2024 年 132 巻 2 号 p. 117-132
Although previous research on hunter-gatherers has shown that cooperative care and resource provisioning are important traits of human life history, the specifics of these behaviors and their relationship to energy acquisition were undetermined. We developed a simulation model of energy investment in reproduction and child raising in hunter-gatherer families based on empirical data from previous research on hunter-gatherer energy acquisition, consumption, and annual mortality. The model calculates the number of children that a hunter-gatherer family can support until reaching adulthood. Using this model, we explored the optimum value for a life history trait, the age of first marriage, in families with different marriage types and with assistance from different age/sex groups. The model results showed that grandparenting could increase the number of children in families, but whether this was advantageous to the grandparents depended on their energy acquisition. The simulation results generally aligned with observed values for mean age at first birth, prevalence of grandparenting, and age/sex of helpers in cooperative breeding, implying that such traits are strongly influenced by energetic constraints.
Throughout the course of their life history, organisms must balance their investment in somatic growth and reproduction. However, optimizing energy investment in humans presents difficulties often not seen in other organisms.
One of the simpler examples of optimizing energy investment can be seen in annual plants, which must maximize seed yield at the end of the growing season, which is also the end of their lifespan. Cohen (1971) suggested that the optimum solution was an instantaneous switch from solely vegetative to solely reproductive growth. Subsequent research applied Pontryagin’s maximum principle to determine the optimum solution for annual (Denholm, 1975; King and Roughgarden, 1982) and perennial plants (Tateno and Watanabe, 1988). The intuitive explanation for this application, provided by Iwasa and Roughgarden (1984), was that the Hamiltonian value represents the increase in reproductive biomass at the end of the growing season, caused by the investment in vegetative and reproductive growth at that point in time. Therefore, optimizing seed yield is equivalent to maximizing the Hamiltonian value throughout the growing season. Reproductive growth always increases seed yield, but not investing in vegetative growth may result in a suboptimal seed yield at the end of the growing season. In contrast, vegetative growth increases a plant’s energy acquisition but requires sufficient time to invest this increase in reproduction and thus becomes increasingly less effective towards the end of the growing season.
In mammals, infants are dependent on their mother’s metabolism until weaning, after which they invest a fixed fraction of their energy budget into growth as juveniles. Upon maturation, all energy previously invested in growth is now invested in reproduction (Charnov, 1991, 1993). Similar to vegetative growth in plants, greater investment in growth increases energy acquisition that can be invested in reproduction, but requires a longer juvenile period, resulting in less time spent as adults and greater mortality before adulthood. Primates are known to have lower rates of energy acquisition relative to body weight (Charnov and Berrigan, 1993), possibly due to the high energy costs of brain tissue (Rolfe and Brown, 1997), which necessitates a longer juvenile period to grow to a given body size, which in turn requires adults to have longer lifespans to have the same number of offspring.
Humans, compared with other primates, have even larger brains (Barrickman et al., 2008) and longer juvenile periods (Boesch and Boesch-Achermann, 2000; Hill et al., 2000; Hill and Hurtado, 1996; Howell, 1979; Jones et al., 1992; Nishida et al., 1991; Sugiyama, 1989) and must find a way to support these increased developmental costs. Isler and van Schaik (2012) showed that a hominid lifestyle cannot support the cost of developing a human brain, even with an increased lifespan. Furthermore, humans are dependent on their parents for provision both as juveniles as well as infants, further raising developmental costs. Another puzzle is the long post-reproductive lifespans of humans, which are not seen in other primates (Hawkes et al., 1998).
Previous research of hunter-gatherers has pointed to cooperative breeding as the solution. Hunter-gatherers are of special interest in studying the life history of humans due to humans being hunter-gatherers for most of our evolutionary history (Lee and DeVore, 1968). Observations of hunter-gatherers, such as the Hadza of northern Tanzania, have shown that grandmothers take part in foraging and raising children, assisting mothers when their babies are youngest and affecting the welfare of her children (Hawkes et al., 1997). This would explain the uniquely human trait of long postmenopausal life spans, which would be selected for if these evolved with mother–child food sharing and thus improved the daughter’s fertility (Hawkes et al., 1998). Fieldwork on three hunter-gatherer tribes, the Ache, Hiwi, and Hadza, showed that adult hunter-gatherer males acquire much more food than other age/sex groups, and human juveniles did not acquire as much as they consumed until the age of sexual maturity, in contrast to chimpanzees which share very little food after weaning and both sexes acquire roughly the same amount of food as they consume, suggesting that male provisioning is necessary for hunter-gatherer reproduction (Kaplan et al., 2000). Further study of the Ache and Hiwi showed that each breeding pair was supported on average by 1.3 non-reproductive adults and that the main food providers were males (Hill and Hurtado, 2009). Mothers and their children in traditional societies are known to receive help from many different groups such as males, older adults, a mother’s children, other kin and non-kin, suggesting that who helps may vary throughout a mother’s reproductive career (Kramer, 2010).
In addition to research on cooperative breeding, it is known that marriage is a universal practice (Murdock, 1949) and that almost all reproduction in hunter-gatherer societies takes place in wedlock (Apostolou, 2007). Based on these findings on energy optimization, cooperative breeding, and marriage, it can be surmised that families in hunter-gatherers serve to enlist the help of male mates as well as post-reproductive family members in investing energy into reproduction, analogously to the switch between somatic/vegetative and reproductive growth in other organisms. If this is true, hunter-gatherer families should be organized in such a way as to maximize energy investment in children. However, whether or not marriage in hunter-gatherers actually serves this role and is timed to optimize energy investment into reproduction as in the switch between somatic and reproductive growth in animals and plants is yet to be determined.
Although much work has been done on the evolution of cooperative breeding and related life history traits in humans (Kokko et al., 2001; Isler and van Schaik, 2012; Smaldino et al., 2013; Loo et al., 2017), our study focuses on how cooperative breeding is viable in the context of the energetic conditions to which extant hunter-gatherers are subject. We decided to focus on families because this has the advantage of being able to discern the smallest possible human groups necessary for the support of a reproductive pair, based on the amount of energy needed to raise a child. If hunter-gatherer families are indeed organized in such a way as to optimize energy investment in reproduction, the energy acquisition and consumption of their age/sex groups should reflect this. While extant hunter-gatherers may not be representations of their prehistoric counterparts (Headland et al., 1989; Solway et al., 1990), studying the energetic constraints present in modern hunter-gatherers could provide insight on the constraints present during our evolution.
One difficulty in determining human life histories is the presence of relatives and postreproductive individuals in providing for reproductive costs. Parents are the reproductive members of the family, and a parent’s death directly prevents new offspring from being born. Conversely, although the death of non-reproductive members may not directly disable reproduction, it may force the family or group to postpone reproduction or even result in starvation due to reduced energy acquisition.
Another difficulty in applying plant models of somatic versus reproductive growth to humans arises due to the qualitative differences between family members: that of individual versus inclusive fitness. Unlike the cells in a plant in which all cells are genetically identical and thus share half of their genes with the seeds they produce, humans can choose to invest in relatives or grandchildren with whom they share less of their genes compared with their own children. With the inclusive fitness gained from grandchildren being half the individual fitness gained from their own children, grandparenting seems less efficient given the same amount of investment. Although there may be other factors influencing this behavior, it is unknown whether or not grandparenting can be explained by seeking to optimize inclusive fitness given the same amount of energy costs.
These difficulties make it difficult to determine the optimal life history using the analytical approach used in plant models, which is to define energy or biomass increase as a set of differential equations and to find a set of controls that maximizes the Hamiltonian value. Therefore, we developed a computer model simulating energy investment in reproduction and child raising in hunter-gatherer families, which calculates the number of children that a family can support to adulthood for a given family composition. The model uses empirical data from previous research on hunter-gatherer energy acquisition, consumption, and annual mortality, which was derived from two populations with differing rates of survival to grandparenthood (Hill et al., 2007). The simulation model can then use this data to compare the number of children that family compositions can support, including ones that may not exist in the observed populations.
By calculating the number of children that various family compositions can support, we examined human life history, focusing on the aforementioned two problems: namely, how hunter-gatherer families support the energetic costs of reproduction; and whether forming the simulated families was viable from the perspective of individuals seeking to optimize their own fitness.
We developed a simulation model that calculates the annual energy balance and mortality of a hunter-gatherer family, with the number of children the hunter-gatherer family can raise in terms of their energy investment as the output. The simulation model establishes marriage age and family composition (i.e. number of wives and absence/presence of grandparents) as the initial state and calculates the number of children that each family is able to raise to adulthood. The amount of energy acquired, energy consumed, and mortality rate for each age/sex group are constants based on data from previous research from Hill and Hurtado (2009) and Kaplan et al. (2000). The model was programmed in Python and the source code is presented in the Supplementary Materials.
Hunter-gatherer energy acquisition and consumptionIn this simulation, energy acquisition refers to the acquisition of food from the external environment, while consumption refers to the calories used by each individual family member for their own growth or maintenance. Sharing food among family members after it has been acquired, (e.g. mothers feeding their children by lactation) is not considered as energy acquisition.
Calculating the optimal age for beginning reproduction for a hunter-gatherer family requires data on the energy acquisition and consumption of each age/sex group. Furthermore, we sought to compare the effects of different values of energy acquisition and consumption on family composition. For this end, we used the mean expected daily energy production/consumption for Ache and Hiwi hunter-gatherers presented by Hill and Hurtado (2009), as these data provided yearly values of hunter-gatherer energy balance, to create time series for the Ache and Hiwi (Figure 1) hunter-gatherer energy acquisition and consumption for use in the simulation model.
Ache and Hiwi daily energy acquisition and consumption, and annual mortality rate used in the simulation model. For the Ache and Hiwi energy data, blue denotes male data, red denotes female data, solid lines denote energy acquisition, and dotted lines denote energy consumption.
The increase in energy acquisition for young hunter-gatherers was approximated as a logistic curve
Energy consumption for hunter-gatherers is also approximated as a logistic curve
The simulation model uses a simplified version (Figure 1) of the annual mortality rate of Ache males and females from Kaplan et al. (2000). The mortality rate is initially high during infancy, decreases to a minimum value in early adulthood, and becomes increasingly higher from late adulthood to the end of the lifespan. Because Kaplan et al. (2000) lacked annual mortality data on individuals past the age of 75, the simulation assumes that all individuals that live to this age will expire within the next year.
Simulation model algorithmThe simulation model algorithm is shown in Figure 2. At the start of the simulation, the marriage age of males and females, defined as the age at which hunter-gatherers begin to invest energy in reproduction; the number of reproductive males and females; and the presence or absence of grandparents are specified as initial conditions. The model then simulates the energy balance and mortality of the family members for a specified number of years.
Flowchart of the simulation model.
For each year in the simulation, the model’s calculations are as follows. First, the energy balance and mortality of the family members are calculated. The model assumes that all food is shared between family members so that the energy balance of the family is equal to the sum of the energy balance of each family member. Children who have attained marriage age are assumed to have married and to have started their own families, and therefore are not included in the energy balance.
If the energy balance of the family is negative, the family is flagged as starving, and it will attempt to restore a positive energy balance by sacrificing unproductive members. The order in which family members are sacrificed follows a ‘greedy algorithm,’ that is, it aims to maximize the number of children who survive to marriage age from a purely energetic perspective, with grandparents being sacrificed first, followed by children in ascending order of age. This is because killing off productive family members would decrease available energy, and killing off children would directly reduce the number of surviving children. Among the children, killing off older members would represent a greater waste of energy and time, so younger members are sacrificed first. If only the parents are surviving and the family’s energy balance is still negative, the family is assumed to have starved to death and the simulation ends. However, children who have attained marriage age before the year of starvation still count toward the number of successfully raised children.
If the family is not starving, the program determines whether the family could give birth to a new child that year. Based on data from Kaplan et al. (2000), it is assumed that the age of last birth is 40; females who are older than this will stop reproducing regardless of the family’s energy balance. The program then checks whether the family’s energy balance is sufficient to support a pregnancy/newborn baby that year. Lastly, the program checks to see if the interbirth interval has passed since the last childbirth. The interbirth interval is set to three years, based on the figure for forager mean of interbirth intervals in Kaplan et al. (2000), unless specified otherwise. Each reproductive female can have up to one new child per year, and the number of children born is determined by the calorie surplus of the family. The year ends with all family members aging by one year. The model repeats these steps for each year and calculates the number of children who attained marriage age for each family at the end of the specified number of years in the simulation.
Unless otherwise specified, all simulations were 40 years long and simulated 1000 families for each starting condition to account for randomness in the results due to mortality rates, and the total number of surviving children was divided by 1000 to calculate the average number of surviving children per family. The source code for the model was written in 64-bit Python 3.9.7 and is included in the Supplementary Materials.
The simplest form of cooperative breeding is a monogamous family with one reproductive male and female sharing resources to invest in their offspring. To determine whether such a family could raise a number of children equal to or greater than the number of parents, we calculated the number of surviving children for two monogamous families each with one reproductive male and one reproductive female, using either Ache or Hiwi data for energy acquisition and consumption. Marriage age varied from age 15 to 30 years for both males and females. The results for monogamous nuclear families are shown in Figure 3.
Relationship between marriage age and average number of surviving children in monogamous Ache (left) and Hiwi families (right). Each colored square represents the average number of surviving children when the male and female(s) marry at the corresponding age. The dark blue area at the top of each graph denotes the age range in which the families starve due to inadequate energy acquisition.
In the Ache simulation, the maximum average number of children (MANC) per family was 1.12 children per family when the marriage age was 21 for males and 17 for females. In the Hiwi simulation, the MANC per family was 0.94 children per family when the marriage age was 21 for males and 25 for females. The low number of surviving children for both simulations, where monogamous families could not support two children, suggests that cooperation from individuals other than the reproductive male and female are necessary for hunter-gatherer reproduction.
Effect of grandparenting on number of children in monogamous familiesPrevious research has posited that the long postreproductive lifespan of humans evolved to allow postreproductive individuals to provision and care for their children’s offspring. We next examined the energetic effects of grandparenting on monogamous families.
In this simulation, three-generation families with grandparents are assumed to be a stable configuration that repeats itself in each generation. Therefore, the state of the family when parents become grandparents should correspond to the initial state of the family at the beginning of the simulation. At the start of this simulation, the father and mother are of marriage age, which is when they begin their reproduction. This means that, when the youngest generation reaches marriage age and begins reproducing, the parents then cease further reproduction and switch to grandparenting. To keep this consistency between generations, this simulation contains an additional condition for reproduction so that parents will only have new children when none of their children have matured.
To gauge the upper limit of the effect of grandparenting, we assumed there was no extra-pair paternity, so that an increase in the number of offspring in the family always equals an increase in fitness for the family members. The age of the grandparents was as young as possible because hunter-gatherer energy acquisition decreases with age. Thus, the grandparents are assumed to be supporting their first child, born when the grandparents were at the age of marriage. Both grandparents were assumed to be paternal, meaning that at the start of the simulation, the age of the grandfather was double the marriage age for men and the age of the grandmother the sum of male and female marriage ages. We simulated families with three conditions: assisted by both grandparents, only the grandfather, and only the grandmother.
The results are shown in Figure 4 for the Ache energy data and in Figure 5 for the Hiwi energy data. The MANC per family was 1.8 for the Ache when assisted by grandfathers and 1.8 for the Hiwi when assisted by both grandparents. The marriage ages corresponding to the maximum number of children was 15 for males and 17 for females in the Ache data, and 16 for males and 24 for females in the Hiwi data. Grandparents increased the number of children in both simulations, with the exception of Ache grandmothers. Although they do not seem to contribute in terms of energy acquisition, it is possible that they have other roles not directly reflected in the energy data, such as assisting in childcare (Kramer, 2010).
Relationship between marriage age and average number of surviving children in Ache monogamous families, supported by both grandparents (A), the grandfather (B), and the grandmother (C).
Relationship between marriage age and average number of surviving children in Hiwi monogamous families, supported by both grandparents (A), the grandfather (B), and the grandmother (C).
Although the highest number of children per family occurred at lower marriage ages, monogamous families with such marriage ages failed to survive in our first simulation due to inadequate energy acquisition. Therefore, such families with ‘grandparents’ may be flukes and not an example of effective grandparenting. Furthermore, the increase in the number of children per family may be at a cost to the fitness of grandparents. Therefore, our next step was to examine the fitness benefits of grandparenting for the grandparents themselves.
Effect of grandparenting on the fitness of grandparentsIn the grandparenting simulation, reproductive adults ceased further reproduction when one of their children matured. This was so that the parents would then become grandparents when the youngest generation began reproduction, like the grandparents at the start of the simulation. Thus, parents choosing to practice grandparenting are choosing to invest energy acquired after one of their children matured into grandchildren instead of additional children of their own. If the ‘cost’ to fitness from having fewer children is smaller than the ‘return’ due to having more grandchildren, grandparenting is advantageous for grandparents as well.
Since we assumed no extra-pair paternity in the previous simulation, all children/grandchildren are genetically related to their grandparents and parents, and inclusive fitness is the same value for either grandparent. Thus, we define inclusive fitness as f = c + g/2, where c is the number of children and g is the number of grandchildren.
In families without grandparenting, all offspring are assumed to each have families with the same number of offspring as the original family, since each offspring’s family is identical in terms of initial age/sex composition and thus energy acquisition. Therefore, as g = c2, inclusive fitness for grandparents who do not practice grandparenting is f = c + c2/2. c is the number of offspring for monogamous families without any outside support, i.e. the results of the first simulation.
In families with grandparenting, the first generation’s reproductive pair will cease reproduction when one of their children matures, changing the number of their offspring to c’, where c’ < c if ceasing reproduction early causes a decrease in children. The first offspring to mature will produce their offspring with assistance from grandparents, increasing the number of their offspring to c”, where c” ≥ c, while other offspring will reproduce in the same manner as the first generation, having c’ children. Therefore, the inclusive fitness for grandparents is
We first calculated the value of c’, and compared them with c. We then calculated the inclusive fitness of grandparents when both grandparents, only the grandfather, only the grandmother, or neither grandparent practiced grandparenting. The results for c and c’ for Ache and Hiwi are shown in Figure 6; the results for c – c’ for Ache and Hiwi, which represents the increase in children when parents forsake grandparenting in favor of having more children, are shown in Figure 7. The results for inclusive fitness are shown in Figure 8 and Figure 9 for the Ache and Hiwi data, respectively.
Relationship between marriage age and average number of surviving children in Ache and Hiwi monogamous families when Ache parents prioritize their own offspring (A), Ache parents cease reproduction for grandparenting (B), Hiwi parents prioritize their own offspring (C), or Hiwi parents cease reproduction for grandparenting (D).
Relationship between marriage age and c – c’, or the difference in the number of children between families where the parents prioritize their own children and families where the parents cease reproduction for grandparenting, in the Ache (left) and the Hiwi (right). Positive values indicate that prioritizing their own children leads to an increase in surviving offspring. Black squares indicate marriage ages at which there was a decrease in fitness.
Relationship between marriage age and inclusive fitness of grandparents in Ache families where both grandparents prioritize their own children (A), both grandparents participate in grandparenting (B), only the grandfather participates in grandparenting (C), and only the grandmother participates in grandparenting (D).
Relationship between marriage age and inclusive fitness of grandparents in Hiwi families where both grandparents prioritize their own children (A), both grandparents participate in grandparenting (B), only the grandfather participates in grandparenting (C), and only the grandmother partitipates in grandparenting (D).
When comparing c and c’, there seems to be no significant difference between the two. The maximum value for c – c’ was 0.096 for the Ache data and 0.074 for the Hiwi data. Conversely, the minimum value for c – c’ was –0.067 for the Ache data and –0.11 for the Hiwi data. In other words, families in which the parents attempted to have more children after one of their children matured did not show a significant increase in the number of children who matured. This implies that the ‘cost’ of grandparenting in terms of having fewer children of one’s own is insignificant.
In Figure 8 and Figure 9, the upper left plot (A) plots the inclusive fitness of grandparents when they do not practice grandparenting and instead invest in their own children. The upper right plot (B) plots the inclusive fitness of grandparents when both grandparents participate in grandparenting. The lower left plot (C) and the lower right plot (D) correspond to inclusive fitness when either the grandfather or grandmother participates in grandparenting, respectively.
Grandparents who participated in grandparenting increased their inclusive fitness relative to those who did not, with the exception of Ache grandparents when only the female participated. Maximum values for the inclusive fitness of grandparents were 2.0 for the Ache data when grandfathers participated, and 1.7 for the Hiwi data when both grandparents participated.
While grandparenting was advantageous for both Ache and Hiwi grandparents over not grandparenting, the maximum inclusive fitness of Hiwi grandparents who practice grandparenting was slightly lower than the maximum number of children who Hiwi parents assisted by grandparents could have. This is in contrast to the Ache results, in which the maximum inclusive fitness for Ache grandparents was higher than the maximum number of children who Ache parents assisted by grandparents could have. This difference, where Hiwi adults gain comparatively more from receiving grandparenting than practicing grandparenting themselves, may explain why the Hiwi are noted as having much lower prevalence of grandparenting than the Ache (Hill et al., 2007).
The marriage ages for maximum inclusive fitness of grandparents in Ache were 20 for males and 19 for females, while in Hiwi it was 19 for males and 27 for females. In the previous simulation, the largest number of children for families with grandparenting occurred at marriage ages where monogamous families were unfeasible due to insufficient energy acquisition. However, the result of this simulation shows that in such families with low marriage ages, the inclusive fitness of grandparents is quite low compared to the maximum possible value and is unlikely to occur, as the grandparents have little to gain from such an arrangement.
Families supported by multiple malesThe Ache, among other hunter-gatherers in South America (Walker et al., 2010), are known for their practice of partible paternity, in which multiple males are believed to contribute to the conception of a single offspring (Ellsworth et al., 2014). Hill and Hurtado (2009) observed that in the Ache and Hiwi, the main food providers in cooperative breeding were young married males and unmarried males of all ages, and noted an example where multiple males related to the father supported a Hiwi family with large energy deficits. How does support by multiple males affect the number of children? To examine this, we simulated hunter-gatherer families supported by two, three, and four males, with one reproductive female, using both Ache and Hiwi energy data. Males are assumed to be the same age for simplicity, and all of their energy acquisition is assumed to be invested in this family. The results are presented in Figure 10 and Figure 11 for the Ache and Hiwi data, respectively.
Relationship between marriage age and number of surviving children in an Ache family supported by one (A), two (B), three (C), or four (D) males.
Relationship between marriage age and number of surviving children in a Hiwi family supported by one (A), two (B), three (C), or four (D) males.
The results show that male support results in a greater number of children in both the Ache and Hiwi data. Families supported by two, three, and four males had a MANC of 2.0, 2.8, and 3.1 for the Ache data and a MANC of 1.7, 2.5, and 3.0 for the Hiwi data. The marriage ages for maximum number of children were 20, 20, 19 for Ache males and 18, 19, 19/20 (tied) for Ache females in families supported by two, three, and four males, respectively. In Hiwi families they were 19, 21, 22 for males and 21, 21, 19 for females in families supported by two, three, and four males, respectively.
In both the Ache and Hiwi data, as the number of males increases, the age range at which families are infeasible due to starvation is reduced until only a lower limit on male age remains, with no limits to female age. The lower limit of male marriage age was 19 for Ache and 18 for Hiwi, which corresponds to the age at which Ache and Hiwi males attain positive energy balance.
The above results show that support from multiple males increases the number of children a reproductive female can raise, and therefore we next examined if this equates to polyandry being advantageous to individual men in terms of the number of children they can have. Figure 12 shows the relationship between the number of males supporting a family, and the number of children per male, assuming the males are solely mating with the reproductive female of this family with equal chances of being the father. While investment by additional males can significantly increase the number of children in a family, each male will have fewer children even assuming that all males mate equally. However, it should be noted that this simulation does not account for cases in which the additional males are not married to the reproductive female, but instead belong to other families that are supporting a family in need.
Relationship between number of males supporting a family and number of surviving children per supporting male in an Ache family (red) and a Hiwi family (blue) supported by one, two, three, or four males.
The results of the first simulation (Figure 3) show that, with energy acquisition only from the parents, even a monogamous family with one father and one mother is difficult to sustain in hunter-gatherer societies. Despite this, many hunter-gatherer societies are known to practice polygyny, although the practice is usually reported as being limited to a minority of men (Apostolou, 2007). How much energy acquisition is required, in addition to that of an average hunter-gatherer family, for polygynous families to be viable?
Figure 13 shows the number of children for a polygynous family with one father and two mothers, based on the Ache and Hiwi energy data. A polygynous family without cooperation from other individuals had a MANC of only 0.88 for the Ache data and 1.23 for the Hiwi data. To see how many additional males’ worth of energy acquisition is needed to support a polygynous family, we simulated polygynous families with two, three, and four males’ worth of energy acquisition. The results, alongside the results for the polygynous family without outside support, are presented in Figure 14 and Figure 15 for Ache and Hiwi data, respectively. Three males’ worth of energy acquisition resulted in a MANC per family of 3.44 for the Ache and 3.30 and for the Hiwi. In other words, a family with two wives and one husband needed roughly three males’ worth of energy acquisition to have a number of children equal to or greater than the number of parents.
Relationship between marriage age and number of surviving children in polygynous families with one father and two mothers using Ache (left) and Hiwi (right) energy data.
Relationship between marriage age and number of surviving children in polygynous Ache families supported by one (A), two (B), three (C) or four (D) males using Ache energy data.
Relationship between marriage age and number of surviving children in polygynous Hiwi families supported by one (A), two (B), three (C) and four (D) males using Hiwi energy data.
The results of our simulation model help quantify several aspects of human hunter-gatherer families in terms of their optimal energy investment in reproduction. Simulations of both monogamous and polygamous families indicate that they require energetic support from other individuals to be viable. The comparison between c and c’, or the number of children in families in which parents continued to have children and families in which parents ceased their own reproduction when one of their children matured, shows that attempting to have more children instead of switching to grandparenting is unlikely to yield an increase in the number of surviving children. This is due to a decline in energy acquisition and aligns with previous research showing that families with middle-aged parents experience an energy deficit (Hill and Hurtado, 2009). This also answers a potential problem with our assumptions on grandparenting—that it would not account for remaining children when parents ceased their own reproduction and switched energy investment to grandparenting. These results show that the decline in energy acquisition in middle-aged parents means that such children are unlikely to survive, and do not affect the total number of children who grow to maturity in the simulation.
Our simulations showed that in the Ache data, the inclusive fitness of grandparents who practiced grandparenting was larger than the number of grandchildren that a family assisted by grandparents could have. This means that declining energy acquisition can result in a situation where investing in grandchildren can yield a greater increase in inclusive fitness, and also benefits the grandparents as well as the parents. Cant and Johnstone (2008) showed that in ancestral humans with female-biased dispersal, grandparenting would be the preferred strategy regardless of any fitness benefit as long as there was any chance of the grandchildren being related, due to asymmetry in relatedness to offspring between older and younger generations of females. In contrast, our results show an example where grandparenting would be the preferred strategy regardless of any intergenerational conflict, which is not incorporated in our model, and instead due to declining energy acquisition in middle and old age. Although it is possible that this decline in energy acquisition is a by-product of intergenerational conflict selecting for early menopause, it points to the possibility of grandparenting being favored due to the difficulty of maintaining high productivity as hunter-gatherers in middle and old age.
Our simulations also show an instance where grandparenting is less beneficial to the grandparents, with the Hiwi grandparents’ inclusive fitness being slightly smaller than the number of grandchildren in a family supported by grandparents. While the inclusive fitness of Hiwi grandparents who practiced grandparenting was higher than that of grandparents who did not, grandparenting was of more benefit to the parents rather than the grandparents. This may explain why previous research showed a much lower prevalence of grandparenting in the Hiwi compared with the Ache (Hill et al., 2007). Comparisons between the energy acquisition of middle-aged hunter-gatherers, and the prevalence of grandparenting in their respective cultures, may be able to deduce if the prevalence of grandparenting is influenced by energy acquisition or is decided by other factors.
Our results also show that support from multiple males who are close to the age of the father were effective at increasing the number of children per family. However, these results do not necessarily support polyandry as an effective strategy, as even with all males having equal mating opportunities, this resulted in fewer children per male the more males were involved. In the Ache, while some ethnographers have mentioned polyandry being frequent (Clastres, 1972), others found it to be rare, with only 1 marriage out of 375 marriages for women being polyandrous (Hill and Hurtado, 1996). In reality, mating opportunities would likely be unequal and parenthood uncertain, which model-based studies have pointed out precludes provisioning resources to offspring as the optimal strategy (Loo et al., 2017). However, the simulations for families supported by multiple males could represent assistance by kin or other married families rather than polyandrous families, which we will discuss later along with optimum marriage ages in each simulation.
The simulation results for polygyny show that increased energy acquisition is necessary for polygynous families to raise sufficient children to equal or surpass the number of parents. This is in line with previous research showing cross-cultural associations between wealth and polygyny (Murdock, 1949), and polygynous Yanomami families receiving more food from others (Hames, 1996). However, this model assumes that all wives are treated equally, which may overestimate the cost of polygyny. There may be a difference in priority among wives such as in rural Ethiopian families (Gibson and Mace, 2007). It should be noted that in observations of the Ache, polygynous relationships, although present, were rare and often temporary in nature (Hill and Hurtado, 1996). While the breakup of such relationships was not due to insufficient food, it is interesting to note that energetically difficult family compositions are also unlikely to last.
Our results showed disparities in the optimum marriage age of males and females. In monogamous families without grandparenting, the optimum marriage age in terms of the number of children was 20 for males and 17 in females for the Ache, and 21 for males and 24 for females in the Hiwi. In families with grandparenting, the optimum age in terms of the inclusive fitness of grandparents was 20 for males and 19 for females in the Ache, and 19 for males and 27 for females in the Hiwi.
For the Ache, the documented age at first marriage is 20.2 for males and 15.2 years for females, although mean age at first birth for females is closer to the simulation results, at 20 years old (Hill and Hurtado, 1996). Ache men from 15 to about 35 years old, which overlaps with the age range in our simulation, are reported as generally marrying women about their own age or two years younger, which is close to the age difference shown in our simulation results. However, the optimum marriage age for the Ache is similar for families supported by either grandparents or males of similar age to the father, so this could be interpreted as supporting either or both family compositions.
For the Hiwi, the optimum marriage ages for monogamous families with and without grandparenting did not align well with previous data, in which the mean age at first birth is 20 for females (Hill et al., 2007). However, in the simulations for families supported by two, three, and four males, the optimum age of marriage for females was 21, 21, and 19, respectively. These results are much closer to the observed values and align with observations that younger monogamous pairs and middle-aged unmarried males contributed the most energy to other married couples (Hill and Hurtado, 2009). Together with our results on the inclusive fitness of Hiwi grandparents, this shows that grandparenting is energetically favorable for the Ache, but not the Hiwi.
Although previous research predominantly attributed cooperative breeding to kin selection, more recent research has pointed out that the effect of kin selection has likely been overestimated and that direct benefits such as improved chances of survival or reproduction for the cooperating individual have been underestimated (Clutton-Brock, 2002). The results of our simulation seem to suggest a mix of these factors. On the one hand, our Ache simulations show an example in which grandparenting increases the number of surviving grandchildren and also benefits the grandparents more than the parents, pointing to kin selection as the explanation. On the other hand, our Hiwi simulations show an example in which grandparenting is of less benefit to the grandparents, and both the Ache and Hiwi simulations showed the effect of younger males in cooperative breeding. While unmarried males may participate in cooperative breeding due to kin selection because they lack mating opportunities of their own, younger married males are also known to participate in cooperative breeding as well (Hill and Hurtado, 2009). This seems less likely to be due to kin selection because such males have mating opportunities of their own and are not affected by the decline in energy acquisition during middle age that makes cooperative breeding the optimal strategy in our simulation. Therefore, other reasons such as mutualism or group augmentation (Clutton-Brock, 2002) seem more likely.
In our simulation results, males tended to have a greater impact than females on the number of offspring who can survive, due to their greater energy surplus as adults. However, one adult male per reproductive female was insufficient to supply the energetic needs of her and her offspring. If this is true, there should be a population bias in favor of males in hunter-gatherer adults. Previous studies have noted that the adult sex ratios of human hunter-gatherers, including the Ache and Hiwi, are male-biased, in contrast to chimpanzee populations which are female-biased (Coxworth et al., 2015). In the Ache, precontact survivors were male-biased, while the post-contact population shows an increasingly female-biased sex ratio (Hill and Hurtado, 1996). In the Hiwi, the infanticide rate is four times higher for females than for males (Hill et al., 2007). Although the implications of male-biased adult sex ratios have been discussed in terms of male strategies in sexual selection (Loo et al., 2017), our study points to a possible reason this surplus of males is necessary. While no individual male would prefer to have more competitors in sexual selection, extra males and their cooperation might be necessary to support the energetic costs of reproduction.
Although our results emphasizing the importance of males in cooperative breeding may seem to contradict previous research theorizing that human longevity evolved from grandmothering (Kim et al., 2012; Hawkes and Coxworth, 2013; Kim et al., 2014), this is likely due to the fact that our study is based on different societies. Our study only used data derived from a few hunter-gatherer groups. Different energetic conditions could lead to different results, which could yield different conclusions about the importance of energetic restrictions on hunter-gatherer family composition. It should also be noted that energy acquisition is not fixed and can change based on behavior. Instead of energy acquisition unilaterally influencing other aspects of hunter-gatherer behavior, both have likely changed over time in an interdependent manner.
One limitation of our research is that since our model focuses solely on the energetic requirements of human reproduction, family compositions in our simulation may be more akin to abstractions representing the transfer of energy between age/sex groups rather than one-on-one depictions of real-life families, and thus are open to interpretation. For example, previous research has noted that meat from hunting is shared widely rather than provisioned directly to a male’s offspring, and that hunting can be motivated by status and mating opportunities rather than provision (Hawkes et al., 2010). This could mean, for example, that males do not directly provision their own families but rather provide collectively for all of the tribe’s families, with hunting successes affecting mating opportunities rather than directly increasing the energy acquisition of a particular family. In this case, our simulation model having x males supporting the family would represent the family being provisioned collectively by male hunters with energy equivalent to x times the average amount of energy acquired by a male hunter, and not an actual group of x men who are exclusively supplying energy to that family. Another example is that although our simulation assumed that the grandparents were paternal when calculating their age at the start of the simulation, because the model itself only uses age/sex groups to calculate energy acquisition and consumption, the results could also apply to maternal grandparents, or unrelated older adults of similar age assisting in reproduction.
Nevertheless, our simulations show the necessity of different age/sex groups in supporting reproduction in hunter-gatherers, and that various traits of hunter-gatherer families, including marriage age and grandparenting, are strongly influenced by energetic conditions.
The authors received no financial support for the research and/or publication of this article.
Conflict of InterestThe authors declare no competing interests.
Author ContributionsHikichi Minori: conceptualization, methodology, software, validation, formal analysis, writing—original draft, visualization. Tateno Masaki: writing—review and editing, supervision, project administration.
