DEMOGRAPHIC CONSTRAINTS O N POPULATION GROWTH OF EARLY H U M A N S Emphasis on the Probable Role of Females in Overcoming Such Constraints
E. A .
Hammel
University of California, Berkeley
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 level of fertility necessary to achieve even inifinitesimal population 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. KEY WORDS:
Fertility; Foraging; Hunter-gatherers; Mobility.
This p a p e r speculates on some d e m o g r a p h i c aspects of the p o p u l a t i o n g r o w t h of early h u m a n s , p e r h a p s including pre-sapiens species. The arg u m e n t s apply to p o p u l a t i o n s in those ecological circumstances in w h i c h extensive foraging was as f u n d a m e n t a l as it seems to be in m o d ern savanna-dwelling h u n t e r - g a t h e r e r s and in w h i c h mortality was as high as suggested by m o d e m hunter-gatherer and archaeological evidence. Received September 29, 1995; accepted January 29, 1996.
Address all correspondence to E. A. Hammel, Department of Demography, Umversity of Cahfornia, Berkeley, 2232 Piedmont Avenue, Berkeley, CA 94720. E-maih gene@ demog, berkeley,edu Copyright 9 1996 by Walter de Gruyter, Inc., New York Human Nature, Vol. 7, No. 3, pp. 217-255. 217
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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 (Hassan 1981; Hill 1993; Howell 1986; Lancaster and King 1985; Lancaster and Lancaster 1983; Zeller 1987; Zihlman 1981) but none have focused on the combined mobility-mortality constraint to growth.
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 (1933 [1798]) and Boserup (1965) 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 lifestyle 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 or mortality (see for example Pennington 1996). Effects could also have been 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 w o m e n in more stable home bases and shifting the mobility requirement more toward male hunters. A shift to more concentrated food resources could have occurred at any point in evolutionary time, in one or more local populations, and 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.
Demographic Constraints on Population Growth of Early Humans
219
They are speculative, intended not to suggest h o w h u m a n 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 A N D ITS DEMOGRAPHY
Figure 1 is an overview of some of the relationships posited for a foraging economy (see also Hawkes et al. 1991; Headland and Reid 1989; Hill and Hurtado 1996; Howell 1986; Hurtado et al. 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 w o m e n 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 w o m e n 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
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demands decrease (lower right). Of course, these relationships are much more complex than is depicted here. For example, as mobility d e m a n d s decrease, density probably increases, with potential concomitant increase in infectious disease, so that mortality might climb to offset growth. In general, our apelike precursors and current primate 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, w h e n doubling times dropped generally below a millennium (and now average about 35 years).
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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 (e.g., the population of Europe during the Pandemic of Justinian or the Black Death), and some species or subspecies may have disappeared (e.g., Neandertal forms). 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 in the long run would have been replaced by others in which it did. 1 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 (trekking, as some Amazonian groups like the Ache do) rather than moving 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 woodland-as-Eden notion of early h u m a n habitat. 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
Demographic Constraints on Population Growth of Early Humans
223
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 nonambulatory child. (See especially Blurton Jones 1986, 1987, 1993, 1994; Blurton Jones and Sibly 1978; Blurton Jones et al. 1989, 1992, 1993; Denham 1974; Harpending 1994; Hawkes et al. 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 h u m a n 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 y o u n g of the great apes upon their mothers. Chimpanzee and gorilla infants are breast-fed for 3 to 5 years, and interbirth 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, 1983; Matessi 1984; Nishida et al. 1990; Richard 1985; Schaller 1963; Teleki et al. 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 y o u n g 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 groups in varying
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degrees of isolation from one another. Broad averages include populations that grew rapidly and those that grew slowly or became extinct (see the critique of the use of broad averages in Hammel and Howell 1987). The arguments in this paper show that there were constraints on growth even for such heterogeneous populations. If the growth of the species depended on sudden accelerations, the constraints here suggested would have been even more drastic for exploding populations than for the populations characterized by a broad average. 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.
Mortality 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 et al. 1983). For this analysis, survivorship for females to the mean age 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. For early h u m a n populations in the ranges here considered, most differences in the overall shape of survivorship were probably induced by changes in mortality up to the mean age of childbearing, but particulary in infant mortality, which is subject to marked variation between populations. Pennington (1996) justly criticizes the use of simplistic approaches to mortality in anthropological populations, but in the mortality range considered here, and for any plausible set of shapes of mortality, the relationship between survivorship to early adulthood and a simple index of overall mortal-
Demographic Constraints on Population Growth of Early Humans
225
ity like expectation of life at birth (see note 1) is rather regular; the implications of that regularity will be discussed below. 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. The implication of this stability assumption is conservative and works against the hypotheses here suggested. As noted above, any local population departing from stability in a sudden spurt of increase would face the mobility-mortality-fertility c o n u n d r u m here posed even more acutely than its stable antecedent.
Fertility Assumptions about fertility rest on the observed general shape of socalled natural fertility, that is, fertility that may be controlled for spacing but is not controlled parity-specifically. I begin analysis by using the fertility schedule reported by Howell for the !Kung (Howell 1979), but I later expand consideration to include recently reported information on the Ache (Hill and Hurtado 1996). The general shape of !Kung fertility is adequate to the initial task, and although the level is low, it is that level that is subjected to experimental manipulation in this analysis. 2 Choosing an age-specific schedule from another group such as the Ache or Hadza or Yanomamo will have an effect on analytic outcomes. Figure 3 compares the proportion of total fertility contributed at each age for !Kung women over age 45, !Kung women observed between 1963 and 1973, the Canadian Hutterites, the Yanomamo, forest-dwelling Ache, and reservation-dwelling Ache. 3 The level of fertility does vary widely between these and other groups, but so does the proportion of fertility experienced at each age. For example, early onset of secondary sterility for the !Kung concentrates a higher proportion of their total fertility in the early portion of the reproductive span, warping the age-specific curve.
Growth 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.
Human Nature, Vol. 7, No. 3, 1996
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Mobility A s s u m p t i o n s about mobility and its c o n s e q u e n c e s for child care are more problematic. The general picture d r a w n is m o r e like that of the !Kung and H a d z a , a m o n g w h o m individual w o m e n are h a r d put to carry two children plus food and have a p p a r e n t l y little assistance in that regard, than that of the Ache, a m o n g w h o m two children are often carried by one w o m a n and also a m o n g w h o m m e n also carry children. A n i m p o r t a n t question is the d e m o g r a p h i c availability of substitute labor for child care and, for any level of such availability, the n e e d for social a r r a n g e m e n t s of labor exchange.
DATA
Early Growth Rates World p o p u l a t i o n g r o w t h rates from 100,000 sP to 2,000 BP, at w h i c h latter date w e have some plausible estimates, are s u g g e s t e d in Table 1. The data s h o w n are a c o m p r o m i s e b e t w e e n alternative estimates of time
Demographic Constraints on Population Growth of Early Humans Table 1.
227
Plausible Population Sizes, Time Points, and Growth Rates
Start Lower Paleolithic End Lower Paleolithic End Upper Paleolithic End Mesolithic End Neolithic End Ancient Empires
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100,000 50,000 25,000 10,000 5,000 2,000
0.001 0.01 1 10 75 300
0.000046 0.000184 0.000154 0.000403 0.000462
15,051 3,763 4,515 1,720 1,500
This table is modeled after Harris and Ross (1987:Tab. 1.1), with some data taken from Durand (1977) and some estimated as indicated m the text. I have recalculated growth rates from the basic population figures. A slowdown in growth rates at any "Mesolithic" transition lends support to theories of environmental overexploltation and nutritional stress (Cohen 1977, 1980, 1989) Increases in growth rates before the advent of plant and ammal domestication support speculations that peripheral hunter-gatherer societies linked by trade networks to richer core regions may have reahzed enhanced marginal productivity of child labor m the gathenng of trade materials (e.g, amber), thus increasing the value of children to the family economy and spurring population growth. of a p p e a r a n c e of the species, the d a t e s of later time points, a n d p o p u l a tion size at t h o s e points. Sensitivity analysis across a r a n g e of d a t e s of a p p e a r a n c e f r o m 50,000 BP to 200,000 BP, initial p o p u l a t i o n sizes bet w e e n 10 a n d 1,000 individuals, a n d p o p u l a t i o n sizes in 25,000 BP bet w e e n 1 a n d 5 million yields a n n u a l g r o w t h rates b e t w e e n 0.00005 a n d 0.00034 before 25,000 BP with c o n s e q u e n t d o u b l i n g times b e t w e e n a b o u t 2,000 a n d 18,000 years. These differences are not c o n s e q u e n t i a l to the analysis.
Mortality Rates The literature p r o v i d e s t w o v e r y carefully d e v e l o p e d life tables for h u n t e r - g a t h e r e r population: h e r e I u s e that of the D o b e !Kung (Hill a n d H u r t a d o 1996; Howell 1979). H o w e l l selects C o a l e - D e m e n y M o d e l West Level 5 (Coale et al. 1983), c h o o s i n g e x p e c t a t i o n of life at birth ( h e r e a f t e r e0) for f e m a l e s equal to 30 to r e p r e s e n t ! K u n g mortality. I u s e the level a n d s h a p e of this m o d e l table initially to define the m o s t favorable p r o b able m o r t a l i t y r e g i m e for early h u m a n s , a n d I u s e the s h a p e of t h e table in m o s t of the s u b s e q u e n t exploration. The e s t i m a t e s p r o v i d e d b y Acsadi a n d N e m e s k e r i (1970) for Late Paleolithic p o p u l a t i o n s (especially Afalou) s u g g e s t a lower e 0 ~ 21. Weiss (1973) s u g g e s t s e0 ~ 15 for A u s t r a l o p i t h e c i n e s a n d e 0 ~ 18 for N e a n d e r t a l s , a n d his e s t i m a t e s for els s u g g e s t sapiens levels of e o well b e l o w 20. O n e of the m o s t carefully excavated sites in the archaeological annals, a n d the o n e w i t h the m o s t
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elaborately analyzed estimates of age at death, the Libben site in Ohio (Howell 1982; Lovejoy et al. 1977; Mensforth and Lovejoy 1985), yields e 0 of 19.6 (my calculations). On the other hand, some rates reported for modern hunter-gatherers are less severe. Early and Peters (1990) estimate e0 ~ 39 for the Yanomamo; Hill and Hurtado (1996) estimate eo -~ 38 for forest Ache, and Blurton Jones et aI. (1992) find Model North Level 6, with e 0 = 32.5, appropriate for the Hadza. Readers can easily relax my assumption of most favorable mortality with e 0 ~ 30, using tools suggested later in this paper. There is also fragmentary evidence for some of our nearest n o n h u m a n relatives, the chimpanzees of the Gombe and Mahale Mountain reserves (Nishida et al. 1990; Teleki et al. 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 e 0 ~ 14 is based on my calculations from the published Gombe data (Teleki et al. 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:Tab. 1). All of these factors suggest examining a range of expectation of life at birth between 15 and 30. The !Kung and Hadza lie at about the top of this range; the Ache and Yanomamo exceed it, but the n o n h u m a n primate and Paleolithic data suggest caution in setting the upper bound much higher than 30. It is important to note that we have no historical evidence suggesting mortality levels with e0 much above 30 until the eighteenth or nineteenth century, although the severity of mortality in historical societies is most likely the result of dense habitation and poor sanitation. Figure 4 summarizes some of the comparative information with survivorship curves. Pennington (1996), using a four parameter model (Ewbank et al. 1983) based on the twentieth-century African standard, shows that e o is marginally useful as a general indicator of mortality level when the shape of mortality experience is strongly altered. I do not attempt to incorporate these possibilities in the present simulations, since there is little information on the basis of which the most critical parameters of a Ewbank model might be estimated for early huntergatherers (especially f~ and K, namely the general slope of survivorship and survivorship at early ages). Indeed, the evidence from the !Kung and Ache would support using the uniformitarian base of standard model life tables for the present purposes. With few exceptions, all empirical life tables and their model derivatives 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
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Demographic Constraints on Population Growth of Early Humans 1-
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Coale-Demeny tables may be distorted by the effects of tuberculosis in many of the nineteenth- and twentieth-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. The under-reporting of infant and child deaths in ethnographic and survey data is pervasive and results in potentially serious biases. 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 9 Positive population growth rates in such mortuary populations 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 outrnigration (or deaths and burial afield) of adults lowers it. Nevertheless the overall patterns of survivorship across such tables show substantial consistency, and it is possible to choose between plausible and implausible tables.
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The published Coale-Demeny tables give expectations for e o 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 "natural fertility" 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"Tab. 11.1) initially here, using the structure of her table as a convenient simulation tool. Later, I utilize data from the Ache (Hill and Hurtado 1996) to expand analysis to include other patterns. First, I recapitulate (with some minor technical alterations) Howell's calculations for the Dobe !Kung.
ESTIMATION OF ALTERNATIVE
SCENARIOS The most important parameter of the simulations for our purposes 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 interbirth interval" over the reproductive life span, which is not our interest. Our interest is in the mean birth interval in the most fecund period, during which women would have the most difficulty consequent on mobility demands because of closely spaced births. PFIBI is only a theoretical estimate for that most fecund decade and takes no account of true onset of risk or of secondary sterility, but empirically it seems 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 much earlier than 17 on average, so that PFIBI for the decade 20-29 is fortuitously well placed; it 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 interbirth interval reported by Howell (1979:Tab. 8.3) for the pre-1950 !Kung. It is also close to the median second interval for women having a first birth in that decade, estimated from Howell's Fig. 7.4. Actually observed birth intervals reported by Howell average around 49 months (1979:Tab. 6.5). Zeller (1987) reports 44 months as the average interbirth interval. Blurton Jones
Demographic Constraints on Population Growth of Early Humans
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(1987:201ff.) reports 55 months for second and higher intervals that are not preceded by an infant death, for bush-dwelling women. Hill and Hurtado (1996:254) report a mean of closed intervals of about 38 months. Computation of closed interbirth 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 total fertility rate (TFR) or net reproduction rate (NRR) require more than the usual interpretation. Computation of the NRR for example takes into account the elimination of deceased w o m e n from the risk pool. The use of marital fertility rates can eliminate w o m e n who never married. A very accurate computation would consider 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 mortality constraints on growth discussed in this paper. 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 in 19631973 showed a TFR of 4.3 (Howell 1979:chaps. 6-9). The forest Ache of Paraguay have a TFR of about 8; their compatriots on the reservation, about 8.5 (Hill and Hurtado 1996:chap. 8). The Yanomamo as reported by Hill and Hurtado (1996) have a TFR of about 6. Hutterite fertility is about the highest known (TFR ~ 12.4). The Hadza appear to have a total
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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 level of fertility necessary to achieve even inifinitesimal population 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. KEY WORDS:
Fertility; Foraging; Hunter-gatherers; Mobility.
This p a p e r speculates on some d e m o g r a p h i c aspects of the p o p u l a t i o n g r o w t h of early h u m a n s , p e r h a p s including pre-sapiens species. The arg u m e n t s apply to p o p u l a t i o n s in those ecological circumstances in w h i c h extensive foraging was as f u n d a m e n t a l as it seems to be in m o d ern savanna-dwelling h u n t e r - g a t h e r e r s and in w h i c h mortality was as high as suggested by m o d e m hunter-gatherer and archaeological evidence. Received September 29, 1995; accepted January 29, 1996.
Address all correspondence to E. A. Hammel, Department of Demography, Umversity of Cahfornia, Berkeley, 2232 Piedmont Avenue, Berkeley, CA 94720. E-maih gene@ demog, berkeley,edu Copyright 9 1996 by Walter de Gruyter, Inc., New York Human Nature, Vol. 7, No. 3, pp. 217-255. 217
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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 (Hassan 1981; Hill 1993; Howell 1986; Lancaster and King 1985; Lancaster and Lancaster 1983; Zeller 1987; Zihlman 1981) but none have focused on the combined mobility-mortality constraint to growth.
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 (1933 [1798]) and Boserup (1965) 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 lifestyle 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 or mortality (see for example Pennington 1996). Effects could also have been 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 w o m e n in more stable home bases and shifting the mobility requirement more toward male hunters. A shift to more concentrated food resources could have occurred at any point in evolutionary time, in one or more local populations, and 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.
Demographic Constraints on Population Growth of Early Humans
219
They are speculative, intended not to suggest h o w h u m a n 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 A N D ITS DEMOGRAPHY
Figure 1 is an overview of some of the relationships posited for a foraging economy (see also Hawkes et al. 1991; Headland and Reid 1989; Hill and Hurtado 1996; Howell 1986; Hurtado et al. 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 w o m e n 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 w o m e n 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
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demands decrease (lower right). Of course, these relationships are much more complex than is depicted here. For example, as mobility d e m a n d s decrease, density probably increases, with potential concomitant increase in infectious disease, so that mortality might climb to offset growth. In general, our apelike precursors and current primate 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, w h e n doubling times dropped generally below a millennium (and now average about 35 years).
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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 (e.g., the population of Europe during the Pandemic of Justinian or the Black Death), and some species or subspecies may have disappeared (e.g., Neandertal forms). 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 in the long run would have been replaced by others in which it did. 1 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 (trekking, as some Amazonian groups like the Ache do) rather than moving 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 woodland-as-Eden notion of early h u m a n habitat. 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
Demographic Constraints on Population Growth of Early Humans
223
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 nonambulatory child. (See especially Blurton Jones 1986, 1987, 1993, 1994; Blurton Jones and Sibly 1978; Blurton Jones et al. 1989, 1992, 1993; Denham 1974; Harpending 1994; Hawkes et al. 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 h u m a n 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 y o u n g of the great apes upon their mothers. Chimpanzee and gorilla infants are breast-fed for 3 to 5 years, and interbirth 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, 1983; Matessi 1984; Nishida et al. 1990; Richard 1985; Schaller 1963; Teleki et al. 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 y o u n g 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 groups in varying
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degrees of isolation from one another. Broad averages include populations that grew rapidly and those that grew slowly or became extinct (see the critique of the use of broad averages in Hammel and Howell 1987). The arguments in this paper show that there were constraints on growth even for such heterogeneous populations. If the growth of the species depended on sudden accelerations, the constraints here suggested would have been even more drastic for exploding populations than for the populations characterized by a broad average. 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.
Mortality 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 et al. 1983). For this analysis, survivorship for females to the mean age 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. For early h u m a n populations in the ranges here considered, most differences in the overall shape of survivorship were probably induced by changes in mortality up to the mean age of childbearing, but particulary in infant mortality, which is subject to marked variation between populations. Pennington (1996) justly criticizes the use of simplistic approaches to mortality in anthropological populations, but in the mortality range considered here, and for any plausible set of shapes of mortality, the relationship between survivorship to early adulthood and a simple index of overall mortal-
Demographic Constraints on Population Growth of Early Humans
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ity like expectation of life at birth (see note 1) is rather regular; the implications of that regularity will be discussed below. 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. The implication of this stability assumption is conservative and works against the hypotheses here suggested. As noted above, any local population departing from stability in a sudden spurt of increase would face the mobility-mortality-fertility c o n u n d r u m here posed even more acutely than its stable antecedent.
Fertility Assumptions about fertility rest on the observed general shape of socalled natural fertility, that is, fertility that may be controlled for spacing but is not controlled parity-specifically. I begin analysis by using the fertility schedule reported by Howell for the !Kung (Howell 1979), but I later expand consideration to include recently reported information on the Ache (Hill and Hurtado 1996). The general shape of !Kung fertility is adequate to the initial task, and although the level is low, it is that level that is subjected to experimental manipulation in this analysis. 2 Choosing an age-specific schedule from another group such as the Ache or Hadza or Yanomamo will have an effect on analytic outcomes. Figure 3 compares the proportion of total fertility contributed at each age for !Kung women over age 45, !Kung women observed between 1963 and 1973, the Canadian Hutterites, the Yanomamo, forest-dwelling Ache, and reservation-dwelling Ache. 3 The level of fertility does vary widely between these and other groups, but so does the proportion of fertility experienced at each age. For example, early onset of secondary sterility for the !Kung concentrates a higher proportion of their total fertility in the early portion of the reproductive span, warping the age-specific curve.
Growth 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.
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Mobility A s s u m p t i o n s about mobility and its c o n s e q u e n c e s for child care are more problematic. The general picture d r a w n is m o r e like that of the !Kung and H a d z a , a m o n g w h o m individual w o m e n are h a r d put to carry two children plus food and have a p p a r e n t l y little assistance in that regard, than that of the Ache, a m o n g w h o m two children are often carried by one w o m a n and also a m o n g w h o m m e n also carry children. A n i m p o r t a n t question is the d e m o g r a p h i c availability of substitute labor for child care and, for any level of such availability, the n e e d for social a r r a n g e m e n t s of labor exchange.
DATA
Early Growth Rates World p o p u l a t i o n g r o w t h rates from 100,000 sP to 2,000 BP, at w h i c h latter date w e have some plausible estimates, are s u g g e s t e d in Table 1. The data s h o w n are a c o m p r o m i s e b e t w e e n alternative estimates of time
Demographic Constraints on Population Growth of Early Humans Table 1.
227
Plausible Population Sizes, Time Points, and Growth Rates
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0.001 0.01 1 10 75 300
0.000046 0.000184 0.000154 0.000403 0.000462
15,051 3,763 4,515 1,720 1,500
This table is modeled after Harris and Ross (1987:Tab. 1.1), with some data taken from Durand (1977) and some estimated as indicated m the text. I have recalculated growth rates from the basic population figures. A slowdown in growth rates at any "Mesolithic" transition lends support to theories of environmental overexploltation and nutritional stress (Cohen 1977, 1980, 1989) Increases in growth rates before the advent of plant and ammal domestication support speculations that peripheral hunter-gatherer societies linked by trade networks to richer core regions may have reahzed enhanced marginal productivity of child labor m the gathenng of trade materials (e.g, amber), thus increasing the value of children to the family economy and spurring population growth. of a p p e a r a n c e of the species, the d a t e s of later time points, a n d p o p u l a tion size at t h o s e points. Sensitivity analysis across a r a n g e of d a t e s of a p p e a r a n c e f r o m 50,000 BP to 200,000 BP, initial p o p u l a t i o n sizes bet w e e n 10 a n d 1,000 individuals, a n d p o p u l a t i o n sizes in 25,000 BP bet w e e n 1 a n d 5 million yields a n n u a l g r o w t h rates b e t w e e n 0.00005 a n d 0.00034 before 25,000 BP with c o n s e q u e n t d o u b l i n g times b e t w e e n a b o u t 2,000 a n d 18,000 years. These differences are not c o n s e q u e n t i a l to the analysis.
Mortality Rates The literature p r o v i d e s t w o v e r y carefully d e v e l o p e d life tables for h u n t e r - g a t h e r e r population: h e r e I u s e that of the D o b e !Kung (Hill a n d H u r t a d o 1996; Howell 1979). H o w e l l selects C o a l e - D e m e n y M o d e l West Level 5 (Coale et al. 1983), c h o o s i n g e x p e c t a t i o n of life at birth ( h e r e a f t e r e0) for f e m a l e s equal to 30 to r e p r e s e n t ! K u n g mortality. I u s e the level a n d s h a p e of this m o d e l table initially to define the m o s t favorable p r o b able m o r t a l i t y r e g i m e for early h u m a n s , a n d I u s e the s h a p e of t h e table in m o s t of the s u b s e q u e n t exploration. The e s t i m a t e s p r o v i d e d b y Acsadi a n d N e m e s k e r i (1970) for Late Paleolithic p o p u l a t i o n s (especially Afalou) s u g g e s t a lower e 0 ~ 21. Weiss (1973) s u g g e s t s e0 ~ 15 for A u s t r a l o p i t h e c i n e s a n d e 0 ~ 18 for N e a n d e r t a l s , a n d his e s t i m a t e s for els s u g g e s t sapiens levels of e o well b e l o w 20. O n e of the m o s t carefully excavated sites in the archaeological annals, a n d the o n e w i t h the m o s t
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elaborately analyzed estimates of age at death, the Libben site in Ohio (Howell 1982; Lovejoy et al. 1977; Mensforth and Lovejoy 1985), yields e 0 of 19.6 (my calculations). On the other hand, some rates reported for modern hunter-gatherers are less severe. Early and Peters (1990) estimate e0 ~ 39 for the Yanomamo; Hill and Hurtado (1996) estimate eo -~ 38 for forest Ache, and Blurton Jones et aI. (1992) find Model North Level 6, with e 0 = 32.5, appropriate for the Hadza. Readers can easily relax my assumption of most favorable mortality with e 0 ~ 30, using tools suggested later in this paper. There is also fragmentary evidence for some of our nearest n o n h u m a n relatives, the chimpanzees of the Gombe and Mahale Mountain reserves (Nishida et al. 1990; Teleki et al. 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 e 0 ~ 14 is based on my calculations from the published Gombe data (Teleki et al. 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:Tab. 1). All of these factors suggest examining a range of expectation of life at birth between 15 and 30. The !Kung and Hadza lie at about the top of this range; the Ache and Yanomamo exceed it, but the n o n h u m a n primate and Paleolithic data suggest caution in setting the upper bound much higher than 30. It is important to note that we have no historical evidence suggesting mortality levels with e0 much above 30 until the eighteenth or nineteenth century, although the severity of mortality in historical societies is most likely the result of dense habitation and poor sanitation. Figure 4 summarizes some of the comparative information with survivorship curves. Pennington (1996), using a four parameter model (Ewbank et al. 1983) based on the twentieth-century African standard, shows that e o is marginally useful as a general indicator of mortality level when the shape of mortality experience is strongly altered. I do not attempt to incorporate these possibilities in the present simulations, since there is little information on the basis of which the most critical parameters of a Ewbank model might be estimated for early huntergatherers (especially f~ and K, namely the general slope of survivorship and survivorship at early ages). Indeed, the evidence from the !Kung and Ache would support using the uniformitarian base of standard model life tables for the present purposes. With few exceptions, all empirical life tables and their model derivatives 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
229
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Coale-Demeny tables may be distorted by the effects of tuberculosis in many of the nineteenth- and twentieth-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. The under-reporting of infant and child deaths in ethnographic and survey data is pervasive and results in potentially serious biases. 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 9 Positive population growth rates in such mortuary populations 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 outrnigration (or deaths and burial afield) of adults lowers it. Nevertheless the overall patterns of survivorship across such tables show substantial consistency, and it is possible to choose between plausible and implausible tables.
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The published Coale-Demeny tables give expectations for e o 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 "natural fertility" 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"Tab. 11.1) initially here, using the structure of her table as a convenient simulation tool. Later, I utilize data from the Ache (Hill and Hurtado 1996) to expand analysis to include other patterns. First, I recapitulate (with some minor technical alterations) Howell's calculations for the Dobe !Kung.
ESTIMATION OF ALTERNATIVE
SCENARIOS The most important parameter of the simulations for our purposes 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 interbirth interval" over the reproductive life span, which is not our interest. Our interest is in the mean birth interval in the most fecund period, during which women would have the most difficulty consequent on mobility demands because of closely spaced births. PFIBI is only a theoretical estimate for that most fecund decade and takes no account of true onset of risk or of secondary sterility, but empirically it seems 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 much earlier than 17 on average, so that PFIBI for the decade 20-29 is fortuitously well placed; it 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 interbirth interval reported by Howell (1979:Tab. 8.3) for the pre-1950 !Kung. It is also close to the median second interval for women having a first birth in that decade, estimated from Howell's Fig. 7.4. Actually observed birth intervals reported by Howell average around 49 months (1979:Tab. 6.5). Zeller (1987) reports 44 months as the average interbirth interval. Blurton Jones
Demographic Constraints on Population Growth of Early Humans
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(1987:201ff.) reports 55 months for second and higher intervals that are not preceded by an infant death, for bush-dwelling women. Hill and Hurtado (1996:254) report a mean of closed intervals of about 38 months. Computation of closed interbirth 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 total fertility rate (TFR) or net reproduction rate (NRR) require more than the usual interpretation. Computation of the NRR for example takes into account the elimination of deceased w o m e n from the risk pool. The use of marital fertility rates can eliminate w o m e n who never married. A very accurate computation would consider 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 mortality constraints on growth discussed in this paper. 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 in 19631973 showed a TFR of 4.3 (Howell 1979:chaps. 6-9). The forest Ache of Paraguay have a TFR of about 8; their compatriots on the reservation, about 8.5 (Hill and Hurtado 1996:chap. 8). The Yanomamo as reported by Hill and Hurtado (1996) have a TFR of about 6. Hutterite fertility is about the highest known (TFR ~ 12.4). The Hadza appear to have a total
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