James Dow. 1976. Systems models of cultural ecology.

People can often sense a super intelligence in cultures. They evolve successfully to adapt people to different changing environments. They "know" how to provide basic psychological and physical necessities. They respond to crises. They are symbolized by religion They evoke powerful sentiments. They have been pictured as having an ethos and eidos. They don't exist apart from people, but their operation as systems often defies the precise understanding of the people who operate them. From one point of view they can be tyrannies over man (Henry. 1963. p. 12), but they are also his salvation and the reason for his survival.

Cultures encode information in tools and in symbols. To change its adaptation to the natural environment a culture must change the ways in which its technologies respond to tools and the way in which people respond to symbols. In general terms, the flow of information must be altered to produce a structural change in the way in which energy is processed. New technologies alter the flow of tools. New ideologies and social structures alter the flow of symbols. Philosophical and religious belief systems can set up channels for the flow of information, so religion as it is passed from generation to generation tends to encode the adaptive structure of a culture as DNA encodes the genetic signals of a species.

This paper discusses a method of building mathematical models [End of Page 953] of information and energy flows within particular culture in order to describe and analyze this adaptation more precisely. Beside describing the adaptive systems in detail, these models allow an examination of their dynamic behavior by means of computer simulation and mathematical analysis. The method does not take a wholly ecological view of culture as a means of relating man to the material world nor a wholly culturological view of culture as a system of symbols, but it endeavors to combine these two views in a systems concept of culture that includes the ecological processing of energy and the culturological structuring of information. It proposes that a culture is a mechanism for processing energy and materials in which control is effected by humanly interpreted information coded in symbols and tools.¹ It follows Roger Keesing's suggestion that the ideational conception of culture be embedded in the real social and ecological world (1974. p 93), but it does not agree with his pessimism that the possibility of analyzing a cultural system in any complete sense is far on the horizon (1974, p. 92); rather, it makes the bold suggestion that the possibility of analyzing cultures as adaptive systems will be within our grasp in the near future.

ENERGY AND INFORMATION IN CULTURAL SYSTEMS

The idea of the superorganic nature of culture put forth by Spencer (1898. pp. 1-7) was developed in relation to anthropology by Kroeber (1917). It pictures culture as a system whose organization transcends that of any one of its components, individual persons, and therefore as a kind of superorganism that has an evolving life of its own. A direct analogy between cultures and living organisms is a facile one to make (Spencer. 1898, pp. 449-462; Radcliffe-Brown, 1952, pp. 179-181). However. differences in changeability and adaptability have been noted, and few deep thinkers have been lured into the trap of making too close an analogy. A significant difference between a living organism and a culture is that in a living organism the components, organs, are in physical contact whereas in a culture the components, composed in some way of people, are seldom in physical contact (Spencer. 1898, p. 457). Thus it has often been proposed that all the links between the components of socio-cultural systems are symbolic communication links.

This is a view of society as a pure control system in which the links are symbolic messages transmitted between the components. However such systems analogs of society suffer two major drawbacks. 1) they are of little practical value to empirical science because their great complexity makes the network mathematics practically unworkable, and 2) they cannot deal with adaptive evolution because they pay scant attention to the material world that is relevant to survival.

Although some sociologists and anthropologists influenced by non-materialistic sociology, cybernetics, and information theory, feel that the links of cultural systems are symbolic messages (Rose, l970) quite a different view of cultural systems is held by ecological anthropologists (e.g. Rappaport, 1967) and cultural materialists (e.g. Harris, 1974) who feel that the functioning of a culture has something to do with its ability to adapt human populations to different environments. Modern ecologists have conceptualized ecosystems as systems for the transfer and control of energy, trophic exchange (Woodwell,1971), and anthropologists feel that these ecosystem concepts should be extended to cultural systems (Anderson, 1973, pp. 183-184). If ecology has shown that animals adapt and survive by extracting energy from their environments, and if one accepts culture as man's means of adaptation, then one can hardly avoid the conclusion that culture must also include systems for the management and control of energy (White, 1959, p. 33). The component interactions of a model explaining the adaptation and evolution of culture cannot be made up solely of information signals alone.

An adequate cultural model should combine flows of information with flows of energy. The proposed modeling method takes its energy ideas from Howard Odum (1971) and adds information flows to arrive at a systems concept of culture. It follows the principles of formalist-deductive theory discussed by Schneider (1974, pp. 24-42) and aims at accomplishing something that is close to what Julian Steward called for in his method of cultural ecology (1955, 1968), a discovery of the mechanism by which a particular culture adapts to its particular environment.

THE CONSTRUCTION OF FLOW DIAGRAMS

In the method, a cultural system is represented graphically by a flow diagram. Energy and material flows are shown by solid lines, information flows, by dashed lines. Material flows can be measured in terms of the energy they carry and then regarded as energy flows in this case, the energy is evaluated as the potential energy that might be [End of Page 955] utilized by the receiver in the culture. For example, the energy of a fossil fuel is evaluated as the heat energy from 100 % efficient combustion, not as the nuclear binding energy which might be used in a thermonuclear reactor, if such a thing existed. Flow lines meet at the components of the system. Flows with a common measure can also meet at other points where they combine in an additive way. Thus the system is represented as a network of components and connections. Energy and materials enter and leave the system only at special locations otherwise their flow is conserved. Thus mathematical relationships between the system variables can be specified.

The components in the diagrams are : 1) sources (Figure 1a), 2) sinks (Figure 1b ), 3) storages (Figure 1c), 4) populations (Figure 1d), and 5) gates (Figure 1e).

1) Sources are places in the environment from which energy and materials flow. Energy sources are primarily living ecosystems and fossil fuels. Materials sources are primarily living ecosystems and mineral deposits.

2) Sinks are places where energy or materials are lost to the cultural system. Sinks in cultural systems differ from heat sinks in ecological energy systems (Odum, 1971, p. 42) in that a sink in a cultural system may absorb potential energy that is unrecoverable by the culture, so one culture might be able to recover energy that would be lost to another culture. For instance heat produced by electrical generation is now lost in industrial cultures, but it might be recovered by another industrial culture if new techniques were used. The nutrients in bones and gristle not eaten by hunters and gathers may or may not be recovered by assistant dog populations in the cultural system. Refuse in peasant culture. may or may not be recycled into food producing fields. Thus entropy in cultural systems is culturally relative.

3) In storages some of the excess of input over output is accumulated and can be recovered when output exceeds input. Living animal and plant populations may be storages, such as when a culture stores plant energy in the form of domestic animals. Rappaport has shown that energy storage in pigs, as in most domestic animals, involves considerable losses (1967, p. 62), however the advantage to man is in the upgraded protein of the animal food. In general as energy and materials move through cultural systems and are stored, they undergo costly transformation that make them useful to man.

4) Populations are the living components of cultural systems. The human population components represent aggregations of human beings as the consumers of food energy, as the producers of work, and as the processors of information ; however, it is important to understand that the effects of human action are felt in other components of [End of Page 956]

Fig. 1. Elements used in constructing cultural systems models

the model as well. For instance humans interpret the information flowing into symbolic gates and operate the technologies represented by the technological amplifiers to be discussed below.

5) Gates are the places at which flows of energy, materials and information are regulated by other control inputs². The regulated flow through gates is conserved. When a control input to a gate is destroyed while doing switching, the output of the control flow to a sink is sometimes not shown in the diagram.

A technological amplifier is a gate at which a flow of energy or materials is regulated by another input of materials in the form of special tools plus an input of work, useful energy provided by humans, animals,or machines.

A symbolic gate is a gate at which a flow is regulated by an input of information. Symbolic gates are means for controlling relatively large flows of energy and materials with coded signals, information, that drain the resources of the culture very little. Information flows are indicated by dashed lines in the system diagram. Humans provide the means by which such signals are interpreted at symbolic gates.

Information in a cultural system is an energy or material flow that is able to influence a much greater energy or material flow. If information is contained in time-coded energy, such as in speech, the energy flow of the information is usually negligible in the overall energy flow of the cultural system. If the information is contained in specially structured materials, such as money, prestige objects, or religious objects, the culture usually provides for the conservation of the materials involved. Symbolic gates are similar to Forester's decision functions (1961. pp.61, 103-108).

APPLICATION OF THE MODELING TECHNIQUE TO PARTICULAR CULTURES

The modeling technique can be integrated and explained more fully by showing now it is applied to the data with which cultural anthropologists work.

Figure 2 is a simple hypothetical model of a band culture. Humans perform work at a rate w to extract food energy at a rate f from the natural environment. Their normal living requires a loss of energy at a rate m over what they put into their subsistence efforts. Since there is an upper limit, w_u, to the rate of useful work comfortably performed by people in this culture, the amplification ratio

cannot fall below

without producing a famine. The ratio

in the gate can be affected from [End of Page 958]

the human side by an input of technology, but it is also affected from the natural side by the density of huntable and gatherable resources within the area of the band. To advance our ability to understand this problem, a more expanded disaggregated model is needed.

Figure 3 shows a disaggregated model which takes into account that the band actually draws its food energy from finite animal and plant populations. The resources exploited by the band are energies stored in living populations which replenish themselves at a given rate. If the band withdraws those resources faster than they are replenished, they will dwindle and become harder to obtain. In the analysis of this situation the anthropocentric energy stored in the plants used by the band is labeled E_pm and the anthropocentric energy stored in the animal populations exploited by the band is labeled E_am. The stored plant energy from which these animals feed is labeled E_pa. In the model, the flows of energy are treated as if they are opposed by forces that tend to resist them in a way proportional to the magnitude of the storages (Odum. 1971,p. 43). Borrowing terminology from electrical engineering, one can call the ratio of the flow to the amount of storage the conductivity L of the connection,

. The conductivity of ordinary connections is fixed, but the conductivity of a connection through a gate is a function of the control input to the gate. For example L_p(w_p) = c_p w_p in the diagram. Thus f_pm = E_pm L_p(wp) . When technology is fixed and tools are sufficient, the conductivity of the gate tends to be a constant multiple of the human work applied :

How much work does a band have to put into gathering in order to withdraw resources at a constant rate if these resources are not replenished at all, a situation that occurs from time to time during [End of Page 959]

the dry season in the Kalahari Desert for example (Thomas, 1959, p. 105) ? Assume that the foods used by the band are seed or storage roots that do not have metabolic losses. Then the law of conservation of energy in the plant population dictates that

Since the withdrawal rate is constant in this hypothetical situation, the supply of energy decreases at a constant rate, and the solution to equation (2) is

This situation is shown graphically in Figure 4. The gatherable resources, E_pm, reach 0 at a time designated as t_z. The human work required to extract the energy at a constant rate, approximating that required to feed a fixed population of persons. is given by the following equation derived from equation (1).

As E_pm approaches zero w_p heads toward infinity as shown in Figure 5. The critical point for the band is reached, of course, as w_p approaches w_u, an upper limit of useful work that the people of the band can put into collecting. This is the point at which the band must change its location or suffer famine.

The same reasoning can be applied to the hunting gate, but different parameters will be involved. With hunting in the picture, w_p + w_a will have to be below some new w_u representing the maximum amount of subsistence work the band can produce. Depending [End of Page 961] on the kind of protein being eaten, limits on the ratio of plant to animal resources may have to be incorporated in the model too.

A simple case of linear decrease of E_pm has just been assumed in an effort to simplify the mathematical relationships in the model. More realistically the cost of supporting people, f_mz, is the constant factor. The effort required to find food and consequently the food requirements of the band increase as the animals and plants become scarcer. A complete solution of the model in Figure 3 should take this into account.

As the model is made more accurate it should also incorporate information about how the group allocates efforts either to hunting or to gathering. A hypothetical optimizing hypothesis about group decision making that could be tested by a cultural systems model is that the members of the band will exploit the resource that gives them the most return for their labor. When this hypothesis is built into the model it produces a convergence of the efficiencies in the work gates. Such a convergence can be expressed mathematically as

By means of mathematical reasoning, which is not given here, it can be proven that this optimization of work pushes the ratio of energies stored in the non-replenishing environmental populations into the following ratio.

Thus the work effort over time is a solution of the following non- linear differential equation.

This gives a better idea of what happens to a hunting and gathering band when it exploits diminishing resources. Work effort can rapidly increase, as shown by the differential equation, and probably provide a clear indicator for decisions to change location. Much more can be learned about the dynamics of such cultural systems when [End of Page 962] real parameters are used in the model and exact solutions of the differential equations are carried out.

So far neither band model inductively incorporates decision-making data. Probably no human decision-making system can maintain a population indefinitely without causing degradation of the environment. One deals realistically with decision-making systems that maintain populations at certain per capita energy inputs for significant periods of time and that have capacities for internal systems modification when faced with the effects of environmental degradation. Actually decisions are made in most bands to alter human activities in such a way as to capture the required amount of energy. Simple models cannot always explain the complexities of how a band keeps the input of energy per capita up to the minimum required to sustain the population. A lot depends on the rate of growth of the different animal and plant populations on which the band depends. If they accumulate anthropocentric energy from the natural ecosystems sufficiently fast, the model in Figure 3 would be an adaptive one in which the output of human energy to the hunting and gathering gates would be governed by the food needs of the members of the band. However one might also be interested in how the nomadic behavior of a band. affected its survival. In that case a model like the one shown in Figure 6 would be more realistic.

The hypothetical model in Figure 6 includes an information flow from the resource populations to the human population and from the human population to the symbolic gates that regulate the amount of work that is put into the exploitation of particular resources. Bands generally exploit all the plant foods they know in a given area and then move on to another area. Therefore the symbolic gate S_p in Figure 6 is shown as a switch that selects which area is going to be gathered. These switching decisions must be made so as to keep f_am + f_pm above the minimum required to support the group and to keep w_p + w_a below w_u. One optimizing strategy is to minimize w_p + w_a while holding f_am + f_pm constant at a convenient level.

It is obviously important to understand how information is used by people of the band to determine what resources will be gathered. A field study can provide the logic used in the gate S_p, either in terms of continuous mathematical functions or in terms of symbolic logic, and this knowledge can be made part of the model. Ethno-ecology and decision-making put into symbolic or mathematical terms improves the cultural systems model so that it generates more realistic predictions about the behavior of the system. The determinacy of models increases as one is able to shunt information circuits around human populations (Figure 7). [End of Page 963]

Cultural systems models are also useful in examining the consequences of certain hypothetical strategies that might be employed by people. The consequences may give indication of why such strategies are, or are not used in the present when a clear memory of past trials may be lost to the modern members of a group.

There is a much larger use for symbolic gates than has been shown so far. Institutions in which money serves as a symbolic control are an important class of such gates in peasant and industrial cultures. The difference between a money regulated market gate and a barter gate is illustrated in Figure 8. When the price is fixed in a market gate, money flows in a constant ratio to materials. [End of Page 965]

More often price responds to storage build-ups of product and money. Figure 9 shows a more sophisticated model of market exchange in which money increases the conductivity of materials. The following equations describe the behavior of the examples in Figure 9.

This produces the following price for fish which can be deduced mathematically. [End of Page 966]

This relationship is more clearly illustrated by the graphs in Figure 10, which show properties similar to what one might expect from a real market. Figure 10a illustrates that the price is inversely proportional to the supply of fish and Figure 10b illustrates that it goes up with the ratio of money to work, a kind of return of labor. This model, however, is still too simple to predict the systems dynamic behavior including a stabilization point for the price. [End of Page 967]

A more elaborate model that can do this is shown in Figure 11, and the equations describing its dynamics are listed in Table 1. The solutions to these first-order non-linear differential equations could most easily be found by means of an analog or digital computer. It is not known under what conditions these particular equations are solvable or what stability properties the solutions have, but mathematicians have been studying such equations, and a framework exists for dealing with these equations (Stern. 1965. p.214, pp. 307-320). [End of Page 968]

These models naturally include economic systems and so provide a type of formal theory of economic processes that need not be tied to money or market mechanisms. They have the potential to describe mixed economies that are neither fully monetized market economies nor isolated tribal economies.

Technological amplifiers are important components of cultural systems. By means of tools man is able to control large flows of energy and materials with small inputs of human work. A technological amplifier is a type of gate that requires an input of special tools in order to amplify an input of work. For example. the gate L_f in Figure 9 is a technological amplifier requiring some sort of in-put of fishing tools like nets, boats, or traps. Cultural systems models can assume that dynamic processes start with an established tool kit at each technological amplifier. The tools have to be supplied now at a certain rate to allow the amplification of human work to take place. If new tools are not supplied, the technological process eventually breaks down because the old tools wear out. If the tools are supplied at an inadequate rate, they limit the amplification of human work. Full amplification will take place if the tools are supplied at a rate above a critical rate. But if the tools are over-supplied, little further amplification takes place. [End of Page 969]

Real technological amplifiers tend to have self-regulating mechanisms that keep the tool input at a level sufficient to maintain the highest amplification but not exceeding that level. Figure 12 is a symbolic representation of such a technological amplifier. When it is operating in a steady state. r₁ equals aw, and the amplification factor is constant at cu. The loss of energy or materials to a sink through flow f_z is a result of the inefficiency of the technological process. In general the ratio of f_z to f_i is constant, but it can change as a result of technological innovation.

EMPIRICAL VALIDATION OF MODELS

The hypotheses generated by this method are models of cultural systems. A means of testing these models is required if the method is to contribute to empirical theory. Most types of cultural systems have been studied well enough to allow preliminary models to be suggested. In the process of developing better models it is important to know what flows to ignore and what degrees of aggregation to use in order to make models valid yet not too complicated. The following steps are suggestions for dealing with the problem of developing simple yet empirically accurate cultural systems models.

1) Isolate human populations with similar materials and energy processing functions.

2) Identify human sub-populations that have theoretical interest.

3) Decide what part of the total surrounding environment is influenced by, and influences, the actions of these populations, and regard the rest of the total surrounding environment as outside the cultural system. [End of Page 971]

4) Isolate the sources of materials and energy.

5) Follow the flows of materials and energy.

6) Look for the points where human action affects these flows.

7) Take note of the effect of symbolic systems on these materials and energy flows.

8) Conceptualize the flows of energy, materials, and information in the terms that have been outlined. Logically build or modify systems components to fit what exists in the data.

9) Make sure that flows of energy and materials are being followed until they leave the system.

10) Eliminate elements and flows that are too small to affect the dynamics of the system.

11) Eliminate elements and flows that do not affect the dynamics of the variables in which there is an interest.

After the framework of a model has been laid out, it should be operationalized and tested. Materials flows are measured in units of mass over time. Energy flows are measured in units of power. The response characteristics of gates are measured by comparing inputs and outputs at different times. How people change their behavior in response to symbols needs to be formalized and quantified. In cases where it is practically impossible to measure a flow, the model should be changed to make it more operational.

Testing a model begins with small components, proceeds to small sub-systems, and terminates, if possible, with the whole cultural system. Small sub-systems should be isolated. and their dynamics should be compared with the dynamics predicted by the subsystem model. Finally the dynamic behavior of the whole model, or of large parts of it, should be analyzed by mathematics, numerical methods, or computer simulation and compared with the culture as it responds to different circumstances. The method of validating models is an iterative, back-to-the-drawing-board method. Whenever a prediction by the model is not congruent with the data, one should go back several steps to change the model. One starts with operationalizing and testing the smallest components of the model and proceeds to larger and larger sub-systems. If the complexity of the model gets out of hand, one should simplify it or content ones self with accurate sub-systems models.

There is no true model of a culture except the culture itself as played out in the daily lives of people. Models can only be evaluated as better or worse at predicting the behavior of certain variables over certain periods of time. A model good for one purpose may not be good for another. [End of Page 972]

What has been described in this paper is merely a method, an approach to the study of cultural systems. It is not a solution to a single problem in cultural anthropology. The value of this method at the moment is not that it solves a problem but that it points the way toward a possible solution of innumerable problems. It is a positivistic reaction against the mystical fatalism that we may never be able to understand in any detail how a cultural system really works. It shows how one can conceptualize particular adaptive cultural systems and work with the logical outcomes of these conceptions until they can be made into adequate useful analogs of empirically real phenomena.

James Dow (born 1934). Assistant Professor of Anthropology at Oakland University, Rochester (Mich.), USA. is presently engaged in research on peasant societies and mathematical models in anthropology. Recent publications : Peasant livelihood Studies in economic anthropology and cultural ecology (1976) (coedited with R. Halperin); The Otomí of the Northern Sierra de Puebla (1975); "A mathematical model of lineage evolution". Social science information 14 (5). 1975. [End of Page 973]

NOTES

1. The pre-theoretical Stance of this paper is opposed to the popular social-science philosophy of methodological individualism, the debate over which has been succinctly summarized by Jarvie (1972, pp. 173-178). Methodological individualism asserts that explanation in the social sciences should be based on models of individual behavior. Methodological individualists, if they will allow themselves to be called by that name, rightly point out that one cannot impute attitudes, behavioral tendencies, expectations, or rationality to entities other than individuals. By asserting that explanations of cultural and social phenomena should be framed in terms of the dynamic properties of the cultural system as a whole, this paper sets forth a type of systemic holism that is opposed to methodological individualism. Yet, because the dynamic structure of a cultural system is determined by the behavioral predispositions of individuals, this holistic form of explanation is not independent of individuals. This systemic holism merely asserts that the explanation of cultural adaptation and evolution requires, above and beyond the knowledge of how individuals behave, the knowledge of how the different behaviors of individuals combine in patterns of which individuals are largely unaware, or, at most, which are perceived by them in subjective or mystical ways. Although there may exist an intersubjective cultural consciousness of cultural dynamics, this paper adopts the position that this intersubjective consciousness when analyzed by the social scientist is inadequate to explain scientifically the adaptation and evolution of a culture. The systemic holism of this paper maintains that such an explanation requires a precise mathematical analysis of how the System works.

2. Analog computer terminology is used in the field of ecological system modeling, and for the time being it seems advisable to continue it here. Although analog computers can be used in cultural systems modeling, general systems theory has been developing autonomously (Bertalanffy, 1972), and the use of this terminology is not meant to suggest that electrical engineering has any particular relevance to anthropology.

BIBLIOGRAPHY

1973 "Ecological anthropology and anthropological ecology". pp. 179-239 in J. J. Honigman (ed.). Handbook of social and cultural anthropology. Chicago, Ill., Rand McNally. [End of Page 974]

1972 "The history and Status of general Systems theory",pp. 21-41 in : G. J. Klir (ed.). Trends in general systems theory. New York, Wiley.

1974 Cows. pigs. wars, and witches The riddles of culture. New York, Random House.

1974 "Theories of culture", pp. 73-97 in Annual review of anthropology, vol. 3. Palo Alto, Calif., Annual Reviews.

1967 Pigs for the ancestors : Ritual in the ecology of a New Guinea people. New Haven, Conn., Yale University Press.

1970 The cybernetics of evolving Systems, vol. 3. New York, Gordon Beach Science Publishers.

1965 Theory of nonlinear networks and systems. Reading, Mass., Addison-Wesley. [End of Page 975]

1968 "Cultural ecology", pp. 337-344 in : International encyclopedia of the social sciences, vol. 4. New York, Macmillan.

1970 "The energy cycle of the biosphere", pp. 26-36 in The biosphere. San Francisco, Calif., Freeman.

JAMES DOW

Systems models of cultural ecology

INTRODUCTION