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Dwight W. Read (1998) 'Kinship based demographic simulation of societal processes'

Journal of Artificial Societies and Social Simulation vol. 1, no. 1, <http://jasss.soc.surrey.ac.uk/1/1/1.html>

To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary

Received: 29-Oct-1997      Accepted: 12-Dec-1997      Published: 3-1-1998


* Abstract

The social boundaries of small scale human societies are defined through culturally defined kin relations that transcend the specifics of the genealogical relationships produced through procreation. Kinship knowledge is culturally defined, distributed knowledge that provides structure for the persons produced through demographic processes. However, the interplay between the demographic system and the cultural system has been difficult to model. Genealogical data are static and do not show how the vagaries of demographic processes affect implementation of a culturally defined, conceptual system. Demographic simulations can provide the dynamic dimension, but usually lack information on how the changing demographic makeup of a population affects application of culturally defined rules relating to marriage, reproduction, residence and the like. This paper presents results obtained from implementation of a multi-agent, demographically driven, simulation of a hunting and gathering group in which each agent is imbued with cultural knowledge that affects decisions to be made about marriage, reproduction and place of residence. The goal is to assess the implications of demographic processes, ego-centered decision making, and culturally determined structures (kin relations, social groupings and the like) for the resulting social system. Questions addressed in the simulation are based on ethnographic observations and it is shown that the simulation provides an effective means to assess the validity of hypotheses about the ethnographic observations.

multi-agent simulation, cultural knowledge, hunting and gathering societies

The question addressed in this paper is: What is the relationship between culture and behavior? The question is an old one and has had widely divergent answers. At one extreme, some have argued that culture is largely the encodification of patterns of behavior that are effective in terms of meeting the pragmatic exigencies of the members of a society. At the other extreme, others have argued that culture defines for the individual the meaning and significance of behavior and thereby directs the behaviors that ensue (Keesing 1973). The position taken here is that there is a dynamic tension between cultural specification of appropriate behavior and the pragmatic reality in which individuals operate, leading both to restriction of behavior through cultural meanings in the short run, and to change in cultural specification through pragmatic necessity in the long run. Simulation is being used as a means to examine this tension by determining specific societal configurations that arise when cultural specifications about appropriate behavior are played out.

The methodological goal is to find a means to fill the inevitable gap in ethnographic data between what can be observed and what would likely be observed if conditions were different. The intent is to use simulation in a quasi-experimental sense. This permits investigation of questions such as: How do outcomes change under different cultural specifications? Do cultural rules provide a means to overcome what otherwise would be lacunae in the ongoing societal system? Using simulation in a quasi-experimental sense to explore the behavior of a system given in the form of a model under change of conditions is not novel; what is different in the application discussed here is a focus on the implications of variation in cultural rules, rather than of parametric values, on the behavior of a model.

Two specific instances of cultural rules are considered, both motivated by the author's previous work on the !Kung San, a hunting and gathering group of southern Africa. One instance relates to decisions women make about spacing of children, and the other to the consequences of cultural rules regulating marriage. The first instance considers alternative models for decision making; the second explores the relationship between culturally specified rules of incest and the extent to which there is residential camp exogamy with respect to marriage.

Both of these have important ramifications for our understanding of societal dynamics of the!Kung San, in particular, and of societal dynamics, in general. For the !Kung San, female decision making about spacing of births affects population dynamics and the latter, in conjunction with variation in resource availability, relates to stresses and strains in resource abundance and scarcity they have had to resolve. Camp exogamy (marrying someone outside of one's living group) relates to general issues about the internal dynamics of their social system and the role kin relationships among camp members plays in how societal members establish themselves as belonging to a camp and thereby gain access to resources (Lee 1976: 77; Marshall 1976: 187-91).

More generally, these are but two examples of the general problem of understanding the interplay between the individual as the locus of both decision making and cultural knowledge, and cultural knowledge as consisting of shared conceptual systems that link individuals into a larger whole in which the meanings of actions and events take on a dimension transcending individual knowledge. Cultural knowledge simultaneously affects and constrains individual behavior through providing shared meanings that actions and events may have, yet is changeable by those same individuals through redefinition and reinterpretation of what constitutes shared meanings.

This dual role, of both directing and being directed, requires, however, a dimension in modeling that is scarcely touched upon by most formalisms yet can be explored through simulations. Let us consider a formal, dynamic model as a 4-tuple, [E, X, P, t]; that is, the model consists of a set of structural equations, E, an n-dimensional vector of time dependent variables, X, a set of parameters, P, and a time dimension, t. Typically, the vector of variables, X, is assumed to be known and the equation set, E, is often some set of differential equations (or possibly difference equations). The parameters are specified in the equations, the state of the system at time t is specified by the vector X(t), and the m-dimensional space (m <= n) determined by the vector of variables, X, (within which occur the values taken on by the vector of variables, X(t), as t varies over a specified time range) forms the state space for the system.

Formalisms of this kind frequently focus on stability properties to characterize the expected state of an ongoing system for a given set of parameter values and initial state vector, X(t0). Stability conditions range from the simple, such as a unique, stable equilibrium in a linear system, to the more complex, such as chaotic, non-linear systems where specification of the system state may only be possible in the form of state space regions in which the system is likely to be found. But whether the system exhibits simple equilibria or chaotic behavior, common is the concern with the manner in which change in the state of the system is driven by the time dimension, t, beginning with some initial state vector, X(t0), and as determined by the set, E, of structural equations and the choice of parameter values.

We can exemplify the formalism in the context of !Kung San population dynamics through a simple model for stabilized population size:

dP(t)/dt = rP(t)(1 - P(t)/K) (1)

where P(t) is the population size at time t, dP(t)/dt is the (instantaneous) rate of growth at time t, r is the net growth rate per female and K is usually interpreted as the carrying capacity. (Or, in words, Equation 1 asserts that the rate of change of population size is proportional to the current population size, but with the proportionality -- the term r(1-P(t)/K) -- decreasing as the population size increases.) The vector, P = <P> is one dimensional; the parameters are r and K, and Equation (1) makes up the set, E, of structural equations and defines the behavior of the system. Equation 1 and variants on it have been widely used for modeling growth in populations. In the deterministic, non-stochastic situation, the system is driven asymptotically to a stable equilibrium value, Pe = K, for r > 0. For groups such as the !Kung San this conclusion is consistent with the observation that hunting and gathering societies necessarily have bounded populations over long time scales (tens to hundreds of generations) by virtue of being constrained by a limited resource base. Equation 1 does not, however, provide a very good model of the process by which population dynamics are played out for a group such as the !Kung San.

There are two significant defects. First, the model eliminates reference to specific individuals by assuming that each individual in the population is characterized by precisely the same parameter values. While that assumption may be less problematic for the parameter, r, it is more problematic for the term (1 - P/K) which represents density dependent reduction of the inherent net growth rate. The assumption in the model is that each female in the population will experience the same reduction in fertility, regardless of her particular situation, such as her current family structure (number, sex and age of children). Second, it uses an artificial means, the term (1 - P/K), to circumvent a much more problematic modeling question, namely the manner in which the realized fertility of women is changing through time. The term (1 - P/K) merely asserts that the inherent net growth rate, r, that would occur at low population levels is modified via some unspecified mechanism in response to the current population size, P. The process by which the net growth rate varies is outside of the scope of the model.

In other words, Equation 1 assumes away precisely what we need to understand. Decision making, in this case on the part of !Kung San women with regard to spacing of offspring, is the process underlying realized fertility rates -- one of the components of net growth rate -- and decision making is done in the context of the current status of each female as measured by her current family structure. But decision making is based upon culturally specified meanings associated with children and the desirability of children. How current family size affects her decision (and the role of other persons in such decisions) is culturally specific and not universal. !Kung San women, when asked about family size and the value placed on children, respond in terms of culturally relevant responses, not individually constructed meanings based upon some assessment of the group's current status with regard to, say, resources. From an etic perspective (i.e., the perspective of an outside observer), spacing of children by !Kung San women is related to postpartum amenorrhea that a large number of studies (see reviews by Gage et al. 1989; Ellison 1994; Vitzthum 1994) have linked to the "duration and intensity of lactation" (Ellison 1994: 267); from an emic perspective (i.e., from the perspective of the culture bearer), nursing of children relates to the desire that the children should "have strong legs, and it is mother's milk that makes them strong . . . a child needs milk till he is three or four years old at least" (Marshall 1976:166). "Needing milk until three or four years old" is a culturally specific meaning assigned to nursing, not a biological imperative.

Their view about family size has an inherent tension between the cultural, "They want children, all the children they can possibly have" (Marshall 1976: 166), and the pragmatic," . . . they explained that they cannot feed babies that are born too close together. . . . A mother had not enough milk to sustain completely two infants at the same time" (Marshall 1976: 166) and ". . . to carry a third child and the food she gathers would be practically impossible for those small women" (Marshall 1976: 168)1. The inherent tension requires that each woman, with each birth, decides, through her behavior, how long this particular child will be nursed. Through that decision she affects her realized fertility as intensive nursing, in conjunction with substantial work effort, is a major factor in temporary reduction of post-partum fecundity2 (Ellison 1994: 269; Wood 1994: 370) via the impact lactation has on ovarian function through an hypothesized effect of the suckling stimulus on the "hypothalamic pulse generator" and/or the triggering role that nursing plays in the release of prolactin (Vitzthum 1994: 313 and references therein).

What we want to understand is the way this local tension between cultural specification and pragmatic limitation plays itself out at the societal level.

Modeling Strategy: Minimum Specification

Hunting and gathering populations, by virtue of dealing with a resource base that is, for the most part, fixed regardless of degree of intensification of foraging and hunting effort3, have population sizes limited by resource availability over time scales measured in tens of decades. Within this general constraint are hunting and gathering populations that vary in their population dynamics from extremes such as the Netsilik Eskimo who suffered from periodic starvation when their expected resource base in the form of migrating caribou did not materialize (Balikci 1970), to groups such as the !Kung San for whom starvation is unknown (Marshall 1976: 107). Given the potential of having a natural, total fertility rate of about 8 children for a woman over her reproductive period (Henry 1961) and typical mortality rates in hunting and gathering societies (upwards of 50% mortality before adulthood followed by low mortality rates during the reproductive years), it is evident that groups such as the !Kung San are, in some manner, engaging in population limitation since their population size remains below the point at which stochastic variation in resource availability could lead to starvation. As Hayden comments "the vast majority of hunter/gatherer populations are and were maintained well below carrying capacity" (Hayden 1972: 205). Are groups such as the !Kung San, however, consciously engaging in population limitation and monitoring current population size against resource availability, or is the limitation an epiphenomenon of practices whose motivation lies not in population regulation but elsewhere? Ethnographic data on the !Kung San argues against the former (Howell 1976; Marshall 1976:166). If so, then it is of interest to know what minimal specification of culturally specified behaviors will have population limitation as an outcome, even if unintentional. The question now becomes: Is the fact of a stable population size an epiphenomenon of decisions whose motivation has no direct relationship to the observed outcome?

This contrasts with other approaches where summary characteristics of a group (such as average birth spacing) are taken as phenomena that need direct explanation. For example, ethnographic data indicate that !Kung San women space children approximately 4 years apart (Howell 1976; Lee 1980) with extended nursing suggested as the primary mechanism for birth spacing (Konner and Worthman 1980; Lee 1980). A common approach takes the fact of spacing as a datum to be embedded into an appropriate theory about behavior. One such theory argues that behaviors maximize Darwinian/Inclusive fitness via an optimization strategy. Using this framework, it is argued that a !Kung San woman's fitness, as measured by energy expenditure, is maximized with a spacing of about 4 years (Blurton Jones 1986). With shorter spacing her energy costs, it is argued, increase due to the extra effort she must use for transportation of children while gathering since !Kung San women take infants and young children with them. With 4 year spacing she will not have a new infant until the current child is old enough to walk the several kilometers that are covered during food gathering.

While the calculations of the energy dynamics are undoubtedly correct, the argument assumes the fact of 4 year birth spacing as a distinct datum needing its own particular explanation rather than considering it as an epiphenomenum of behavior whose basis lies elsewhere. Previously I have published a model for !Kung San population dynamics based upon the assumption that each woman acts in her self interest within the context of cultural specification of what constitutes appropriate behavior (Read 1986). The model posits the 4 year birth spacing as an epiphenomenum of self-interested decision making rather than as a global property requiring a causal explanation such as the adaptive value of 4 year spacing4. The model made two culturally based assumptions:

Assumption 1: !Kung San women have a desire for as many children as possible


Assumption 2: !Kung San women are concerned for, and make decisions to promote, the well-being of their family,

where family well-being includes, but is not limited to, ability of a woman to adequately nurse a newborn and to carry infants with her when foraging for resources. These two assumptions are based on comments elicited from !Kung San women by Lorna Marshall as discussed above.

The model assumes each women has some set of activities, [A1, . . . , An] (such as gathering, preparing food, and so on, where neither the list of activities nor the number of tasks is fixed but can vary from one woman to another) which engage her time and energies. It is assumed that each women has a limited energy/time budget, E, which can be partitioned between these activities and the care of offspring. It is further assumed that each woman will allocate some minimal amount of energy/time, call it EI, to each infant (see Assumption 2), and some total amount of energy/time, call it EA, to activities that she engages in. The only assumption made about EI and EA is that n*EI + EA <= EMax, where EMax is the maximum amount of energy/time she can spend on both child care and activities and n is her current number of infants. It is assumed that each woman is free to vary both the set of activities, [A1, . . . , An], and the amount of energy/time, Ej, spent on activity Aj.

In addition to the two cultural assumptions, several observations about the dynamics of foraging are incorporated in the model. It is argued that as population size increases (and hence density increases since the geographical area available to the !Kung San is limited by the presence of other groups in the same region) the amount of energy/time required for foraging activities with the same nutritional output must increase. It follows, then, that if EA increases sufficiently a !Kung San woman must eventually reduce n*EI, and the only means for reducing n*EI consistent with her desire to adequately care for her offspring is to change the value of n via birth spacing (see Assumption 2). It is further assumed in the model that women are knowledgeable of means either to limit fertility, such as intensive and extended nursing, or practice abortion and, in extreme cases, infanticide, as a way to space offspring5. Note that the latter two methods are likely to occur regularly only when culturally reinforced. Conversely, it is assumed that if n*EI + EA << EMax ( "<<" = "much less than") then she will decrease the spacing between offspring (see Assumption 1). Consistent with this aspect of the model, interbirth spacing has decreased by about 8 months when more sedentarized !Kung San women are compared with less sedantarized !Kung San women (Lee 1980).

Under these assumptions it was shown that there will, in the deterministic model, be a stable equilibrium, Pe, for population size due to two factors. First, as population size increases, foraging costs increase and women with infants will delay future pregnancies, hence the average fertility rate is reduced. Second, when there is sufficient reduction in realized fertility rate for enough women, population size will decline and with a decline in population size foraging costs will decrease and spacing will now be reduced, thereby raising the average realized fertility rate. In other words, the model demonstrates that there is a dynamic, feedback relationship among birth spacing, population size, and the cultural valuation placed on children and the well-being of the family. This behavioral response by individual women in response to the current cost of foraging as mediated through her family structure thereby establishes a link between lactation amenorrhea and a nonconservative factor (i.e., a factor that varies directly with population size) that was argued to be absent by Gage et al. (1989)in their critique of attempts to use lactational amenorrhea alone as a causative mechanism when accounting for population regulation6. The realized birth spacing achieved through this process will reach an equilibrium value at the spacing that stabilizes the population size. Further, the average spacing needed for stabilizing the population size is determined by the age specific mortality rate and the length of the active reproductive period.

The cultural implication of the decision making in this process needs to be emphasized. Malthusian parameters will ensure that the population size is stabilized within tens of generations when there is a bounded resource base whose abundance is relatively impervious to intensification. The positive cultural valuation placed on the well being of the family allows for decision making on the part of the woman that then has the effect of circumventing the Malthusian parameters, not because women are aware of the long term consequences of high fertility rates but because it happens that when she acts in her self-interest as defined by her culture, the consequence, even if unintended, is stabilization of the population size below a value where Malthusian parameters would otherwise come into play. In contrast, other hunting/gathering groups such as the Netsilik Eskimo faced periodic starvation because there were no cultural practices that had the consequence of stabilizing population size below the value that could be supported without starvation in the long run, given the variation that took place in the availability of their resources, mainly in the form of unpredictability of caribou during their fall migration to winter feeding areas.

In more general terms, the !Kung San example highlights the problems that arise when societal characteristics are viewed as individually needing explanatory accounts without first determining if the characteristic in question arises as an epiphenomenon of other, perhaps simpler, behaviors. Another example of this caveat derived from the simulation is discussed at the end of this chapter and relates to the number of persons making up a residential camp among the !Kung San.

Simulation Model

Simulation has become a standard technique in small population demography and has had focus on three broad topics: (1) vital rates and small population dynamics, (2) fertility variability, and (3) the interplay between genetics and demography (Leslie and Gage 1989: 30) The simulation model constructed here differs from this previous work as the goal is to determine the consequences of culturally mediated decision making on demographic parameters and how the appearance of emergent social structure can arise from such decision making. The demographic simulation is being used quasi-experimentally (Howell and Lehotay 1978) both to determine the relative role of cultural factors on demographic properties and to work out the interplay between an objective demographic background and a culturally constructed foreground that overlays this background and frames decision making.

The simulation model is written in Turbo PascalTM and is based on person records that keep track of information such as: year of birth, sex, current age, marital status, spouse, offspring, kin relations (specified via kin terms), name giver/name receiver relations and camp membership. The simulation used a year as a time unit.

Each simulation year the age of alive persons is increased, age specific mortality rates are applied to each currently living person, the marital status of females is noted and spouses are found (if possible) for post menarche, unmarried females (or females whose spouse has died), married women of reproductive years are exposed to fertility rates according to the model selected, and when there are births, kinship lists are updated (see Figure 1).

Fertility Models

While population growth and decline is driven by the net growth rate, net growth rate can be thought of as determined by the current fertility rate so long as the age specific mortality schedule does not change. Since the intent of the simulations is to focus on the effect of variation in fertility rates due to decision making by women, age-specific mortality rates are kept constant. This permits modeling to focus on fertility rates.

Three types of models were constructed for fertility rates: (1) density dependent, (2) threshold, and (3) birth spacing. Density dependent fertility refers to models where the current fertility rate, r, for all women decreases with increase in population density. Density dependent fertility underlies models such as Equation (1) and has been widely used to model constrained population growth. However, as discussed above, the way in which population density leads to change in behavior on the part of females is usually not addressed in these models. The threshold fertility is a first attempt to introduce a behavior component. Rather than assuming a direct, but unexplained, relationship between fertility and population density, the threshold model posits a conservative tendency on the part of females to not change behavior until an external factor, the cost of foraging for food, dictates that change must occur. Finally, the birth spacing model presumes that women modify the spacing of offspring in accordance with both the time/energy demands of foraging and her current family structure as measured by the age and number of infants. Each model is assessed for qualitative goodness of fit to data on the actual birth spacing realized by !Kung San women.

Model 1 (Density Dependent Fertility)

The density dependent model is based on Equation 1 and takes the form:

r = r0(1 - P/K) (2)

where K is a parameter that specifies the equilibrium population size, r0 is the intrinsic fertility rate (r0 = 8 births per female per reproductive period in all simulations), r is the current, realized fertility rate (note that in equation (2) r is the fertility rate whereas in equation (1) r is the net growth rate) and P is the number of adult women. The model separates the net growth rate of equation (1) into two parts, the realized fertility rate which is assumed to be density dependent and a fixed, age dependent mortality rate. Consequently, the parameter, K, in equation (2) is an overestimate of the stabilized population size since equation (2) does not include mortality rates. A fixed, age-specific mortality schedule is used in this and all other simulations.

The value of r is used to stochastically determine if a woman has a birth or not each year that she can become pregnant. If a woman has a birth in year n it is assumed in all simulations she cannot have a birth in year n+1 but can again have a birth in year n + 2, thus making the minimum birth spacing (as measured by the difference in age of successive offspring) 2 years. In a year when she can potentially give birth, she will have an offspring with probability determined by r. A value of K = 800 was used in the simulation based on Model 1, leading to a population size of about 400.

Model 2 (Threshold)

The threshold model assumes that no reduction in fertility takes place until a total "energy expenditure" value reaches a fixed threshold and then the fertility rate, r, drops to 0. The "energy expenditure" is composed of two parts. One part is proportional to the current number of living children below a fixed infant age, IA. The parameter, IA, can be interpreted as the age at which nursing stops. The model assumes the value of IA is fixed and the same for all women. The other part of the "energy expenditure" is proportional to the current population size so that:

E = n*Wt + P/K (3)

where E is the total energy expenditure for a woman, n is the number of children below the infant age, IA, Wt is a weighting factor that represents the energy expenditure per infant, and K is a constant that translates population size into energy cost equivalents per women per infant (and represents in summary fashion her total cost in doing all activities other than caring of infants).

The value of E is computed each simulation year for each woman and if E < T, T the threshold value, then the inherent fertility rate is used for her current fertility rate. If E > = T then r = 0. Thus,

r = 0 if E >= T

r = r0if E < T (4)

This model corresponds, for example, to having births as often as possible until a threshold value is reached beyond which a newborn infant cannot be kept alive. Note that in this model a large population size can drive a woman's fertility rate to 0 even if she currently has few or no children. Typical values used in the simulation were T = 16, K = 25, and Wt = 6. These led to a stabilized population size of around 400 persons.

Model 3 (Birth Spacing)

The birth spacing model is similar to the threshold model except that the age for an infant is not fixed but determined by the current population size:

IA= 4 *(P/K) (5)

Equation 5 relates a woman's current willingness to have an offspring to the time/energy she must expend on obtaining resources. The energy expenditure per woman is computed in the same manner as for Model 2:
E = n*Wt + P/K (6)

and equation (4) is used for assigning the current fertility rate of a woman. This model captures the notion that a choice to have another child is affected by both (1) the current amount of time/energy spent on obtaining resources (which affects the number of years she will nurse, hence the age for an infant) and (2) her cost of having currently having n infants.

Different from the threshold model are the parameter values. Typically in the simulation runs, Wt = T = 16, and K = 300 when using Model 3. With these parameter values the model is driven by changes in IA as population size changes. Whereas the parameter, K, in Model 2 served as a translation factor for changing population size into energy units, by setting Wt = T in Model 3, K becomes a proxy measure for carrying capacity. In addition, setting Wt = T has the effect of changing the fertility rate to 0 if the female has 1 infant, though the definition of an infant changes with the current population size. The effect is to space offspring according to the current value of IA since the fertility rate is reduced to 0 when a woman currently has 1 infant regardless of the population size.

For all models two conditions had to be satisfied before a woman could give birth: (1) a woman must be between the ages of menarche and menopause and (2) a woman must be married to a currently alive male. The second condition matches the ethnographic observation that "illegitimate" children are very rare in groups such as the !Kung San, if only because women are almost always married. Polygyny was not incorporated (though it occurs in about 10% of !Kung San marriages (Marshall 1976: 263)) and when a husband died a new husband would be found unless the woman has reached menopause.

Marriage had two conditions that must be satisfied in accordance with ethnographic observation: (1) a husband is older than his wife and (2) a husband is not substantially older than his wife. For the purposes of the simulation a male must be at least 3 years older than a female, but not more than 8 years older. These assumptions are not stringent and mainly have the effect of sometimes shortly extending the period of time between a women reaching puberty and obtaining a husband.

Population Growth And Birth Spacing: Results

In all simulations the initial cohort consists of 80 adults with sex assigned randomly and with an age distribution varying from menarche to the end of the reproductive period. All simulations were run sufficiently long so as to eliminate transient effects due to the structure of the initial cohort. Graphs of population size against time, and of the average birth spacing per women against time, are presented here.

Model 1: K = 800.

The model and parameter value provide a baseline model showing stochastic effect in what otherwise is simple density dependent population growth as given by Equation 1. The simulation was run for 1200 years and approximately the first 500 years are needed to arrive at a steady state (see Figure 2). The upper curve gives the population size and the lower curve the average spacing of births.

It can be seen in Figure 2 that stochastic variation in population size is substantial. Average birth spacing varies to some extent, but not in a consistent manner with population size. Because the parameter, K, is compared to the current number of adults rather than total population size, there are time lags between change in fertility rate and realized effect on growth or shrinkage in the number of adults. The "jaggedness" and quasi-periodicity of the peaks in the stabilized population size reflect both these stochastic and time lag effects.

Model 2

Several choices of parameters were used to ascertain the effect of placing greater emphasis on female decision making. Four results are presented here.

Model 2a: Wt = 0, T = 16, K = 25.
These parameters correspond to a fixed fertility pattern on the part of females, with current fertility either being the inherent fertility rate or 0, depending upon the current population size. The definition of an infant (here and in other simulations in this section) is set at IA= 5. As can be seen in Figure 3, the threshold model is highly periodic and corresponds to a crash and boom regime. Population size increases rapidly since female fertility is not affected by initial population growth until the threshold value is reached. At this point fertility goes to 0 for all females and the population crashes. The time lag between fertility change and when change has an effect on the adult population size introduces the periodicity in the trajectory of the population curve. Birth spacing is generally unaffected until the population is close to its minimum value when a sufficient number of women have experienced 0 fertility over a long enough period of time to cause the average spacing of births to increase.

While the pattern is not characteristic of !Kung San population dynamics, a regime such as this probably characterized groups such the Netsilik Eskimo who suffered periodic starvation due to unexpected and substantial changes in their resource base.

Model 2b: Wt = 3, T = 16, K = 25.
With Wt = 3 the model assumes women are taking into account both their energy expenditure for the care of infants as well as the cost of procuring resources. The non-zero value for Wt implies that females with more infants will restrict their fertility prior to females with fewer infants, making fertility patterns more in attune with current family structure and not driven solely by the cost of procuring resources as is true in Model 2a.

As can be seen in Figure 4, the periodicity in population size remains but is substantially attenuated by the decision making on the part of females that takes into account their current energy/time expenditure on infants. Also striking is the increasing interdependence between birth spacing and population size, with the peak in birth spacing occurring shortly after the peak in population size. The attenuation in the heights of the peaks and valleys seen in Figure 4 is due to females with infants restricting their fertility prior to when reduction of fertility would take place were it responding only to resource procurement costs as in Model 2a.

Model 2c: Wt = 6, T = 16, K = 25.
The value of Wt = 6 shows the effect of placing more emphasis on the cost of infants, causing the threshold value to be reached with fewer infants than is true for Model 2b. As can be seen in Figure 5, there is further attenuation of the extremes in population size. Overall population size is decreasing in comparison to Model 2b as the threshold value, T = 16, is reached with lower population sizes; that is, the P/K term will contribute an amount that makes E > T at smaller population levels for the same number of infants in comparison to Model 2b. In effect, female decision making that places more emphasis on the cost of infants reduces the equilibrium population size.

The latter result is of considerable interest as it indicates that measures such as population size as a percentage of total carrying capacity are not particularly meaningful without taking into consideration the cultural dimensions of how women are responding culturally to costs such as time spent in procuring resources, and how this may affect decision making with regard to reproduction. The simulation suggests that even with identical resources and identical resource procurement methods, the magnitude of the stabilized population size will vary (for the threshold model) according to the relative importance a female places on the cost of caring for offspring in comparison with her desire to have additional offspring.

Model 2d: Wt = 15, T = 16, K = 200.
This is an extreme case with females deciding not to have additional offspring if they currently have more than one infant, and deciding not to have another offspring if they currently have one infant and there are even just moderate resource procurement costs. The larger value of K is needed to keep the stabilized population size at the same order of magnitude as the previous models.

The general effect is one of slightly decoupling the linkage between birth spacing and population size. In Figure 6, for example, there are only 5 major peaks for birth spacing, in comparison to the 7 peaks in each of Figure 4, and the peaks are not as evenly spaced.

Model 3: Wt = 16, T = 16, K = 400.

The value of IA is computed in each simulation cycle via IA= 4 * (P/K), where P is the current number of adults. For small values of P, IA > 0 and for P > K, IA > 4. As discussed above, this model corresponds to statements by the !Kung San women indicating that they do not want to have additional children unless they can properly care for them. For small population sizes where resources may be plentiful and little time is needed for their procurement, women may have adequate time to care for infants closer together in age than is the case when resources are harder to come by. Ethnographically, it has been noted that the spacing of births by !Kung San women has decreased with increased sedentarization; i.e., when resource procurement time is reduced. This model corresponds to Read's deterministic model as it allows for both decrease and increase in birth spacing.

In comparison to Model 1, Model 3 leads to better tracking of population size in relationship to resources as measured by less pronounced stochastic variation. In comparison to Models 2a - 2c, change in fertility rates and their delayed consequences at the level of adult populations are not as severe. In Models 2a - 2c time lags are more or less synchronous across all women as the component of the energy/time budget driven by population size affects all women equally regardless of the number of offspring. In contrast, time lags in Model 3 are female specific and determined primarily by her current reproductive history. Hence there is less synchrony across females and time lags lead neither to as regular nor as pronounced a periodic pattern as occurs with Models 2a - 2c.

As can be seen in Figure 7, birth spacing is tracking population size. Perhaps unexpected, though, is the result that relatively little change in birth spacing is needed to maintain the population at a stabilized value.

Birth Spacing

All three models lead to a stabilized population size infant spacing. Spacing of 0 or 1 year is excluded in all models as discussed above. Average birth spacing is approximately equal for all three models (see Table 1) and comparable to the


Model Mean (x) Standard Deviation (s) Number of Females
Model 1 3.70 1.84 306
Model 2c 3.47 1.46 249
Model 3 3.90 1.31 201

44.1 month average spacing (n = 55) observed for the more nomadic !Kung San women (Lee 1980: 336). Differences among the models arise, however, in the frequency distribution of birth spacing for each model. For Model 1, spacings of 2 or 3 years are most common, with longer spacing occurring substantially less often (see Figure 8). In Model 2, frequency of spacing drops off more smoothly, with spacing of 2 - 4 years the most common values, reflecting the fact that when fertility changes at the threshold value all women are affected equally regardless of their current family structure (see Figure 9). In Model 3 the modal value is 3 year spacing with spacing of 4 years also common. Spacing fewer than 3 years is rare (see Figure 10). Thus, although the average birth spacing is comparable across the three models (which primarily reflects the fact that all three models arrive at stabilized population values), only Model 3 leads to a birth spacing frequency distribution that approximates the actual birth spacing by !Kung San women. Common values for birth spacing are 3 and 4 years and seldom is less than 3 years (Howell 1976: 145).

Marriage Rules

In the above models it has been required that a woman be married before she will have offspring and that post-pubescent, unmarried woman attempt to marry in each cycle of the simulation. The only limitation on choice of a spouse is expressed in terms of age. However, as is true for all societies, options on spouse choices are expressed through incest rules. While some of these rules are shared with other societies, such as genealogical parent or genealogical child prohibited as a spouse, others are cultural specific and can only be expressed via relationships defined through their kinship terminology. To state these rules requires a brief excursion into an abbreviated description of !Kung San kinship terminology and world of kin based on descriptions of !Kung San kinship presented by Marshall (Marshall 1976).

!Kung San Kinship Terminology

Ultimately, it is kin that comprise the social world of the !Kung San. The context within which individuals operate is the social world of kin and excludes those with whom there is no kin relationship. Kin relationship is determined through their conceptual system of kin as expressed in their kinship terminology. Elsewhere (Read 1974; Read 1984; Read and Behrens 1990) I have argued that kinship terminologies are conceptual structures whose form is determined by an internal logic that leads to a structured system of symbols (kin terms). This conceptual structure determines kinship relationships and kinship relationships so determined are distinct from, but can be related to, genealogical relationships calculated through the reckoning of relationships based on parent/child links. While for a terminology such as the American/Anglo Kinship Terminology, kin term relationships such as Mother, Grandfather, etc. can be expressed simply using genealogical concepts (e.g., a Grandfather is either a mother's father or a father's father), such is not the case for the terminology of the !Kung San. There is no complete mapping of genealogical relationships onto kin term relationships. In practice, genealogical relationships are of secondary concern (if of concern at all) and kinship relationships are determined not through identifying the genealogical relationship between ego and alter (as might be done by two persons using the American/Anglo terminological system) but through identifying kin term relationships: "If I call so-and-so by the kin term, X, and you call so-and-so by the kin term Y, then I am your Z and you are my W" would be a typical calculation, with no concern for the actual genealogical relations among the persons in question.

Kin Terms

The consanguineal part of the !Kung San terminology can be expressed via two sets of kin terms. The first set is used for members of the nuclear family (but not exclusively) and consists of 7 terms. The terms are (with approximate transliterations given in parentheses and quotes): ba ("father"), tai ("mother"), !ha ("son"), khai ("daughter"), !go ("elder brother"), !kwi ("elder sister") and tsi ("younger sibling"). The last three terms (but not the other four) are also used for persons outside of the nuclear family.

The second set of terms consist of 4 generational and sex terms: tsu ("male, odd generation with respect to ego"), //ga ("female, odd generation with respect to ego"), !gun!a ("male, even generation with respect to ego"), and tun ("female, even generation with respect to ego"). While the use of odd and even generation in the transliteration seems to suggest a need for genealogical reckoning, such is not the case and the usage of the terms need not correspond to the actual genealogical generation of alter with respect to ego. Non-genealogical usage of the terms can be seen in the following two examples. Example 1: If ego calls alter1 by, say, the term tsu, and alter1 calls alter2 by, say, the term tai, then ego calls alter2 by the term tun since alter2 is female and 1 generation removed from alter1 by virtue of alter1 using the kin term, tai ("mother"), for alter2. Example 2: If ego calls alter1 by the term tun, and alter1 calls alter2 by the kin term tsu, then ego uses the kin term !gun!a for alter2 since alter2 must be male and, according to the kin terms, an even number of generations away from ego (whether or not, in fact, ego and alter2 are an even number of generations apart as reckoned genealogically). In other words, the proper usage of the terms can be expressed via kin term equations, such as "tsu of tun is !gun!a," without reference to genealogical relationships.

Name Relationship
The !Kung San make the genealogical aspect even more irrelevant by another aspect of the terminological system, namely the way in which name-giving and name-receiving affect kin relationships. There is a standard list of 41 female and 48 male names (Marshall 1976: 225) and when a child is born, s(he) will be given one of these names. Which one depends upon the relative for whom the parents decide to name the child. The child and the relative whose name is given to the child then stand in a special name-receiving and name-giving relationship that creates a conceptual identity between the two of them. This has two effects on kin term relationships. First, for anyone in a name-giving relationship to ego's parent's or ego's children, ego will use either the term tsu or the term //ga, according to the sex of alter (since such a person, when identified with the parent or child name-receiver in ego's nuclear family is now, conceptually, a person in an odd generation with respect to ego). For anyone in a name-giving relationship with a sibling of ego, ego will use the appropriate sibling term (either !go or !kwi, depending on sex, since the name-giver is conceptually older with respect to ego). Second, ego will use the same generational kin terms as does name-giver for all relatives except members of ego's nuclear family (ego always uses the nuclear family terms for members of the nuclear family) regardless of ego's actual generational distance to the person in question. For example, ego will use the term tsu for his "uncles" if ego received the name of one of his "grandfathers," but if instead ego had received the name of one of his "uncles," ego would use the term !gun!a for all other "uncles." (The shift to name-giver as a focal point for kin reckoning is slightly more extensive than outlined here, but this much suffices for the purpose of the simulation.)

Some rules apply to the choice of relatives selected to be name-givers. First born sons are to be named for their father's father, first born daughters are generally named for their mother's mother, second born sons are often named for their mother's father, and second born daughters can be named for their father's mother.

Incest Rules

As has been noted in ethnographic accounts on the !Kung San, marriage need not be exogamous with respect to one's natal camp. When queried, the !Kung San indicate that it is permissible to marry someone from one's own camp. In reality, though, marriages almost never occur between members of the same camp. The ethnographically suggested reason is that no one in one's natal camp is marriageable without violating incest rules (Marshall 1976: 252). Though suggested as a reason, it has never been empirically verified. The intent of the simulation, then, is to determine the extent to which de facto camp exogamy arises out of adherence to incest rules.

Unfortunately, the ethnographic data on incest are not clearly expressed in terms of !Kung San conceptualizations but are given in terms of our own kinship categories. For some of the incest rules this is not problematic. For example, marriage with any member of the nuclear family would be unthinkable, as well as with parents' siblings. Though expressed in terms of our concepts, all of these relations are easily enough restateable using !Kung San kin term relationships. But in the primary work on !Kung San marriage rules, Lorna Marshall goes on to indicate that incest also excludes 1st, 2nd and 3rd cousins (Marshall 1976: 255). Since cousins in general, and the distinction of 1st, 2nd and 3rd cousins in particular, are not part of !Kung San kinship conceptualizations, some estimate of the kind of relationships involved must be made. As a first approximation, what we call 1st, 2nd and 3rd cousins are all relations in an even generation with respect to ego, so we might express the marriage prohibition using the kin terms !gun!a and tun. However, this is too strong as all !Kung San outside of the nuclear family will be called by one of the four generational terms. Further, a proper marriage for a female is with a male with whom she uses the !gun!a term.

A possible resolution arises via the simulation. The nature of the !Kung San terminology requires that kin relationships be calculated for offspring as they are born and named since kin relationships cannot be calculated from demographic information on parent/child relationships regardless of how detailed the genealogical information may be. This implies that when a female has a child in the simulation, the relationship of the offspring to at least its close kin needs to be identified, and vice-versa. In effect, the simulation must do what happens culturally; namely, with the birth of a child there is identification via a birth ritual of the fact that a new person has entered the kinship world of the parents and their close kin and the child is given a kinship position to each of these persons, and vice-versa.

This suggests that in the simulation, and with each birth, the person record of the new born person should include a list for each kin term of those persons who are the newborn's close kin. Further, the kin term list for each close kin should be augmented by the new born as a new relative. This permits defining incest as follows.

Simulation Incest Rule: Marriage between ego and alter will be incestuous if alter is in any of the kinship lists of ego, and vice-versa.
Since the purpose of the simulation is to be experimental, it is possible to examine the consequence of this, or even less restrictive, incest rules with respect to the degree of camp exogamy that ensues.

Kin Terms: Implementation

Kinship identification was done as follows. Each person record has a set of linked list person record pointers with one such list for each kin term. The initial cohort begins with no kin relationships. When a offspring is born and named, the "child pointers" for the two parents are updated, and the two parents are added to the newborn's "parent pointers." If the "mother" already has children, their "sibling pointers" are updated and the "sibling pointers" for the newborn are also updated. Next, all kin referred to in the parents' "kin pointer" lists are updated according to the kin term relationship of the newborn to each kind of "kin pointer" and conversely, the newborn's "kin pointers" are updated according to the newborn's relationship computed via the newborn's "mother" and her set of "kin pointers." For example, if she has a pointer to a particular person record in her !gun!a pointer list, a newborn female will be added to that person record's //ga pointer list since the offspring is "female, odd generation" with respect to the !gun!a of a "mother". Conversely, the newborn's tsu pointer list will be updated with a pointer to the person record in question (since the person record in question must be that of a male person and the male person is "odd generation" with respect to the newborn).

!Kung San Naming System: Implementation

Prior to these allocations the newborn is named and, as discussed above, the kin term relationships affected by the name-giving, name-receiver relationship are updated. Naming takes place by selecting a name randomly from names of the appropriate sex that appear in the "kin pointer" lists of the two parents, subject to the rule about the naming of 1st and 2nd born offspring. The !Kung San also restrict using the same name for living offspring and this rule is also applied in the simulation. If there is no available name (such as occurs with the initial cohort and in the first few years of the simulation) then a name is selected randomly from the fixed list of names.

The simulation was run on a 486 PC under Dos 6.2 with some modifications made in the basic procedure outlined above. First, it was discovered--unexpectedly-- that even with the limited calculation of kin term relationships (that is, kin relationships are identified for a newborn only as far out as the kin listed in parents' "kin pointer" lists), the four generational kin term lists became quite long, indicating that the kin term system is very effective in identifying for individuals an extensive kinship network simply through each generation only learning who are the close kin of one's parents, and vice-versa. To keep the lists to a manageable size, only even generation kin pointers were updated since incest, outside of the nuclear family, is expressed in terms of the "even generation" kin. Further, as the concern is with the incidence of in-camp marriages, only even-generation kin in one's camp were added to the kin pointer lists. But even with these limitations the results are striking and unambiguous. Before discussing these results, though, the implementation of camp membership rules needs brief discussion.

Camp Membership

In addition to kin relationships, marriage also affects camp affiliation. Camp affiliation is crucial for access to resources as each camp is associated with a water hole and the resources in the area around the waterhole belong to the members of the camp. Other !Kung San cannot access these resources without first establishing temporary membership in a camp and membership depends upon kin relationships. Camp affiliation also comes to the fore at time of marriage. Upon marriage, the newly married couple will normally live in the bride's camp (with the groom providing bride-service) until the eldest child reaches puberty. Hence the first born child is initially associated with her/his mother's camp. At this time the couple will decide to either remain in the bride's parents' camp, or take up residence in the groom's parents' camp with the basis for the decision unclear in ethnographic accounts, but probably taking into account the relative position of the two camps with respect to resources, among other considerations. If the couple returns to the groom's parents' camp, then all subsequent children will be born in the groom's camp.

Camp residence on a week-to-week basis can be fluid, but camp movement is based on kin or other social relationships. Temporary relocation in other camps is related to spatial variation in resource availability and provides a mechanism to even out seasonal and other variation in resources. Because of the need for first having close relations with someone already in a camp before temporary residence can be established, the degree of camp exogamy that accrues through the incest rules is central to knowing how the !Kung San societal system works itself out in view of stochastic variation in resource availability. In other words, cultural rules about incest have significant pragmatic consequences for intercamp mobility.

For the purposes of the simulation, all couples move to the bride's camp upon marriage and whether or not they return to his natal camp when a child reaches puberty depends upon the current size of the respective camps. This procedure was implemented via the following rule:

The value of 30 is used as camps tend to average about 30 persons.

Since an empty camp would mean that there are unexploited resources, it is further assumed that if her camp > 30 and his camp > 30 and there is an empty camp, then the couple will reside in the empty camp. There are no ethnographic data on "empty camps" as the fluidity of !Kung San society will lead to relocation in camps with abundant resources via kin relationships long before camp membership drops to zero. For purposes of the simulation the initial cohort was distributed equally in 12 camps.

Results: Implications Of Incest Rules

Two questions were addressed with the inclusion of incest rules in Model 3. First, do the incest rules have an effect on the overall, demographic characteristics of the population? Second, what effect do the incest rules have on the proportion of marriages within versus between camps? For the first question, comparison was made between the previous simulations and the simulations that resulted when an incest rule constrained possible marriages. Comparison focused on the overall, qualitative appearance of the simulated populations with respect to stochastic variation through time and changes in the average birth spacing.

Since the parameter values for both the time scale and stabilized population size differ for these simulations from what was the case with the previous simulations involving population size and birth spacing only, a baseline case, without an incest rule constraint, is presented based on Model 3 but using parameter values of K = 300 and t = 600, the values used in all simulations in this section (see Figure 11). The simulation reaches a steady state with a stabilized population in about 200 years.

The results of three simulations are considered, each based on Model 3. All three simulations calculate kinship relationships, determine camp membership and enact marriage according to incest rules. The three simulations differ in the specification of what constitutes incest. In order to test whether or not camp exogamy was the consequence of an incest rule for marriages, the spouse procedure for all simulations in this section searches first within the camp of a female to see if there is an eligible male. If so, that male (or a random choice if more than 1 male is eligible) is selected as spouse. If not, the search is then extended to all other camps to see if an eligible male can be found. If so, that male (or a random choice if more than one male is eligible) is selected as spouse.

In the first simulation, Model 3a, incest excludes male parents, siblings, and children and relatives for whom the term !gun!a is used. In the second simulation, Model 3b, the incest rule is relaxed so that it only excludes ego's genealogically defined 1st and 2nd cousins among all relatives for whom the term !gun!a is used, in accordance with the specification provided by Marshall. The third simulation, Model 3c, relaxes the incest rule further and only excludes parents, parents' siblings, children and siblings. Only one of the demographic comparisons is illustrated (see Figure 12) as the population curves and birth spacing patterns are largely unaffected by the cultural rules on incest. The lack of a qualitative difference in overall demographic effect stems from the fact that the incest rules primarily affect the male to whom a female is married, not the likelihood of her being married and of having offspring. Figure 12 displays the results for Model 3a and it can be seen that the overall pattern is similar to the data presented in Figure 11.

The primary difference among the simulations occurs in the proportion of women who marry exogamously. As can be seen in Table 2,


Incest Type Marriages in Camp/Total Marriages Total Population
Model 3a (!gun!a Incest) 2/91 = 0.02 270
Model 3b (Cousin Incest) 16/67 = 0.24 243
Model 3c (Parental Incest) 22/74 = 0.30 281

in the least restrictive case, Model 3c, where only parent, parents' siblings, siblings and children are incestuous, about 1/3 of the marriages are within camps. Adding cousin incest (1st and 2nd cousins) produces Model 3b and the added incest has a relatively minor additional effect on camp exogamy. With !gun!a incest included (Model 3a), that is incest that includes close relatives for whom a female uses the term !gun!a, there is virtually complete camp exogamy (and in other runs there were either 0 or at most 1 endogamous marriages). Evidently a cultural rule of making close relatives for whom the term !gun!a is used incestuous suffices to create de facto camp exogamy. That there are pragmatic reasons for making camp exogamy efficient with respect to the distribution of persons over resources via camp membership suggests that the cultural rule may be the result of interplay between the kinship system as a cultural phenomenon, on the one hand, and the extent to which redistribution of persons in camps is aided or hindered by culturally specified incest rules.

One unexpected result emerged from the simulation and has to do with the amount of variation in the total number of persons in a camp. The implicit assumption made by some researchers has been that without a mechanism and reason by the !Kung San to limit camp size, camp sizes would follow a pattern different than what is empirically observed. Suggestions have been made, for example, that the empirically realized modal value of about 30 persons per camp is the consequence of fissioning processes driven by increasing rate of conflicts as camp size increases. In this scenario both camp sizes and number of larger camps would be greater than the empirically observed values unless there are countervailing tendencies, and conflict over consensus making in small groups has been suggested as having the effect of keeping camp sizes near the modal value of about 30 persons per camp (Johnson 1983).

From the viewpoint of the simulations, the cultural rule that has been implemented for camp membership limits the locus of change in camp identity primarily to the bride's and the grooms' respective camps7. The limited opportunity within the simulation for change in camp identification would seem to suggest that camp size could vary widely depending upon the reproductive success of a few families.

However, the simulation suggests that accounting for both the empirically observed mean and the variation about the mean does not require appeal to any additional structuring property such as fission due to within camp conflict. Stochastic effects obviously affect the realized camp size, but striking is the consistency between camp size distribution in the simulation and camp size distribution across the !Kung San population. In Figure 13, the output of the three simulations (each with summary values as given in the Table 2) are rank ordered and the rank orderings are graphically compared. It can be seen visually in Figure 13 that the actual distribution of camp sizes is closely paralleled by the simulated data, regardless of the incest rule. In other words, the observed distribution of camp sizes needs no explanation beyond (1) the number of camps8, (2) the population size and (3) a stabilized population size. The lack of relationship between the incest rule and the pattern of camp sizes relates to the fact that camp sizes are determined by demographic parameters and decisions by a couple to remain or not remain in her natal camp, whereas the different incest rules are primarily affecting the kin relatedness of spouses.


The results of the simulations suggest that human social processes are not likely to be well-understood without taking into account the interplay between cultural specification and pragmatic exigency. That interplay can lead to radically different results as indicated in the differences between Model 2 and Model 3. Model 2 assumes, in effect, that women should have as many children as possible -- a viewpoint that has its adherents in the Western world today. Model 2 shows that behavior consistent with such a culturally specified valuation can lead to drastic boom and bust cycles that are maintained by the culturally reinforced behavior. It is intriguing (and initially unexpected) that the severity of the cycles is substantially ameliorated once women in the simulation have feedback between number of infants and realized fertility rate. In effect, as decision making reflects individual circumstances, the synchronous behavior of women becomes decoupled and periodicity is less likely to occur. The decoupling is even more complete in Model 3. Yet, paradoxically, the basis for the decoupling is culturally specified meanings and valuations conformed to by all women in the simulation -- a different kind of synchrony.

The second set of simulations illustrates the way in which culturally specified meanings imposed on empirical phenomena (e.g., culturally defined kinship relations and incestuous marriages) has a dynamic affected by individual decision making but then produces consequences at a global level that also determines the range of possibilities for individual decision making. That is, the kinship terminological system constructs for the individual !Kung San a kinship world (the global level) within which all social activity takes place. Individuals know where they are located in terms of kinship relations they have to other !Kung San. At the same time the overall structure of kin relations in which they find themselves embedded is a consequence of a myriad of decisions made in terms of locally important pragmatic exigencies (such as: Which one of our relatives shall be the name giver for our newborn child?) that have had globally important structural implications for individual decision making, Individual decision making, such as the decision to remain or not remain in the bride's camp when the first child reaches puberty, is embedded in, and affected by, this constructed universe of kin relations -- that is, the kinship networks that link the !Kung San and constrain the range of possible decisions.

By culturally making the close relatives for whom a female ego uses the term !gun!a incestuous, !Kung San marriages become exogamous with respect to the camp, thereby creating a new set of possibilities (camps linked via marriages) for solving the pragmatic problem of balancing numbers of persons against available resources. The cultural specification of incest works in this manner because the nature of the terminology happens to ensure that camp members are tightly intertwined via kin relationships even if their genealogical linkages are much looser. The way in which the terminological system links sets of relatives in a camp is illustrated by the results of the simulation. Figure 14 presents the personnel of one of the 12 camps produced through the simulation and the genealogical relationships of the persons in the camp. Even though the simulation begins with unrelated individuals and relocation with respect to camps is primarily by grooms taking up residence with their brides (since the total population size in the simulation ensures that on the average most camps will have fewer than 30 persons), a camp becomes a highly interconnected set of individuals at the level of kinship even though, in this example, the camp is composed of four genealogically distinct "extended families." The !gun!a and tun kin relationships are identified for just one women in Figure 14. From these it can be seen that she is tightly interwoven with all families through her kinship relationships even where no genealogical connections are apparent.

This paper has been motivated by using simulation as a way to explore the interplay between culture and behavior, between shared meaning and individually based pragmatic decisions. Cultural knowledge has been explicitly made part of the modeling process in order to consider not only the consequences of behavior directed by cultural specification, but to explore what would happen under alternative scenarios such as a less inclusive incest rule. The results obtained here suggest that explicit embedding of cultural concepts is both fruitful and necessary. However, change in the simulation is exogenous to the simulation and produced by the researcher changing parameter values or rewriting computer code, not by means of the "actors" in the simulation restructuring the simulated system in accordance with individual and collective interests. The dynamics of the latter is what we understand poorly but what we want ultimately to understand and this will require more than making models more sophisticated. It will require new approaches to modeling, what we are calling "artificial culture" (Read and Gessler 1996} and aimed at understanding the interplay among mind, environment and society.


* Notes

1Similar comments about the difficulty of providing enough food for a family have been elicited from other hunter/gatherer groups. For example, with reference to groups in South Australia, Tiechelmann writes: "A mother who had already killed two of her children said -- "how could I accompany my husband, and how could I supply food enough were I to bring up so many children?" (Tiechelmann 1841: 13) quoted in (Hayden 1972: 213).

2The relationship between months of breast feeding and months of amenorrhea is well-illustrated by worldwide data on women from 21 countries provided by (Bongaarts and Potter 1983). Their data are well fit by a second degree polynomial that implies an almost 1-1 equivalence between months of breast feeding and months of amenorrhea when breast feeding extends beyond about 30 months.

3Intensification of foraging and hunting can lead to degradation of resource availability. Habitat productivity, except for a few examples such as the use of fire to create more open country habitat, is not augmented via intensification of foraging and hunting procedures as can occur with agricultural production and intensification.

4It should be noted that, as demonstrated in the simulations, an average spacing of 4 years will arise when a population with a mortality schedule and actual reproductive period for women comparable to that of the !Kung San has a zero net growth rate, regardless of the factors affecting the spacing of offspring. This follows from the fact that the average spacing of offspring that must occur in order to maintain a zero net growth rate is determined by the mortality schedule and the length of the actual reproductive period. Thus the average birth spacing can be treated as responding to adaptive pressures only if it is assumed there are no factors driving the population size to an equilibrium value.

5While Howell (1976: 147) has argued that !Kung San women do not control their fertility artificially through means such as herbal teas, this does not rule out the possibility that !Kung San women can affect time of next pregnancy through a decision to continue or terminate breast-feeding. The strong evidence for the role of breast-feeding, particularly as practiced by !Kung San women, in post-partum amenorrhea along with the keen awareness of hunting and gathering groups about the biological world make it unlikely that they are unaware of the role of breast-feeding in producing temporary fecundity reduction. Such awareness may be mediated culturally in terms of how it is expressed; e.g., the quote presented above regarding the need to nurse for 3 to 4 years to ensure strong legs

6Gage et al. noted correctly that lactational amenorrhea, by itself, does not regulate population growth. They further argued that no link between lactational amenorrhea and a nonconservative factor (i.e., an extrinsic factor whose quantity varies with population density) had been established by those that proposed not only the existence of lactational amenorrhea but lactational amenorrhea as a causative mechanism in population regulation.

7In reality, other kin relations such as sibling relations are also used to justify camp membership.

8The number of camps relates to the number of permanent waterholes.


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