KYKLOS, Vol. 53 – 2000 – Fasc. 2, 161–172

What Happened to the Neanderthals? – The Survival Trap

João Ricardo Faria*

I. INTRODUCTION Neanderthals inhabited Europe and Near East from approximately 135.000 to 34.000 years ago. Beginning 50.000 years ago, in Eastern Europe, the Neanderthal populations disappeared and were replaced by Modern Humans (Humans, for short). In Western Europe the replacement happened around 34.000 years ago. Nevertheless, there is enough evidence showing Neanderthals and Humans coexisted for a long time (Leakey 1994). There are four principal hypotheses that have been advanced by archaeologists and paleoanthropologists to explain the decline and eventual extinction of the Neanderthals (e.g., Caird 1994, Shreeve 1995, Stringer and Gamble 1993, Trinkaus and Shipman 1994). These conjectures are mainly based in anatomical and cultural differences between Humans and Neanderthals. The first hypothesis assumes that competition between Neanderthals and Homo sapiens led to extinction of the Neanderthals. A slower birth rate and shorter life-span, or a greater mortality rate in comparison with Humans, or a relative technological disadvantage, made them out-competed and completely replaced in few generations by H. sapiens (Zubrow 1989). This is a common inference in any standard model of competing species (see, for example, Braun 1979). Two further hypotheses stress the negative impact of the contact between Humans and Neanderthals. One proposes that Neanderthals could have been killed through wars against H. sapiens. The other proposes that the contact be-

* School of Finance and Economics, University of Technology, Sydney, Broadway NSW 2007, Australia. Phone: +61– 2 – 9 514 7782; Fax: +61– 2 – 9 514 7711. E-mail: Joao. Faria@uts. edu. au. I would like to thank, without implicating, Chris Bajada, Francisco G. Carneiro, Carl Chiarella, Sophia Delipalla, M. Leon-Ledesma, Flávio Menezes, Robert de Rozario, and the referees for helpful comments.

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tween Neanderthals and Humans facilitated the propagation of diseases that devastated the Neanderthal populations. In contrast, a fourth hypothesis assumes a positive feedback between both populations. It proposes that there was some interbreeding between Neanderthals and H. sapiens, whose genes eventually became dominant. The background of these conjectures lies in the debate between the theories of human evolution: the Regional Continuity model, associated with Wolpoff (1989), which stresses the long-lasting contact and cooperation between Humans and ancient hominids (among them the Neanderthals); and the Out of Africa model, associated to Stringer (1990), that emphasises the replacement of ‘ancients’ by the Homo sapiens. There are other theories that lie somewhere between the views of Wolpoff and Stringer, as Brauer’s ‘hybridisation and replacement’ model and Smith’s ‘assimilation’ theory (see Shreeve 1995, Trinkaus and Shipman 1994). One of the objectives of this paper is to demonstrate to archaeologists and other scientists the potential that economic analysis may have in integrating and unifying the conjectures and evidence about the Neanderthal extinction 1. The paper presents a simple model that takes into consideration the four hypotheses outlined above. The model introduces migration into Brander and Taylor (1998) Ricardo-Malthus model of renewable resource use. The set up is simple; a native population (Neanderthals) exploits the natural resources of its region. The incoming population of H. Sapiens affects this dynamics. The results are quite appealing: 1) The model has multiple equilibria. One of them is a stable equilibrium with a positive Neanderthal population. This shows that the theories above, considered individually or together, do not suffice to guarantee the Neanderthal extinction. 2) The actual equilibrium with no Neanderthal population is also stable. 3) The third equilibrium with positive Neanderthal population is a saddle point, which is coined the survival trap. The path to extinction or survival of The Neanderthal population depends on the relationship between the initial conditions and the survival trap.

II. THE MODEL The basic model describes how natural resources, Neanderthals and Humans interact. It is composed by a system of three non-linear ordinary differential equations. Each one describing the rate of growth of natural resources, Nean1. Therefore, this paper follows the tradition of applying economic analysis into prehistorical problems initiated by Smith (1975, 1992).

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derthal population and Human population. The system is able to represent the theories presented in the introduction. It captures economic and demographic features behind the Neanderthal fate, such as migration, resource competition, and on the one hand, warfare and disease transmission, and on the other, cooperation and interbreeding, between Neanderthals and Humans. Since Neanderthal and Human populations are hunters and gathers, they use renewable resources. In this sense, natural resources are supposed to be renewable. Two different forces affect the rate of growth of natural resources: natural and populational. Populational forces are related to the way Neanderthals and Humans use and exploit the environment. Natural forces are the forces that affect the rate of growth of renewable resources that do not depend on Neanderthal and Human populations, such as climate, soil, etc. These forces have two important aspects. First, concerning the populational forces, Humans and Neanderthals compete for natural resources. It implies that Human exploitation and consumption of natural resources decrease the rate of growth of renewable resources, which allow less resources for Neanderthals, and, vice-versa. Therefore, natural resources are excludable goods for both populations. Concerning to the role of natural forces, they are captured, as usual, by a logistic functional form 2. The rate of growth of renewable resources is given by the following equation: . S = rS(1 – S ) – zNS – hMS K

(1)

In equation (1), S represents the renewable resource stock at time t, N is the Neanderthal population, and M is the migrant. population of H. Sapiens. Observe that the growth rate of natural resources (S/S) consists of two terms: 1) the logistic functional form for the biological growth (divided by S): r(1 – KS ), where K is the carrying capacity and r is the intrinsic growth rate; and 2) the exploitation of the natural resource by Neanderthals (zNS) and Humans (hMS). Where z and h stand for the rate of exploitation of natural resources from Neanderthals and Humans respectively 3. From equation (1) it is clear that Humans and Neanderthals compete for natural resources. From the discussion in the introduction, many hypothesis have been put forward to explain how the Neanderthal population was affected by the incoming Homo sapiens. The rate of growth of the Neanderthal population is supposed 2. See Faria (1998). 3. As will become clear in the model, it is not necessary to compare z with h. Even if both populations differ in the way they exploit the environment, using different technologies, none of the results depend on which of them is more efficient, that is, if z > h, or, vice versa.

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to have been affected by interbreeding with Humans, by infectious diseases transmitted by Humans and, finally, by wars and genocides carried out by Humans. Furthermore, the rate of growth of the Neanderthals should reflect their fertility, which is linked to the efficiency in exploiting the environment. . N = N(ag(M) – bf(M) – F(w)M + nzS – c)

(2)

. Equation (2) describes the rate of growth of the Neanderthal population (N/N). The first term inside the brackets captures the birth rate of Neanderthals and their interbreeding with H. Sapiens, where g(M) represents the interbreeding function with Humans, (g(0) = 1, g′(M) < 0), and a is a positive constant. The rate of growth of the Neanderthal population is a negative function of the death rate, which is affected by infectious diseases transmitted by Humans, f(M), (f(0) = 1, f ′(M) > 0), where b is a positive constant 4. The effect of wars and genocide is captured by the term F(w)M, where the loss of Neanderthal life is given by the function F of wars, w, (F′(w) > 0, F(0) = 0) 5. The forth term is the fertility function of the Neanderthal population, it depends on their efficiency in exploiting their environment, where n > 0. Finally, the positive constant c (close to zero) is a natural rate of decreasing of the Neanderthal population. Naturally, if the Neanderthal population is affected by the Humans, the Human population dynamics also must reflect the impact of such contact. The growth rate of the Humans is affected by wars and by the interbreeding with Neanderthals. It is assumed that infectious diseases are passed from Humans to Neanderthals, so, Human population is not affected by any disease that might have been passed from Neanderthals. The incoming Human population is also affected by the migration of other humans, attracted by the economic gains in migrating. As Human population growth is accelerated by the decrease of Neanderthals, a sort of intra-competition among humans might have emerged. The equation below spotlights how these variables determine the dynamics of the Human population: . M = M(q – G(w) – eM) (Y(x) – N ) (1 + u) S

(3)

. Equation (3) describes the rate of growth of Human population (M/M). The first term in the right hand side (RHS) is the natural growth rate of Human popula4. This is a very simple way to model disease transmission, it implicitly assumes that all Neanderthals susceptible, when in contact with Humans, are infected. See Stannard (1993) for the relation between migration and disease and Bailey (1975) for the models of infectious diseases. 5. Here the conflict is not modelled along the lines of Lanchester (1956) (see Hirshleifer 1991, as well), which stresses the relation between force sizes and fighting parameters.

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tion, where q is the difference between birth and death rates; G(w) is the loss of life in wars (G′(w) > 0, G(0) = 0); and eM represents the intra-competition of Humans. The second term in the RHS stands for the economic opportunity cost of migration. This term depends positively on the relative Neanderthal density (N/S) and negatively on the economic gains in migrating (Y). Y is affected by climate shocks, x. The constant (1 + u), where u lies in the [0,1) interval, captures the genetic contribution of Neanderthals to Human population. Followers of the ‘Out of Africa’ model would assume u = 0 (no genetic contribution), and others u > 0. Therefore, when we refer to the extinction or replacement of the Neanderthal population, it does not imply that we are following the ‘Out of Africa model’. In order to address the theories exposed in the introduction, we must pay attention to four parameters in the above model. The parameters are: h, the human’s rate of exploitation of natural resources; w, the occurrence of wars between Humans and Neanderthals; b, the rate at which infectious diseases spread from Humans to Neanderthals and, finally, a, which stands for the effect of interbreeding on Neanderthals. The model captures the four theories used to explain the Neanderthal extinction: 1) Competitive Model: h > 0, and w = a = b = 0. 2) Genocide Model: w > 0, and h = a = b = 0. 3) Disease Model: b > 0, and w = a = h = 0. 4) Interbreeding Model: a > 0, and w = b = h = 0. The dynamical system of equations (1)–(3) is a generalisation of all theories. Notice that when M = 0, Brander and Taylor (1998) model becomes a particular case of our model.

III. MULTIPLE EQUILIBRIA The dynamical system (1)–(3) presents multiple steady-states equilibria 6. Three of them have direct interest for our discussion. Basically these equilibria are related to Human migration. Migration is pushed by economic incentives. The benefits of migration are given by the abundance of natural resources, and/ or low cost of exploitation of the environment. The cost to migrate is associated . . . 6. A steady-state equilibrium satisfies the following condition: S = N = M = 0.

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to the Neanderthal density relative to the amount of natural resources available. Greater is this density, lower is the Human migration. The first equilibrium is the one in which the Neanderthal population does not become extinct. This equilibrium occurs because there is no incentive to Human migration. When there is no Human migration, the competition and contact among populations is low, which allows their coexistence. This equilibrium is stable. The second equilibrium is also stable. It is characterised by the extinction of the Neanderthal population. It is related to the migration of Human population. In this equilibrium there are incentives for Humans to migrate. So by increasing their density relatively to Neanderthals their competition and contact increase, which drives Neanderthals to extinction. Given these two stable equilibria, there is a logical and mathematical need for an unstable equilibrium to separate them. This unstable equilibrium is called the survival trap. In this equilibrium the Neanderthal population does not become extinct. However, as it is an unstable equilibrium, it is fragile and any disturbance from it can decide the final fate of the Neanderthals, by driving them to one of the stable equilibria. That is, to complete extinction or coexistence. However, in order to study these equilibria, the following inequalities are assumed: i) nzr > c(r/K + zY(x)), given that c is close to zero 7; and ii) r > hM. The second inequality assumes that the intrinsic growth rate of natural resources is greater than the impact of the Human population on the environment. This is a delicate question since by the overkill hypothesis (due to Martin 1967) Humans are considered a causative factor of the great megafaunas extinctions, which occurred approximately 10.000 years ago (see Smith 1991). Nevertheless, for the period analysed, 30.000 to 40.000 years ago, there is no evidence that the population of Humans in Europe engaged in such destructive behaviour. The first steady-state equilibrium occurs when the economic opportunities to migrate are fully exhausted: Y(x) = N/S, as a consequence the term (q – G(w) – eM) is assumed to be positive. This yields the following values for the endogenous variables 8: M* =

nzr – c(rK–1 + zY(x)) >0 (F(w) + b(1 + f ) – a(1 – g) nz (rK–1 + zY(x)) + hnz n

(4)

7. Inequality one is just a mathematical condition to guarantee the non-negativity of one of the solutions. It is likely to be fulfilled since c is a very small number. Inequality one has no economic meaning. 8. For mathematical convenience assume that f (M) = (1 + f ) M, and g(M) = (1 – g) M, where g > 1.

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S* =

r – hM* > 0 rK–1 + zY(x)

N* = Y(x)S* > 0

(5) (6)

The trace and determinant of the jacobian matrix J* of the non-linear system (1)–(3) evaluated at the fixed point, (4)–(6), are the following 9: trJ* =

rK–1 (hM* – r) <0 rK–1 + zY(x)

detJ* = (q – G(w) – eM*) N * M * (hnz + (hM* – r) (a(1 – g) – b (1 + f) – F(w)) (1/S*)) > 0

(7)

(8)

which suffices to qualify the fixed point (4)–(6) as stable 10. The important characteristic of this equilibrium is that the Neanderthal population does not become extinct. Therefore, our model does not necessarily lead to the extinction of the Neanderthals; despite taking into account the four distinctive theories created to explain their disappearance. Furthermore, this equilibrium is stable. This holds true even when each one of the theories is considered individually (the proof is available from the author upon request) 11. The second steady-state equilibrium, in which the Neanderthal population disappears, is characterized by positive economic opportunities to migrate: Y(x) > N/S. The steady-state values for N, M, and S are the following: N* = 0 q – G(w) >0 e S* = K(1 – h M* ) > 0 r M* =

(9) (10) (11)

The determinant and trace of the jacobian matrix J* of the non-linear system (1)–(3) evaluated at the fixed point, (9)–(11), are the following: 9. Without loss of generality, in all equilibria examined we are assuming u = 0. 10. The local stability can be assessed simply noticing that when the trace of J* is negative (positive), the fixed point is stable (unstable), the only exception occurs when the determinant of J* is negative, in this case we have a saddle point whatever the sign of the trace of J*. When the trace of J* is equal to zero, we have a vortex. See Tu (1994). 11. Note that climatic change has a major role in this equilibrium, since changes in the climate (changes in x), affect the opportunity cost of migration, which change the position of this equilibrium point. For the impact of climatic change on Human migration see Stringer and McKie (1997).

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detJ* = (hM* – r) (G(w) – q) Y(x) > 0

(12)

trJ* = hM* – r + Y(x) (G(w) – q) < 0

(13)

The equilibrium is stable as well. In this equilibrium the Neanderthal population is extinct and replaced by Human population. This is the actual equilibrium. The third steady-state equilibrium also occurs when there are economic incentives to migrate, Y(x) > N/S: q – G(w) >0 e F(w)M* + bf(M*) – ag(M*) + c S* = >0 nz n N* = (r(1 – S* ) – hM*)z –1 > 0 K M* =

(14) (15) (16)

The determinant and trace of the jacobian matrix J*, of the non-linear system (1)–(3) evaluated at the fixed point, (14)–(16), are the following: detJ* = z2nS*N*(Y(x) – N* ) (G(w) – q) < 0 S N* trJ* = (Y(x) – ) (G(w) – q) – r S* < 0 S* K

(17) (18)

As the determinant of J* is negative this steady-state equilibrium is a saddle point. It remains a saddle point equilbrium for the specific models as well (the proof is available from the author upon request). The equilibrium (14)–(16), is coined the survival trap. The reason for this name arises from the fact that there are two stable equilibria in the model, one with positive Neanderthal population and another with no Neanderthal population, which is the actual case. Given any initial conditions for N, M and S, it is impossible to predict what the final outcome of the Neanderthal population will be (if it will survive or disappear). This problem occurs because both equilibria (with extinction or survival) are stable. Hence, the existence of a third equilibrium is necessary to separate the stable fixed points, and this equilibrium is a saddle point 12. As a saddle point, the survival trap is unlikely to be reached and to guarantee the coexistence of both populations, since there are just a few stable separatrices approaching the saddle point in the steady-state. This equilibrium is just 12. It is useful to note that the origin (S*, N*, M*) = (0, 0, 0), is an unstable node equilibrium.

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a weak survival trap because it is reached only by chance. Furthermore, any perturbation of this equilibrium (for example, a climate change) can definitely drive the Neanderthals to coexistence or extinction 13. Therefore, it is the relationship between the initial conditions and the survival trap that will drive the Neanderthal population to survival or extinction. As a consequence, any analysis on the fate of the Neanderthals has to take into consideration the existence of the survival trap. In the present model, its existence is related to the opportunity cost of migration. The survival trap is the equilibrium in which the Neanderthals survive, even when the net economic gains to migrate are not fully exhausted. The workings of the model can be visualised through Figure 1.

Figure 1

13. This point is acknowledged in the last page of Stringer and Gamble (1993, p. 219): ‘There was nothing inevitable about the triumph of the Moderns, and a twist of Pleistocene fate could have left the Neanderthals occupying Europe to this day’.

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Where points A and B are the stable equilibria and T is the survival trap. At point B, Neanderthals become extinct, and at point A they coexist with Humans. Note that if point E represents the initial conditions (for Human and Neanderthal population and availability of natural resources), the Neanderthal population will end up extinct (point B). However, if the initial conditions are given by F, the Neanderthal population will survive (point A). If the initial conditions are at point G, the populations will be ride to the survival trap. It is important to stress the fact that the survival trap is an unstable equilibrium. Therefore, any small perturbation taking the equilibrium out of T can define the final fate of the Neanderthals, to coexistence or extinction. At the survival trap there exists economic opportunities to migrate, any perturbation on these opportunities can push the equilibrium out of T, and decide the final outcome of the Neanderthals. Notice that despite the fact of the closeness between points E, F, and G, the long run implications cannot be more different. The relation between E, F and G and the survival trap, T, is essential in any discussion on the fate of the Neanderthals.

IV. CONCLUDING REMARKS This paper has presented a model that integrates and unifies the conjectures on the Neanderthal extinction. It is shown that the model has multiple equilibria. Three of them were studied. The first is a stable equilibrium with positive Neanderthal population. Its existence is a strong result since it demonstrates that the theories of Neanderthal extinction, considered individually or together, are not sufficient to drive the Neanderthal population to extinction. The other equilibria are the actual equilibrium with no Neanderthal population, which is also stable, and the survival trap equilibrium, which is a saddle point. The path to extinction or survival of the Neanderthals depends on the relationship between the initial conditions and the survival trap. The survival trap is the equilibrium in which the Neanderthals survive even when the net economic gains to Human migration are not fully exhausted. This model can be adapted to examine other problems like the colonial expansion of Europeans in America. As pointed out by Deacon (1997), the Neanderthal demise has a close parallel to the colonisation of Europeans in America and the extinction or diminishing number of many native tribes. Therefore, the importance of our model is that it integrates, in a simple framework, many features of human history such as migration, resource competition, and on the one hand, warfare and disease transmission, and on the other, cooperation and interbreeding, between different populations. 170

WHAT HAPPENED TO THE NEANDERTHALS? REFERENCES Bailey, N. (1975). The Mathematical Theory of Infectious Diseases. London: Hafner Press. Brander, J. A. and M. S. Taylor (1998). The simple economics of Easter island: A Ricardo-Malthus model of renewable resource use, American Economic Review. 88: 119 -138. Braun, M. (1979). Differential Equations and their Applications. Berlin: Springer-Verlag. Caird, R. (1994). Ape Man: The Story of Human Evolution. New York: Macmillan. Deacon, T. (1997). The Symbolic Species. New York: W. W. Norton & Co. Faria, J. R. (1998). Environment, growth and fiscal and monetary policies, Economic Modelling. 15: 113 –123. Hirshleifer, J. (1991). The technology of conflict as an economic activity, American Economic Review. 81: 130 –134. Lanchester, F. W. (1956). Aircraft in warfare: The dawn of the fourth arm, in: J. R. Newman (ed.), The World of Mathematics. New York: Simon and Schuster: 4: 2138 – 2157 Leakey, R. (1994). The Origin of Humankind. London: Weindenfeld & Nicholson. Martin, P. (1967). Prehistoric overkill, in: P. S. Martin and H. E. Wright, Jr. (eds.), Pleistocene Extinctions. New Haven: Yale University Press. Smith, V. L. (1975). The primitive hunter culture, pleistocene extinction, and the rise of agriculture, Journal of Political Economy. 83: 727–755. Smith, V. L. (1991). Hunting and gathering economies, in: J. Eatwell, M. Milgate and P. Newman (eds.), The New Palgrave: The World of Economics. London: Macmillan: 330 – 338. Smith, V. L. (1992). Economic principles in the emergence of humankind, Economic Inquiry. 30: 1– 13. Stannard, D. E. (1993). Disease, human migration, and history, in: K. F. Kiple (ed.), The Cambridge World History of Human Disease. Cambridge: Cambridge University Press: 35 - 42. Shreeve, J. (1995). The Neanderthal Enigma. London: Penguin. Stringer, C. (1990). The emergence of modern humans, Scientific American. December: 98 –104. Stringer, C. and C. Gamble (1993). In Search of the Neanderthals. London: Thames and Hudson. Stringer, C. and R. McKie (1997). African Exodus. London: Pimlico. Trinkaus, E. and P. Shipman (1994). The Neandertals. New York: Vintage Books. Tu, P. N. V. (1994). Dynamical Systems. Berlin: Springer-Verlag. Wolpoff, M. H. (1989). Multiregional evolution: the fossil alternative to Eden, in: P. Mellars and C. Stringer (eds.), The Human Revolution: Behavioural and Biological Perspectives on the Origins of Modern Humans. Edinburgh: Edinburgh University Press: 62 –108. Zubrow, E., (1989). The demographic modelling of Neanderthal extinction, in: P. Mellars and C. Stringer (eds.), The Human Revolution: Behavioural and Biological Pespectives on the Origins of Modern Humans. Edinburgh: Edinburgh University Press: 212 – 231.

SUMMARY This paper proposes a model that unifies and integrates four conjectures put forward to explain the extinction of the Neanderthals. The model shows that these hypotheses, considered together or individually, are not sufficient to guarantee the extinction of the Neanderthals. Moreover, a survival trap related to the economic incentives of Homo sapiens’ migration is essential to explain the fate of the Neanderthals.

ZUSAMMENFASSUNG In dieser Arbeit wird ein Modell vorgeschlagen, das vier bekannte Hypothesen über die Gründe für das Aussterben des Neandertalers integriert. Das Modell zeigt, dass diese vier Hypothesen weder zu-

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JOÃO RICARDO FARIA sammen noch einzeln eine ausreichende Erklärung für das Aussterben des Neandertalers liefern. Um dessen Schicksal wirklich erklären zu können, muss darüber hinaus ein entscheidender Einfluss angenommen werden, der mit den ökonomischen Migrationsanreizen beim Homo sapiens zusammenhängt.

RÉSUMÉ Cette étude propose un modèle qui réuni et intègre quatre hypothèses connues sur les causes de l’extinction de l’homme du Neandertal. Le modèle met en évidence que ces quatre hypothèses ne sont capables ni ensemble ni à elles seules de donner une raison concluante de la disparition de l’homme du Neandertal. Afin de pouvoir bien expliquer son sort, il faut supposer une influence décisive liée aux incitations économiques à la migration chez l’homo sapiens.

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