Evolution of dispersal under spatio-temporal heterogeneity.

Theoretical studies over the past decades have revealed various factors that favor or disfavor the evolution of dispersal. Among these, environmental heterogeneity is one driving force that can impact dispersal traits, because dispersing individuals can obtain a fitness benefit through finding better environments. Despite this potential benefit, some previous works have shown that the existence of spatial heterogeneity hinders evolution of dispersal. On the other hand, temporal heterogeneity has been shown to promote dispersal through a bet-hedging mechanism. When they are combined in a patch-structured population in which the quality of each patch varies over time independently of the others, it has been shown that spatiotemporal heterogeneity can favor evolution of dispersal. When individuals can use patch quality information so that dispersal decision is conditional, the evolutionary outcome can be different since individuals have options to disperse more/less offspring from bad/good patches. In this paper, we generalize the model and results of previous studies. We find richer dynamics including bistable evolutionary dynamics when there is arrival bias towards high-productivity patches. Then we study the evolution of conditional dispersal strategy in this generalized model. We find a surprising result that no offspring will disperse from a patch whose productivity was low when these offspring were born. In addition to mathematical proofs, we also provide intuition behind this initially counter-intuitive result based on reproductive-value arguments. Dispersal from high-productivity patches can evolve, and its parameter dependence behaves similarly, but not identically, to the case of unconditional dispersal. Our results unveil an importance of whether or not individuals can use patch quality information in dispersal evolution.

Evolutionary stability of cooperation in indirect reciprocity under noisy and private assessment.

Indirect reciprocity is a mechanism that explains large-scale cooperation in humans. In indirect reciprocity, individuals use reputations to choose whether or not to cooperate with a partner and update others' reputations. A major question is how the rules to choose their actions and the rules to update reputations evolve. In the public reputation case where all individuals share the evaluation of others, social norms called Simple Standing (SS) and Stern Judging (SJ) have been known to maintain cooperation. However, in the case of private assessment where individuals independently evaluate others, the mechanism of maintenance of cooperation is still largely unknown. This study theoretically shows for the first time that cooperation by indirect reciprocity can be evolutionarily stable under private assessment. Specifically, we find that SS can be stable, but SJ can never be. This is intuitive because SS can correct interpersonal discrepancies in reputations through its simplicity. On the other hand, SJ is too complicated to avoid an accumulation of errors, which leads to the collapse of cooperation. We conclude that moderate simplicity is a key to stable cooperation under the private assessment. Our result provides a theoretical basis for the evolution of human cooperation.

Ancestral social environments plus nonlinear benefits can explain cooperation in human societies.

Human cooperation (paying a cost to benefit others) is puzzling from a Darwinian perspective, particularly in groups with strangers who cannot repay nor are family members. The beneficial effects of cooperation typically increase nonlinearly with the number of cooperators, e.g., increasing returns when cooperation is low and diminishing returns when cooperation is high. Such nonlinearity can allow cooperation between strangers to persist evolutionarily if a large enough proportion of the population are already cooperators. However, if a lone cooperator faces a conflict between the group's and its own interests (a social dilemma), that raises the question of how cooperation arose in the first place. We use a mathematically tractable evolutionary model to formalise a chronological narrative that has previously only been investigated verbally: given that ancient humans interacted mostly with family members (genetic homophily), cooperation evolved first by kin selection, and then persisted in situations with nonlinear benefits as homophily declined or even if interactions with strangers became the norm. The model also predicts the coexistence of cooperators and defectors observed in the human population (polymorphism), and may explain why cooperators in behavioural experiments prefer to condition their contribution on the contributions of others (conditional cooperation in public goods games).

Reputation structure in indirect reciprocity under noisy and private assessment.

Evaluation relationships are pivotal for maintaining a cooperative society. A formation of the evaluation relationships has been discussed in terms of indirect reciprocity, by modeling dynamics of good or bad reputations among individuals. Recently, a situation that individuals independently evaluate others with errors (i.e., noisy and private reputation) is considered, where the reputation structure (from what proportion of individuals in the population each receives good reputations, defined as goodness here) becomes complex, and thus has been studied mainly with numerical simulations. The present study gives a theoretical analysis of such complex reputation structure. We formulate the time change of goodness of individuals caused by updates of reputations among individuals. By considering a large population, we derive dynamics of the frequency distribution of goodnesses. An equilibrium state of the dynamics is approximated by a summation of Gaussian functions. We demonstrate that the theoretical solution well fits the numerical calculation. From the theoretical solution, we obtain a new interpretation of the complex reputation structure. This study provides a novel mathematical basis for cutting-edge studies on indirect reciprocity.

Non-zero-sum neutrality test for the tropical rain forest community using long-term between-census data.

For community ecologists, "neutral or not?" is a fundamental question, and thus, rejecting neutrality is an important first step before investigating the deterministic processes underlying community dynamics. Hubbell's neutral model is an important contribution to the exploration of community dynamics, both technically and philosophically. However, the neutrality tests for this model are limited by a lack of statistical power, partly because the zero-sum assumption of the model is unrealistic. In this study, we developed a neutrality test for local communities that implements non-zero-sum community dynamics and determines the number of new species (N sp) between observations. For the non-zero-sum neutrality test, the model distributed the expected N sp, as calculated by extensive simulations, which allowed us to investigate the neutrality of the observed community by comparing the observed N sp with distributions of the expected N sp derived from the simulations. For this comparison, we developed a new "non-zero-sum N sp test," which we validated by running multiple neutral simulations using different parameter settings. We found that the non-zero-sum N sp test rejected neutrality at a near-significance level, which justified the validity of our approach. For an empirical test, the non-zero-sum N sp test was applied to real tropical tree communities in Panama and Malaysia. The non-zero-sum N sp test rejected neutrality in both communities when the observation interval was long and N sp was large. Hence, the non-zero-sum N sp test is an effective way to examine neutrality and has reasonable statistical power to reject the neutral model, especially when the observed N sp is large. This unique and simple approach is statistically powerful, even though it only employs two temporal sequences of community data. Thus, this test can be easily applied to existing datasets. In addition, application of the test will provide significant benefits for detecting changing biodiversity under climate change and anthropogenic disturbance.

Impact of social dominance on the evolution of individual learning.

A major question in cultural-evolution studies is the phenotype of individual learners. Evidence suggests that social dominance is one influential factor, where socially subordinate individuals are more apt to learning of trial-and-error type than the dominants. Despite the accumulating evidence, the evolutionary dynamics leading to such outcomes remains largely elusive, partly because of the cost of individual learning. Here, we provide an evolutionary game framework to study the influence of social dominance on individual's learning decisions. We show that subordinates are indeed more apt to individual learning, because they gain a lot when individual learning is successful but lose little when it fails. We also predict that an evolutionary limit-cycle, in which dominants' and subordinates' behavior change over evolutionary time, may occur in such a case. We additionally showed that group-wide knowledge-gain is poor in egalitarian groups compared to moderately despotic ones. Our model sheds light onto the consequence of tactics played between dominants and subordinates for the evolution of individual learning.

Fecundability and Sterility by Age: Estimates Using Time to Pregnancy Data of Japanese Couples Trying to Conceive Their First Child with and without Fertility Treatment.

Fecundability, the probability of conception in a month or in a menstrual cycle, varies across and within age groups for both women and men. Fertility treatment has become common in a number of countries including Japan, but its impact on the age pattern of fecundability is unknown. By utilizing the previously collected data on time to pregnancy (TTP) of Japanese couples trying to conceive their first child, the present study aimed to estimate fecundability and sterility by women's age and to assess how the estimates may differ by including or excluding assisted conceptions. Duration between discontinuing contraception and conception (including both natural and assisted) resulted in a live birth was called TTP-all, and the duration ending with natural conception was called TTP-natural. TTP-natural was censored when a participant received fertility consultation or treatment. A zero-inflated beta distribution model was used to estimate a proportion of sterile (zero probability of conception) and a distribution of fecundability for each age group. Parameters of the distribution were estimated using the maximum likelihood method. When TTP-all and TTP-natural were used, the sterile proportion of the whole sample was, respectively, 2% and 14%, and the median (interquartile range) of fecundability was, respectively, 0.10 (0.04, 0.19) and 0.11 (0.05, 0.19). The median (interquartile range) of fecundability was 0.18 (0.10, 0.29) for women aged 24 years or younger and 0.05 (0.02, 0.13) for 35-39 years old when TTP-all was used, and the estimates were quite similar with those based on TTP-natural: it was 0.18 (0.10, 0.29) for women aged 24 years or younger and 0.06 (0.00, 0.15) for 35-39 years old. Exclusion of assisted conceptions resulted in larger proportions of sterility, but it had little impact on median or interquartile ranges of fecundability estimates. Fecundability is overall lower at higher ages, while interquartile ranges are overlapping, suggesting that inter-individual variability of fecundability within an age group is as large as the variability across age groups.

Coevolutionary dynamics of genetic traits and their long-term extended effects under non-random interactions.

Organisms continuously modify their living conditions via extended genetic effects on their environment, microbiome, and in some species culture. These effects can impact the fitness of current but also future conspecifics due to non-genetic transmission via ecological or cultural inheritance. In this case, selection on a gene with extended effects depends on the degree to which current and future genetic relatives are exposed to modified conditions. Here, we detail the selection gradient on a quantitative trait with extended effects in a patch-structured population, when gene flow between patches is limited and ecological inheritance within patches can be biased towards offspring. Such a situation is relevant to understand evolutionary driven changes in individual condition that can be preferentially transmitted from parent to offspring, such as cellular state, micro-environments (e.g., nests), pathogens, microbiome, or culture. Our analysis quantifies how the interaction between limited gene flow and biased ecological inheritance influences the joint evolutionary dynamics of traits together with the conditions they modify, helping understand adaptation via non-genetic modifications. As an illustration, we apply our analysis to a gene-culture coevolution scenario in which genetically-determined learning strategies coevolve with adaptive knowledge. In particular, we show that when social learning is synergistic, selection can favour strategies that generate remarkable levels of knowledge under intermediate levels of both vertical cultural transmission and limited dispersal. More broadly, our theory yields insights into the interplay between genetic and non-genetic inheritance, with implications for how organisms evolve to transform their environments.

The components of directional and disruptive selection in heterogeneous group-structured populations.

We derive how directional and disruptive selection operate on scalar traits in a heterogeneous group-structured population for a general class of models. In particular, we assume that each group in the population can be in one of a finite number of states, where states can affect group size and/or other environmental variables, at a given time. Using up to second-order perturbation expansions of the invasion fitness of a mutant allele, we derive expressions for the directional and disruptive selection coefficients, which are sufficient to classify the singular strategies of adaptive dynamics. These expressions include first- and second-order perturbations of individual fitness (expected number of settled offspring produced by an individual, possibly including self through survival); the first-order perturbation of the stationary distribution of mutants (derived here explicitly for the first time); the first-order perturbation of pairwise relatedness; and reproductive values, pairwise and three-way relatedness, and stationary distribution of mutants, each evaluated under neutrality. We introduce the concept of individual k-fitness (defined as the expected number of settled offspring of an individual for which k-1 randomly chosen neighbors are lineage members) and show its usefulness for calculating relatedness and its perturbation. We then demonstrate that the directional and disruptive selection coefficients can be expressed in terms individual k-fitnesses with k=1,2,3 only. This representation has two important benefits. First, it allows for a significant reduction in the dimensions of the system of equations describing the mutant dynamics that needs to be solved to evaluate explicitly the two selection coefficients. Second, it leads to a biologically meaningful interpretation of their components. As an application of our methodology, we analyze directional and disruptive selection in a lottery model with either hard or soft selection and show that many previous results about selection in group-structured populations can be reproduced as special cases of our model.

Familiarity with humans affect dogs' tendencies to follow human majority groups.

Recently, copying others' behaviour has attracted attention among researchers. It aids individuals in reducing uncertainty about the knowledge of the environment and helps them in acquiring an adaptive behaviour at a lower cost than by learning it by themselves. Among the copying strategies, conformity, which is the copying of behavioural decisions presented by the majority, has been well studied and reported in many animals, including humans. The previous study showed that dogs did not conform to their multiple conspecific individuals; however, dogs have evolved to increase their adaptability while living with humans, and it is plausible that dogs have selected appropriate behaviour according to the behaviour of humans. Therefore, we investigated which factors influenced the choice of dogs in a situation where they have to choose one of two numerically unbalanced human groups. The results showed that the dogs followed the human majority group under certain conditions, depending on the familiarity with the human demonstrators. These results are important in considering the significance of groups for dogs and the factors of group formation, and will also provide a clue as to how dogs have penetrated into human society.

Evolution of dispersal in a spatially heterogeneous population with finite patch sizes.

Dispersal is one of the fundamental life-history strategies of organisms, so understanding the selective forces shaping the dispersal traits is important. In the Wright's island model, dispersal evolves due to kin competition even when dispersal is costly, and it has traditionally been assumed that the living conditions are the same everywhere. To study the effect of spatial heterogeneity, we extend the model so that patches may receive different amounts of immigrants, foster different numbers of individuals, and give different reproduction efficiency to individuals therein. We obtain an analytical expression for the fitness gradient, which shows that directional selection consists of three components: As in the homogeneous case, the direct cost of dispersal selects against dispersal and kin competition promotes dispersal. The additional component, spatial heterogeneity, more precisely the variance of so-called relative reproductive potential, tends to select against dispersal. We also obtain an expression for the second derivative of fitness, which can be used to determine whether there is disruptive selection: Unlike the homogeneous case, we found that divergence of traits through evolutionary branching is possible in the heterogeneous case. Our numerical explorations suggest that evolutionary branching is promoted more by differences in patch size than by reproduction efficiency. Our results show the importance of the existing spatial heterogeneity in the real world as a key determinant in dispersal evolution.

Evolution of cumulative culture for niche construction.

A mathematical model of the joint evolution of learning and niche construction in a spatially subdivided population is described, in which culture is used to practice niche construction and can evolve by accumulating small improvements over generations. Individuals allocate their lifetimes to social learning, individual learning, niche construction to improve the environment, and exploitation of resources according to their genetically determined strategies. The coordinated optimal strategy (COS) is defined as the allocation strategy which maximizes the equilibrium fecundity of the population, as opposed to the convergence stable strategy (CSS), which is the strategy favored by natural selection. Both the COS and CSS are analytically derived and compared. It turns out that, although the levels of the CSS in terms of culture and the environmental quality can be high in a highly viscous population, they are in general much lower than those of the COS. It is argued that the discrepancy between the CSS and COS stems from the producer-scrounger structure inherent in the model. Analysis of transient dynamics reveals that the level of culture and the environmental quality may temporarily undergo drastic increases after sudden changes in parameter values, although they eventually drop down to low values due to the genetic adaptation of the time allocation strategy to the new cultural and environmental backgrounds. Implications of the results for human evolution are discussed.

Evolution of self-limited cell division of symbionts.

In mutualism between unicellular hosts and their endosymbionts, symbiont's cell division is often synchronized with its host's, ensuring the permanent relationship between endosymbionts and their hosts. The evolution of synchronized cell division thus has been considered to be an essential step in the evolutionary transition from symbionts to organelles. However, if symbionts would accelerate their cell division without regard for the synchronization with the host, they would proliferate more efficiently. Thus, it is paradoxical that symbionts evolve to limit their own division for synchronized cell division. Here, we theoretically explore the condition for the evolution of self-limited cell division of symbionts, by assuming that symbionts control their division rate and that hosts control symbionts' death rate by intracellular digestion and nutrient supply. Our analysis shows that symbionts can evolve to limit their own cell division. Such evolution occurs if not only symbiont's but also host's benefit through symbiosis is large. Moreover, the coevolution of hosts and symbionts leads to either permanent symbiosis where symbionts proliferate to keep pace with their host, or the arms race between symbionts that behave as lytic parasites and hosts that resist them by rapid digestion.

Spatial heterogeneity and evolution of fecundity-affecting traits.

It is widely recognized that spatial structure in a population has some, and occasionally great, impacts on ecological and evolutionary dynamics. However, it has been observed that in the homogeneous Wright's island model with a certain standard demographic assumption, spatial structure does not affect the fitness gradient of a fecundity-affecting trait. The location and convergence stability of singular strategies thus remain unchanged. Furthermore, evolutionary branching is impossible for small dispersal rates, and for a wide class of fecundity functions, evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatially homogeneous structure thus often inhibits evolutionary branching. Here we study the impact of spatial heterogeneity on evolutionary dynamics. We consider an infinite Wright's island model, where different islands have different capacity and fecundity consequences, and therefore the population is spatially heterogeneous. Through the analysis of metapopulation fitness, we derive its first-order and second-order derivatives with respect to mutant's trait, which are explicitly represented in terms of fecundity derivatives. The selection gradient turns out to be a biased average of local selection pressures in different patch types. We find that evolutionary branching is generally favored in the presence of spatial heterogeneity. We also find a simple condition under which evolutionary branching is particularly favored. Applications to public-goods cooperation and emergent evolutionary branching to cooperators and defectors are discussed.

Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution.

A finite-population, discrete-generation model of cultural evolution is described, in which multiple discrete traits are transmitted independently. In this model, each newborn may inherit a trait from multiple cultural parents. Transmission fails with a positive probability unlike in population genetics. An ancestral process simulating the cultural genealogy of a sample of individuals is derived for this model. This ancestral process, denoted by M-, is shown to be dual to a process M+ describing the change in the frequency of a trait. The age-frequency spectrum is defined as a two-dimensional array whose (i,k) element is the expected number of distinct cultural traits introduced k generations ago and now carried by i individuals in a sample of a particular size n. Numerical calculations reveal that the age-frequency spectrum and related metrics undergo a critical transition from a phase with a moderate number of young, rare traits to a phase with numerous very old, common traits when the expected number of cultural parents per individual exceeds one. It is shown that M+ and M- converge to branching or deterministic processes, depending on the way population size tends to infinity, and these limiting processes bear some duality relationships. The critical behavior of the original processes M+ and M- is explained in terms of a phase transition of the branching processes. Using the results of the limiting processes in combination, we derive analytical formulae that well approximate the age-frequency spectrum and also other metrics.

Emergence of opinion leaders in reference networks.

Individuals often refer to opinions of others when they make decisions in the real world. Our question is how the people's reference structure self-organizes when people try to provide correct answers by referring to more accurate agents. We constructed an adaptive network model, in which each node represents an agent and each directed link represents a reference. In every iteration round within our model, each agent makes a decision sequentially by following the majority of the reference partners' opinions and rewires a reference link to a partner if the partner's performance falls below a given threshold. The value of this threshold is common for all agents and represents the performance assessment severity of the population. We found that the reference network self-organizes into a heterogeneous one with a nearly exponential in-degree (the number of followers) distribution, where reference links concentrate around agents with high intrinsic ability. In this heterogeneous network, the decision-making accuracy of agents improved on average. However, the proportion of agents who provided correct answers showed strong temporal fluctuation compared to that observed in the case in which each agent refers to randomly selected agents. We also found a counterintuitive phenomenon in which reference links concentrate more around high-ability agents and the population became smarter on average when the rewiring threshold was set lower than when it was set higher.

Evolution of emotional contagion in group-living animals.

Emotional contagion refers to an instantaneous matching of an emotional state between a subject and an object. It is believed to form one of the bases of empathy and it causes consistent group behavior in many animals. However, how this emotional process relates to group size remains unclear. Individuals with the ability of emotional contagion can instantaneously copy the emotion of another group member and can take relevant behavior driven by this emotion, but this would entail both cost and benefit to them because the behavior can be either appropriate or inappropriate depending on the situation. For example, emotional contagion may help them escape from a predator but sometimes induce mass panic. We theoretically study how these two aspects of emotional contagion affect its evolution in group-living animals. We consider a situation where an environmental cue sometimes indicates a serious event and individuals have to make a decision whether to react to them. We show that, as the group size increases, individuals with the ability of emotional contagion would evolutionarily weaken their sensitivity to environmental cues. We also show that a larger group yields a larger benefit to them through such evolutionary change. However, larger group size prevents the invasion of mutants with the ability of emotional contagion into the population of residents who react to environmental cues independently of other group members. These results provide important suggestions on the evolutionary relationship between emotional contagion and group living.

Forward and backward evolutionary processes and allele frequency spectrum in a cancer cell population.

A cancer grows from a single cell, thereby constituting a large cell population. In this work, we are interested in how mutations accumulate in a cancer cell population. We provide a theoretical framework of the stochastic process in a cancer cell population and obtain near exact expressions of allele frequency spectrum or AFS (only continuous approximation is involved) from both forward and backward treatments under a simple setting; all cells undergo cell divisions and die at constant rates, b and d, respectively, such that the entire population grows exponentially. This setting means that once a parental cancer cell is established, in the following growth phase, all mutations are assumed to have no effect on b or d (i.e., neutral or passengers). Our theoretical results show that the difference from organismal population genetics is mainly in the coalescent time scale, and the mutation rate is defined per cell division, not per time unit (e.g., generation). Except for these two factors, the basic logic is very similar between organismal and cancer population genetics, indicating that a number of well established theories of organismal population genetics could be translated to cancer population genetics with simple modifications.

Inclusive fitness analysis of cumulative cultural evolution in an island-structured population.

The success of humans on the globe is largely supported by our cultural excellence. Our culture is cumulative, meaning that it is improved from generation to generation. Previous works have revealed that two modes of learning, individual learning and social learning, play pivotal roles in the accumulation of culture. However, under the trade-off between learning and reproduction, one's investment into learning is easily exploited by those who copy the knowledge of skillful individuals and selfishly invest more efforts in reproduction. It has been shown that in order to prevent such a breakdown, the rate of vertical transmission (i.e. transmission from parents to their offspring) of culture must be unrealistically close to one. Here we investigate what if the population is spatially structured. In particular, we hypothesize that spatial structure should favor highly cumulative culture through endogenously arising high kinship. We employ Wright's island model and assume that cultural transmission occurs within a local island. Our inclusive fitness analysis reveals combined effects of direct fitness of the actor, indirect fitness through relatives in the current generation, and indirect fitness through relatives in future generations. The magnitude of those indirect benefits is measured by intergenerational coefficients of genetic relatedness. Our result suggests that the introduction of spatial structure raises the stationary level of culture in the population, but that the extent of its improvement compared with a well-mixed population is marginal unless spatial localization is extreme. Overall, our model implies that we need an alternative mechanism to explain highly cumulative culture of modern humans.

The effect of fecundity derivatives on the condition of evolutionary branching in spatial models.

By investigating metapopulation fitness, we present analytical expressions for the selection gradient and conditions for convergence stability and evolutionary stability in Wright's island model in terms of fecundity function. Coefficients of each derivative of fecundity function appearing in these conditions have fixed signs. This illustrates which kind of interaction promotes or inhibits evolutionary branching in spatial models. We observe that Taylor's cancellation result holds for any fecundity function: Not only singular strategies but also their convergence stability is identical to that in the corresponding well-mixed model. We show that evolutionary branching never occurs when the dispersal rate is close to zero. Furthermore, for a wide class of fecundity functions (including those determined by any pairwise game), evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatial structure thus often inhibits evolutionary branching, although we can construct a fecundity function for which evolutionary branching only occurs for intermediate dispersal rates.