To what degree does increasing life span tend to favor further increases in life span due to an enhanced effect of cooperative, altruistic behavior? Can this create runaway extension of life span in species with greater levels of such behavior? Our own species is the example in mind when asking these questions, as illustrated by the Grandmother hypothesis as an explanation for the exceptional longevity of humans in comparison to other primate species. Our intelligence makes us better at cooperation, which allows natural selection to operate at ever older ages, because individuals in later life contribute to the success of their descendants.
Equally, we can ask whether longevity is necessary for cooperative, altruistic behavior to be selected. If species are too short-lived perhaps there is less selection pressure for the emergence of cooperative behaviors. The authors of this paper mount the argument that species without long periods of overlapping shared experience will tend to be less likely to evolve altruism, but - inconveniently - this doesn't appear in nature in any long-lived species. This makes it hard to argue any of the points in this paper on the basis of evidence rather than model-based speculation.
Many primate species engage in unidirectional or reciprocal cooperation with others. Dyadic interactions with relatives or other individuals are particularly common among humans. This cooperative behaviour has presumably evolved because it increases the fitness of the individual who performs the behaviour by yielding either indirect or direct fitness gains. Direct fitness gains via reciprocity are often not immediate but rather occur with a time delay to be realised in a future interaction between the cooperation partners.
A human baby born today in an industrialised country can expect to share most of its lifetime with a peer from its birth cohort due to high lifespan equality (i.e. most individuals live similarly long). High lifespan equality arises from a rectangularised survival function, which captures the fact that most individuals will survive to a similar age. What is true for humans today, however, need not be true in general. Across the tree of life, species show an astounding diversity of survival functions, with remarkable differences even between human populations. In this work we ask how different survival functions determine, firstly, life expectancy, secondly, the expectancy of overlapping life among two peers of a birth cohort ("shared life expectancy"), and thirdly, the proportion of shared life expectancy in relation to life expectancy ("proportion of life shared"). A low proportion of life shared adds uncertainty to the future availability of reciprocal cooperation partners and thus may hinder the evolution of cooperation.
Using population models, we find that while the proportion of life shared can vary vastly for similar life expectancies, almost all changes to mortality schedules that result in higher life expectancies also result in higher proportions of life shared. From our results we can infer that selection pressures which increase life expectancy almost always increase the proportion of life shared, or in other words lifespan equality, and vice versa. A co-occurrence of both carries therefore little indication as to whether high proportions of life shared may aid the evolution of high life expectancies through enhancing cooperative behaviour, or whether high life expectancies inevitably co-occur with high proportion of life shared, which then may be a precondition for the evolution of cooperation.