermore the results also suggest that traits directly involved in the density-regulating process, such as various competitive strategies or interference behaviours, are likely candidates for evolution through group selection, since they are not constrained by the ecological population structure to the same degree as other traits are. Laboratory experiments on group selection may provide some support for this hypothesis, since many traits that have been shown to be involved in the response to group selection are either directly or indirectly responsible for determining the strength of intraspecific competition.
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A bimolecular catalytic surface reaction is extended to include diffusion which yields mobilized coverage on the surface. We consider the reaction occurring in a tubular reactor with a convection flow where the reactants also diffuse. An initial boundary value problem in one-dimensional reaction-diffusion-convection equations is used in describing the model. We combine singular perturbation analysis with numerical simulations in studying the solution behavior in parameter space. We track the reaction front and the cause of period-2 oscillations. Compared with the case of having no surface diffusion, we observe regular oscillations instead of irregular oscillations. Compared with the nondiffusive nonconvective model, we obtain rich spatiotemporal patterns including stationary, oscillatory reaction fronts and multiple steady states.
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Limited dispersal is often thought to facilitate the evolution of altruism by increasing the degree of relatedness among interacting individuals. Limited dispersal can have additional effects, however, such as local population regulation, that inhibits the evolution of altruism. Many models of structured populations assume that a viscous stage of the life cycle alternates with a global mixing stage, which allows the advantages of interactions among close relatives without the disadvantages of local population regulation. Here we analyse a computer simulation model of pure population viscosity, in which offspring are always deposited close to parents and no global mixing stage exists. As expected, limited dispersal generates a high coefficient of relatedness among interacting individuals. Patches of altruists, however, are unable to export their productivity to other regions of the landscape and are easily invaded by selfish types from neighbouring patches. Unlike models of alternating viscosity, in which high relatedness and local population regulation can be decoupled, these two opposing effects are inextricably linked in purely viscous populations, which therefore are not conducive to the evolution of altruistic traits.
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In statistical physics we study macroscopic properties of matter on the basis of constituent particles, and in theoretical population biology we study features of populations on the basis of behaviors of individuals or, more basically and generally, on the basis of properties of self-replicating entities such as genes or chromosomes. Let us refer to any object that we broadly regard as a unit of replication as a ‘replicon’, thereby extending the original meaning used by molecular geneticists. Each replicon has a definite genetic state and undergoes birth and death. Therefore, in addition to ‘attraction and repulsion’, interactions between replicons typically includes ‘attacking and helping’, which affects the birth and death of recipients. The particular mode of interaction depends on a replicon’s state. This state is inherited from its parent replicon, and we can therefore study what type of interaction is prevalent in a population by examining that population’s dynamics. This is simply the evolution of behavior by natural selection.
The normal physiology of the hypothalamic-pituitary-testicular axis in man is reviewed. According to current concepts, LH plays an important role in the initiation and maintenance of spermatogenesis by stimulating Leydig cell production of high concentrations of T within the testes. FSH is thought to be important in spermatid maturation (spermiogenesis) during the initiation of spermatogenesis by stimulation of Sertoli cells. Studies of selective gonadotrophin replacement in experimentally-induced hypogonadotrophic hypogonadal men demonstrate that qualitatively normal sperm production can be achieved by replacement of either LH or FSH alone, but both LH and FSH are necessary to maintain quantitatively normal spermatogenesis. Studies of gonadotrophin replacement in spontaneously-occurring hypogonadotrophic men suggest that the requirement for FSH activity to stimulate sperm production is greatest during the initiation of sperm production at the time of puberty. The initiation of spermatogenesis in postpubertal men with acquired hypogonadotrophic hypogonadism and the maintenance of spermatogenesis after its initiation can often be achieved with LH activity alone.
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Cooperation in organisms, whether bacteria or primates, has been a difficulty for evolutionary theory since Darwin. On the assumption that interactions between pairs of individuals occur on a probabilistic basis, a model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game. Deductions from the model, and the results of a computer tournament show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established. Potential applications include specific aspects of territoriality, mating, and disease.
Article
The evolution of cooperation among unrelated individuals is studied in a lattice-structured habitat, where individuals interact locally only with their neighbors. The initial population includes Tit-for-Tat (abbreviated as TFT, indicating a cooperative strategy) and All Defect (AD, a selfish strategy) distributed randomly over the lattice points. Each individual plays the iterated Prisoner's Dilemma game with its nearest neighbors, and its total pay-off determines its instantaneous mortality. After the death of an individual, the site is replaced immediately by a copy of a randomly chosen neighbor. Mathematical analyses based on mean-field approximation, pair approximation, and computer simulation are applied. Models on one and two-dimensional regular square lattices are examined and compared with the complete mixing model. Results are: (1) In the one-dimensional model, TFT players come to form tight clusters. As the probability of iteration w increases, TFTs become more likely to spread. The condition for TFT to increase is predicted accurately by pair approximation but not by mean-field approximation. (2) If w is sufficiently large, TFT can invade and spread in an AD population, which is impossible in the complete mixing model where AD is always ESS. This is also confirmed by the invasion probability analysis. (3) The two-dimensional lattice model behaves somewhat in between the one-dimensional model and the complete mixing model. (4) The spatial structure modifies the condition for the evolution of cooperation in two different ways: it facilitates the evolution of cooperation due to spontaneously formed positive correlation between neighbors, but it also inhibits cooperation because of the advantage of being spiteful by killing neighbors and then replacing them.
Article
Group selection can overcome individual selection for selfishness and favour altruism if there is variation among the founders of the spatially distinct groups, and groups with many altruists become substantially larger (or exist longer) than groups with few. Whether altruism can evolve in populations that do not have an alternation of local population growth and global dispersal (“viscous populations”) has been disputed for some time. Limited dispersal protects the altruists from the non-altruists, but also hinders the export of altruism. In this article, we used the Pair Approximation technique (tracking the dynamics of pairs of neighbours instead of single individuals) to derive explicit invasion conditions for rare mutants in populations with limited dispersal. In such viscous populations, invading mutants form clusters, and ultimately, invasion conditions depend on the properties of such clusters. Thus there is selection on a higher level than that of the individual; in fact, invasion conditions define the unit of selection in viscous populations. We treat the evolution of altruism as a specific example, but the method is of more general interest. In particular, an important advantage is that the spatial aspects can be incorporated into game theory in a straightforward fashion; we will specify the ESS for a more general model.
Article
The evolution of cooperation is studied in a lattice-structured population, in which each individual plays the iterated Prisoner's Dilemma game with its neighbors. The population includes Tit-for-Tat (TFT, a cooperative strategy) and All Defect (AD, a selfish strategy) distributed over the lattice points. An individual dies randomly, and the vacant site is filled immediately by a copy of one of the neighbors in which the probability of colonization success by a particular neighbor is proportional to its score accumulated in the game. This "score-dependent fertility model" (or fertility model) behaves very differently from score-dependent viability model (viability model) studied in a previous paper. The model on a one-dimensional lattice is a analysed by invasion probability analysis, pair-edge method mean-field approximation, pair approximation, and computer simulation. Results are: (1) TFT players come to form tight clusters. When the probability of iteration w is large, initially rare TFT can invade and spread in a population dominated by AD, unlike in the complete mixing model. The condition for the increase of TFT is accurately predicted by all the techniques except mean-field approximation; (2) fertility model is much more favorable for the spread of TFT than the corresponding viability model, because spiteful killing of neighbors is favored in the viability model but not in the fertility model; (3) eight lattice games on two-dimensional lattice with different assumptions are examined. Cooperation and defects can coexist in the models of deterministic state change but not in the models of stochastic state change.
Systematics and the Origin of Species The evolution of cooperation in a lattice-structured popula-tion Score-dependent fertility model for the evolution of cooperation in a lattice
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The spatial dilemmas of evolution
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