A general model of the public goods dilemma

An individually costly act that benefits all group members is a public good. Natural selection favours individual contribution to public goods only when some benefit to the individual offsets the cost of contribution. Problems of sex ratio, parasite virulence, microbial metabolism, punishment of noncooperators, and nearly all aspects of sociality have been analysed as public goods shaped by kin and group selection. Here, I develop two general aspects of the public goods problem that have received relatively little attention. First, variation in individual resources favours selfish individuals to vary their allocation to public goods. Those individuals better endowed contribute their excess resources to public benefit, whereas those individuals with fewer resources contribute less to the public good. Thus, purely selfish behaviour causes individuals to stratify into upper classes that contribute greatly to public benefit and social cohesion and to lower classes that contribute little to the public good. Second, if group success absolutely requires production of the public good, then the pressure favouring production is relatively high. By contrast, if group success depends weakly on the public good, then the pressure favouring production is relatively weak. Stated in this way, it is obvious that the role of baseline success is important. However, discussions of public goods problems sometimes fail to emphasize this point sufficiently. The models here suggest simple tests for the roles of resource variation and baseline success. Given the widespread importance of public goods, better models and tests would greatly deepen our understanding of many processes in biology and sociality.     

Bottom-up derivation of population models for competition involving multiple resources

This paper provides first-principles derivations of population models for competition involving multiple resources with different competition types, based on resource partitioning between individuals. The following two cases are investigated. The first is the case in which the resource competed for and its competition type change depending on life stages from scramble to contest competition, or from contest to scramble competition. The second is the case in which individuals compete for two resources simultaneously with scramble and contest types, respectively. In both cases, population models are derived analytically, and in particular, the Hassell model is derived in the second case. The nature of reproduction curves and the stability properties of three population models derived are compared with each other. These models provide three representative models for competition involving both scramble and contest types.     

Hamilton's rule, imprinting and parent-offspring conflict over seed mass in partially selfing plants

When genes in the offspring control the provisioning of the seed, the optimal seed size can be calculated exactly by applying Hamilton's rule. When seed size is a compromise between mother and offspring, we predict that outcrossing plant species produce larger seeds than selfers. This trend was found in the British flora and in a number of well-studied plant families. The analysis was extended to imprinting, a conditional strategy in which a gene in the offspring takes more resources when derived from the father than from the mother. The conditions for imprinting to be selected were rather restrictive. The analysis is relevant for the current debate about the evolution of imprinting in Arabidopsis thaliana.     

Why do large mothers produce large offspring? Theory and a test

To explain the general tendency of large mothers to produce large offspring, we developed two models in which either the rate at which each single offspring extracts resources from the mother or the rate at which the mother supplies resources to all the offspring is limited (terminal- or upper-stream-limitation on resource transport, respectively). We also reanalyzed the data of Erythronium japonicum to test the models. The terminal-stream-limitation model predicted that the optimal offspring size that maximizes the fitness of the mother increases with an increase in the maximum rate of resource extraction by each single offspring. Thus, large mothers produce large offspring if the maximum resource extraction rate is high in those mothers. The upper-stream-limitation model predicted that the optimal offspring size decreases with an increase in the maximum rate of resource supply by the mother to all the offspring. In E. japonicum, the maximum growth rate of a seed was independent of the number of seeds of a plant, suggesting that the resource extraction rate is limited at the individual seed level. The maximum growth rate was high in large plants and had a strong positive effect on final seed mass. Thus, the results were consistent with the terminal-stream-limitation model.     

Interspecific Competition Models Derived from Competition Among Individuals

This paper demonstrates how discrete-time models describing population dynamics of two competing species can be derived in a bottom-up manner by considering competition for resources among individuals and the spatial distribution of individuals. The competition type of each species is assumed to be either scramble, contest, or an intermediate between them. Individuals of two species are distributed over resource sites or patches following one of three distribution functions. According to the combination of competition types of the two species and the distribution of individuals, various interspecific competition models are derived. Furthermore, a general interspecific competition model that includes various competition models as special cases is derived for each distribution of individuals. Finally, this paper examines dynamics of some of the derived competition models and shows that the likelihood of coexistence of the two species varies greatly, depending on the type of spatial distribution of individuals.     

Do social insects support Haig's kin theory for the evolution of genomic imprinting?

Although numerous imprinted genes have been described in several lineages, the phenomenon of genomic imprinting presents a peculiar evolutionary problem. Several hypotheses have been proposed to explain gene imprinting, the most supported being Haig's kinship theory. This theory explains the observed pattern of imprinting and the resulting phenotypes as a competition for resources between related individuals, but despite its relevance it has not been independently tested. Haig's theory predicts that gene imprinting should be present in eusocial insects in many social scenarios. These lineages are therefore ideal for testing both the theory's predictions and the mechanism of gene imprinting. Here we review the behavioral evidence of genomic imprinting in eusocial insects, the evidence of a mechanism for genomic imprinting and finally we evaluate recent results showing parent of origin allele specific expression in honeybees in the light of Haig's theory.     

Parental modifiers,antisense transcripts and loss of imprinting

The kinship theory of genomic imprinting has explained parent-specific gene expression as the outcome of an evolutionary conflict between the two alleles at a diploid locus of an offspring over how much to demand from parents. Previous models have predicted that maternally derived (madumnal) alleles will be silent at demand-enhancing loci, while paternally derived (padumnal) alleles will be silent at demand-suppressing loci, but these models have not considered the evolution of trans-acting modifiers that are expressed in parents and influence imprinted expression in offspring. We show that such modifiers will sometimes be selected to reactivate the silent padumnal allele at a demand-suppressing locus but will not be selected to reactivate the silent madumnal allele at a demand-enhancing locus. Therefore, imprinting of demand-suppressing loci is predicted to be less evolutionarily stable than imprinting of demand-enhancing loci.     

Parental conflict does not necessarily lead to the evolution of imprinting

For some genes, the epigenetic state (whether they are expressed) depends on whether the gene is inherited through the mother or the father. Such imprinting, or parent-specific gene expression (PSGE), occurs in mammals, including humans, and higher plants. The theory that PSGE solves genetic conflict between mother and father is widely accepted. We argue, however, that the conditions for PSGE to evolve are restricted. With respect to seed size, PSGE can only evolve when the developing offspring has a strong effect on its own resource acquisition. When seed size is close to the optimum for the maternal parent, there is no internal conflict in the offspring because maternally and paternally derived genes both favour increased seed size. Although the literature generally suggests that the maternal parent controls seed size, a number of observations suggest an additional role for the paternal parent. Here, we critically evaluate these studies and suggest a rigorous methodology for establishing paternal effects on seed size, which can be applied to the model species Arabidopsis thaliana.     

Resource exploitation and relatedness: implications for offspring size variation within broods

Much of the theory on offspring size variation within a brood relies on unequal maternal allocation of resources to each embryo. However, maternal allocation strategies are subject to an inherent conflict between mothers and offspring: individual offspring, being more closely related to themselves than to their siblings, should always prefer a larger share of the available resources than that which is optimal from their mother's perspective. Thus, in species where mothers cannot unilaterally impose a resource allocation strategy, offspring can respond to this conflict by competing for more resources than is maternally optimal. Here we show that variation in offspring size within a brood can arise as a by‐product of competition between siblings over a common resource, even when 1) there are no competitive inequalities within families, and 2) maternal investment per brood is fixed. Moreover, we show that size variance among offspring increases with increasing levels of competition, brought about by decreasing relatedness among siblings. Conflict thus offers a simple, testable and, potentially general, explanation for the wide variability in offspring size seen in nature. This extends explanatory hypotheses for offspring size variation beyond those of maternal effects, under which most explanations have been subsumed to date.     

Population structure inhibits evolutionary diversification under competition for resources

A model is presented that explores how population structure affects the evolutionary outcome of ecological competition for resources. The model assumes that competition for resources occurs within groups of a finite number of individuals (interaction groups), and that limited dispersal of individuals between groups (according to Wright's island model of population structure) results in genetic structuring of the population. It is found that both finite-sized interaction groups and limited dispersal can have substantial effects on the evolution of resource exploitation strategies as compared to models with a single, infinitely large, well-mixed interaction group. Both effects, in general, tend to select for less aggressive competitive strategies. Moreover, both effects also tend to reduce the likelihood of the evolutionary diversification of resource exploitation strategies that often occurs in models of resource competition with infinite populations. The results are discussed in the context of theories of the evolutionary diversification of resource exploitation strategies and speciation.     

How should parents adjust the size of their young in response to local environmental cues?

Models of parental investment typically assume that populations are well mixed and homogeneous and have devoted little attention to the impact of spatial variation in the local environment. Here, in a patch‐structured model with limited dispersal, we assess to what extent resource‐rich and resource‐poor mothers should alter the size of their young in response to the local environment in their patch. We show that limited dispersal leads to a correlation between maternal and offspring environments, which favours plastic adjustment of offspring size in response to local survival risk. Strikingly, however, resource‐poor mothers are predicted to respond more strongly to local survival risk, whereas resource‐rich mothers are predicted to respond less strongly. This lack of sensitivity on the part of resource‐rich mothers is favoured because they accrue much of their fitness through dispersing young. By contrast, resource‐poor mothers accrue a larger fraction of their fitness through philopatric young and should therefore respond more strongly to local risk. Mothers with more resources gain a larger share of their fitness through dispersing young partly because their fitness in the local patch is constrained by the limited number of local breeding spots. In addition, when resource variation occurs at the patch level, the philopatric offspring of resource‐rich mothers face stronger competition from the offspring of other local mothers, who also enjoy abundant resources. The effect of limited local breeding opportunities becomes less pronounced as patch size increases, but the impact of patch‐level variation in resources holds up even with many breeders per patch.     

东方田鼠家群个体体重、攻击性及胆量对其扩散的影响

扩散作为动物适应生存环境的重要特征之一,受到自身生物学特征及环境等方面的制约。以家群形式生活和子代雄鼠扩散为主的东方田鼠,其成员个体是否因领地食物和空间资源竞争导致体重小、攻击性弱及胆小个体先行扩散。以新鲜马唐叶片构建三块密集均质的食物斑块,在食物斑块周边以透明玻璃设置观测箱,采用透明塑胶管连接三块食物斑块作为动物扩散的通道,构建东方田鼠扩散行为观测装置。将东方田鼠家群子代成员投放至带有自身家群气味的食物斑块,测定成员个体在食物斑块上的觅食行为序列过程和参数,以及向其他食物斑块扩散的行为过程和参数以及家群中先行扩散个体体重、攻击性及胆量占所有家群数的比率,检验成员个体的体重、攻击性及胆量对扩散的影响。结果发现,体重小、攻击性弱和胆小个体的觅食启动时间极显著地大于体重大、攻击性强和胆大个体的,但其先行扩散的比率却显著地大于体重大、攻击性强和胆大个体的;然而体重小、攻击性弱及胆小个体的扩散开始时间显著或极显著地大于体重大、攻击性强及胆大个体的。结果揭示,东方田鼠家群成员随着年龄的增长和对食物及空间资源竞争的加剧,体重大、攻击性强及胆大个体会迫使体重小、攻击性弱及胆小个体先行扩散。     

Social immunity of the family: parental contributions to a public good modulated by brood size

Social immunity refers to any immune defence that benefits others, besides the individual that mounts the response. Since contributions to social immunity are known to be personally costly, they are contributions to a public good. However, individuals vary in their contributions to this public good and it is unclear why. Here we investigate whether they are responding to contributions made by others with experiments on burying beetle (Nicrophorus vespilloides) families. In this species, females, males and larvae each contribute to social immunity through the application of antimicrobial exudates upon the carrion breeding resource. We show experimentally that mothers reduce their contributions to social immunity when raising large broods, and test two contrasting hypotheses to explain why. Either mothers are treating social immunity as a public good, investing less in social immunity when their offspring collectively contribute more, or mothers are trading off investment in social immunity with investment in parental care. Overall, our experiments yield no evidence to support the existence of a trade-off between social immunity and other parental care traits: we found no evidence of a trade-off in terms of time allocated to each activity, nor did the relationship between social immunity and brood size change with female condition. Instead, and consistent with predictions from models of public goods games, we found that higher quality mothers contributed more to social immunity. Therefore our results suggest that mothers are playing a public goods game with their offspring to determine their personal contribution to the defence of the carrion breeding resource.     

Sink-limitation and the size-number trade-off of organs: production of organs using a fixed amount of reserves

To analyze the nature of size-number trade-off of organs, we develop models in which the effects of sink-limitation in the growth of organs and the loss of resources by maintenance respiration are taken into consideration. In these models, the resource absorption rate of an organ is proportional to either its absolute size or its surface area and either the initial size of an organ or the total initial size of the organs produced is fixed. In all models, organs are produced using a fixed amount of reserved resources and no additional resources become newly available for their growth. We theoretically show that size-number trade-offs are nonlinear if the resource absorption rate of an organ is proportional to the absolute size of the organ and the initial size of the individual organs is fixed or if the resource absorption rate of an organ is proportional to the surface area of the organ. In these nonlinear size-number trade-offs, the size of individual organs increases less rapidly than in linear trade-offs with a decrease in the number of organs and the total size of organs is an increasing function of the number of organs produced. This implies that increasing the number of organs produced is advantageous in terms of resource-use efficiency. In contrast, size-number trade-off is linear if the resource absorption rate of an organ is proportional to the absolute size of the organ and there is a linear trade-off between the initial size of organs and their number. To exemplify the effects of those size-number trade-offs on the life-history evolution, we calculate the optimal offspring sizes that maximize the number of offspring successfully being established. In the case of nonlinear size-number trade-offs, the optimal offspring sizes are smaller than the optimal offspring size in the case of linear size-number trade-offs, namely, that in the model of Smith and Fretwell (1974). Our optimal offspring size depends on the metabolism of organ development; the optimal offspring size decreases with an increase in maintenance respiration rate relative to the growth coefficient of organs.     

Clutch-size behavior and coexistence in ephemeral-patch competition models

Systems of patchy, ephemeral resources often support surprisingly diverse assemblages of consumer insects. Aggregation of consumer individuals over the landscape of patches has been suggested as one mechanism that can stabilize competition among consumer species. One mechanism for larval aggregation is the laying of eggs in clutches by females traveling among patches to distribute their total fecundity. We use simulation models to explore the consequences, for coexistence of competitors, of larval aggregation that arises from clutch laying. Contrary to some previous treatments, we find that clutch laying can be strongly stabilizing and under certain conditions can be sufficient to allow competitors to coexist stably. We extend these models by considering clutch size as a variable that responds to the abundance of resource patches. Such a relationship might be expected because females should lay their eggs in fewer but larger clutches when the cost of travel among patches is high (because patches are rare). When females adjust clutch size in response to resource abundance, coexistence can be easiest when resource patches are scarce and most difficult when resources are abundant.     

Asymmetry within social groups: division of labour and intergroup competition

Social animals vary in their ability to compete with group members over shared resources and also vary in their cooperative efforts to produce these resources. Competition among groups can promote within‐group cooperation, but many existing models of intergroup cooperation do not explicitly account for observations that group members invest differentially in cooperation and that there are often within‐group competitive or power asymmetries. We present a game theoretic model of intergroup competition that investigates how such asymmetries affect within‐group cooperation. In this model, group members adopt one of two roles, with relative competitive efficiency and the number of individuals varying between roles. Players in each role make simultaneous, coevolving decisions. The model predicts that although intergroup competition increases cooperative contributions to group resources by both roles, contributions are predominantly from individuals in the less competitively efficient role, whereas individuals in the more competitively efficient role generally gain the larger share of these resources. When asymmetry in relative competitive efficiency is greater, a group's per capita cooperation (averaged across both roles) is higher, due to increased cooperation from the competitively inferior individuals. For extreme asymmetry in relative competitive efficiency, per capita cooperation is highest in groups with a single competitively superior individual and many competitively inferior individuals, because the latter acquiesce and invest in cooperation rather than within‐group competition. These predictions are consistent with observed features of many societies, such as monogynous Hymenoptera with many workers and caste dimorphism.     

Cooperation and the common good

In this paper, we draw the attention of biologists to a result from the economic literature, which suggests that when individuals are engaged in a communal activity of benefit to all, selection may favour cooperative sharing of resources even among non-relatives. Provided that group members all invest some resources in the public good, they should refrain from conflict over the division of these resources. The reason is that, given diminishing returns on investment in public and private goods, claiming (or ceding) a greater share of total resources only leads to the actor (or its competitors) investing more in the public good, such that the marginal costs and benefits of investment remain in balance. This cancels out any individual benefits of resource competition. We illustrate how this idea may be applied in the context of biparental care, using a sequential game in which parents first compete with one another over resources, and then choose how to allocate the resources they each obtain to care of their joint young (public good) versus their own survival and future reproductive success (private good). We show that when the two parents both invest in care to some extent, they should refrain from any conflict over the division of resources. The same effect can also support asymmetric outcomes in which one parent competes for resources and invests in care, whereas the other does not invest but refrains from competition. The fact that the caring parent gains higher fitness pay-offs at these equilibria suggests that abandoning a partner is not always to the latter''s detriment, when the potential for resource competition is taken into account, but may instead be of benefit to the ‘abandoned’ mate.     

Competition over Personal Resources Favors Contribution to Shared Resources in Human Groups

Members of social groups face a trade-off between investing selfish effort for themselves and investing cooperative effort to produce a shared group resource. Many group resources are shared equitably: they may be intrinsically non-excludable public goods, such as vigilance against predators, or so large that there is little cost to sharing, such as cooperatively hunted big game. However, group members'' personal resources, such as food hunted individually, may be monopolizable. In such cases, an individual may benefit by investing effort in taking others'' personal resources, and in defending one''s own resources against others. We use a game theoretic “tug-of-war” model to predict that when such competition over personal resources is possible, players will contribute more towards a group resource, and also obtain higher payoffs from doing so. We test and find support for these predictions in two laboratory economic games with humans, comparing people''s investment decisions in games with and without the options to compete over personal resources or invest in a group resource. Our results help explain why people cooperatively contribute to group resources, suggest how a tragedy of the commons may be avoided, and highlight unifying features in the evolution of cooperation and competition in human and non-human societies.     

Kin competition within groups: the offspring depreciation hypothesis

Where relatives compete for the same resources (kin competition) and each obtains an equal share, this can favour the evolution of elevated dispersal rates, such that most resource competition is among non-relatives. We show that this effect evaporates as among-sibling dominance increases to the point where the allocation of resources is maximally unequal. We restore a kin-competition effect on emigration rates from dominance-ranked family groups by showing that where siblings form queues to inherit the breeding positions, the length of the queue affects the fitness of all individuals by depreciating the rank of subsequent offspring. Incorporating this 'offspring depreciation' effect decreases optimal queue lengths, increases dispersal rates and explains the otherwise paradoxical use of sinks by cooperatively breeding birds in stable environments. The offspring depreciation effect also favours the evolution of small, but consistent, clutch sizes and high reproductive skew, but constrains the evolution of alloparenting.