An act of strong altruism involves giving a fitness advantage to others at net personal cost to the benefactor1,2. Strong altruism presents a special case in evolutionary biology because its cost to the altruist appears to contradict the self-interested incentives of natural selection. Its resilience to defection despite the cost is explained by the indirect benefits that return to an altruist from interactions that are positively assorted by kin recognition, population viscosity, reciprocity, or other structuring mechanisms3,4,5. The evolution of strong altruism is inhibited, however, when the very structures that promote indirect benefits also promote competition amongst the beneficiaries6. This benefits-cancelling effect of competition may sustain only weak altruism, without net cost to the altruist, or suppress cooperation altogether7. A challenge remains therefore to explain the widespread occurrence of altruistic traits and cooperative behaviours generally, in crowded environments8,9,10,11,12.

Strong altruism occupies the +/− quartile of pairwise interaction space in the Hamiltonian classification3,13 completed by +/+ mutually beneficial (including weakly altruistic), −/+ selfish and −/− spiteful interactions. The +/− interaction of strong altruism, henceforth referred to as ‘altruism’, can achieve an evolutionarily stable strategy (ESS) when its beneficiaries are kin. Specifically, kin selection must satisfy Hamilton's rule:

in which the altruist's net cost c to personal fitness in delivering fitness benefit b is compensated by beneficiaries with coefficient of relatedness r returning inclusive fitness r·b to the altruist3. Coefficient r quantifies the benefits arising from positively assorted interactions. In pairwise interactions, assortative mixing is a necessary pre-requisite for altruism by kin selection, and/or trait selection on synergistic benefits4,14.

Altruism is inhibited when relatives compete for its benefits6,8,15,16. Competition means that one individual's gain is another's loss; competitive interactions amongst relatives therefore result in beneficiaries gaining from altruism only at the expense of other relatives of the altruist. For example, if mutual altruism raises personal fitness in the form of b − c extra offspring, then their displacement of other relatives of the altruist by population regulation incurs an inclusive fitness cost r′·(b − c), where r′ is the relatedness of those relatives to the altruist. Hamilton's rule can accommodate this supplementary cost by reconfiguring relatedness with respect to the ‘economic neighbourhood’ that encompasses competition with relatives, with a devaluation of r that has the effect of inhibiting altruism15. Unless r′ < r, altruism is unsustainable with inelastic population regulation8,16. Recent life-cycle models have shown how elasticity in regulating mechanisms can offset this inhibitory effect of competition, even to the extent that competition favours altruism when it brings trait-selected synergistic benefits11,12,17.

Even with elastic population regulation and synergistic benefits, the requirement for strong population structure and/or positive synergies to overcome inhibition by competition assumes that the driver for altruism is an opportunity to collect the positive benefits of the altruistic act. In ecologically realistic scenarios of crowding, however, the driver for altruism can be something altogether more mundane and ubiquitous: release from competition amongst non-altruists. Competition is widespread and largely inevitable in the natural world and conditions that provide positive synergies are possibly too rare to explain the ubiquity of altruism. Here we contest the prevailing view that altruism requires stronger kin or trait selection in crowded conditions, by showing that its models have yet to embrace fully the evolutionary tenet that traits spread when their carriers have higher fitness than the population average (even if the trait carries no intrinsic benefit). Prior work on the evolution of altruism has focused solely on the impacts of altruists on beneficiaries, calibrating Hamilton's rule against a non-altruism alternative of no interaction. Whilst this alternative is appropriate to density-independent dynamics, it ignores a basic principle of population regulation, that the payoff for mutual competition is negative relative to no interaction.

We consider an environment in which competition lowers the payoff for non-altruists with other non-altruists, as well as for altruists with beneficiaries. For example cooperative hunting and breeding in groups of African wild dogs (Lycaon pictus) brings fitness benefits that may depend on prevailing conditions of competitor density18. The alternative to altruism amongst kin in this globally competitive environment is competition amongst non-altruist (‘defector’) kin. Their competition with each other presents a bleak prospect against which altruism prevails relatively easily, even with negligible population structure and without requirement for r′ < r, or elastic regulation, or synergistic benefits. We find that competitive environments facilitate altruism by devaluing its alternatives, as opposed to improving its opportunity. This prediction is consistent with the observation in wild dogs that group size increases individual fitness more strongly under higher competitor density18. We demonstrate the broad scope of our theoretical analysis by modelling it with the simplest games between altruist and defector strategies and the most generic dynamics of altruistic phenotypes and genotypes invading a density-regulated population of non-altruists. These games and models underpin understanding of all empirical cases of cooperative behaviours amongst taxa ranging from bacteria to vertebrates and we point to examples of both conferred benefits and public goods benefits. We discuss the reasons why density regulation amongst non-altruists has been ignored in previous theory of altruism in the presence of competition.

We start with a conventional Prisoner's Dilemma game, in which unilateral defection pays better than mutual altruism and mutual defection pays better than unilateral altruism. We interpret its pairwise interactions as products of density-dependent competition and we analyse the inclusive fitness required to escape the dilemma. We then model the influence of interactions amongst defectors on the threshold of relatedness necessary for an ESS with altruism, always assuming a Prisoner's Dilemma for personal fitness. Our method aligns with recent life-cycle models in recognizing that competition and inclusive fitness have independent causal factors, of resource limitation and population structure respectively11,12. Accordingly, we decouple the effects of competition from those of inclusive fitness by allocating all competitive effects to payoffs in personal fitness. Inclusive fitness is then calculated on payoffs resulting from interactions that include competition, instead of being calculated as a supplement to pre-competition inclusive fitness. This approach greatly simplifies accounting procedures by obviating the need to specially add the effects of competition into the inclusive fitness payoffs. Thus we treat the change in personal fitness b − c for mutual altruism as the average payoff obtained in the presence of competition amongst altruists selected with average relatedness r. Competition may render b − c negative relative to no interaction and we consider both positive and negative scenarios. Model predictions depart from those of previous theory only when we factor in the presence of competition to the payoff for mutual defection. Competition renders this payoff negative relative to no interaction and we therefore refer to it as a fitness cost d (see ref. 19 for discussion of such costs generally). We will demonstrate that this method of accounting for competition perfectly maps the game-theoretic payoffs onto Lotka-Volterra interaction coefficients for density-dependent population dynamics.