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

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What Happened to the Neanderthals?– The Survival Trap

João Ricardo Faria*

I. INTRODUCTION

Neanderthals inhabited Europe and Near East from approximately 135.000 to34.000 years ago. Beginning 50.000 years ago, in Eastern Europe, the Nean-derthal populations disappeared and were replaced by Modern Humans (Hu-mans, for short). In Western Europe the replacement happened around 34.000years ago. Nevertheless, there is enough evidence showing Neanderthals andHumans coexisted for a long time (Leakey 1994).

There are four principal hypotheses that have been advanced by archaeolo-gists and paleoanthropologists to explain the decline and eventual extinction ofthe Neanderthals (e.g., Caird 1994, Shreeve 1995, Stringer and Gamble 1993,Trinkaus and Shipman 1994). These conjectures are mainly based in anatomi-cal and cultural differences between Humans and Neanderthals.

The first hypothesis assumes that competition between Neanderthals andHomo sapiens led to extinction of the Neanderthals. A slower birth rate andshorter life-span, or a greater mortality rate in comparison with Humans, or arelative technological disadvantage, made them out-competed and completelyreplaced in few generations by H. sapiens (Zubrow 1989). This is a commoninference in any standard model of competing species (see, for example, Braun1979).

Two further hypotheses stress the negative impact of the contact betweenHumans and Neanderthals. One proposes that Neanderthals could have beenkilled 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 Chi-arella, Sophia Delipalla, M. Leon-Ledesma, Flávio Menezes, Robert de Rozario, and the refe-rees for helpful comments.

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tween Neanderthals and Humans facilitated the propagation of diseases thatdevastated the Neanderthal populations.

In contrast, a fourth hypothesis assumes a positive feedback between bothpopulations. It proposes that there was some interbreeding between Neander-thals and H. sapiens, whose genes eventually became dominant.

The background of these conjectures lies in the debate between the theoriesof human evolution: the Regional Continuity model, associated with Wolpoff(1989), which stresses the long-lasting contact and cooperation between Hu-mans and ancient hominids (among them the Neanderthals); and the Out of Af-rica model, associated to Stringer (1990), that emphasises the replacement of‘ancients’ by the Homo sapiens. There are other theories that lie somewhere be-tween the views of Wolpoff and Stringer, as Brauer’s ‘hybridisation and re-placement’ model and Smith’s ‘assimilation’ theory (see Shreeve 1995, Trink-aus and Shipman 1994).

One of the objectives of this paper is to demonstrate to archaeologists andother scientists the potential that economic analysis may have in integrating andunifying the conjectures and evidence about the Neanderthal extinction1. Thepaper presents a simple model that takes into consideration the four hypothesesoutlined 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. Oneof them is a stable equilibrium with a positive Neanderthal population. Thisshows that the theories above, considered individually or together, do not suf-fice to guarantee the Neanderthal extinction. 2) The actual equilibrium with noNeanderthal population is also stable. 3) The third equilibrium with positiveNeanderthal population is a saddle point, which is coined the survival trap. Thepath to extinction or survival of The Neanderthal population depends on the re-lationship between the initial conditions and the survival trap.

II. THE MODEL

The basic model describes how natural resources, Neanderthals and Humansinteract. It is composed by a system of three non-linear ordinary differentialequations. Each one describing the rate of growth of natural resources, Nean-

1. Therefore, this paper follows the tradition of applying economic analysis into prehistoricalproblems initiated by Smith (1975, 1992).

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derthal population and Human population. The system is able to represent thetheories presented in the introduction. It captures economic and demographicfeatures behind the Neanderthal fate, such as migration, resource competition,and on the one hand, warfare and disease transmission, and on the other, coop-eration and interbreeding, between Neanderthals and Humans.

Since Neanderthal and Human populations are hunters and gathers, they userenewable resources. In this sense, natural resources are supposed to be renew-able. Two different forces affect the rate of growth of natural resources: naturaland populational. Populational forces are related to the way Neanderthals andHumans use and exploit the environment. Natural forces are the forces that af-fect the rate of growth of renewable resources that do not depend on Neander-thal and Human populations, such as climate, soil, etc. These forces have twoimportant aspects. First, concerning the populational forces, Humans and Ne-anderthals compete for natural resources. It implies that Human exploitationand consumption of natural resources decrease the rate of growth of renewableresources, which allow less resources for Neanderthals, and, vice-versa. There-fore, natural resources are excludable goods for both populations. Concerningto the role of natural forces, they are captured, as usual, by a logistic functionalform2. The rate of growth of renewable resources is given by the followingequation:

S. = rS(1 – ) – zNS – hMS (1)

In equation (1), S represents the renewable resource stock at time t, N is the Ne-anderthal population, and M is the migrant population of H. Sapiens. Observethat the growth rate of natural resources (S

./S) consists of two terms: 1) the lo-

gistic functional form for the biological growth (divided by S): r(1 – ), whereK is the carrying capacity and r is the intrinsic growth rate; and 2) the exploi-tation of the natural resource by Neanderthals (zNS) and Humans (hMS).Where z and h stand for the rate of exploitation of natural resources from Ne-anderthals and Humans respectively3. From equation (1) it is clear that Humansand Neanderthals compete for natural resources.

From the discussion in the introduction, many hypothesis have been put for-ward to explain how the Neanderthal population was affected by the incomingHomo 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 popu-

lations differ in the way they exploit the environment, using different technologies, none of theresults depend on which of them is more efficient, that is, if z > h, or, vice versa.

SK

SK

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to have been affected by interbreeding with Humans, by infectious diseasestransmitted by Humans and, finally, by wars and genocides carried out by Hu-mans. Furthermore, the rate of growth of the Neanderthals should reflect theirfertility, 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 andtheir interbreeding with H. Sapiens, where g(M) represents the interbreedingfunction with Humans, (g(0) = 1, g′(M) < 0), and a is a positive constant. Therate of growth of the Neanderthal population is a negative function of the deathrate, which is affected by infectious diseases transmitted by Humans, f(M),(f(0) = 1, f ′(M) > 0), where b is a positive constant4. The effect of wars and gen-ocide is captured by the term F(w)M, where the loss of Neanderthal life isgiven by the function F of wars, w, (F ′(w) > 0, F(0) = 0)5. The forth term is thefertility function of the Neanderthal population, it depends on their efficiencyin 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 Hu-man population dynamics also must reflect the impact of such contact. Thegrowth rate of the Humans is affected by wars and by the interbreeding withNeanderthals. It is assumed that infectious diseases are passed from Humans toNeanderthals, so, Human population is not affected by any disease that mighthave been passed from Neanderthals. The incoming Human population is alsoaffected by the migration of other humans, attracted by the economic gains inmigrating. As Human population growth is accelerated by the decrease of Ne-anderthals, a sort of intra-competition among humans might have emerged. Theequation below spotlights how these variables determine the dynamics of theHuman population:

M. = M(q – G(w) – eM) (Y(x) – ) (1 + u) (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 popula-

4. This is a very simple way to model disease transmission, it implicitly assumes that all Neander-thals susceptible, when in contact with Humans, are infected. See Stannard (1993) for the rela-tion 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, aswell), which stresses the relation between force sizes and fighting parameters.

NS

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tion, where q is the difference between birth and death rates; G(w) is the lossof life in wars (G′(w) > 0, G(0) = 0); and eM represents the intra-competitionof Humans. The second term in the RHS stands for the economic opportunitycost of migration. This term depends positively on the relative Neanderthaldensity (N/S) and negatively on the economic gains in migrating (Y). Y is af-fected by climate shocks, x. The constant (1 + u), where u lies in the [0,1) in-terval, captures the genetic contribution of Neanderthals to Human population.Followers of the ‘Out of Africa’ model would assume u = 0 (no genetic contri-bution), and others u > 0. Therefore, when we refer to the extinction or replace-ment 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 at-tention to four parameters in the above model. The parameters are: h, the hu-man’s rate of exploitation of natural resources; w, the occurrence of wars be-tween Humans and Neanderthals; b, the rate at which infectious diseasesspread from Humans to Neanderthals and, finally, a, which stands for the effectof interbreeding on Neanderthals. The model captures the four theories used toexplain 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 particularcase of our model.

III. MULTIPLE EQUILIBRIA

The dynamical system (1)–(3) presents multiple steady-states equilibria6.Three of them have direct interest for our discussion. Basically these equilibriaare 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 doesnot become extinct. This equilibrium occurs because there is no incentive toHuman migration. When there is no Human migration, the competition andcontact among populations is low, which allows their coexistence. This equilib-rium is stable.

The second equilibrium is also stable. It is characterised by the extinction ofthe Neanderthal population. It is related to the migration of Human population.In this equilibrium there are incentives for Humans to migrate. So by increasingtheir 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 needfor an unstable equilibrium to separate them. This unstable equilibrium iscalled the survival trap. In this equilibrium the Neanderthal population does notbecome extinct. However, as it is an unstable equilibrium, it is fragile and anydisturbance from it can decide the final fate of the Neanderthals, by drivingthem to one of the stable equilibria. That is, to complete extinction or coexist-ence.

However, in order to study these equilibria, the following inequalities are as-sumed: i) nzr > c(r/K + zY(x)), given that c is close to zero7; and ii) r > hM.The second inequality assumes that the intrinsic growth rate of natural re-sources 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). Neverthe-less, for the period analysed, 30.000 to 40.000 years ago, there is no evidencethat the population of Humans in Europe engaged in such destructive behav-iour. The first steady-state equilibrium occurs when the economic opportunitiesto 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 endo-genous variables8:

M* = > 0 (4)

7. Inequality one is just a mathematical condition to guarantee the non-negativity of one of the so-lutions. It is likely to be fulfilled since c is a very small number. Inequality one has no economicmeaning.

8. For mathematical convenience assume that f (M) = (1 + f ) M, and g(M) = (1 – g) M, where g > 1.

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

n

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S* = > 0 (5)

N* = Y(x)S* > 0 (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 following9:

trJ* = < 0 (7)

detJ* = (q – G(w) – eM*) N * M * (hnz + (hM* – r)(a(1 – g) – b (1 + f) – F(w)) (1/S*)) > 0 (8)

which suffices to qualify the fixed point (4)–(6) as stable10.The important characteristic of this equilibrium is that the Neanderthal pop-

ulation does not become extinct. Therefore, our model does not necessarilylead to the extinction of the Neanderthals; despite taking into account the fourdistinctive theories created to explain their disappearance. Furthermore, thisequilibrium is stable. This holds true even when each one of the theories is con-sidered individually (the proof is available from the author upon request)11. The second steady-state equilibrium, in which the Neanderthal populationdisappears, 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 (9)

M* = > 0 (10)

S* = K(1 – h ) > 0 (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 (posi-

tive), 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 thetrace 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 equi-librium point. For the impact of climatic change on Human migration see Stringer and McKie(1997).

r – hM*rK–1 + zY(x)

rK–1 (hM* – r)rK–1 + zY(x)

q – G(w)e

M*r

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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 popula-tion is extinct and replaced by Human population. This is the actual equilib-rium.

The third steady-state equilibrium also occurs when there are economic in-centives to migrate, Y(x) > N/S:

M* = > 0 (14)

S* = > 0 (15)

N* = (r(1 – ) – hM*)z–1 > 0 (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) – ) (G(w) – q) < 0 (17)

trJ* = (Y(x) – ) (G(w) – q) – r < 0 (18)

As the determinant of J* is negative this steady-state equilibrium is a saddlepoint. It remains a saddle point equilbrium for the specific models as well (theproof is available from the author upon request).

The equilibrium (14)–(16), is coined the survival trap. The reason for thisname arises from the fact that there are two stable equilibria in the model, onewith positive Neanderthal population and another with no Neanderthal popula-tion, which is the actual case. Given any initial conditions for N, M and S, it isimpossible to predict what the final outcome of the Neanderthal population willbe (if it will survive or disappear). This problem occurs because both equilibria(with extinction or survival) are stable. Hence, the existence of a third equilib-rium is necessary to separate the stable fixed points, and this equilibrium is asaddle point12.

As a saddle point, the survival trap is unlikely to be reached and to guaranteethe coexistence of both populations, since there are just a few stable separa-trices 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.

q – G(w)e

F(w)M* + bf(M*) – ag(M*) + cnz

nS*K

N*S

N*S*

S*K

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a weak survival trap because it is reached only by chance. Furthermore, anyperturbation of this equilibrium (for example, a climate change) can definitelydrive the Neanderthals to coexistence or extinction13.

Therefore, it is the relationship between the initial conditions and the sur-vival 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 intoconsideration the existence of the survival trap. In the present model, its exist-ence is related to the opportunity cost of migration. The survival trap is theequilibrium in which the Neanderthals survive, even when the net economicgains 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 wasnothing inevitable about the triumph of the Moderns, and a twist of Pleistocene fate could haveleft 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 pointB, Neanderthals become extinct, and at point A they coexist with Humans. Notethat if point E represents the initial conditions (for Human and Neanderthalpopulation and availability of natural resources), the Neanderthal populationwill 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 areat point G, the populations will be ride to the survival trap. It is important tostress the fact that the survival trap is an unstable equilibrium. Therefore, anysmall perturbation taking the equilibrium out of T can define the final fate ofthe Neanderthals, to coexistence or extinction. At the survival trap there existseconomic opportunities to migrate, any perturbation on these opportunities canpush 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, thelong run implications cannot be more different. The relation between E, F andG and the survival trap, T, is essential in any discussion on the fate of the Ne-anderthals.

IV. CONCLUDING REMARKS

This paper has presented a model that integrates and unifies the conjectures onthe Neanderthal extinction. It is shown that the model has multiple equilibria.Three of them were studied. The first is a stable equilibrium with positive Ne-anderthal population. Its existence is a strong result since it demonstrates thatthe theories of Neanderthal extinction, considered individually or together, arenot sufficient to drive the Neanderthal population to extinction. The other equi-libria are the actual equilibrium with no Neanderthal population, which is alsostable, and the survival trap equilibrium, which is a saddle point. The path toextinction or survival of the Neanderthals depends on the relationship betweenthe initial conditions and the survival trap. The survival trap is the equilibriumin which the Neanderthals survive even when the net economic gains to Humanmigration are not fully exhausted.

This model can be adapted to examine other problems like the colonial ex-pansion of Europeans in America. As pointed out by Deacon (1997), the Nean-derthal demise has a close parallel to the colonisation of Europeans in Americaand the extinction or diminishing number of many native tribes. Therefore, theimportance of our model is that it integrates, in a simple framework, many fea-tures of human history such as migration, resource competition, and on the onehand, warfare and disease transmission, and on the other, cooperation and in-terbreeding, between different populations.

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World of Mathematics. New York: Simon and Schuster: 4: 2138–2157Leakey, 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 Ex-

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SUMMARY

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

ZUSAMMENFASSUNG

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

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sammen noch einzeln eine ausreichende Erklärung für das Aussterben des Neandertalers liefern. Umdessen Schicksal wirklich erklären zu können, muss darüber hinaus ein entscheidender Einfluss an-genommen werden, der mit den ökonomischen Migrationsanreizen beim Homo sapiens zusammen-hängt.

RÉSUMÉ

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