Despite growing evidence that the long female post-reproductive lifespan may not be unique to humans and may not even require an adaptive explanation , grandmothering remains among the leading hypotheses for the evolution of human longevity. This is due in part to the fact several (though, importantly, not all) empirical studies of contemporary and historical populations have shown that helpful grandmothers may benefit the fitness of their grandchildren. But such findings do not necessarily speak directly to the evolution of increased longevity via grandmothering because studies of extant modern humans cannot demonstrate that the observed benefits are (i) applicable to human ancestors or (ii) sufficiently large to offset the costs associated with reducing adult mortality.
The motivation for our article was to employ an evolutionary model to test whether inclusive fitness benefits gained via grandmothering could in fact be large enough for selection to favour increased longevity . We found no effect of grandmothering on longevity. However, the authors of the comment  have alerted us to problems with two of our model's assumptions: (i) that every adult male has the same probability of serving as a mate, regardless of his age, and (ii) that mutations can increase longevity (or, in other words, decrease adult mortality) at no expense to reproductive potential. Here, we take up both of these issues in turn.
In our model, females choose their mates randomly from among all adult males. Thus, male fertility is limited only by mortality. Hawkes et al. argue that male reproduction into old age allows selection to favour increased longevity through males in our model (see also ). They introduce a different rule, whereby females preferentially choose to mate with young adult males, as seen in primates in which male fertility is mediated by rank. Hawkes et al. demonstrate that over many tens of thousands of time-steps longevity does not increase as rapidly when females preferentially mate with young adult males (, fig. 1). Yet, selection favours increased longevity even when male fertility is limited by female mate-choice (see below).
The second issue has more bearing on the interpretation of our original results. A central component of the grandmother hypothesis is the trade-off between somatic and reproductive effort, whereby: ‘Increased “somatic effort” that slowed ageing would come at the cost of lower “reproductive effort” at younger ages’ (, p. 1336). We did not include a trade-off between somatic effort (longevity) and reproductive effort (total reproductive potential) in the original model for two reasons. First, to the best of our knowledge the life-history literature provides no clear guide as to what mathematical form this trade-off should take. Second, had we included a trade-off between longevity and reproductive potential and found no effect of grandmothering, we would have been left unable to distinguish whether this result was due to insufficient inclusive fitness benefits or to an unreasonably steep trade-off. In any case, it is now clear that our decision to do without this trade-off had an important unintended consequence. Hawkes et al. show that the mean xL values observed in our experiments are close to the value provided by Fisher's fundamental theorem, even in simulations without grandmothering. It appears that the decision not to include a trade-off between longevity and reproductive potential ultimately hindered our ability to assess the effects of grandmothering on longevity. We agree with the comment: the results reported in figs. 2 and 3 of our research article should be viewed as inconclusive concerning the effect of grandmothering on the evolution of longevity.
While Hawkes et al. recognize the problem associated with the lack of a trade-off between longevity and reproductive potential, they do not address this issue in their modified version of our model. Indeed, they note that selection favours increased longevity—even in simulations that do not include grandmothering—because decreased adult mortality helps ensure that females survive deeper into their own reproductive periods. But just as before, these decreases in adult mortality come at no cost to fertility. Clearly, the trade-off between longevity and reproductive potential will need to be addressed in order to provide a better test of the grandmother hypothesis.
We have begun to investigate the effect of including a trade-off between longevity and reproductive potential with a one-sex (female only) model in which adult mortality (μ) is modelled as a single haploid locus with multiple alleles (mutation rate 0.05, mutation size 0.001). Mortality at young ages follows Siler's model, as before. However, once an individual reaches sexual maturity (age 15), adult mortality is represented by a constant value (μ). At the beginning of each simulation, all agents possess an adult mortality rate of μ = 0.03. This model includes a rather simple trade-off between reproductive potential and adult mortality rate. Mutations that decrease female i's adult mortality rate (and thus increase her longevity) also decrease her total reproductive probability (TRPi) as follows: where t represents the strength of the trade-off. TRP is capped at 8, so that agents cannot increase TRP above this limit by increasing their adult mortality rate. Furthermore, the mortality rate cannot fall below 0.001, and agents are culled if they live to an age of 100. To learn about the evolutionary dynamics of the model under different conditions we vary t and the size of the benefits associated with grandmothering. TRPi is used to calculate age-dependent fertility as described in Kachel et al.  given w = 35. In baseline simulations, grandmothers provide no help. In simulations that include grandmothering, eligible grandmothers can decrease the weaning age of their matrilineal grandchildren from 5 years to 1 year old and decrease their matrilineal grandchildren's pre-adult mortality. We run the experiments (20 simulations each) for 200 000 time steps, long enough for mean adult mortality to reach equilibrium in all cases (figure 1). The source code and ODD (overview, design concepts and details) protocol for this model are freely available upon request.
The results demonstrate the importance of the trade-off between reproductive potential and adult mortality (figure 1). When t is low, selection favours increased longevity even when grandmothers have no effect on the weaning age or survival of their grandchildren (figure 1a) for the same reason cited by Hawkes et al.: decreasing adult mortality allows females to experience more of their reproductive period. However, under conditions in which the cost of decreasing one's adult mortality is higher, selection does not favour increased longevity, even when the benefits associated with grandmothering are relatively large. Figure 1 illustrates that the degree to which the inclusive fitness benefits of grandmothering are large enough for selection to increase longevity beyond the level observed when grandmothers play no role at all depends not only on the type and the size of the benefits provided by helpful grandmothers but also on the value of t. These results suggest that the grandmother hypothesis may be applicable only within a relatively narrow (and intermediate) range of t. The weakness of selection acting on older females is likely to explain why there exists a threshold value of t beyond which selection does not favour increased longevity, despite the benefits associated with grandmothering. In any case, it would appear that the nature of the trade-off between adult mortality and reproductive potential in ancestral females (and possibly males) must be characterized before one can conduct an appropriate evolutionary test of the grandmother hypothesis.
We are grateful for Hawkes et al.'s comment. Making one's assumptions explicit and sharing them with others often leads to advances that are not possible by arguing over the subtle nuances and vague phrases of verbal models. The next iteration of the model will be better for having gone through this process and for including new ways of modelling male fertility as well as new findings on the nature of the trade-off between reproductive potential and adult mortality. Kirkwood & Shanley (, p. 27) remind us that until the grandmother hypothesis can be demonstrated quantitatively in an evolutionary context with parameter values that are appropriate to human ancestors, it ‘remains a matter of speculation’. We agree, and we join Hawkes et al. in expressing our hope that the problems we encountered in the first attempt at testing whether the grandmother hypothesis holds in an evolutionary context will not deter future work aimed at quantifying how helpful grandmothers must be in order to play an evolutionarily significant role in human-like longevity.
We thank Annette Baudisch and John Hawks for their helpful correspondence.
The accompanying comment can be viewed at http://dx.doi.org/10.1098/rspb.2010.2720.
- Received March 4, 2011.
- Accepted March 17, 2011.
- This Journal is © 2011 The Royal Society