Title: The tradeoff between number and size of offspring in humans and other primates

Abstract: Life-history theory posits a fundamental trade-off between number and size of offspring that structures the variability in parental investment across and within species. We investigate this ‘quantity–quality’ trade-off across primates and present evidence that a similar trade-off is also found across natural-fertility human societies. Restating the classic Smith–Fretwell model in terms of allometric scaling of resource supply and offspring investment predicts an inverse scaling relation between birth rate and offspring size and a −¼ power scaling between birth rate and body size. We show that these theoretically predicted relationships, in particular the inverse scaling between number and size of offspring, tend to hold across increasingly finer scales of analyses (i.e. from mammals to primates to apes to humans). The advantage of this approach is that the quantity–quality trade-off in humans is placed into a general framework of parental investment that follows directly from first principles of energetic allocation.

Authors: Robert Walker, Michael Gurven, Oskar Burger, Marcus Hamilton

I have a biased perspective but I think this is a really good paper. It combines the classic model of the quantity/quality tradeoff in life history theory developed by Smith and Fretwell with a recent model by Charnov and Ernest (citations below).

The Smith-Fretwell model basically says that the relative cost of a kid C is the total energy budget mom has to put toward making kids R divided by the number of kids she has N. so C = R/N. This also means that the number of kids then is given by N = R/C. This is a pretty straight forward model that works well. So the higher the cost of an average kid to an average mother in a species or population the fewer kids the average mom will have. We know from life history theory that mom's energy budget R is a function of her mass and that a 3/4 power allometry of body mass is a pretty reasonable estimate for this energy budget. We also know that a reasonable estimate of the cost of a kid seems to be mass at weaning, which is a linear function of mom's mass - about .3M among mammals where M is mom's mass. This means that on average mammal offspring are dependent on their moms for energy until they are about 1/3 her size (Charnov 1993 and others). Anyway, these two observations can be placed into the Smith-Fretwell model to predict another well-known allometric relationship, the -1/4 power scaling of fertility rate with body mass. This happens because R is proportional to M^3/4 and C is proportional to M^1 so we get that N can be predicted by M^3/4 divided by M^1 which gives us M^-1/4. Or we can use these same expressions to look at the relationship between the number and size of offspring, which is predicted to be an inverse relationship (N/R = 1/C ~ M^-1). Our analysis demonstrates that the theory predicts the actual empirical trends in humans and primates.

If this is kind of thing is new to you just realize that when we look for patterns across large numbers of species - like all mammals or all birds - we find these really consistent relationships where a lot of important traits seem to be largely constrained (or at least well-predicted) by the average adult mass of the species. Three of these traits used here are metabolic rate, which is taken to be energy budget, the size of the offspring when its independent from its mom (important because that's when the mom can start making new kids if she wants so its a key constraint on fertility), and these two predict another - that fertility rate is slower with larger animals than with smaller ones.

We need to keep in mind that mass at weaning is generally a good proxy for the measure we are really interested in which the energetic cost of the offspring to the mother. For primates and in humans in particular, however, this may not be a good approximation. Human mothers invest much more in their offspring as human kids are often dependent long after they are weaned.

We take this into account by looking at mass of the offspring at ages older than the typical age at weaning and find that the model works better as a result. So this basic prediction of life history theory, that a tradeoff exists between the number and size of offspring, is met with data on human groups (natural fertility, small-scale populations) and among primates. There are some other points to the paper as well and we hope people find it interesting and that it provokes further research in this area. comments welcome of course.

I'll post a stable link to the pdf of the paper as soon as I can but something is wacky with UNM's server so I can't right now. [Ok, here's a link to a pdf of the paper.] If you are on a computer that has access to the proceedings of the royal society then you should be able to get it here.

best,

Oskar

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Charnov, E.L. & Ernest, S.K.M. 2006 The offspring-size/clutch-size trade-off in mammals.

*Am. Nat.*

**167**, 578–582, (doi:10.1086/501141).

Charnov, E.L. 1993 Life history invariants: some explorations of symmetry in evolutionary ecology. Oxford, UK: Oxford University Press.

Smith, C.C. & Fretwell, S.D. 1974 The optimal balance between number and size of offspring.

*Am. Nat.*

**108**, 499–506, (doi:10.1086/282929).

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