Viscous Populations Research Articles

The Time Evolution of in Protoplanetary Disks as a Way to Disentangle between Viscosity and MHD Winds

As the classic viscous paradigm for protoplanetary disk accretion is challenged by the observational evidence of low turbulence, the alternative scenario of MHD disk winds is being explored as being potentially able to reproduce the same observed features traditionally explained with viscosity. Although the two models lead to different disk properties, none of them has been ruled out by observations—mainly due to instrumental limitations. In this work, we present a viable method to distinguish between the viscous and MHD framework based on the different evolution of the distribution in the disk mass (M d )–accretion rate () plane of a disk population. With a synergy of analytical calculations and 1D numerical simulations, performed with the population synthesis code Diskpop, we find that both mechanisms predict the spread of the observed ratio in a disk population to decrease over time; however, this effect is much less pronounced in MHD-dominated populations compared with purely viscous populations. Furthermore, we demonstrate that this difference is detectable with the current observational facilities: we show that convolving the intrinsic spread with the observational uncertainties does not affect our result, as the observed spread in the MHD case remains significantly larger than in the viscous scenario. While the most recent data available show a better agreement with the wind model, ongoing and future efforts to obtain direct gas mass measurements with Atacama Large Millimeter/submillimeter Array and next-generation Very Large Array will cause a reassessment of this comparison in the near future.

A simulation test of the prediction that density-dependent dispersal promotes female-biased sex allocation in viscous populations.

A classic result of sex-allocation theory is that the sex ratio is predicted to be invariant with respect to the rate of dispersal. However, a recent mathematical analysis has suggested that if individuals are able to adjust their probability of dispersal according to the local density of their neighbourhood, then a lower rate of dispersal will be associated with greater female-bias. Here, we perform a computer simulation test of this prediction. Our simulation data provide strong qualitative support for the prediction, and a Monte Carlo randomization test of significance allows us to reject the null hypothesis of the invariance relationship.

Paternal genome elimination promotes altruism in viscous populations.

Population stieveness has lang been thocht tae forder the evolution o altruism. Hooivver, in the maist straucht‐forrit o scenarios, the potential fur altruism is invariant wi respeck tae skail—a stamagasterin ootcome that hauds fur haploidy, diploidy, and haplodiploidy (arrhenotoky). Here we pit forrit a kin‐walin model fur tae airt‐oot hoo population stieveness affects the potential fur altruism in species wi male paternal genome drap‐oot (PGD), takkin tent o altruism enactit by baith females and males, forby baith young‐anes and aulder‐anes. We find that: 1) PGD forders altruistic ongauns relative tae the ither inheritance seestems, forby tae a degree that depends on the extent o paternal genome kythin. 2) Unner PGD, skail maks mair muckle the potential fur altruism amang young‐anes and gars it less likely amang aulder‐anes. 3) The genetics o PGD can lead tae kenspeckle differences in sex‐specific potentials fur altruism, even wioot onie sex‐differences in ecology.

Density-dependent dispersal promotes female-biased sex allocation in viscous populations

A surprising result emerging from the theory of sex allocation is that the optimal sex ratio is predicted to be completely independent of the rate of dispersal. This striking invariance result has stimulated a huge amount of theoretical and empirical attention in the social evolution literature. However, this sex-allocation invariant has been derived under the assumption that an individual's dispersal behaviour is not modulated by population density. Here, we investigate how density-dependent dispersal shapes patterns of sex allocation in a viscous-population setting. Specifically, we find that if individuals are able to adjust their dispersal behaviour according to local population density, then they are favoured to do so, and this drives the evolution of female-biased sex allocation. This result obtains because, whereas under density-independent dispersal, population viscosity is associated not only with higher relatedness—which promotes female bias—but also with higher kin competition—which inhibits female bias—under density-dependent dispersal, the kin-competition consequences of a female-biased sex ratio are entirely abolished. We derive analytical results for the full range of group sizes and costs of dispersal, under haploid, diploid and haplodiploid modes of inheritance. These results show that population viscosity promotes female-biased sex ratios in the context of density-dependent dispersal.

Death happy: adaptive ageing and its evolution by kin selection in organisms with colonial ecology.

Standard evolutionary theory, supported by mathematical modelling of outbred, dispersed populations predicts that ageing is not an adaptation. We recently argued that in clonal, viscous populations, programmed organismal death could promote fitness through social benefits and has, in some organisms (e.g. Caenorhabditis elegans), evolved to shorten lifespan. Here, we review previous adaptive death theory, including consumer sacrifice, biomass sacrifice and defensive sacrifice types of altruistic adaptive death. In addition, we discuss possible adaptive death in certain semelparous fish, coevolution of reproductive and adaptive death, and adaptive reproductive senescence in C. elegans. We also describe findings from recent tests for the existence of adaptive death in C. elegans using computer modelling. Such models have provided new insights into how trade-offs between fitness at the individual and colony levels mean that senescent changes can be selected traits. Exploring further the relationship between adaptive death and social interactions, we consider examples where adaptive death results more from action of kin than from self-destructive mechanisms and, to describe this, introduce the term adaptive killing of kin. This article is part of the theme issue 'Ageing and sociality: why, when and how does sociality change ageing patterns?'

Mobility can promote the evolution of cooperation via emergent self-assortment dynamics.

The evolution of costly cooperation, where cooperators pay a personal cost to benefit others, requires that cooperators interact more frequently with other cooperators. This condition, called positive assortment, is known to occur in spatially-structured viscous populations, where individuals typically have low mobility and limited dispersal. However many social organisms across taxa, from cells and bacteria, to birds, fish and ungulates, are mobile, and live in populations with considerable inter-group mixing. In the absence of information regarding others’ traits or conditional strategies, such mixing may inhibit assortment and limit the potential for cooperation to evolve. Here we employ spatially-explicit individual-based evolutionary simulations to incorporate costs and benefits of two coevolving costly traits: cooperative and local cohesive tendencies. We demonstrate that, despite possessing no information about others’ traits or payoffs, mobility (via self-propulsion or environmental forcing) facilitates assortment of cooperators via a dynamically evolving difference in the cohesive tendencies of cooperators and defectors. We show analytically that this assortment can also be viewed in a multilevel selection framework, where selection for cooperation among emergent groups can overcome selection against cooperators within the groups. As a result of these dynamics, we find an oscillatory pattern of cooperation and defection that maintains cooperation even in the absence of well known mechanisms such as kin interactions, reciprocity, local dispersal or conditional strategies that require information on others’ strategies or payoffs. Our results offer insights into differential adhesion based mechanisms for positive assortment and reveal the possibility of cooperative aggregations in dynamic fission-fusion populations.

How Sex-Biased Dispersal Affects Sexual Conflict over Care

Existing models of parental investment have mainly focused on interactions at the level of the family and have paid much less attention to the impact of population-level processes. Here we extend classical models of parental care to assess the impact of population structure and limited dispersal. We find that sex differences in dispersal substantially affect the amount of care provided by each parent, with the more philopatric sex providing the majority of care to young. This effect is most pronounced in highly viscous populations: in such cases, when classical models would predict stable biparental care, inclusion of a modest sex difference in dispersal leads to uniparental care by the philopatric sex. In addition, mating skew also affects sex differences in parental investment, with the more numerous sex providing most of the care. However, the effect of mating skew holds only when parents care for their own offspring. When individuals breed communally, we recover the previous finding that the more philopatric sex provides most of the care even when it is the rarer sex. We conclude that sex-biased dispersal is likely to be an important yet currently overlooked driver of sex differences in parental care.

Higher relatedness mitigates mortality in a nematode with lethal male fighting.

According to kin selection theory, individuals show less aggression towards their relatives. Limited dispersal promotes interactions among relatives but also increases competition among them. The evolution of cooperation in viscous populations has been subject of mainly theoretical exploration. We investigated the influence of relatedness on aggression in males of entomopathogenic nematode Steinernema longicaudum that engage in lethal fighting. In a series of invitro experiments, we found that both competitor male group size and relatedness influence male mortality rates. Higher relatedness led to progressively lower rates of male mortality. In experimentally infected insects, wherein large numbers of males and females interact, the proportion of dead and paralysed (=terminally injured) males was higher when infection was established by infective juveniles originating from a mixture of three lines than in those infected by a single line. The results collectively show that Steinernema longicaudum males recognize their kin and consequently male mortality rates are lower in groups consisting of more related males. Furthermore, this monotonic negative relationship between aggression and relatedness suggests that kin selection benefits are still substantial even under extreme competition. Our experiments also suggest that kin recognition in entomopathogenic nematodes has a genetic basis rather than being strictly based on environmental cues. We discuss our findings within the theoretical context of the evolution of altruistic/cooperative behaviour in structured populations.

Cooperation is related to dispersal patterns in Sino-Tibetan populations.

There is growing recognition in both evolutionary biology and anthropology that dispersal is key to establishing patterns of cooperation. However, some models predict that cooperation is more likely to evolve in low dispersal (viscous) populations, while others predict that local competition for resources inhibits cooperation. Sex-biased dispersal and extra-pair mating may also have an effect. Using economic games in Sino-Tibetan populations with strikingly different dispersal patterns, we measure cooperation in 36 villages in southwestern China; we test whether social structure is associated with cooperative behaviour toward those in the neighbourhood. We find that social organization is associated with levels of cooperation in public goods and dictator games and a resource dilemma; people are less cooperative towards other villagers in communities where dispersal by both sexes is low. This supports the view that dispersal for marriage played an important role in the evolution of large-scale cooperation in human society.

Sex-biased dispersal, kin selection and the evolution of sexual conflict.

There is growing interest in resolving the curious disconnect between the fields of kin selection and sexual selection. Rankin's (2011, J. Evol. Biol. 24, 71-81) theoretical study of the impact of kin selection on the evolution of sexual conflict in viscous populations has been particularly valuable in stimulating empirical research in this area. An important goal of that study was to understand the impact of sex-specific rates of dispersal upon the coevolution of male-harm and female-resistance behaviours. But the fitness functions derived in Rankin's study do not flow from his model's assumptions and, in particular, are not consistent with sex-biased dispersal. Here, we develop new fitness functions that do logically flow from the model's assumptions, to determine the impact of sex-specific patterns of dispersal on the evolution of sexual conflict. Although Rankin's study suggested that increasing male dispersal always promotes the evolution of male harm and that increasing female dispersal always inhibits the evolution of male harm, we find that the opposite can also be true, depending upon parameter values.

Invasion of cooperators in lattice populations: Linear and non-linear public good games

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open.Here we examined the dynamics of individual based stochastic models of the NVD. We analyze the dynamics in well-mixed and viscous populations. We show in both cases that coexistence between cooperators and defectors is possible; moreover, spatial aggregation of types in viscous populations can easily lead to pure cooperation. Furthermore we analyze the invasion of cooperators in populations consisting predominantly of defectors. In accordance with analytical results, in deterministic systems, we found the invasion of cooperators successful in the well-mixed case only if their initial concentration was higher than a critical threshold, defined by the replicator dynamics of the NVD. In the viscous case, however, not the initial concentration but the initial number determines the success of invasion. We show that even a single mutant cooperator can invade with a high probability, because the local density of aggregated cooperators exceeds the threshold defined by the game. Comparing the results to models using different benefit functions (linear or sigmoid), we show that the role of the benefit function is much more important in the well-mixed than in the viscous case.

Evolution of Helping and Harming in Viscous Populations When Group Size Varies

Recent years have seen huge interest in understanding how demographic factors mediate the evolution of social behavior in viscous populations. Here we study the impact of variation in group size on the evolution of helping and harming behavior. Although variation in group size influences the degree of relatedness and the degree of competition between groupmates, we find that these effects often exactly cancel, so as to give no net impact of variation in group size on the evolution of helping and harming. Specifically, (1) obligate helping and harming are never mediated by variation in group size, (2) facultative helping and harming are not mediated by variation in group size when this variation is spatial only, (3) facultative helping and harming are mediated by variation in group size only when this variation is temporal or both spatial and temporal, and (4) when there is an effect of variation in group size, facultative helping is favored in big groups and facultative harming is favored in little groups. Moreover, we find that spatial and temporal heterogeneity in individual fecundity may interact with patch-size heterogeneity to change these predictions, promoting the evolution of harming in big patches and of helping in little patches.

Short Versus Long Term Benefits and the Evolution of Cooperation in the Prisoner's Dilemma Game

In this paper I investigate the evolution of cooperation in the prisoner's dilemma when individuals change their strategies subject to performance evaluation of their neighbours over variable time horizons. In the monochrome setting, in which all agents per default share the same performance evaluation rule, weighing past events strongly dramatically enhances the prevalence of cooperators. For co-evolutionary models, in which evaluation time horizons and strategies can co-evolve, I demonstrate that cooperation naturally associates with long-term evaluation of others while defection is typically paired with very short time horizons. Moreover, considering the continuous spectrum in between enhanced and discounted weights of past performance, cooperation is optimally supported when cooperators neither give enhanced weight to past nor more recent events, but simply average payoffs. Payoff averaging is also found to emerge as the dominant strategy for cooperators in co-evolutionary models, thus proposing a natural route to the evolution of cooperation in viscous populations.

Co-evolution between sociality and dispersal: The role of synergistic cooperative benefits

Explaining the evolution of sociality is challenging because social individuals face disadvantages that must be balanced by intrinsic benefits of living in a group. One potential route towards the evolution of sociality may emerge from the avoidance of dispersal, which can be risky in some environments. Although early studies found that local competition may cancel the benefits of cooperation in viscous populations, subsequent studies have identified conditions, such as the presence of kin recognition or specific demographic conditions, under which altruism will still spread. Most of these studies assume that the costs of cooperating outweigh the direct benefits (strong altruism). In nature, however, many organisms gain synergistic benefits from group living, which may counterbalance even costly altruistic behaviours. Here, we use an individual based model to investigate how dispersal and social behaviour co-evolve when social behaviours result in synergistic benefits that counterbalance the relative cost of altruism to a greater extent than assumed in previous models. When the cost of cooperation is high, selection for sociality responds strongly to the cost of dispersal. In particular, cooperation can begin to spread in a population when higher cooperation levels become correlated with lower dispersal tendencies within individuals. In contrast, less costly social behaviours are less sensitive to the cost of dispersal. In line with previous studies, we find that mechanisms of global population control also affect this relationship: when whole patches (groups) go extinct each generation, selection favours a relatively high dispersal propensity, and social behaviours evolve only when they are not very costly. If random individuals within groups experience mortality each generation to maintain a global carrying capacity, on the other hand, social behaviours spread and dispersal is reduced, even when the latter is not costly.

A general ploidy model for the evolution of helping in viscous populations

There is growing interest in understanding how kin selection drives the evolution of social behaviours in viscous populations. A key result, that has inspired much work on this topic, is the exact cancellation of the genetic relatedness and kin competition effects of dispersal in the simplest models of population viscosity, such that a reduction in the rate of dispersal neither promotes nor inhibits the evolution of helping behaviour. This theoretical result has been demonstrated for populations characterised by haploid, diploid and haplodiploid modes of inheritance. Here we develop a model of general ploidy that recovers these three scenarios as special cases and allows examination of scenarios that have not been considered previously. Specifically, we: clarify the importance of the implicit assumption of monandry in previous models; show that the cancellation result obtains in some models of ploidy but not in others; and reveal that the cancellation result obtains for different reasons in different models of ploidy. The cancellation result therefore hinges upon a population's genetic system as well as its demography.

EVOLUTION OF HELPING AND HARMING IN HETEROGENEOUS POPULATIONS

There has been much interest in understanding how demographic factors can mediate social evolution in viscous populations. Here, we examine the impact of heterogeneity in patch quality--that is, the availability of reproductive resources for each breeder--upon the evolution of helping and harming behaviors. We find that, owing to a cancellation of relatedness and kin competition effects, the evolution of obligate and facultative helping and harming is not influenced by the degree of viscosity in populations characterized by either spatial or temporal heterogeneity in patch quality. However, facultative helping and harming may be favored when there is both spatial and temporal heterogeneity in patch quality, with helping and harming being favored in both high-quality and low-quality patches. We highlight the prospect for using kin selection theory to explain within-population variation in social behavior, and point to the need for further theoretical and empirical investigation of this topic.

How dispersal influences parent–offspring conflict over investment

Models that investigate family conflicts over parental investment have generally ignored population structure above the level of the family. Here, we extend conventional models to assess the impact of spatial population structure and limited dispersal on the intensity and resolution of parent‐offspring conflict. Although one might naively predict that limited dispersal should reduce parent‐offspring conflict, due to increased local relatedness, we show that this is not necessarily the case. Parent‐offspring conflict may actually become more intense when dispersal is limited because local competition among related young can reduce the cost of any decline in maternal productivity, favoring greater selfishness on the part of the offspring. We also investigate the impact of limited dispersal on the resolution of parent‐offspring conflict when the young can solicit extra resources by means of costly begging. Our model predicts that begging will be more intense when dispersal is limited but that the impact of dispersal on size then depends on the effect of parental supply on offspring demand. When greater supply leads to reduced demand, we find that parental investment should be higher in more viscous populations. By contrast, when greater supply leads to greater demand, parental investment should be lower in more viscous populations. Key words: begging, kin selection, local competition, model, offspring demand. [Behav Ecol]

Sexual conflict in viscous populations: The effect of the timing of dispersal

In recent years, there has been increasing theoretical and empirical examination of how sexual conflict can arise between males and females. However, much this work has implicitly assumed that interactions take place in panmictic populations with complete dispersal, where interactions are between unrelated individuals. Here, we examine the consequences of limited dispersal and population structure for the evolution of a male phenotype that is associated with the males pre- and post-copulatory reproductive success, using an inclusive-fitness based analysis applied to group-structured populations. We show that: (i) the sex-specific timing of the dispersal phase of the life cycle can drive the evolution of sexual conflict; (ii) the inclusive fitness of a female in this conflict is determined solely by direct (i.e. personal) effects on its own competitive ability. Our analysis is supported by results from individual-based simulations of multi-level selection. Our results support the suggestion that kin selection can influence the evolution of sexual conflict, but reveal that such a role might be more complex than previously appreciated when sex-specific life histories are taken into consideration. We discuss the implications of our results for sexual conflict in various species of insects, but focus primarily on dipteran flies of the family Sepsidae.

Evolution of reproductive effort in viscous populations: the importance of population dynamics

I present two ecological models for the evolution of reproductive effort in viscous populations with empty sites. In contrast with previous studies, I show that limited dispersal needs not have a positive effect on the evolutionarily stable allocation of resources to fecundity versus survival. Rather, depending on the feedback between the trait and the population dynamics, population viscosity may have no effect or even lead to a decrease in the evolutionarily stable reproductive effort when individuals can degrade their environment during their lifetime. I show that the different evolutionary outcomes can be explained by the asymmetry in the level of kin competition resulting from investing into juveniles or into adults.

Space‐Time Relatedness and Hamilton’s Rule for Long‐Lasting Behaviors in Viscous Populations

Genes affect not only the behavior and fitness of their carriers but also that of other individuals. According to Hamilton's rule, whether a mutant gene will spread in the gene pool depends on the effects of its carrier on the fitness of all individuals in the population, each weighted by its relatedness to the carrier. However, social behaviors may affect not only recipients living in the generation of the actor but also individuals living in subsequent generations. In this note, I evaluate space-time relatedness coefficients for localized dispersal. These relatedness coefficients weight the selection pressures on long-lasting behaviors, which stem from a multigenerational gap between phenotypic expression by actors and the resulting environmental feedback on the fitness of recipients. Explicit values of space-time relatedness coefficients reveal that they can be surprisingly large for typical dispersal rates, even for hundreds of generations in the future.