Computationally Modelling the Human Carrying Capacity of Neolithic and Bronze Age
Wessex
Harry R. Erwin, PhD
School of Computing and Technology
University of Sunderland
Requirements:
“Carrying capacity” (K) can be defined in many ways. For example in ecology, it has been defined as the equilibrium population size of a species that can be supported by a region. In
anthropology, it has been defined as the maximum human population that the region can support without progressive degradation (Dewar 1984) (Zubrow 1975). These definitions are
somewhat simple, ignoring the possibility that there may be no equilibrium—the population can cycle or even vary chaotically, and that the environment may be modified by the species
to increase or reduce the population that it can support. Moore (1983) suggests that periodic famines and other processes (“minima”, e.g., fluctuations of the weather) influence human
survivability and so set K, and discusses two further objections: K being set based on “minima” requires some criterion for the time interval between, and the fact that humans seem frequently to use biologically arbitrary cultural criteria to set K. Finally, technological change affects the human population that can be supported in an area. These issues make reaching a simple definition of carrying capacity difficult, and this study does not attempt that. Rather, it uses modelling techniques to explore the dynamics of a prehistoric human population.
The primary interest of this study is to explore how the variation in assumptions might influence the population dynamics that the model produces. The parameters to be input by the user will include initial age distribution of the population, the model of food productivity per person as a function of the weather and other processes (but not in the detail seen in Zubrow (1975)), a model of mortality by year class, children produced per woman, and
assumptions about internal exchange of resources. The simulation uses a time step of one month, runs for a user-defined period, and reports the age distribution of the population yearly in a form suitable as input to a spreadsheet for analysis or graphing. Food distribution in modelled in one of two ways:
1. Fixed production per person (no density-dependent effects),
2. Fixed total production with egalitarian distribution (everyone goes without if someone goes without), Note that this produces excess mortality of children during famine.
Food production is modelled as the sum of:
1. Constant production (per person or total)
2. Randomly varying production (per person or total) with a normal distribution
3. Cyclically varying production (per person or total)
The age distribution is input as an initial male and female population count for each age between 0 and 80. The mortality model incorporates background mortality based on Coale
and Demeny’s Western Region life tables (1983), following McCaa (1998) and additional mortality due to malnutrition (Collins, Myatt et al. 1998) (Sear). The childbirth model includes a nominal rate of 0.25 pregnancies per month modified by BMI, age, and current status. The age-related effect is a reduction of 50% between ages 25 and 35, and another 50% between 35 and 39. The effect of BMI is modelled as linear between 17.5 (no fertility) and
19.0 (full fertility). McCaa (1998) makes some interesting points about paleodemography that are used in this model. He indicates the dominant factor in defining the age distribution for a stable population (and likely the age distribution of burials) is fertility (GRR), not mortality, and that is likely to be culturally controlled. Since GRR is defined a posteriori, rather than a priori, the model instead uses a desired GRR, representing a cultural standard
and implemented as the delay until weaning of an infant. If an infant dies prior to the end of the interval, the mother immediately becomes fertile again. Finally, the expected lifespan at
birth is set to 20 years, as variation there does not affect the results markedly.
Differences in the mortality of the sexes have to be modelled, as otherwise the lower BMI of females makes them more vulnerable to malnutrition. A mortality ratio of about 3 after puberty balances this.
Individual persons, not couples, are modelled. Significant parameters include BMI, age, sex, and dependent children (for mothers). The model does not reflect the variation in BMI and
other parameters found in the real population, producing years where all children of a given age die of malnutrition. Fertility is computed from current status, age and BMI. BMI is modelled as dependent on age and sex (NCHS 2000), and adjusted for nutritional status.
Nutritional status is modelled as a fraction of the full diet needed by each age/sex combination to avoid malnutrition. A pregnant or lactating woman is treated as requiring 2700 kcal/day and an adult man, 3000. Adult women otherwise require 2200 kcal/day, and
children 1000 + 100*age kcal/day.
A random number seed is input so that simulation runs are repeatable. Java 5.0 is used as the programming language so that the model can run on any computer.
Design and Methods:
Each year is modelled by stepping through twelve months. The year starts in April, at which point the food production for the year is computed and the level of malnutrition. Food requirements will be defined in terms of caloric intake—protein, fats, and other dietary components are not modelled separately.
Results:
1. The first series of scenarios investigate non-population-density-limited systems well below the carrying capacity of the region. GRR is set to 2, corresponding to a pregnancy interval of 3 years. The principal factor in determining whether the population is sustainable is whether or not there is enough food to allow the children to grow to adulthood, and the key parameter is the fraction of the full diet available.
Population grows with a constant 0.9 diet and falls for 0.85. When periodic variation in the food available over four years is introduced, with a mean availability of 1.0 and a minimum of 0.8 times, it results in slow population decline, and a minimum of 0.85
results in rapid population growth. When random variation is introduced, a standard deviation of about 0.15 is tolerable, and 0.2 is too great.
2. The second series of scenarios introduce population limits the population by introducing malnutrition. A constant availability of food for 3000 adult males, results after 100 years in a population of about 4400 with a standard deviation of about 200.
There appears to be a cyclic malnutrition cycle in the data. 10% periodic variation in the food available results in a population mean of about 4300, but with a standard deviation of almost 600. With 20% variation, the female population tends to outnumber the male population. The population mean becomes about 3650, with a standard deviation of about 560. For random variation, a standard deviation of 0.15 results in a mean of about 3930 and a standard deviation of 750. For a standard deviation of 0.2, the system becomes unstable and dies out.
3. The final series of scenarios investigate changing the interval between children. GRR is now set to 6, corresponding to a pregnancy interval of a year. In all cases, the
results are very similar to the previous results.
Discussion:
The implications are interesting. First, the relative vulnerability of various segments of the population to malnutrition results in unexpected population structures. The male population, being relatively protected from starvation, dominates unless social factors produce relatively higher death rates. Second, periodic variation in food supplies results in lower mean populations and much greater variation. Random variation in the food supply is very important. It is tolerable up about 15%, but at 20%, the population tends to grow too much and then starve. Since records of agricultural production show a variability that exceeds those
values, it suggests that population control measures should be important. Monument construction is the sort of optional activity that can take place during good years to reduce the surplus that would otherwise fuel unsustainable population growth. It is also clear that the male population has to be managed to maintain a balance with the female population and prevent excessive population growth.
Conclusions:
The model is very simple and yet calibration already exceeds the data available. Further development is likely to be useful in identifying the factors that have to be considered in understanding Neolithic and Early Bronze Age societies.
References Cited:
Coale, A. and P. Demeny (1983). Regional Model Life Tables and Stable Populations. New
York, Academic Press.
Collins, S., M. Myatt, et al. (1998). "Dietary treatment of severe malnutrition in adults."
American Journal of Clinical Nutrition 68: 193-199.
Dewar, R. E. (1984). "Environmental Productivity, Population Regulation, and Carrying
Capacity." American Anthropologist 86(3): 601-614.
McCaa, R. (1998). Calibrating Paleodemography: The Uniformitarian Challenge Turned.
American Association of Physical Anthropology Annual Meeting.
Moore, J. (1983). "Carrying capacity, cycles and culture." Journal of Human Evolution 12:
505-514.
NCHS (2000). Body mass index-for-age percentiles. 2005.
Sear, R. Size, body condition and adult mortality in rural Gambia: a life history perspective.
Zubrow, E. B. W. (1975). Prehistoric Carrying Capacity: a Model. Menlo Park, CA,
Cummings Publishing Company.
