On the evolution of intergenerational division of labor, menopause and transfers among adults and offspring.

We explain how upward transfers from adult children to their elderly parents might evolve as an interrelated feature of a deepening intergenerational division of labor. Humans have a particularly long period of juvenile dependence requiring both food and care time provided mainly by younger and older adults. We suggest that the division of labor evolves to exploit comparative advantage between young and old adults in fertility, childcare and foraging. Eventually the evolving division of labor reaches a limit when the grandmother's fertility reaches zero (menopause). Continuing, it may hit another limit when the grandmother's foraging time has been reduced to her subsistence needs. Further specialization can occur only with food transfers to the grandmother, enabling her to reduce her foraging time to concentrate on additional childcare. We prove that this outcome can arise only after menopause has evolved. We describe the conditions necessary for both group selection (comparative steady state reproductive fitness) and individual selection (successful invasion by a mutation), and interpret these conditions in terms of comparative advantages.

Sexual dimorphism and sexual selection: a unified economic analysis.

We develop a life history model with two sexes, and study the optimal energy allocation strategy of males and females. We join Darwin and others in suggesting that the origin of sexual dimorphism and sexual selection is the difference between male and female reproduction costs. Due to this assumed cost difference, the resulting Bellman equations of gene dynamics in our two-sex life history model imply a large "energy surplus" on the part of males. This allows the male form to devote energy to the development of some costly male traits that help the males to compete for access to females. These costly male traits are sexually dimorphic. Using this life history model, we are able to explain important features of sexual dimorphism, as well as why males often transfer less to their offspring than do females, and why only females have a menopause.

A two-sex life history model of handicap signaling.

The males of many species (such as peacocks) develop excessively large traits, which appear to interfere with their agility and hence survival probability. Moreover, it is also observed that females seem to prefer mating males with such clumsy traits. Zahavi (1975) proposed a handicap theory to explain this phenomenon, suggesting that this trait/preference interaction is a way in which strong males can signal their viability by yielding a handicap in terms of a clumsy trait size. This paper presents a two-sex model of selfish genes that generates this particular male-female interaction, and characterizes the conditions behind a handicap equilibrium. We first show the female dominance result of Bateman (1948) in this two-sex model, and then specify the relevant equilibrium conditions, including the incentive compatibility condition for females, the individual rationality condition for males, and the stability condition of population composition. Identifying these conditions helps us understand the various features of the searching/signaling of sex selection in evolution.

The co-evolution of intergenerational transfers and longevity: an optimal life history approach.

How would resources be allocated among fertility, survival, and growth in an optimal life history? The budget constraint assumed by past treatments limits the energy used by each individual at each instant to what it produces at that instant. We consider under what conditions energy transfers from adults, which relax the rigid constraint by permitting energetic dependency and faster growth for the offspring, would be advantageous. In a sense, such transfers permit borrowing and lending across the life history. Higher survival and greater efficiency in energy production at older ages than younger both favor the evolution of transfers. We show that if such transfers are advantageous, then increased survival up to the age of making the transfers must co-evolve with the transfers themselves.