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Demographic Constraints on Population Growth of Early Humans: with Emphasis on the Probable Role of Females in Overcoming Such Constraints

E. A. Hammel

Departments of Demography and Anthropology

University of California, Berkeley CA 94720

Address :

E. A. Hammel

P O Box 921

Inverness, CA 94937

(415) 663-1843 (voice)

(415) 663-9219 (fax -- call voice number first)

email: gene@demog.berkeley.edu

Key words:

fertility, foraging, hunter-gatherers, mobility

Biographical Information

E. A. Hammel is Professor in the Graduate School in Demography and Anthropology at the at the University of California, Berkeley. He received his PhD in Anthropology at Berkeley in 1959, conducted ethnographic field work in California, New Mexico, Peru, Mexico, and the Balkans, archaeological field work in California and New Mexico, and has published analyses in archaeology, ethnography, semantic analysis, statistical applications, biological anthropology, and demography. He is a member of the National Academy of Sciences and of the American Academy of Arts and Sciences. Recent publications include:

The elderly in the bosom of the family: la famille souche and nuclear hardship reincorporation. In Aging in the past: demography, society, and old age (David Kertzer and Peter Laslett, eds.). Berkeley: University of California Press (in press).

Economics 1: Culture 0. Fertility change and differences in the northwest Balkans 1700-1900. In Rethinking reproduction: culture and political economy in demographic behavior, S. Greenhalgh (ed), pp. 225-258. Cambridge: Cambridge University Press.

Gender and the academic career in North American anthropology: differentiating intramarket from extramarket bias. (With Carl Mason, Ariadne H. Prater, and Robert T. Lundy). Current Anthropology 36:366-80.

Fertility decline in Prussia 1875-1910: a pooled cross-section time series analysis. (P. Galloway, E. A. Hammel and R. D. Lee). Population Studies 48:135-58.

Abstract

The human population grew at very low average rates for most of its existence. Mortality was reasonably severe and expectation of life at birth was low. The fertility necessary to achieve even inifinitesimal growth under such mortality implies birth intervals sufficiently short to conflict with the ability to care for and carry children in a mobile foraging economy. Techniques for the control of mortality, especially of children before puberty and of women in childbirth, and of child care exchange, probably developed by females, may have been essential in permitting population growth under conditions of mobile foraging. Figures

1 Relationships between Technology, Knowledge, Social Structure, and Population Growth in a Primitive Foraging Economy

2 Hypothetical Relationships between Mortality, Fertility, and Mobility for Early Humans

3 PFIBI as a Function of Growth Rate for Plausible Levels of Mortality

4 Survivorship Curves for Model West Females 3, 5, 7, the Libben Site, and the Chimpanzee
Tables

1 Plausible Population Sizes, Time Points, and Growth Rates

2 Computation of Fertility Rates and Associated Measures:

An Example from the Dobe !Kung

3 Fertility Estimates for Posited Rates of Growth under Different Mortality Scenarios

4 Multiple Regression of PFIBI on Growth Rate and Mortality Level

5a Production under Combinations of Cooperation for Two Women, A and B, with C Children and P (Equal) Production

5b Production under Combinations of Cooperation for Two Women, A and B, with C Children and P (Unequal) Production

INTRODUCTION

This paper speculates on some demographic aspects of the population growth of early humans, perhaps including pre-sapiens species. The arguments apply to populations in those ecological circumstances in which extensive foraging was as fundamental as it seems to be in modern savanna-dwelling hunter-gatherers and in which mortality was as high as suggested by modern hunter-gatherer and archaeological evidence. Population growth would have been difficult, given the probable constraints of relatively high mortality, the high fertility necessary to offset such mortality to achieve a positive growth rate, the short birth intervals implied by such fertility, the need for infant care and transport, and high mobility in a foraging economy. Females may have played an important role in overcoming these impediments to growth. Similar issues have been addressed by other authors but none have focussed on the combined mobility-mortality constraint to growth (Hassan 1981, Hill 1993, Howell 1986, Lancaster and King 1985, Lancaster and Lancaster 1983, Zeller 1987, Zihlman 1981). Theoretical Considerations The interrelationships between culture, demography, and the resource base are complex. Most attempts to specify causality in a complete fashion show reciprocal and synergistic effects, and it has always been challenging to reconcile the classic theories of Malthus and Boserup on the constraints and spurs to population growth (Hammel and Howell 1987, Howell 1986, R. D. Lee 1986, 1987, 1988, 1992, Wachter 1987). Important achievements, requiring at least some minimal density of population and concomitant social structure, although not necessarily stimulated by density, might have been (1) socially and culturally facilitated easing of the mortality constraint, (2) labor substitution in child care, and (3) shifts in resource exploitation that allowed more stable home bases with less female foraging. The example of plant domestication and development of a more sedentary life style is commonly accepted as an instance of the last factor; its effects could have been direct, through possible (although still disputed) nutritional effects on fecundity and/or indirect, through lessening the need for extensive mobility by women. It is the last point on which I concentrate in this paper. Shifts to more intensive hunting or fishing, yielding richer food sources, could have had such effects long before plant domestication, concentrating women in more stable home bases and shifting the mobility requirement more toward male hunters. A shift to more concentrated food resources could have been at any point in evolutionary time and could have occurred in one or more local populations, and could have occurred more than once. I concentrate here on a presumed earlier ecological adaptation in which a major shift away from foraging had not yet occurred and assume that that shift had not occurred before the emergence of early humans.

These conjectures imply culturally driven shifts in ecological exploitation that changed the selective pressures on group-dwelling individuals. They are speculative, intended not to suggest how human evolution "really happened" but to set up a critical framework using demographic concepts not previously employed, within which to examine still more carefully the evidence of the laboratory and the spade.

The Foraging Economy and its Demography.

Figure 1 is an overview of some of the relationships posited for a foraging economy (see also Hawkes, O'Connell, and Blurton Jones 1991, Headland and Reid 1989, Hill and Hurtado 1995, Howell 1986, Hurtado, Hawkes, and Kaplan 1985, R. B. Lee 1979). Reciprocal interactions between the resource base and culture (in its most general sense) give rise to an economic system situated in some ecological context. The search for subsistence makes certain demands on mobility, as the members of a local population scour the resource base for sustenance. These mobility demands can have an effect on mortality at several levels, notably maternal, infant-child, and in old age. Mobility may make insupportable demands on pregnant and lactating women so that their mortality may be higher than otherwise. Mobility demands may work unfavorably on the survival of closely spaced infants and children. The elderly may not be able to keep up on the march and may not survive as they otherwise might. Mobility demands may also diminish fecundability through arguable effects of body fat and estrogen level. All of these factors, but especially infant-child and maternal mortality, constrain birth intervals among surviving women to be sufficiently long to permit mobility and survival but sufficiently short to produce the requisite number of surviving births to offset mortality. Old age survival may have feedback effects on the process by providing child care for weaned but not yet fully ambulatory children. Population growth itself may have density dependent effects on technology, knowledge, and social structure. The theoretical relationships in Figure 1 can of course be elaborated; I present only a skeleton.

Figure 2 presents this scheme as a ternary phase diagram, each of the constraints forming a side of the triangle. Where mortality is high, fertility low, and mobility high, a population can be on the edge of extinction (lower left). Fertility cannot increase without easing the mobility constraint, but if the mobility constraint eases and fertility increases, or if mortality decreases, at least some growth is possible (center). This center zone of slight positive growth is characterized by some combination of medium to high mortality, medium to high fertility, and medium mobility demands. Growth does not become strongly positive until mortality falls even further, or fertility stays high or increases, and mobility demands decrease (lower right). Of course, these relationships are much more complex than depicted. For example, as mobility demands decrease, density probably increases, with potential concomitant increase in infectious disease, so that mortality climbs to offset growth. In general, our apelike precursors and current cousins are probably close to the lower left of this diagram, and the succession of species over time is a record of movement through consistently more expansive ecological niches under the posited conditions, rotating clockwise across the diagram. Our own species, and perhaps some precursors moved into the middle region of the diagram. Only after the Late Paleolithic, perhaps via Epipaleolithic and Mesolithic transitions in extractive economy, and ultimately with plant domestication, could our species have begun to edge toward the right of the diagram, still remaining close to the center until barely two or three centuries ago when doubling times dropped generally below a millenium. Outline of the Problem Among large primates, the human species has increased remarkably since its first appearance. The number of human beings in the world has increased without obvious reversals since the beginning, although individual and even regional populations have decreased from time to time (for example the population of Europe during the Pandemic of Justinian or the Black Death). The overall rate of population increase has itself apparently increased, possibly also monotonically, yielding a kind of double exponential increase. Fertility must have exceeded mortality on average across all populations to achieve any growth, and individual populations in which fertility did not exceed mortality would have been replaced by others in which it did.

The conditions of life of early humans for most of their existence probably made substantial demands for mobility, as foraging populations moved in daily and seasonal cycles. If ethnography and guesses about the ecology of early humans are good guides, much of the diet consisted of heavy and bulky vegetal materials, and this preponderance should have been even more marked in the very earliest times, before the development of hafted weapons, traps, nets, and other hunting devices found in the specialized technologies of middle or late Paleolithic to modern hunter-gatherers. Of course, if one's view of early humans is that of roving packs of den-dwelling carnivores (see the discussion of these issues by Ingold 1995), the arguments in this paper are probably moot. Similarly, if early humans simply roamed at large rather than in daily cycles out from home bases, the need to carry food would have been minimal, being consumed en passant, and these arguments would again be moot. Thus, some degree of localization is necessary for these arguments. Mobility demands might have lessened if dietary sources consisted of or shifted to emphasize meat, as they might in cold steppe conditions, or fish/shellfish, as they might in riverine, maritime, or lacustrine environments. Cold steppe seems an unlikely locale for emergence of humans, as do maritime environments, with riverine or lacustrine settings at the edge of forest or savanna perhaps more likely. Still, it is not clear that the biomass available in fish and shellfish to hominids as yet unaware of clever catching devices or the use of dams and fish-stupefying drugs could have provided the sustenance necessary for population growth. This paper is admittedly based on a Serengeti- or jungle-as-Eden notion of early human habitat, or as one commentator has remarked, even of !Kung as Urmensch. We can never be certain if early human habitats were like that, but it is plausible that they might have been. Women with closely spaced births would have been hard put to sustain demands for mobility in such environments if they also had to carry substantial amounts of food back to a home base as well as more than one non-ambulatory child. (See especially Blurton Jones 1986, 1987, 1993, 1994, 1993, Blurton Jones, Hawkes, and O'Connell 1989, Blurton Jones and Sibly 1978, 1992, Denham 1974, Harpending 1994, Hawkes, O'Connell, and Blurton Jones 1991, Howell 1979, R. B. Lee 1972, 1979, 1980)

The undeveloped condition of the human neonate requires unusually long physical dependency until the young can be as mobile as the parents (Campbell 1974, Lewin 1984, Lovejoy 1980, Trevathan 1987). Whereas among other primates the young can cling to the mother's hair and thus lessen maternal effort in carrying, if our early ancestors were as glabrous and their children as leggy as their descendants, they had no such advantage. The physical independence of human children is also delayed by the need to acquire cultural knowledge, like language, required for adult functioning. While human infants are in some ways less dependent on their mothers for lactational sustenance than ape infants, because human technology has provided supplemental feeding, they continue to be dependent even longer than ape offspring in respect of mobility and independent survival. This is not to ignore the exceptionally long nutritional and emotional dependence of the young of the great apes upon their mothers. Chimpanzee and gorilla infants are breast fed for 3 to 5 years, and inter birth intervals are 5-8 years. Yet the physical mobility of young apes is not as delayed in development as that of young humans, and the foraging ability of female apes may be relatively unimpeded by the presence of their young, perhaps because localization of favorite sleeping places is much less than the localization of home bases among H. sapiens. (See Fossey 1979, Fossey 1983, Matessi 1984, Nishida, Takasaki, and Takahata 1990, Richard 1985, Schaller 1963, Teleki, E. E. Hunt, and Pfifferling 1976, Zeller 1987) The emergence of the mortality-fertility-mobility conflict discussed here of course depends on other events and behaviors, such as the loss of body hair, increases in the dependence of the young as language and cultural knowledge had to be acquired, the development of carrying devices such as slings or baskets that permitted food and children to be carried, movement into ecological zones that required more mobility, and so on. Limitations of the Analysis
Using Broad Averages This analysis is cast in terms of broad averages for the species, even though the population overall consisted of small local populations in varying degrees of isolation from one another. Broad averages mask underlying stochastic variation in the demographic fortunes of breeding populations and the probable evolutionary mechanics of the survival and expansion of some populations at the expense of others (see the critique of the use of broad averages in Hammel and Howell 1987). However, in this analysis, the use of broad average rates is a conservative choice, since it works against the hypotheses put forth. If human population growth resulted primarily from sudden accelerations, the constraints here suggested must have been more serious than for the necessarily more modest broad average of growth rates that includes those populations that did not grow or became extinct. Similarly, since human populations were likely to grow more rapidly at their geographical edges where density and competion were lower than at their centers, it is likely that population growth was generally characterized by movement into more demanding environments, perhaps often with higher mobility demands. Thus, if Eden were a jungle filled with succulent fruits, movement into savanna would have required more mobility than the prior average.

Assumptions about mortality here are uniformitarian (Howell 1976). I do not employ empirical tables from archaeological or ethnographic data except by comparison. Such empirical tables, however carefully constructed, are problematic because of small sample size, failure of underlying assumptions (e.g., stability, stationarity), underenumeration of infant and child deaths, difficulties in age determination, or questionable treatment of right-censored individuals in age intervals. Instead, I use well-understood Coale-Demeny model tables and examine only the effects of mortality level, not of differences in the shape of the survivorship curve (Coale, Demeny, and Vaughan 1983). For this analysis, survivorship for females to the end of childbearing is the critical range, and the shape of that function is relatively similar across human and even other higher primate forms, even though the levels may differ remarkably. For example, for any level in the ranges here considered, the four models of the Coale-Demeny set (East, West, South, North) differ only by about a percentage point in survival to the mean age of childbearing.

It is important to note that the Coale-Demeny tables are for stable populations. It is virtually impossible that any particular foraging population was ever stable, even though the population of the species as a whole might have been stable and indeed practically stationary for much of its existence. An alternative analytic approach would be to use stable-population rates but employ stochastic microsimulation to generate large numbers of small and unstable populations for aggregative analysis. I take the simpler and more direct approach here, reserving the more complex technique for later analysis.

Assumptions about fertility rest on the observed general shape of so-called "natural fertility", that is, fertility that may be controlled for spacing but is not controlled parity-specifically. I employ the fertility schedule reported by Howell for the !Kung (Howell 1979), since it is the best documented schedule for hunter-gatherers. The very low fertility of the !Kung has been attributed by different authors to low estrogen levels induced by low body fat, to conscious spacing in order to accommodate mobility demands, and to the pathogenic effects of sexually transmitted disease. See Howell (1979) for early suggestion of the possible effects of low fat levels on fertility, of mobility constraints in Blurton Jones (1986, 1987, 1993, 1994), Blurton Jones, Hawkes and O"Connell (1989), Blurton Jones et al. (1992), Blurton Jones, Hawkes and Draper (1993) and counter arguments emphasizing STDs by Pennington and Harpending (1993) and Harpending (1994).

STD effects have little impact on this analysis. Early onset of secondary sterility for the !Kung concentrates a higher proportion of their total fertility in the early portion of the reproductive span. The effect of this (compared to the Hutterites, for example) is small. The average birth interval for !Kung women aged 20-29 is about a month shorter than it would be if they had the same shaped age-specific fertility curve as the Hutterites or typical natural fertility European peasant populations.

Assumptions about population growth rates are based on admittedly sketchy evidence. However, in the plausible range of rates here examined, all of which are very close to stationarity, differences have virtually no impact on the analysis.

Assumptions about mobility and its consequences for child care are more problematic. The general picture drawn is more like that of the !Kung and Hadza, among whom individual women are hard put to carry two children plus food and have apparently little assistance in that regard, than that of the Ache, among whom two children are often carried by one woman and also among whom men also carry children. An important question is the demographic availability of substitute labor for child care, and for any level of such availability, the need for social arrangements of labor exchange. DATA
Early Growth Rates World population growth rates 100,000 BP to 2,000 BP, at which latter date we have some plausible estimates are suggested in Table 1.

The data shown are a compromise between alternative estimates of time of appearance of the species, the dates of later time points, and population size at those points. Sensitivity analysis across a range of dates of appearance from 50,000 BP to 200,000 BP, starting population sizes between 10 and 1,000 individuals, and population sizes in 25,000 BP between 1 and 5 million yield annual growth rates between 0.00005 and 0.00034 before 25,000 BP with consequent doubling times between about 2,000 and 18,000 years. These differences are not consequential to the analysis. Mortality Rates One of the most carefully developed life tables for a hunter-gatherer population is that of the Dobe !Kung (Howell 1979); Howell selects Coale-Demeny Model West Level 5 (Coale, Demeny, and Vaughan 1983), with expectation of life at birth (hereafter e0) for females of 30 to represent !Kung mortality. The fit to the empirical data is very good. I use this table to define the most favorable probable mortality regime for early humans. The estimates provided by Acsadi and Nemeskeri (1970) for Late Paleolithic populations (especially Afalou) suggest a lower e0 ~ 21. Weiss (1973) suggests e0 ~ 15 for Australopithecines and e0 ~ 18 for Neandertals, and his estimates for e15 suggest sapiens levels of e0 well below 20. One of the most carefully excavated sites in the archaeological annals, and with the most elaborately analyzed estimates of age at death, the Libben site in Ohio (Howell 1982, Lovejoy et al. 1977, Mensforth and Lovejoy 1985), yields e0 of 19.6 (my calculations). There is also fragmentary evidence for some of our nearest non-human relatives, the chimpanzees of the Gombe and Mahale Mountain reserves (Nishida, Takasaki, and Takahata 1990, Teleki, E. E. Hunt, and Pfifferling 1976). These animals appear to have an expectation of life at birth of between 10 and 14, reach sexual maturity around age 6 or 8 and seem not to survive past about 40 or 45. This value of e0 ~14 is based on my calculations from the published Gombe data (Teleki, E. E. Hunt, and Pfifferling 1976: 571). I have been unable to discover by recalculation how the published estimates were made. I have also used the raw data from Nishida et al (1990: 89). Data for other apes are roughly comparable (Zeller 1987, Table 1). Blurton Jones (1992), following Dyson (1977) finds Model North Level 6, with e0 = 32.5 appropriate for the Hadza.

All of these factors suggest examining a range of expectation of life at birth between 15 and 30. It is important to note that we have no historical evidence suggesting mortality levels with e0 much above 30 until the 18th or 19th century, although the severity of mortality in historical societies is most likely the result of dense habitation and poor sanitation.

With few exceptions, all empirical life tables are distorted in one way or another. Standard period life tables combine the experience of different cohorts, between which there have at least in recent history been remarkable mortality changes. The classic Coale-Demeny tables may be distorted by the effects of tuberculosis in many of the 19th and 20th century populations on which they are based. Tables from ethological, ethnographic and archaeological evidence are often based on very small samples, so that sampling error can play a large role. Archaeological life tables (or what I call mortuary life tables) are especially problematic because of differential burial practices and preservation by sex and age. They are usually computed under assumptions of stationarity and zero migration. These last assumptions are seldom justified, and their violation can wreak havoc with the computations. Positive population growth rates yield a high number of infant and child deaths and lower the apparent expectation of life at birth, while population decline achieves the opposite. Under-recovery of infant and child deaths greatly raises the computed expectation of life at birth, while the outmigration (or deaths and burial afield) of adults lower it. Nevertheless the overall patterns of survivorship across such tables show substantial consistency, and it is possible to choose between plausible and implausible tables.

The published Coale-Demeny tables give expectations for e0 of 30, 25, and 20; I have extrapolated to include expectations of 17.5 and 15. I use Model West because it imposes the lowest level of mortality up to the mean age of childbearing and thus runs counter to the arguments expressed in this paper; it is a conservative choice. Fertility Rates Given some mortality schedule, some rate of growth, and assuming a particular shape to the age-specific fertility schedule, calculation of the fertility level necessary to achieve the posited rate of growth is straightforward. I follow Howell (1979: Table 11.1) here, using the structure of her table as a convenient simulation tool. First, I recapitulate (with some minor technical alterations) her calculations for the Dobe !Kung in Table 2. ESTIMATION OF ALTERNATIVE SCENARIOS The most important parameter of the simulations is the peak fertility implied birth interval, PFIBI (Table 2). PFIBI is the expected

waiting time to a birth for women reaching age 20 or having had a birth between age 20 and 29. It is not the same as the commonly reported "average inter birth interval" over the reproductive life span, which is not our interest; our interest is in the mean birth interval in the most fecund period, at which women would have the most difficulty consequent on mobility demands because of closely spaced births. PFIBI here is only a theoretical estimate in that most fecund decade and takes no account of true onset of risk or of secondary sterility, but it seems empirically not far off the desired mark. First births among the !Kung and most other closely observed hunter-gatherer populations occur at about age 19 or 20 and probably seldom earlier than 17, so that PFIBI for the decade 20-29 is fortuitously well placed; thus PFIBI is not much contaminated by including the waiting time to first birth. Its value for the !Kung as calculated above is about 4.5 years (54 months), which is close to the 51 month average implied inter birth interval reported by Howell (1979: Table 8.3) for the pre-1950 !Kung. Actually observed birth intervals reported by Howell average around 49 months (1979: Table 6.5). Zeller (1987) reports 44 months as the average inter birth interval. Blurton Jones (Blurton Jones 1987: 201-101) reports 55 months for second and higher intervals that are not preceded by an infant death, for bush-dwelling women. The generally accepted consensus seems to be "about 4 years." Computation of closed inter birth intervals is deceptively simple. It does not include left-censored women who have never had a first birth, nor does it include the time at risk of right-censored women who were fecundable. Neither does it include time after the last observed birth of women who have reached secondary sterility prematurely for pathological reasons. Thus the computation of the ordinary indices of population fertility, like the TFR or NRR require more than the usual interpretation. Computation of the NRR for example takes account of the elimination of deceased women from the risk pool. The use of marital fertility rates can take account of the elimination of women who are never married. A very accurate computation would take account of actual exposure to risk, involving interruption of marriages, spousal separation, and similar factors, and it would also take into account the onset of secondary sterility before menopause. For all of these reasons I use PFIBI since it reflects the ability of females to reproduce unconstrained by factors other than mortality; birth intervals computed from observed births will always be shorter than those calculated as the reciprocal of the birth rate, so that PFIBI is a conservative estimator of the mobility and morality constraints on growth discussed in this paper. It is also close to the median second interval for women having a first birth in that decade, estimated from Howell's Figure 7.4. PFIBI is important because if fertility increases enough to maintain some posited rate of growth, PFIBI must shorten, and it may shorten enough to impede the mobility of foraging women, with potential negative feedback results in mortality.

PFIBI is always equal to or shorter than the interval between surviving children that actually conflicts with mobility demands. The operative interval is that between children who survive at least to about age 5 or 6; deaths to children younger than that age will lengthen the operative interval by about 12-18 months under natural fertility conditions and net of secondary sterility or interruption of conjugal relations. Nevertheless, I use PFIBI in developing the initial argument because it is easy to estimate. Later I use arguments from the age structure appropriate to the life tables to discuss the need for child care, and thus embed information on surviving children.

!Kung fertility is the lowest natural fertility level known. Women surviving past age 45 had a total fertility rate of 4.7; those observed 1963-73 showed a TFR of 4.3 (Howell 1979, Ch. 6-9). The forest Ache of Paraguay have a TFR of about 8, their compatriots on the reservation about 8.5 (Hill and Hurtado 1995, Ch. 8). The Yanomamo as reported by Hill and Hurtado (1995) have a TFR about 6. Hutterite fertility is about the highest known (TFR ~ 12.4). The Hadza appear to have a total fertility rate of 6.2 (Blurton Jones et al. 1992: 174). My estimates of PFIBI for these groups are 1.9 years for the Hutterites, 4.5 for the !Kung, 3.0 to 3.5 for the Ache, 3.9 for the Yanomamo, and about 3.5 for the Hadza.

For the range of growth rates .00001, .0001, and .0005 that might be suggested as broadly representative of species-wide human demography before the end of Classical times, I explore the effect of mortality levels with expectations of life at birth of 30, 25, 20, 17.5, and 15. The simulation procedure is simple. Using the structure of Table 2, I select a mortality level and a growth rate, then iteratively scale the age specific fertility vector and recompute until the desired growth rate is achieved. The results of this exploration are shown in

Table 3. For purposes of later statistical estimation I include in the table examples with expectation of life at birth of 30 years but with much higher growth rates, .01 and .02, and for the !Kung.

(Readers who wish to conduct further simulation experiments may use the structure of Table 2 or Table 3 in the same way. Those who wish a machine-readable Excel spreadsheet of the two tables may download them from the author's U. C. B. Department of Demography home page, http://demog.berkeley.edu/~gene; the filenames are nrrkung.xls (Table 2) and nrrsims.xls (Table 3). In Netscape, simply select the filename, and Netscape will let you download it. Launch Excel (or some other spreadsheet program that can read Excel files) and open the file from within Excel or that program. Readers may use the spreadsheets to challenge some of the assumptions in this analysis, for example the mortality levels; they may have to hand-enter appropriate values from the Coale-Demeny tables to do so.)

The relationships between these variables can also be estimated by regression from the simulation results. The elasticity of PFIBI with respect to expectation of life at birth is about 0.8, while that with respect to growth rate is about -.04 (Table 4). Mortality level in this range of growth rates thus has the major effect.

Carrying out these simulations as above is tedious for more than a few values of e0 and of fertility, and the relationships can also be estimated by a more general regression as (R. Lee, personal communication),

ln(PFIBI) = ln(lu) -u*r- (f(b20-29,TFR)) * 2.05

where u is the mean age of childbearing, lu is survivorship to that age, r is the growth rate, b20-29 is the birth rate between maternal ages 20 and 29, and 2.05 is the ratio of all births to female births. Since lu cannot be readily obtained from model life tables without interpolation, and since in the model tables in the narrow range examined here lu is linearly related to e0, I use e0 as a proxy for lu.

Figure 3 shows the estimated values of PFIBI for combinations of e0 and r, and a few superimposed points approximately representing information on some ethnographically known hunter-gatherer populations. Again, at the very low growth rates considered here, from zero perhaps to .0005, the major determinant of differences in PFIBI is mortality level, not growth rate. Analysis is thus robust to assumptions about growth rate but sensitive to assumptions about mortality level. THE MORTALITY CONSTRAINT AND ITS ALLEVIATION The importance of technological advances that lower mortality to increases in population growth has been clearly manifest since the last part of the 19th century, principally through the efficacy of general public health measures. Such sanitation methods would have had little impact on small and isolated forager populations. However, the development of techniques for nursing the sick could have had a major impact. No animal except our species engages in intensive nursing care other than parental care of the young. Nursing, even if it only takes the form of provision of warmth, food, and emotional support can have important effects. Depression and shock are diminished, metabolic demands are lowered, and predators are kept at bay. If nursing also includes attending to parturient females, the effects are multiplied; the nurse can save not only the mother but also the unborn child, and by virtue of saving the mother often also the previously born child. The advent of midwifery and the establishment of birthing as a socially situated rather than individual occasion must have been notable events in the history of the species. Even among the !Kung, although no technical midwifery is practiced, and women in theory have their births alone, in practice other women keep them company, build a fire, and give comfort and protection (Howell 1979). Female aid to parturient females has been observed in other mammals but is rare (bats, Indian elephants, dolphins, langurs, lorises). Male orangutans have been reported to assist in delivery. (Kuntz 1994, McFarling 1994, Trevathan 1987:108-117). Much of the behavior of "assisting" females seems to "imitate" the behavior of the parturient female (e.g., straining), also nudging or cradling the newborn. Surrogate breastfeeding, observed in some human groups but unreported for other species, also contributes to survival of the young. Care directed to the maintenance of mothers and children diminishes the need for high fertility to achieve some rate of growth and, lowers the maternal depletion and other morbidities that might otherwise keep mortality high, and in general lowers the net physiological cost and reproductive inefficiencies of heavy subsistence activity.

Care of the aged is another human idiosyncracy. Protracted senescence is a rare phenomenon in the animal world, although the phenomenon of senescence itself is ubiquitous among mammals (Anon. 1995, Carnes and Olshansky 1993, Hill 1993, Hill and Hurtado 1991, Kirkwood 1981, Kirkwood and Rose 1991, Lancaster and King 1985, Matessi 1984, Rogers 1993, Washburn 1981, Williams 1957, Williams 1966). Other than humans, only elephants and some species of whales appear to show protracted senescence. Post-menopausal apes, for example, are rarely reported in the wild (Nishida, Takasaki, and Takahata 1990, Richard 1985, Teleki, E. E. Hunt, and Pfifferling 1976). Figure 4

compares the female survivorship curves for Coale-Demeny Models West females at levels 3, 5 and 7, those I have computed for the Libben site (both sexes), the Gombe female chimpanzee and for the female forest Ache reported by Hill and Hurtado (Hill and Hurtado 1995). Survivorship past menopause, which occurs at about the same age in humans and chimpanzees, is virtually absent for the chimpanzee, modest for the Libben population, and substantial for the model tables and the Ache. The figure reinforces Howell's conclusion (1982) that life at Libben was much more difficult than anything human adults experienced in the last two hundred years. Nevertheless, Libben survivorship after age 20 is clearly more like that of the model human tables than like that of the chimpanzee.

What evolutionary advantage is enjoyed by virtue of protracted human senescence? The minds of the elderly before the advent of writing and indeed of widespread literacy were the sole transgenerational storehouse of cultural knowledge. Such knowledge is particularly useful where the stock of knowledge does not increase much from generation to generation but where annual variability in living conditions is high. Rozenzweig (1994) demonstrates the utility under these conditions of coresident elderly in semi-arid regions of India. That protracted senescence is also reported for elephants is illuminating; old elephants, for example, can be expected to have more experience in finding distant water sources in times of drought. Similarly, human elderly can remember a larger number of adaptive responses and their efficacy than can the young. The efficacy of such knowledge would have been enhanced by the development of language, especially of those aspects of language that express the future and the conditional. Care of the elderly under these circumstances gives the young a survival advantage. The elderly are also useful caretakers of weaned but not yet fully ambulatory children. If sufficiently robust, they can carry them, if not, they can watch them. Such baby-minding is particularly effective if there are base camps in which a few elderly can tend a larger number of children.

All of the foregoing behaviors are socially situated and culturally symbolized in societies that we know about. Perhaps at some distant point the propensity to give care was genetically specified or induced, and the mechanisms that led to concentration of such tendencies were the ordinary ones of natural selection acting on biological diversity. It cannot have been long, however, before such behaviors were institutionalized and the survival of groups with such institutions was enhanced over the survival of other groups without such institutions, because the growth rates of the former could more easily exceed those of the latter even under conditions of substantial exogenously induced variability. Natural selection then acted on social and cultural diversity, even though the mechanisms of behavioral maintenance and transmission were quite different from the biological. The view taken here is explicitly one of the co-evolution of the organism and of culture and society, but not in any teleological sense. THE MOBILITY CONSTRAINT The foregoing arguments claim that at expectable mortality levels and rates of growth near zero, mobility pressures on individual women could have been sufficient to work against high fertility and the consequent short birth intervals. Both maternal and infant-child mortality could increase if fertility were high under high-mobility conditions. The need to nurse a new infant might lead to premature weaning and death of that older child. Where parental investment in children is high, such losses are inefficient to the reproducing individuals. Maternal depletion leading to higher death rates in the reproductive years is also inefficient, losing all of the investment in the reproducing female without recovering it through her survival to the end of childbearing. Maternal depletion also leads to lower work performance in obtaining food for the mother and other members of the group.

How reasonable is the view of the mobility constraint? The need for mobility should diminish in very lush environments. If daily foraging occurred, for example, within patches no larger than a few square kilometers, if there were no long term base camps, and if a local population simply advanced to a new foraging area each day, women would not have to move long distances in their daily search and might be able to carry more than one child, first from one foraging area to the next, and then within the new area. The Ache seem to follow a pattern like this (Hill and Hurtado 1995). Similarly, if the food sources were of very high quality, for example meat, fish, and shellfish or nuts high in fat found in concentrated groves (acorns, for example), the need for mobility might be lessened, depending on the quality and distribution of those resources. The picture we have of foraging may be biased by the fact that most foraging populations observable today are in refuge areas (Headland and Reid 1989, Lee 1979, Sahlins 1972, Wilmsen 1989). The constraints posited in this paper may thus apply more to populations expanding (or driven) into less favorable environments, notably arid or semi-arid environments in which the accessible edible biomass may be less than in other zones.

For all of these reasons one's guesses about ecological circumstances are crucial to evaluation of when the constraints suggested in this analysis may have been operative. If we think of early humans as existing in a challenging savanna environment rather than in a lush tropical one, or as omnivorous foragers rather than very efficient carnivores, the scenario presented may well apply to them. On the other hand it might apply only to human populations which, having first emerged in another kind of environment, later expanded into or were driven into one more like that of foragers like the !Kung. It probably would not apply to such foragers if they found themselves moving into environments in which the hunting of large game became the predominant subsistence activity, as we might posit for the Upper Paleolithic or some later groups such as the Eskimo. The scenario seems most appropriate to groups without highly developed hunting technologies and in which women provide much of the subsistence, in bulky vegetal foods. LABOR SUBSTITUTION The conflict with mobility experienced by individual women with closely spaced births could be alleviated by child care exchange of various kinds. Women currently without a child to be carried could carry another woman's child. Men could carry children. Children could be tended by the elderly.

A precondition for such arrangements is the demographic availability of alternative caregivers. The ratio of caregivers to children needing such care can be estimated from the model tables for different rates of growth (Wachter, personal communication, Coale, Demeny, and Vaughan 1983). I use these tables in an exploratory way, even though they give results for stable populations, and it is unlikely that any local population of interest would be stable.

If we define those who need to be carried as fetuses in the second trimester and later, plus all children under age 5 (all called "needers" here), and if we define potential caregivers as females aged 10-60 (all called "carriers" here), there are abundant carriers per needer under conditions of stationarity, from about 2.7 per needer when e0 = 30 to about 1.5 when e0= 15, and between about 2.3 and 1.6 for these levels of e0when r = .005, a level of growth we might take as an upper limit.

However, it is not clear why one female would carry the child of another, since under the foraging conditions posited carrying even one child would diminish the productivity of the carrier. We might suppose that close kin would be more likely to offer such child care services, either on purely altruistic grounds or in expectation of other services returned. The two most likely candidates would be mothers and sisters. We can estimate the number of unencumbered mothers and sisters per women from the life table and related data; that estimate ranges between about 0.90 and 1.0 across the range of e0 between 30 and 15, and for growth rates between 0 and .005. Estimation was as follows. The probability that a reproductive woman will have a living mother is approximately the ratio of females aged 40-60 to those aged 20-40. If the number of children surviving to adulthood is distributed as Poisson, then if r = 0, NRR = 1, and the number of daughters surviving to adulthood should be distributed as Poisson with [[lambda]] = 1. Under these circumstances, a woman chosen randomly from the population can expect on average to have one sister. Estimating the annual birth rate as 2.05*GRR/25, with GRR taken from the Coale Demeny tables for r = 0 and r = .005, and taking survivorship to age 5 as an estimate of survival past the first year, one can estimate the probability that some sister has either not had a birth in the last 5 years or has had a birth in the last 5 years but the child has not survived, so that the sister is unencumbered. Where b = the probability of birth in a year and s = l5/l0, this estimate is (1-b)**5 + (1-(1-b)**5) *s . Since mothers may have to satisfy the demands of more than one daughter, estimation should take into account the possibility that more than one daughter might need a carrier. While all mothers have on average only one daughter, those that have any daughters have on average two. Thus the number of unencumbered mothers is the ratio noted times the probability that the sister will be unencumbered. The sum of unencumbered mothers plus unencumbered sisters is the number of potential carriers for a woman who needs a carrier. (Estimation by microsimulation techniques would be superior, since it would allow examination of this problem under conditions of instability, and that problem is being pursued separately.)

Under these circumstances, help available from close female kin would be barely sufficient even under perfect altruism or exchange. The efficacy of such patterns of assistance depends in any case on the relative productivity of the partners. Suppose a woman with no children can produce one unit of output, with 1 child a half unit, and with two children can produce nothing. Suppose two women equally productive in foraging and child care. Table 5a shows the results.

From Table 5a we see that if A has 2 children and B none, the production of A is zero and of B 1 so that joint production is 1 unit . If A gives one child to B, the production of each is .5 so that joint production is again 1. Where producers are equally effective, there is no economic advantage to substitute child care. Where one participant is less productive in the food quest, there is an advantage to giving excess child care burdens to that participant, since having the more productive partner produce food is more effective than having the less productive partner do so. This result is shown in Table 5b.

In this instance if A has 2 children and B none, joint production is .5, and if A gives one child to B, joint production is .75, gained through removing B from production and into child care. The most efficient allocation of labor for the short run is to give child care responsibilities to the less productive workers, for example the elderly or adolescents. The greater is the disparity in food production between food producers and child caretakers, the greater is the advantage in this allocation of labor. The obvious limiting case is that in which the food production capability of the child caretaker is zero. If one child caretaker can care for more than one child at a time, any such advantage is multiplied. If there are economies of scale in having child caretakers work jointly (e.g., if one woman can care for two children by herself but two women can jointly care for six, a situation recognized by any nursery school teacher), the advantage is again multiplied. Thus, simple exchange between workers of equal productivity is the worst solution, while the establishment of creches supervised by several persons of low food-generating productivity is the best solution. Elderly women who are beyond prime working age would seem the optimal caretakers, since their productivity and efficiency as caretakers is likely to be higher than that of males; pre-pubescent females not yet capable of much food-producing work might also be useful, but child caretaking might impede their education in food-producing, especially in situations in which knowledge of the environment is not a trivial matter. What is important about this discussion of labor exchange is not the specifics of the examples but the fundamental necessity of differential food-providing capacity across and of social arrangements between individuals in order for labor substitution (of this or any other kind) to work.

These outcomes may have some bearing on the rarity with which adult males in the prime ages assist in child care. If the goods produced by males (for example, meat) are of high value either calorically or culturally, the most efficient allocation of labor is to leave the responsibility for child care with women. Societies that have institutionalized such practices would have an advantage. Of course the cultural value of goods produced by males may be calorically illusory, and it is not difficult to offer other conjectures for the low level of male contribution to child care. CONCLUSIONS This paper offers speculations about the interactions between mortality levels and the growth rates apparently experienced by early humans. Those growth rates can have been achieved only if fertility were sufficiently high. If fertility were sufficiently high, birth intervals would have to have been sufficiently short. A conflict may have arisen in foraging environments, since women may not have been able to forage and also carry more than one child, if a next child were born before a previous child were fully ambulatory. Various scenarios for solution of this conflict are discussed, including technological change, altruistic behavior, the participation of post reproductive survivors, elaboration of child care exchange relationships, but especially the amelioration of mortality.

Analysis shows that at mortality levels worse than e0 = 25, it would in many environments and under most circumstances have been difficult for women to forage extensively and also maintain the fertility necessary to achieve even the modest growth rates presumably obtaining in the earliest periods. Some populations may have had temporarily higher growth rates by virtue of higher fertility, but the burden of short birth intervals could have fallen hard on the women, and the levels of maternal depletion and of maternal and child mortality might well have worsened, bringing growth to even lower levels. Only in periods of fortuitously low mortality could a fertility level commensurate with mobility demands have provided higher growth, but such fluctuations would have been balanced by periods of fortuitously higher mortality. Until some stable amelioration of mortality levels was achieved, or until the need for mobility was decreased, could fertility have yielded higher growth rates, either at a relatively low level because mortality was eased or at a higher level because mobility was eased.

Among homeostatic populations (Lee 1987, Wachter 1987) there are general advantages to a homeostasis produced by relatively low levels of mortality and fertility, i.e. low-pressure rather than high-pressure regimes (Wrigley and Schofield 1981). Such regimes are subject to smaller stochastic fluctuation and thus less vulnerable to downside risk. Moving upwardly away from homeostasis even if only modestly but in a sustained way is facilitated by social and cultural diminution of mortality, which is intrinsically stabilizing in the first place, since it lowers the "pressure" of the demographic regime. An alternative is to reduce mobility constraints, for example through child care arrangements, so that fertility can rise to yield growth. However, ameliorating the mobility constraint and achieving higher fertility results in an intrinsically less stable outcome, because the demographic regime is still at higher "pressure" than it might otherwise be for the same growth rate. The more stable outcome resulting in some growth relies on lowering mortality. One may question the assumptions that primeval human mortality was no better than about e0 = 25, but there is no evidence to support the claim that it was less severe.

From this analysis we may speculate that not only was the development of culture facilitative of the expansion of the human species but that it was essential, whether directed toward easing of the mobility constraint or of the mortality constraint, although the latter is deemed to be a more reliable path. The amelioration of mortality had three plausible effects: one at birth, one at parturition, and one at menopause. The first of these enhanced survival to the onset of childbearing. The second enhanced survival to the end of childbearing. The third enhanced survival beyond reproduction, permitted knowledge to accumulate for longer periods, spread the burden of childrearing, and decreased the workload of reproducing females. All of these factors have positive effects on reproductive success, but those focusing on reproducing females have the greatest effect, since saving and maintaining a reproducing female is more efficient than simply saving a potential adult, life for life.

Fertility could of course have been higher, and growth could have been sustained at relatively high levels of mortality in very abundant environments in which mobility was not a serious constraint, although under these conditions the risk of extinction or of sudden expansion is higher. If humans originated in such environments, they did not stay in them. When humans moved into more demanding environments, mobility would have had to increase. Sudden expansion could have pushed human populations into such new areas. Even though hunter-gatherers and foragers are now refuge populations, even though they have been peripheral to regions of higher density and abundance at least since the development of plant domestication, and even though at some point some such populations were peripheral to others that lived in richer environments, there must have been movement into more difficult circumstances as humans expanded territorially and numerically. It is the demography of expansion, not of ultimate origin, that is the issue. The easing of mortality or mobility constraints must have occurred before or during such expansion, favoring those populations that had experienced or were experiencing the changes.

It is of course entirely possible that stochastically generated spurts of growth in a local population that were for some reason sustained might have led to density-dependent improvements in extractive technology or social organization. Such improvements might have allowed a homeostatic pause at a new level, and the human population might have grown by progression across a large number of such platforms. Nevertheless, at each such step the constraints discussed in this paper could well have been in play.

If the demographic reasoning used here is informative, it suggests that without the complex amelioration of mortality, coupled with the development of culture as an elaborated transgenerational knowledge system, the numbers of humans might otherwise have remained more like those of our ape cousins. Malthus saw technology as enhancing food supply and the expansion of population, checked by limits to survival and by the control of fertility. He did not contemplate the easing of the positive checks, for example of mortality, as an important factor and saw exogenous technological improvement and consequent population growth simply as driving populations closer to the limits of survival. Boserup saw the growth of technology as driven by the need to survive and thus by population density, but the technological changes she envisaged were again those involved in production and distribution, not in the easing of constraints. Of course no modern observer can doubt the importance of the easing of mortality for population growth; that easing clearly is responsible for the major expansion of world population since 1900 and perhaps to some extent since 1800. From the simple exercises and speculations of this paper, however, we see that the easing of the mortality constraint may have been important to sapiens from the beginning of its existence. Similarly, cultural innovations leading to easing of mobility demands, whether strictly technological (Malthus) or social (Boserup), could also have played a role. Women can be expected to have played an important role in achieving mortality reduction and in creating the social mechanisms for labor substitution in child care that would have reduced mobility demands.

Acknowledgements

I am indebted to Nicholas Blurton-Jones, Monique Borgerhoff-Mulder, Bill Chu, Diana Friou, Nancy Howell, Mark Jenike, Ronald Lee, and Kenneth Wachter for comments on a draft of this paper, and to Friou for bibliographic assistance. None of the aforementioned are responsible for errors of fact or interpretation.

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              Start Lower   End Lower    End        End        End        End          
              Paleolithic   Paleolithic  Upper      Mesolithi  Neolithic  Ancient      
                                         Paleolith  c                     Empires      
                                         ic                                            
Date BP             100000  50000        25000      10000      5000       2000         
Population           0.001  0.01         1          10         75         300          
(millions)                                                                             
r                           0.000046     0.000184   0.000154   0.000403   0.000462     
Doubling                    15051        3763       4515       1720       1500         
Time                                                                                   

A slowdown in growth rates at any "Mesolithic" transition lends support to theories of environmental over-exploitation and nutritional stress (Cohen 1977, Cohen 1980, Cohen 1989). Increases in growth rates before the advent of plant and animal domestication support speculations that peripheral hunter-gatherer societies linked by trade networks to richer core regions may have realized enhanced marginal productivity of child labor in the gathering of trade materials (e.g., amber), thus increasing the value of children to the family economy and spurring population growth.

Table 2

Computation of Fertility Rates and Associated Measures

An Example from the Dobe !Kung

  Age     Midpoin  Birth      Fem.Birth    Av.      PYL        Childre  Daughters  D*MP     
             t     Rate       Rate         Wait                   n                         
15-19        17.5  0.135      0.0659       7.41     2.72131     0.3674     0.1793  3.1374   
20-24        22.5  0.242      0.1181       4.13     2.56565     0.6209     0.3030  6.8173   
25-29        27.5  0.203      0.0991       4.93     2.39235     0.4856     0.2370  6.5174   
30-34        32.5  0.152      0.0742       6.58     2.21079     0.3360     0.1640  5.3296   
35-39        37.5  0.119      0.0581       8.40     2.02427     0.2409     0.1176  4.4083   
40-44        42.5  0.071      0.0346       14.08    1.83918     0.1306     0.0637  2.7083   
45-49        47.5  0.016      0.0078       62.50    1.65848     0.0265     0.0129  0.6151   
PFIBI=     4.5153  TFR=            4.6900           MACB=      27.4096  CEB=        2.2080  
GRR=       2.2887  NRR=           1.07748           r=         0.00272  DBLT=          254  

Table 3

Fertility Estimates for Posited Rates of Growth under Different Mortality Scenarios

    e0      PFIBI     GRR    TFR        NRR      MACB         r       CEB     DBLT    
        15    2.67   3.8565  7.9027    1.00027    26.81   0.00001000  2.049    69284  
                                                                      7               
        15    2.67   3.8658  7.9218    1.00268    26.81   0.00010000  2.054     6931  
                                                                      7               
        15    2.64   3.9075  8.0072    1.01350    26.81   0.00050000  2.076     1386  
                                                                      8               
      17.5    2.99   3.4464  7.0623    1.00027    26.93   0.00001000  2.049    69281  
                                                                      7               
      17.5    2.99   3.4548  7.0794    1.00270    26.93   0.00010000  2.054     6931  
                                                                      7               
      17.5    2.95   3.4922  7.1561    1.01355    26.93   0.00050000  2.077     1386  
                                                                      0               
        20    3.31   3.1151  6.3834    1.00027    27.02   0.00001000  2.049    69296  
                                                                      7               
        20    3.30   3.1227  6.3990    1.00271    27.02   0.00010000  2.054     6931  
                                                                      7               
        20    3.27   3.1566  6.4685    1.01360    27.02   0.00050000  2.077     1386  
                                                                      1               
        25    4.11   2.5142  5.1520    1.00027    27.23   0.00001000  2.049    69284  
                                                                      7               
        25    4.10   2.5204  5.1647    1.00273    27.23   0.00010000  2.054     6931  
                                                                      8               
        25    4.05   2.5480  5.2212    1.01371    27.23   0.00050000  2.077     1386  
                                                                      3               
        30    4.86   2.1247  4.3539    1.00027    27.41   0.00001000  2.049    69301  
                                                                      7               
        30    4.85   2.1300  4.3647    1.00274    27.41   0.00010000  2.054     6931  
                                                                      8               
        30    4.80   2.1534  4.4128    1.01380    27.41   0.00050000  2.077     1386  
                                                                      5               
        30    3.70   2.7940  5.7253    1.31534    27.41   0.01000000  2.695       69  
                                                                      4               
        30    2.81   3.6750  7.5308    1.73012    27.41   0.02000000  3.55        35  
!Kung   30    4.52   2.2887  4.6900    1.07748    27.41   0.00272269  2.208      255  
                                                                      0               

           Coefficien  Std. Error    Std.        t-Value   Elasticity1  P-Value     
               t                     Coeff.                                         
Intercept  .462        .045          .462        10.263                 <.0001      
e0         .145        .001993       1.094       72.936    .792         <.0001      
r          -103.059    2.364         -.654       -43.597   -.037        <.0001      

Table 5a

Production under Combinations of Cooperation for Two Women, A and B, with C Children and P (Equal) Production

            A              
              C      0      1      2      
              P      1      .5     0      
       C      P         Joint Output     
       0      1      2      1.5    1      
B      1      .5     1.5    1      .5     
       2      0      1      .5     0      

Table 5b

Production under Combinations of Cooperation for Two Women, A and B, with C Children and P (Unequal) Production

            A              
              C      0      1      2      
              P      1      .5     0      
       C      P         Joint Output     
       0      .5     1.5    1      .5     
B      1      .25    1.25   .75    .25    
       2      0      1      .5     0