Autocatalysis in cultural ecology: model ecosystems and the dynamics of biocultural evolution

BioSystems, 17 (19~15) 259--272

259

Elsevier Scientific Publishers Ireland Ltd.

AUTOCATALYSIS IN C U L T U R A L ECOLOGY: MODEL ECOSYSTEMS AND THE DYNAMICS OF ]3IOCULTURAL E V O L U T I O N

GEBHARD GEIGER Max-Pianck-Institut fiir Physik und Astrophysik, Institut fiir Astrophysik, Karl-Schwarzschild-Strasse 1, 8046 Garching (F.R.G.)

(Received March 12Lh, 1984) (Revision received J'aly 12th, 1984) Using a well-known mathematical model frequently applied in theoretical population dynamics, certain ecological mechanisms are investigated that are inherent in the organic evolution of cultural capacities in man. Culture is argued to, involve ecological interactions exhibiting analogies to the interaction of chemical species in autocatalytic biomc4ecular reactions. In the model, biocultural evolution proceeds by more and more broadening ecological niches and, thus, releasing competitive selection pressure on the populations involved. This, in turn, facilitates the maintenance of polymorphism in these populations as well as the individual acquisition of organic traits through learn!ing and cultural transmission. The result is that the genetic variance in phenotypic expressions decreases at an acce]Leratedrate. Keywords: Autocatalysis, Cultural ecology; Biocultural coevolution; Population dynamics.

Introduction Among the many intricate theoretical questions posed by evolutionary biology, one is c o n f r o n t e d with t he problem of how to explain the capacities of h u m a n self-organization in evolutionary terms. It is widely accepted t o d a y among the scientific comm u n i t y t h a t these capacities, which are usually referred ~o as " c u l t u r e " , have evolved from less c o m p l e x organic systems by the same processes as any other form of life, namely, by th e r an dom creation o f genetic variation and natural selection. On t he ot her hand, the e x t r e m e variety of phenot ypi cal l y distinct forms o f h um an existence leave it difficult to trace the phyletic pathways of h u m a n cultural capacities back t o the preh u m a n forms of life. Some theorists even c o n t e n d that the h um an phyl ogeny can be described best ~ a sequence of abr upt evolutionary changes (Gould and Eldredge, 1977; Eldredge and Tattersall, 1 9 8 2 ) t h r o u g h each o f which muc h genetic variance in p h e n o t y p i c expressions was lost, eventually

leaving H o m o sapiens as a tabula rasa species with regard to genetic constraints on organic reaction ranges {environmental determinism}. Recently, Cavalli-Sforza and Feldman (1981) as well as Lumsden and Wilson {1981} have published detailed investigations of various aspects inherent in the genetical evolution of cultural capacities in man. Lumsden and Wilson's b o o k is especially concerned with the " c o e v o l u t i o n a r y circuit" through which genetical and cultural evolution drove each ot her forward, thus giving the impression of a self-accelerating process similar to the autocatalytic chemical reactions known from biomolecular genetics (Eigen and Schuster, 1979}. The mathematical framework of m o d e r n popul at i on genetics applied in these investigations proved a useful tool to treat analytically genetic fitness differentials arising from varied, culturally codetermined, environmental and social interactions. A major difficulty in these approaches seems to be, however, to give the term " c u l t u r e " an adequate operational definition which can be incorporated

0303-2647]85]$03.30 © 1985 Elsevier Scientific Publishers Ireland Ltd. Published and Printed in Ireland

260 in the calculus, thus establishing the correspondence between abstract variables and specific cultural observables. For instance, the concept of culturgen (Lumsden and Wilson, 1981) denoting cultural traits as objects of natural selection has become subject to some criticism based on its alleged lack of realistic content (Leach, 1981, Cloninger and Yokoyama, 1981). In the present approach to biocultural evolution, we concentrate on concepts of cultural ecology in order to avoid the numerous difficulties in assessing individually acquired and culturally transmitted traits in terms of genotypic fitness. There are a number of different schools in current anthropology focussing on population-environment interactions as major subprocesses of human biological and sociocultural adaptations (for review and discussion see, e.g. Steward, 1968; or Winterhalder, 1980). The corresponding variety of theoretical perspectives and methodological approaches is matched by the c o m m o n fundamental postulate that ecological factors provide significant, causal agents affecting human biocultural evolution. In particular, White (1959, pp. 33--57), Adams (1975) and others largely identify ~he rates of matter and energy conversion inherent in human ecological as well as social interactions with the rates of cultural development and differentiation (see also White, 1954). It is the aim of the present investigation to explicate these aspects of biocultural evolution in terms of certain principles of theoretical population dynamics. The ranges of significance and validity of theories of cultural ecology have been subject to vigorous debate among contemporary anthropologists (for review and references see, e.g. Winterhalder, 1980). Instead of dealing with the details of this controversy here, we develop certain basic aspects of the ecological approach to biocultural evolution in analytic terms, and test the results of the analysis against various empirical features of hominid evolution. Accordingly, we dis-

pense with the specification of culture in terms of customs, symbols or social relations in hominid populations, and give an exclusively functional, processual characterisation of the notion of culture instead. First, a simple mathematical model frequently considered in population dynamics is applied in order to simulate certain basic processes of organic evolution (mutation, selection, adaptation). Then an equation is established which describes the enhanced synthesis of organic matter by an intelligent toolusing species. The species is supposed to live partly upon these artificially reproduced organic resources. It is shown that the reproduction of the species and the synthesis of its resources can be interpreted as autocatalytic reactions in the sense that the respective reproduction rates are increasing functions of the concentrations of the reactants involved. The rate constant entering the resource reproduction rate is referred to as the (overall) cultural capacity of the intelligent model species. This definition is justified by intuitive arguments. Thus, culture is characterised as a mode of ecological interaction. Finally, the Darwinian evolution toward larger cultural capacities in a lineage of species with increasing intelligence and learning abilities is investigated. In the model, the genetic variation for cultural capacities is assumed to correlate with certain ranges of phenotypic variability within which differences in selective value arise from individually acquired traits transmissible through learning. There is thus a time-lag between the formation of genetic dispositions conferring advanced capacities of self-organization on individuals, and the development of novel p h e n o y t y p e s (emergence and spread of cultural innovations). Hence, effective mechanisms of maintained polymorphism are necessary in order to exploit the hidden variation for cultural capacities. The following analysis demonstrates that the ecological niches accessible to the model species broaden in a straightforward manner

261 as the subsistence techniques improve, with the consequent release of the competitive selection pressure on the populations involved. This favours the maintenance of polymorphism in these populations, which, in turn, extends the time-span available for the exploitation of previously hidden adaptive potentials through individual learning and tradition. The latter step leads to further ecological release and thus closes the feedback loop in the "coevolutionary circuit".

identical ecological niches of 81 and S:, whereas ~ < 1 indicates a partial overlap (0 < /]) or complete separation (/] = 0) in the respective resources. Then the competition between S, and $2 is described b y dX1 = k l ( N , - X I - - / ] X 2 ) X 1 -- d l X 1

(3a)

= k2 (N2 - X 2 - I~X,)X2 - d2X2

(3b)

dt dX: dt

The basic equations In order to give a simple description of organic evolution and natural selection in analytic terms (which is suitable to stimulate macro-evolutiom~y processes in secular timescales; see Geigel:, 1983), a species or population $1 is considered whose density X~ obeys a Lotka-Volterra type of equation o f logistic growth dXl

-- k l ( N I -- J~'l) X ! --

dt

dX,

(I)

where the reproduction rate k , N ~ ~ 0 and death rate d, > 0, and the coefficient N, is proportional to the available amount of food and other resources. The species is supposed to live in a steady and homogeneous environment so that k,, N~ and d~ can be treated as constants. Linear stability analysis of the stationary solution X, <°~ = N l -

d,/bl = K,

The ecosystem (Eqn. 3) has frequently been analyzed in theoretical population dynamics. For the sake of completeness, a few elementary results must be summarized briefly here. Before the mutants appear we have the steady state X~ (°)=K~

and

X2 ( ° ) = 0

(4)

For given saturation levels K, and, similarly, K2 the state (Eqn. 4) is stable against invasion b y $2 if K2 >/]KI

(5)

does n o t hold. If on the other hand, this inequality is satisfied and/] = 1, the new stable state XI <°) = 0, X2 <°) = K2 > K1 is attained. When $2 completely differs from S1 in its choice of resources, $1 coexists with S: and the total population number is increased to

(2) X1 (°) + X2 (°) = K, + K2

shows that Eqn. 2 is stable against small random perturbations if the saturation level (or "carrying capacity") K~ in Eqn. 1 is positive. Let now a mutant subpopulation $2 appear in S~ by genetic mutations or immigration, and let $2 be characterized by population parameters k2, N2 and d2 (all positive and constant). The mutants compete with S, for a share/3 (0 ~ # ~< 1) in the available resources. The case # = 1 implies

(6)

In the intermediate range 0 ( /] ( 1 of overlapping ecological niches, two cases must be distinguished. If ilK2 > KI in addition to K: > /]K~ then $1 again becomes extinct and yet, the final population number X2 ¢°~ = K2 is still larger than the initial one. On the other hand, in the case of /]K2 <~ KI both populations coexist, X I <°> = ( K l - - / ] K 2 ) / ( 1

--/]2)

(7a)

262 X2 (°) = (K2 - ~KI)/(1 - ~2)

(7b)

(10b) upply

so that dA _

X1 (°) + X2 (°) -

K l + K2

1+~

> K1

X ~

d

inactivation

(9a)

(9b)

where k and d denote the respective reaction constants. The chemical with concentration A, in turn, is supposed to be supplied at the same rate at which X is inactivated so that the overall concentration X + A remains constant. Hence, this assumption may be referred to as the condition o f quasi-closedness or, equivalently, dynamical equilibrium of the system composed of X and A. The corresponding rate equations then read dX -dt

=

kAX--

dX

supply =

-d-X dt

(10c)

the latter of which gives the conservation relation

k ) 2X

+ ( d-~ t )

(8)

The model ecosystem (Eqn. 3) exhibits certain basic properties of Darwinian evolution. Natural selection operates so as to lead to an increasing exploitation of resources and ecological niches. Successive mutations will be rejected if they do n o t increase the overall degree of adaptation (reproductive capacities evaluated in terms of K) of the populations involved. Niche variation (/~ < 1) is favoured when new resources become accessible which are rich enough to sustain polymorphism. Otherwise only one of the competing species will be selected for survival (competitive exclusion). As has been pointed o u t by Nicholis and Prigogine (1977), the population dynamics (Eqn. 1) is isomorphic to the rate equation of an autocatalytic production of a chemical substance (concentration X) that interacts with a finite reservoir of another reactant A according to the reaction scheme A + X

kAX

dt

(10a)

A + X = N = constant

(11)

so that Eqn. 10a adopts the form of Eqn. 1. The significance of the analogy between Eqns. 1 and 9 for the present approach is to be found in the conditions Eqn. 10c and Eqn. 11 of quasi-closedness. Their application to the system composed of the species $1 and the amount A~ = N~ - XL of its actual resources may serve in explicating the concept of adaptation. If in a steady and homogeneous environment dA l -- - -

dt

dXl ¢

- -

dt

(12)

$1 would either reproduce suboptimally or overexploit the reservoir A,. For the remainder of the present analysis we therefore assume that all species concerned o b e y balance equations of the form Eqn. 11 and are in this sense adaptive. The assumption implies that disequilibrium ecologies violating Eqn. 11 become sooner or later subject to saturation phenomena re-establishing the dynamical preservation of the total amount of matter present ("mature", or "climax" stage of an ecosystem; see Odum, 1969). Alternatively, it may be based on timeaverages over dynamical variations when the evolution of ecosystems in secular, as against dynamic, time-scales is considered (Geiger, 1983). For instance, in ecologies of the Lotka-Volterra t y p e with strongly fluctuating population numbers matter preservation indeed holds in time-scales much larger than the Lotka-Volterra cycles (Goel et al., 1971). The assumption of ecological equilibrium will be further discussed in the final section.

263 The preceding considerations can be generalised straightforwardly so as to extend to ecological interactions that are usually regarded as characteristic of human culture. Here, in a first approximation culture is understood as l~he capacity to manipulate purposely the environment and, more specifically, organic reproduction rates in human resource bases (Greenwood and Stini, 1977, p. 400). This view, which reflects conceptions of cultural ecology as applied to human subsistence activlities (Steward, 1968; Netting, 1971), is discussed in some more detail in the next section. Consider a species which has acquired the capability to use tools and specialises on the enhanced reproduction of its organic resou:mes. This m o d e of ecological interaction can be described by a reaction scheme similar to Eqn. 9,

dA

kAX-

-

dt

,2A+X

(13a)

where the reaction rate is proportional to the density X of the species. The occurrence of X on both sides of Eqn. 13a shows X as an intermediate whose concentration remains unchanged, whereas A catalyzes its own production. Furthermore, the system (13a) is supposed to be open to interaction with the reservoir R which furnishes the matter and energy necessary for the enhanced synthesis of A. If g in (13a) is sufficiently small, the depletion of the reservoir is slow, and[ R may be treated as a constant. This approximation breaks d o w n when we consider the case of large g below. We further supplement (13a) by its rever~e process h 2A+ X , X+A+R (13b) which symbolizes two effects, firstly, an enhanced consumption and decomposition of A by X, and, secondly, the recycling of the decomposed organic matter A into the reservoir R. Under the conditions (Eqn. 10b) and R = constant the respective rate equations read

dX

(14a)

dX

+ gARX-

(14b)

hXA 2

dt

The existence of a non-trivial solution requires

stationary

A (°) = d / k = g R / h = constant

Choosing g R = ~ d and h = ~k, we get dA

dX

dt

dt

--=--(1+ cA)--

(15)

so that X = N-

g

R+A+X

dX --= dt

~-' In (1 + ~A)

(16)

whereby N is an integration constant measuring the "carrying capacity" of a characteristic environment of X. Note that lim~_,~ X(a) = N and lim~_. 0 X(~ ) = N - A. Evidently, the mathematical framework developed" thus far is based on principles of competitive selection, with the coefficients N, k, d, etc. describing epigenetic interactions between species-specific phenotypes and environmental features. Now it is wellknown that neo-Darwinian synthetic theory requires finite genetic variance in phenotypic expressions exposed to natural selection, be the selection mechanisms frequency~lepend e n t or density
264 density-dependent selection, no dominance and random mating by Geiger (1984). Hence the assumption of non-zero genetic variance in selected traits, on which the following analysis depends, is approximately, though implicity, expressed by the present competition equations. On the other hand, Eqns. 14a and b differ from other models of competition and density~lependent selection that have been extensively discussed in the literature in recent years (e.g. Roughgarden, 1979; Turelli and Petty, 1980). In the present model, selective advantages are evaluated in terms of genetically constrained capacities to manipulate resource reproduction rates which, in turn, control population growth. There is thus one step b e y o n d Eqns. 1 and 10 made explicit in the simulation of populationenvironment interactions, which leads to the cubic terms in Eqns. 14 and 15 as well as higher-order non-linearities in the competition Eqns, 18a, b obtained below. The concept o f cultural capacity The biological evolution of the human capacities of social communication, cooperation and environmental interaction is clearly a many-factored process of extreme complexity. It involves such diverse phenomena as brain size and functional differentiation, individual learning abilities, tools, language, plasticity of social organisation, etc. and their multiple interplay (see e.g. Wilson, 1975). In the coevolutionary context, at least, these phenomena have to be treated from one c o m m o n viewpoint, namely, the extent to which they confer on organisms the ability to extract as much matter and energy from their environments as is needed for survival and reproduction. Some biologists, anthropologists and sociologists seem to give less weight to this aspect by defining culture in terms of modes and devices of information processing other than genetic inheritance that is, transmission of behaviours, skills and knowledge through teaching

and individual learning (Bonner, 1980, Cavalli-Sforza and Feldman, 1981). On the other hand, cultural ecologists (Steward, 1968; White, 1959, Chap. 2; Netting, 1971; Adams, 1975) have insisted on the point that, when viewed functionally, the sociocultural capacities of prehistoric and m o d e m man are subfunctions of certain processes of matter and energy conversion (cultivation, reproduction and recycling of natural resources) which constitute "the dynamics behind the entire cultural system" (Adams, 1975, p. 281}. However rough the conversion scheme (13) may seem in comparison with real ecological interactions in hominid populations it simulates precisely these global ecological effects and thus retains an important c o m p o n e n t of the concepts of culture and cultivation. Similarly, the rate constant entering Eqns. 15 and 16 serves as an approximate measure of the overall efficiency with which the model species assumed in Eqns. 13 and 14 reproduces, consumes and recycles its resources. Therefore, ~ may be termed the cultural capacity of this species which, on its part, may be regarded as a model of a species of intelligent tool-using beings. This definition is in fact a modified restatement of Adams' (1975, p. 271} main thesis that "the rate of cultural change is proportional to the rate of energy conversion carried o u t within the system". Reaction schemes similar to (13} have also been used by White (1959, pp. 40--55) to analyse the connexions between culture, tools and rates of energy conversion in human environmental interactions. White maintains that culture can be understood as the human exosomatic, traditional organisation of customs, tools, language, beliefs, etc. which functions so as to exploit natural resources serving the needs of man. He extends the use of the term " t o o l " to cover all the material means employed by man to set conversion processes such as (13) into operation. Taking this view as a reasonable contribution to cultural evolutionism, we may indeed propose that the framework

265 of the Eqns. 14a, b retains a significant connotation of more broadly circumscribed concepts of culture used elsewhere in evolutionary anthropology. No other than this restricted meaning of the term " c u l t u r e " is intended when a is treated as the overall cultural capacity of a tool-using species here. Nor do we engage in the extensive anthropological debate on the question of whether all sociocultural phenomena in man can be reduced to (i.e. explained in terms of) cultural ecology, as some cultural ecologists seem to suggest (White, 1959, p. 55; Adams, 1975, p. 104). This question leads beyond the scope of the present investigation. In the following sections the evolution of the cultural capacity a as a selected trait is investigated. Starting from u = 0, a succession of species with increasing a and mean characteristic population size

random genomic substitutions and environmental transformations in time-scales r much larger than the inverse relaxation rate of Eqn. 18 which will, in general, lead to changes in the control parameters ("evolution in secular time-scales") (Geiger, 1983). However, we only consider variations in a here. This restriction will be discussed in the next paragraph. The selection model reviewed in the preceding section is then applied to Eqn. 18. The stability analysis proceeds exactly as outlined above and yields results analogous to Eqns. 5--8. In these relations one must only substitute K~ and K2 by K ( a l ) and K(a2), respectively. Choosing /3 = 1 (which will be justified below), the evolution of a satisfies

X (°) (a) = K(a) = N - a-l In (1 + a d / k )

This result follows straightforwardly from the competitive structure and stability behaviour of the system (Eqn. 18) which guarantee that only those m u t a n t phenotypes will be successful which are characterized by

(17)

is considered, whereby N, k, d and 3 are kept constant throughout. Evolution proceeds by inva.,;ion of previously existing populations with a = a2 by mutants carrying the cultural capacity a = a2 so that competition sets in (compare Eqns. 3, 10 and 16),

dX(a ~)

-

k s 1-1 { e ( a , [ N - X ( a , ) - ~ X ( a : ) ] )

dt - 1 )X(a,)dX(a:) _ ka2_ ~ (e(~ ~ [N :/t

dX(al)

(18a)

X(a2)--3X(a,)])

- 1 } X ( a 2 ) - dX(a2)

(18b)

The obvious assumption is made that the "control parameters" (as opposed to the dynamical variables) N, k, d, 3 and a are determined by epigenetic interactions between the genome and characteristic environment of a population, thus specifying reproductive differentials among species-specific phenotypes. We further assume long-term

dK(a)

dX(°)(a)

dr

dr

d~

- - = f(r) > 0 dr

> 0

(19a)

(19b)

One thus gets an evolutionary sequence of stable population equilibria of increasing degrees of adaptation evaluated in terms of g(~). Several qualifications have to be made concerning the reality of the assumptions adopted so far. From our present knowledge of the emergence of cultural patterns in the hominid line (e.g. Montagu, 1962) it is obvious that biocultural evolution has made strong impact on all conceivable population parameters. Consequently, in the present model the birth and death coefficients should be treated as variables in a as well. Since changes in these parameters are quite general features of organic evolution, however, we neglect these effects here and concentrate exclusively on the investigation of (13)

266 which retains certain characteristics of the notion of culture. Similarly, one must expect that the richness of the ecological niches accessible to hominid populations in natural history were strongly dependent on these populations technological skills such that a function N(a) in Eqns. 16--18 might seem more appropriate than N = constant. However, the impact of advanced subsistence techniques on the amount of available resources has already been taken into account. Expressed in terms of a, Eqn. 10b reads

[

dA(a)l = dX(a) A supply

(20)

This means that larger a and X(a) require an increase in supply rate which is not provided b y processes o f the t y p e (13), b u t depends on the acquisition of new resources. Furthermore, Eqn. 20 may also serve for estimating the degree ~ to which the ecological niches of t w o consecutive species with a, and a2 > a, overlap:

[dA(al)/dt]supply [dA(~2)/dt]supply

X(al) X(a2)

As we consider only continuous evolutionary changes in a here, the "local" approximations a2 ~> al and ~ ~ 1 always suffice. The system (13) suggests an interpretation as a schematic model of ecologies of the agrarian t y p e in which manipulations of resource reproduction rates (tillage and stock-breeding; see (13a) and intensified fertilization (recycling; see 13b) are the prevailing modes of environmental interaction. However, agricultural systems have appeared very recently in human natural history and, hence, could not have been of much impact on the processes of organic differentiation and natural selection. Nonetheless, effects of cultural ecology less pronounced than agriculture were already operating in earlier hominid populations. For instance, the use of fire as the artificial

extraction of heat from organic matter acts in the sense of (13), if heat is included among the natural resources A. The primary source of energy for all organic life is solar radiation catalyzing the production of plant tissue from which, in turn, heat can be extracted by firing techniques. Thus the use of fire can be understood straightforwardly as an artificially enhanced production and consumption of energy exercised by tool-using intelligent beings. Another example of pre-agrarian forms of cultivation and intensified resource reproduction is given by interspecific aggression and competition. Deliberately killing other predators preying on the same game species as the early hunter-gatherers (Wilson, 1975) acts so as to increase the rate constant in {13). Finally, slash-and-bum ecological strategies, ethnographically recorded among hunter-gatherers, probably represent the oldest techniques to increase the net primary productivity of human ecosystems (Stewart, 1956). Other examples of the reproduction and recycling of biomass and the harnessing of the chemical energy contained in it have been extensively dealt with by White {1959, Chap. 2) under the rubric of "energy and tools". The impact of learning on biocultural evolution In Fig. 1 we have schematically drawn X ¢°> as given by Eqn. 17 as a function of the ratio d/k for various values of a and for an imaginary environment o f the "carrying capacity" N in dynamical equilibrium. Various ecological niches are distributed over the environment which codetermine the equilibrium values A C°) = d/k. The straight line a = 0 demarcates the set Of niches 0 ~< d/k <. N whose broadness (evaluated in terms of the adaptedness K they require) has an absolute upper boundary fixed by the environmental "limiting factors" (Odum, 1969) which also determine the carrying capacity N. The curved lines give

267

x(O)

x(O)

N N

d/k •const.

N-d/k 0

N

0

d/k

Fig. 1. Populatiol~ n u m b e r X(0) as a f u n c t i o n o f the r a t i o d / k for various values o f t h e overall "cultural c a p a c i t y " ~. F o r ~ > 0 t h e curved lines s h o w t h a t X(°) remains finite in ecological niches w i t h d / k > N w h e r e p o p u l a t i o n s at zero cultural c a p a c i t y could n o t exist.

X (°) as a function of d / k for s > 0. For every d/k, X (°l~ ( s ) is n o t only increased above X (°) (0), but also remains positive in finite ranges d/k > N. Hence, our model species with s "> 0 m a y penetrate ecological niches where they could n o t exist otherwise, that is, at zero cultural capacity. In the asymptotic case s -* oo the entire carrying capacity N of the conceived environment is employed on behalf of a highly skilled species which transforms the total inflow of organic matter and other supplies into optimal population size according to Eqn. 20: lima-® (dA/dt~upply = dN. It is obvious from the preceding sections that evolution toward higher s is governed by the principle of competitive exclusion. As s approaches infinity, however, competitive selection pressure between consecutive species operating at higher and higher s releases. This ~ illustrated in Fig. 2 where we have plotted X (°) as a function o f s for fixed d/k. At low s, fluctuations As yield large increments, and, for negative As, decrements ~ X (°) in mean population size,

0t

Fig. 2. Population number X(°) (a) for fixed ratio d/k and biotic capacity N. whereas dX~°)/ds -~ 0 for s -~ ~ . Linear stability analysis of Eqn. 18 shows that the rate co at which Eqn. 18 relaxes to a new stationary state after some variation As occurred is given by

dX~°)(s)

w = kAs(1 + s d / k ) - ds

(21)

so that for the mean duration ~-1 of maintained polymorphism between the unperturbed and the m u t a n t subpopulations we get -1

lim ¢o-1= lira

kAa(l+sd/k)~

=

(22) If the present model correctly simulates certain evolutionary mechanisms essential to hominid phylogeny, it predicts a tendency toward competitive exclusion between the early hominid species sharing their habitats, whereas temporary coexistence becomes more likely as biocultural evolution proceeds. Unfortunately, the present fossil evidence still seems to be too inconclusive to support or falsify this proposition empirically (for

268

review and discussion of this question see Cronin et al., 1981). T h e present assumption that there is finite genetic variance in p h e n o t y p i c expressions exposed to natural selection is made somewhat mo r e explicit now. We suppose in first a p p r o x i m a t i o n t hat there is a steady source o f genetic variation which leads to f ( r ) = p = co n s tan t in Eqn. 19. If the genetic variance in a were always very high, Eqn. 19 would yield d X (°)

d X (°) da

d X (°)

dr

da

da

dr

(23)

This relation is schematically depicted in Fig. 3. The situation changes when individual learning and tradition c ont r i but e to t he specification o f a. The presence o f variation for a then means a certain disposition to learning in individuals, and reproductive fitness becomes a f unc t i on of individually acquired traits. Correspondingly, increases in cultural capacity are e xpe c t e d to arise from hidden adaptive potentials which will n o t

x{O)

(X

N

N-d/k

~

{Z}

0 Fig. 3. The evolution of the cultural trait a and mean characteristic population size X(0) over secular timescales r in case of constant average rate of evolution and complete genetic determination of a.

yield selective advantages in time-scales shorter than one generation (as an absolute lower boundary). The resulting phase-shift between mutations and the d e v e l o p m e n t o f new p h e n o t y p e s through learning is of the order of magnitude T = n A a ( k N ) - ' , where (kN )-' is approximately the duration of one generation and n is a positive integer which will generally be large. Effective mechanisms of maintained hidden variation thus become codeterminants o f the evolutionary success o f mutants which will express higher values o f a after the time T, if t hey are n o t counterselected immediately after their first appearance. These effects give a modified evolutionary rate (compare Eqn. 21). da dr

~

[

dXC°)~ '

~oT/Aa - p N n(1 + a d / k ) d--a--_]

(24) where ( c o T / A a ) - ' is the ratio of the timescales of the maintenance o f non-stationary fluctuations h a arouns a, and of learning and cultural transmission. F o r sufficiently small a one has ( w T / A a ) -~ ~ 1. In this case mutants are exposed to strong competitive selection, and the large relaxation rates co o f the system Eqn. 18 prevent the developm e n t of traits expressing high individual flexibility. For large a, when ( w T / A a ) -1 /> 1, competitive selection pressure on mutants eases. Every m u t a t i o n contributing to an increase in a becomes m ore likely t o carry through its selective advantage witho u t restriction, and the genetic variance in p h e n o t y p i c expressions is eventually reduced. The global evolution o f a t hen obeys Eqn. 24 and d X (°~

dX <°> da

dr

da

dr

pN n(1 + a d / k )

(25)

as sketched in Fig. 4. The steep quasi-exponential rise of a may be com pared with

269

X{0)

N

B

,.,x(O)lo

N-dlk 0

! ~0

Fig. 4. T h e e v o l u t i o n o f t h e trait a a n d average p o p u l a t i o n size X(0) over secular time-scales r. It is a s s u m e d t h a t Q~ is c o d e t e r m i n e d b y individual l e a r n i n g a n d c u l t u r a l t r a d i t i o n . T h e s t r a i g h t line labelled ~ X ( ° ) (r) r e p r e s e n t s a r o u g h a p p r o x i m a t i o n t o X(°) (r), w i t h t h e f a c t o r (1 + c ~ d / k ) -~ neglected in E q n . 25.

certain conspicuous gross features of hominid evolution such as the accelerated increase in brain size (Pilbeam, 1972) which it parallels qualitatively. On the other hand, the present model predicts a very slow increase in mean population size. This, however, is consistent with the data and semi-empirical hypotheses on overall Pleistocene population growth which has been estimated at about 0.001% or less per year, and probably did n o t vary considerably during that period (Cohen, 1980; Hassan, 1~)80). The expiring o f the coevolutionary circuit As noted abc,ve, in the limit a -+ ¢¢ the basic assumptions of the model ecosystem (13) break down. The secondary production rate at which A is synthesizes at the expense of the matter and energy supplies R is clearly limited by the rates of certain

biological growth and decay processes as well as environmental changes such as photosynthesis, ecological succession (Odum, 1969), or seasonal variation in climate and weather. Increases in a far beyond these limiting rates can, at best, be attained by intensified depletion of the primary resources R whose concentration can then no longer be treated as a constant. One must therefore expect that somewhere on the steep section of the a-curve in Fig. 4 a transition to intrinsically non-stationary ecosystems occurs when depletion and consumption of natural resources proceed faster than biomass can be refurnished by biological processes in dynamic equilibrium. In fact, it is well-known that the emergence of advanced agriculture and intense forestry in history shifted the h u m a n ecosphere away from the " m a t u r e " equilibrium states in which the ratio A ' / R ' of the "standing crop biomass" A' (as a subset of A) and the a m o u n t R' of primary plant tissue acting as a reservoir of nutrients (as a subset of R) adopts some stable optimum value. Agrarian systems moved more and more towards unbalanced ecologies in which the ratio A ' / R ' is suboptimal, implying an ever higher consumption of the primary matter and energy resources R (Odum, 1969). In the present model the emergence of large cultural capacities, the expiring of competitive selection, and the rise of intrinsically unbalanced ecologies virtually coincide. This is expected to happen w h e n the timescales T of the spread of technological innovations ("history of civilization") become much shorter than those of competitive selection (¢o -I >> T/Aa). The model admits an order of magnitude estimate of the time r0 of the onset of the history of civilization when the factor (1 + ~d/k) -1 is omitted in Eqn. 25. In this approximation the integration of Eqn. 25 from r = 0, X (°) (0) = N - d/k to r = r~ X (°) (r0) ~ N, r0 ~

nd #kN

(26)

270 shows that r0 is determined essentially by the inverse average rate p-1 of evolution. Since in our representation p is not simply proportional to the rate o f genomic substitution (which can be estimated) (see e.g. Lewontin, 1974) but also covers the complicated transformation of genetic dispositions into phenotypic expressions, it may be determined indirectly by inserting the estimated Pleistocene population growth rate of 10 -s year -1 for dX~°~/dr in Eqn. 25 so that ~ ~- 10 -s nN -~ year -~. Relation, Eqn. 26, then yields ro ~- lO s ( d / k ) years -~ 10 5 N y e a r s where d / k = N - X ~°) (0) ~ N by order of magnitude. An appropriate choice for N would be the typical size of local huntergatherer groups extrapolated backward from living primitive societies. Such extrapolations have frequently been carried o u t in the literature (Wilson, 1975, Cohen, 1980; Hassan, 1980) with the widely agreed result of N ~ 102. These estimates leave r0 of the order of some million years which roughly covers the Pliocene-Pleistocene period. Hence, within the approximations on which the present model is based the empirical timescales of hominid evolution are reproducible numerically.

Summary and conclusions A simple mechanism of biocultural evolution has been proposed which is based on three obvious assumptions. First, the phylogenetic succession of species is simulated by a model of competitive selection. Secondly, "culture" is characterized as a m o d e of ecological interaction arising from the intelligent manipulation of natural resources, and exercised by tool-using species. Thirdly, the capacities of individual learning and tradition are adaptive traits exposed to natural selection. Once these conceptions are translated into an appropriate analytic framework a variety of empirical features of hominid evolution can be explained in a

straightforward manner. The model correctly predicts the widening range of accessible ecological niches and the decrease in immediate genetic impact on p h e n o t y p e as biocultural evolution proceeds. The essence of the present approach, however, is expressed in Fig. 4 which reflects t w o fundamental characteristics of hominid evolution, namely, the self-accelerating increase in mental capacity, with characteristic population size varying much less drastically. The former phenomenon is explained by a kind of autocatalysis mechanism (Hart, 1959; Wilson, 1975, pp. 566--568, Stebbins, 1982), meaning that every successful evolutionary step toward larger cultural capacity provides selective advantages for prospective moves in the same direction. The latter is clearly a saturation effect (limits imposed on Malthusian growth by the condition of ecological equilibrium). The impact of ecological constraints on human prehistoric population regulation is still a matter of controversy (see various contributions to the b o o k edited by Cohen et al. (1980), and Hayden (1981)). In particular, Hayden has questioned the empirical significance of "carrying capacity" and other notions related with ecological equilibrium in view of constantly fluctuating environmental conditions throughout man's natural history. Commentators on Hayden's conclusions such as Cohen (1981) and Druss (1981) have argued, however, that periodic variations in the resource bases of early man must be expected to m o d i f y the effects of ecological equilibrium and saturation rather than remove them completely. Similar arguments can be drawn from the mathematical analysis of ecological cycling which demonstrates that time-averages of fluctuating population numbers and resources may simulate the presence of population equilibria in secular time-scales (Goel et al., 1971; Geiger, 1983). Now, the present model suggests on the basis of relation (Eqn. 16) that as long as the overall saturation level N is invariant, the mean population size X

271 remains bounded even for moderate ~, since X(a) depends exclusively on the resources A(~) according to Eqn. 20. Correspondingly, rapid population growth as is to be observed since the Neolithic age may have been possible only due to marked increases (i.e. non-cyclic changes) in N which, however, are characteristic of inherently unsteady ecosystems.

Acknowledgement The author wishes to thank the Deutsche Forschungsgemeinschaft, Bonn, by which the present work was sponsored.

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