Joint determination of biological encephalization, economic specialization

Resource and Energy Economics 33 (2011) 426–439

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Resource and Energy Economics journal homepage: www.elsevier.com/locate/ree

Joint determination of biological encephalization, economic specialization§ Richard D. Horan a,*, Jason F. Shogren b, Erwin H. Bulte c a

Michigan State University, United States University of Wyoming, United States c Wageningen University, The Netherlands b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 1 June 2009 Accepted 1 February 2010 Available online 4 June 2010

In this paper, we develop a paleoeconomic model of the coevolution of economic specialization and encephalization—the common physiological measure of intelligence as reflected by brain mass relative to total body mass. Our economic analysis links ecological and social intelligence theories of increased encephalization in early hominins through a model in which both economic and ecological feedbacks jointly determined the evolutionary incentives. We focus on degrees of specialization affected by coordination costs with and without market exchange. Our results suggest encephalization would be a process characterized by diminishing returns to behavioral advances. In terms of the long-running debate in economics over whether specialization increases or decreases intelligence, our results suggest from an evolutionary perspective the answer depends on economic/social institutions and how these influence ecological interactions. ß 2010 Elsevier B.V. All rights reserved.

Keywords: Bioeconomics Hominin evolution Positive feedbacks Australopithecus

1. Introduction A central theme of Tom Crocker’s research is that economic and ecological systems are jointly determined (e.g., Crocker and Tschirhart, 1992)—the two systems are fundamentally linked through a series of feedback processes. As a consequence, risks to environmental health and ecosystem services

§ This paper was presented at the Crockerfest Workshop in Centennial, WY. Thanks to Tom Crocker for the inspiration for this work. Thanks also to Klaas van’t Veld and other workshop participants, as well as Arthur Robson, for their many helpful comments. * Corresponding author. E-mail address: [email protected] (R.D. Horan).

0928-7655/$ – see front matter ß 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.reseneeco.2010.05.005

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are endogenous (Shogren and Crocker, 1999). Crocker has applied this concept to a diverse set of topics ranging from groundwater policy (Crocker et al., 1991), invasive species management (Settle et al., 2002), health care policy (Chen et al., 2002), and human capital formation (Agee and Crocker, 1998). Our paper serves to illustrate how the concept of joint determination is relevant even for the coevolution of human economic behaviors, specifically specialization, and the most important of all human physiological traits—encephalization. Greater encephalization means increased brain mass relative to total body mass, and is widely seen as a measure of intelligence (Williams, 2002). Our model builds on Agee and Crocker’s (1998) results in the area of human capital formation, and it addresses a debate in the economic literature initiated by Adam Smith. Smith (1965) proposed that specialization and intelligence, two of the key drivers of economic growth, are fundamentally linked. He theorizes specialization and intelligence are substitutes, whereby specialization reduces (the need for) intelligence because an individual only requires knowledge about his or her specialized skill. More recently, Becker and Murphy (1992) find a complementary relation may hold in some instances: investments in specialization and human capital are reinforcing when specialization is limited by coordination costs. But these results are less clear cut when human choices generate environmental impacts affecting utility. Agee and Crocker (1998) show how incorporating environmental relations in a model of human capital development produces economic and ecological feedback processes that can lead to ambiguous results. They stop short of modeling the thickening of markets via specialization, but they do propose that more research is needed on the role of ecosystem interactions in this process. In effect, this earlier work focuses on human investments in knowledge as opposed to evolutionary investments in intelligence. Herein we take things one step further. We investigate the role of economic and ecological feedbacks at the evolutionary level, shedding light on fundamental processes of what makes us human—the co-evolution of human physiology, behavior, and our natural environment. The origin of human intelligence is at the core of understanding human beginnings. Researchers measure a species’ intelligence by the encephalization quotient (EQ): the ratio of actual brain size to the predicted brain size based on body mass (Williams, 2002). Human EQ is far greater than the EQ of any other known animal. For instance, Williams calculates the EQ for humans to be 62.9, almost three and one half times the largest EQ among all other extant primates 18.5 for Gorilla Gorilla. Scientists generally accept that human intelligence is the result of runaway selection—a selfreinforcing selection process, often described as a co-evolutionary arms race, fueled by positive feedbacks between humans (or hominins) interacting with each other or with their environment (e.g., Ofek, 2001). Debate remains, however, on the processes involved. Theories generally fall into one of two categories. First, the social intelligence hypothesis posits that social interactions drive runaway selection (Robson, 2005).1 For instance, Robson (2005) and Ofek (2001) describe various ways in which individuals gain from having improved rationality or intelligence relative to others, resulting in runaway selection for this trait. Alexander (1990, p. 4) argued humans had ‘‘become so ecologically dominant that they in effect became their own principal hostile force of nature.’’ That is, the encephalization process came about from within-group and cross-group social competition and coordination. Competition and coordination enabled us to achieve such dominance over our ecosystem we were no longer subject to ecological pressures. Flinn et al. (2005, p.15) write, ‘‘In this evolutionary scenario, the primary selective pressures acting on hominins – particularly in regard to the brain – came from their dealings with other hominins rather than with climate, predators, and food directly.’’ Only social pressures mattered and these spurred runaway selection for intelligence. These theories, however, do not address why hominin social environments developed differently and spurred unique outcomes as compared to our closest primate relatives (see Flinn et al., 2005). Moreover, if complex social interactions did spur encephalization, why has encephalization apparently ceased, or declined (Ruff et al., 1997) today when humans have developed the most complicated and ecologically dominant society the world has ever known?

1 The label ‘‘social intelligence hypothesis’’ is used in economics, while other labels have been adopted in other fields. For instance, in human behavioral ecology, Flinn et al. (2005) use instead the label Ecological Dominance-Social Competition (EDSC) model, as proposed by Alexander (1987, 1990).

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The second class of explanations is based on the ecological intelligence theory—intelligence coevolves with ecological or physiological relations (Robson and Kaplan, 2003). For instance, Robson and Kaplan (2003) model investments in somatic capital co-evolving with investments in reduced mortality—so as to reap the future gains of somatic investments. The underlying argument is these investments would have paid off for early human hunters, as hunting is highly skill-intensive. Galor and Moav (2002) focus on humans’ somewhat unique ability (relative to most predators) to fashion tools and technology as a driving force (see also Wood and Strait, 2004), as there are positive feedbacks between innovation and human capital. Another theory suggests adding meat to the diet provided high-value nutrition that spurred brain development (see O’Connell et al., 2002). As explanations of the encephalization process, these ecologically-based theories have difficulty explaining the significant amount of encephalization that occurred long before hominins were hunters. The EQ of the first instance of Homo, Homo habilis, had already doubled relative to our nearest relatives today, the chimpanzee (Pan troglodytes) (Williams, 2002). These hominins were still largely foragers, scavengers (not yet organized hunters), and prey for more powerful predators (O’Connell et al., 2002). It is now understood that meat was only a fall-back resource for early Homo (O’Connell et al., 2002). Moreover, earlier hominins like Australopithecus, which had an approximately 34% larger EQ than chimpanzees (Williams, 2002), likely were unable to access meat and marrow from carcasses (Wood and Strait 2004). So how did this early encephalization begin? Our analysis links ecological and social intelligence theories. We expand on prior work by exploring feedbacks between the ecosystem and hominin behaviors when hominins first moved into the savanna, long before they were hunters. We explore how cooperation through specialization could have co-evolved with the hominin resource base to drive encephalization, as changes in encephalization should be expected to accompany changes in foraging behavior (Foley and Lee, 1991). We first focus on specialization that does not involve highly differentiated tasks (i.e., markets are thin) and is limited by coordination costs. Next, we examine how the results change for higher levels of specialization, combined with exchange markets and no coordination costs. Our results are consistent with Agee and Crocker, and they illustrate conditions under which Becker and Murphy’s and Smith’s results each hold at the evolutionary level. 2. Foraging and evolution: Australopithecus The earliest bi-pedal hominins moved into the patchy savannas of Africa after these habitats originated following a period of climate change around 6 million years ago (Cerling et al., 1997; Foley and Lee, 1989). We refer to these first hominins in the savanna as Australopithecus, though technically Australopithecus emerged as a result of the ensuing evolutionary forces. We model this evolutionary process, focusing on how behavioral choices influence encephalization. We begin by developing a model of population growth and foraging, since these processes are what ultimately determine evolutionary changes. 2.1. Resource and population dynamics We develop a predator–prey model of population dynamics, focusing on a single Australopithecus (predator) population, denoted N, and a single resource (prey) stock, denoted X. The resource stock is denominated by its nutritional or energetic value, which amounts to scaling biomass by a nutritional parameter having units such as kcal/kg. We model the resource stock as a renewable resource that evolves according to:   X X˙ ¼ rX 1   NF K

(1)

where r is the intrinsic growth rate of the resource, K is the resource’s carrying capacity, and F is the per capita consumption of the resource by early hominins. Logistic growth is not necessary for our results; the key element is that hominin harvests influence the resource stock.

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Australopithecus population growth – or fertility – depends on the available food supply, which holds with force for people living close to subsistence (see Frisch, 1978; Hansson and Stuart, 1990; Nerlove, 1991, 1993; Dasgupta, 1995). Following conventional models of predators (e.g., McGehee and Armstrong, 1977; Robinson and Wilson, 1998), population dynamics are:   F N˙ 1 ¼G¼r S N

(2)

where G is per capita fertility, r is a growth parameter, and S is a subsistence level. The population shrinks (grows) whenever per capita consumption is below (exceeds) the subsistence level. Let S be an increasing, convex function of the physiological factor encephalization, e, as greater encephalization is costly in terms of energy requirements.2 2.1.1. Foraging model Australopithecus are believed to have had foraging patterns similar to chimpanzees, which forage primarily for collected foods (e.g., fruits and easily accessible plant parts) (Kaplan et al., 2000; Foley and Lee, 1991; O’Connell et al., 2002).3 It is also believed that tools were not used to any significant degree during this period (Foley and Lee, 1989; Wood and Strait, 2004). Tools would have been of little use for accessing and processing collected foods. Individuals have T amount of time available to obtain food, which must be allocated between searching for food, Ts, and processing food, Tp. The per capita amount of food encountered and consumed is given by the augmented Schaefer production function (Clark, 1990), F ¼ ½T s ½1  cðn; eÞgðn; aÞqðe; aÞX

(3)

In (3), the coefficient q is an individual’s encounter rate for the resource, which is an increasing function of encephalization, e, qe > 0.4 Assume q also depends on a habitat area parameter, a, with qa < 0: search effort is less effective when X is spread over a larger area. We also assume, for simplicity, qae = 0. The encounter rate is modified by the function g, which is increasing and concave in the size of the search party, n  N, and decreasing in land area, ga < 0, with gan > 0. This is consistent with Kurland and Beckerman (1985), who discuss how search parties that fan out and communicate can increase per capita encounters relative to searches by individuals.5 We view this collaboration as a division of labor over the hunting area, with each individual specializing in searching along a particular trajectory. In this sense, production described by Eq. (3) is consistent with the approach of Becker and Murphy (1992), except that specialization herein does not require a significantly differentiated skill set among individuals. Following Becker and Murphy (1992), collaboration is costly. Collaboration costs (e.g., communication costs) reduce the effective search effort level, defined as Ts[1  c(n,e)] with c 2 [0,1] and c(1,e) = 0. For c < 1, per unit marginal costs of collaboration increase at an increasing rate, cn, cnn > 0. Total and marginal per unit costs of collaboration are decreasing in e, i.e., ce, cne < 0; encephalization 2 The subsistence parameter reflects a number of biological processes. For instance, the subsistence rate should vary directly with the mortality rate, and mortality should increase, given a fixed pelvis size, when encephalization increases (i.e., higher mortality during birth). Encephalization also requires energy that can alternatively be used to reduce natural mortality (Kaplan et al., 2000). Subsistence implicitly depends on the total time spent working, defined below as the fixed value T, and does not vary as a function of labor allocations across different tasks (e.g., searching for food, processing food). Rather, each task has the same energy requirement per unit time. This is a common, though implicit, assumption in foraging models (e.g., Robinson and Wilson, 1998). 3 Other food categories include extracted foods (e.g., seeds, roots, and nuts), and hunted foods (e.g., vertebrate meat) (Kaplan et al., 2000). It is difficult to force all food resources neatly into these three traditional categories, as accessibility and processing times may vary considerably within each class. But it would be unwieldy to model a large number of highly-differentiated resources. We use these three categories, noting the set of collected foods may extend slightly beyond traditional definitions. For instance, we assume Australopithecus only foraged for collected foods. This hominin, however, likely foraged for the most easily accessible extracted and hunted foods (e.g., tiny animals), and so we implicitly include those in our definition of collected foods. 4 Subscripts refer to partial derivatives. 5 We speculate that the cognitive and behavioral preconditions for such a coordination and communication strategy to be successful are significant—arguably explaining why the evolutionary trajectory of humans is distinct from that of non-hominin foragers.

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improves communication and planning, both vital to coordination. How we model coordination costs differs slightly from Becker and Murphy (1992)—we assume these costs are a function of encephalization, e, and operate as a reduction in effective search time rather than an output cost.6 In sum, harvests follow the basic Schaefer production function when n = 1. Coordination increases output at a diminishing rate when n > 1. In addition to locating food, individuals also spend effort on food processing.7 Let processing time per unit of the resource be given as b, which is fixed since collected foods do not require any special physiological capital or tools to process. Individuals take group size, n, and all biological parameters as fixed, though later we show the optimal group size is chosen at the group level to be an endogenous function of the resource base. Their labor allocation is then determined in this model from their time constraint: Ts ¼

T ½1 þ b½1  cðn; eÞgðn; aÞqðe; aÞX

(4)

Assume processing time for collected foods is not too substantial, such that b[1  c(n,e)]g(n,a)q(e,a)X < 1; which implies search time accounts for more than 50% of the total available foraging time. Using relations (3) and (4), per capita food consumption is: F¼

T½1  cðn; eÞgðn; aÞqðe; aÞX ð1 þ b½1  cðn; eÞgðn; aÞqðe; aÞXÞ

(5)

Per capita consumption in (5) depends on n and the value of the resource stock. The value of n is a group level choice that requires cooperation among individuals or that could be achieved via a group leader.8 Alternatively, competition among groups having different cooperation strategies may lead to the fittest groups surviving, resulting in a value of n that maximizes fitness G (Kurland and Beckerman, 1985). Specifically, the optimal group size solves:

@F Tqðe; aÞX ¼ ½½1  cðn; eÞg n ðn; aÞ  cn ðn; eÞgðn; aÞ ¼ 0 @n ð1 þ b½1  cðn; eÞgðn; aÞqðe; aÞXÞ2

(6)

which implies the term in brackets must vanish. The implicit solution to (6) is n(e,a), with:

@n cn g a  ½1  cg na ¼ >0 @a ½1  cg nn  cnn g  2cn g n

(7)

@n cne g þ ce g n ¼ >0 @e ½1  cg nn  cnn g  2cn g n

(8)

Expression (7) indicates coordination increases when resources are distributed over a larger area (i.e., resource density falls), which is consistent with extant primate behavior in such environments (Foley and Lee, 1989).9 Coordination increases because the returns to coordination increase—they spend more time searching (as opposed to processing) when the resource density falls, which increases Ts and the returns to coordination. This expression implies group sizes would have likely increased when hominins first moved into the savanna, which was characterized by a lower density of nutritional 6 Other specifications for the time cost, such as a lump sum reduction in the total time for work, T, yield analogous results, but add significantly greater analytical complexity. 7 Processing time can influence the set of foods over which a species will forage (Robinson and Wilson, 1998); Wood and Straight (2002) argue primitive hominins such as Australopithecine may have been unable to access the energy embedded in extractive and hunted foods. 8 There is evidence suggesting that foraging societies are able to regulate fertility in order to promote overall fitness. Such evidence exists for contemporary foraging societies, and Marceau and Myers (2006) argue that Paleolithic people also controlled their populations. They suggest that various methods of population control may have been used including ‘‘culturally-demanded abstinence, disruption of the menstrual cycle through extended breast feeding, abortion, direct and indirect infanticide (particularly female infanticide) and even dietary cannibalism’’. 9 Coordination could also increase to confront an increase in predation risks in the open savanna (Foley and Lee, 1989).

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resources than the forest habitats which the hominins previously occupied (Kurland and Beckerman, 1985).10 Expression (8) indicates greater encephalization increases the returns to coordination by increasing search productivity and decreasing coordination costs. Encephalization is complementary to coordination. If coordination is also complementary to the encephalization process such that coordination and encephalization are joint complements, then co-evolution drives increases in both encephalization and coordination. We show this holds in the next section on evolution. 2.1.2. Evolution of encephalization after moving into the savanna We use adaptive dynamics (Brown and Vincent, 1987; Rice, 2004) to model evolutionary changes in e. Encephalization is a ‘‘slow variable’’ since it evolves on a much slower time scale than N and X, which we call the ‘‘fast variables’’. Changes in encephalization occur after the fast variables have equilibrated at their steady state values (Rice, 2004). Following Diekmann and Law (1996), Lande (1979), and Krakauer and Jansen (2002), encephalization evolves according to:

e˙ ¼ me N

   @G Sð@F=@eÞ  Fð@S=@eÞ  ¼ me N  r   @e X¼X  S2   X¼X   ð @ F= @e Þ  ð @ S= @e Þ  ¼ me N  r  S

(9)

X¼X 

where me is a mutation rate and the superscript * denotes N and X are evaluated at their conditional steady state values—that is, conditional on the current value of e. The final equality in (9) arises because F* = S in a conditional steady state involving the ‘‘fast’’ variables N and X. Since F* endogenously depends on foraging behavior, so does the evolution of e. Expression (9) indicates the encephalization trait e increases (decreases) when its marginal benefit from increased food production exceeds (is less than) its marginal cost from increased subsistence. An equilibrium emerges when the marginal values are equal. Suppose prior to entering the savanna, hominins were in an evolutionary equilibrium, i.e., e˙ ¼ 0. Hominins likely focused their foraging efforts on collected foods both prior to and after their move to the savanna, though these resources would have been less dense in the new ecosystem (Foley and Lee, 1989; Kurland and Beckerman, 1985). This reduced density is modeled by a larger value of a.11 Starting from an initial equilibrium that would have satisfied ½@F=@ejX¼X  ¼ @S=@e, we want to know how this relation would have been affected in the short run by an increase in a (later, we explore how the long-run evolutionary equilibrium value of e is affected by an increase in a). That is, how does the increase in a alter the marginal incentives for encephalization, so as to move e out of equilibrium?12 The increase in a will not affect S, and so the evolutionary impact depends on how an increase in a affects ½@F=@ejX¼X  .13 If @½@F=@ejX¼X  =@a > 0, the marginal benefits of encephalization increase and e increases; if @½@F=@ejX¼X  =@a < 0, the reverse happens. Define Lðe; a; nðe; aÞ; X  ðe; aÞÞ ¼ ½@F=@ejX¼X  , where X*(e,a) is the conditional steady state value of X, implicitly defined by the steady state condition F* = S.14 The marginal affect of a on ½@F=@ejX¼X  is: dð½@F=@ejX¼X  Þ ¼ La þ LX  Xa þ Ln na da 10

(10)

Kurland and Beckerman (1985) use a less formal model to develop the same result. They also might have found resources to be supported by a different carrying capacity, though this feature would not affect evolutionary outcomes. The reason is that the evolutionary equilibrium condition [@F/@e]jX=X* = @S/@e is independent of the carrying capacity, since X* is determined from Eq. (2). From Eq. (1), the equilibrium population, N*, does depend on the carrying capacity. By Eq. (9), N* impacts the speed of evolution, but not the evolutionary equilibrium. 12 The evolutionary equilibrium condition [@F/@e]jX=X* = @S/@e implicitly defines the evolutionary equilibrium value e(a). The sign of e0 (a) indicates how changes in a affect the equilibrium value of e. We initially focus on shorter run impacts as a change in a moves e out of equilibrium. Later, we describe the equilibrium impacts. 13 A decrease in the density of food will increase the caloric requirement of searching for one unit of food, as searching longer will require more calories. However, the extra time searching comes at the expense of time spent processing. Since these tasks require the same energy per unit time, there is no net change in subsistence requirements. 14 The steady state hominin population level is then determined from the steady state condition rX*(1  X*/K) = NF*. 11

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Eq. (10) indicates three key effects are at work: (i) La, a direct foraging productivity effect; (ii) LX  Xa , an ecological feedback effect as the resource stock adjusts in response to the change in harvest pressure; and (iii) Lnna, an economic feedback effect as group sizes adjust in response to the lower density. The partial derivatives of L are:

La ¼

TX  3

ð1 þ b½1  cgqX  Þ

½ce ðg a q þ gqa Þð1  b½1  cgqX  Þ þ qe ½1  cðg a ð1  b½1

 cgqX  Þ  2b½1  cg 2 X  qa Þ > <0

LX  ¼

Ln ¼

Tð1  b½1  cgqX  Þð½1  cgqe  ce gqÞ 3

ð1 þ b½1  cgqX  Þ

TX  qðce g n  cne gÞ 2

ð1 þ b½1  cgqX  Þ

>0

(11)

>0

(12)

(13)

The sign of La is ambiguous because an increase in a reduces search productivity, resulting in less time processing and more time spent searching. The sign will be negative if the reduction in search productivity dominates, which we believe is the most likely case, as labor reallocations can be secondary to productivity effects. In that case, the net effect is a reduction in foraging productivity. This implies, in the absence of ecological and economic feedbacks in Eq. (10) (i.e., if LX  ¼ Ln ¼ 0), a reduction in resource density should reduce the incentives for encephalization. In what follows, however, we show how the presence of the ecological and economic feedbacks reverses this result. The sign of LX is positive, as a larger equilibrium resource stock yields larger productivity when there is greater encephalization. To sign the term LX  Xa in expression (10), we must sign Xa , which is:

@X  X  ðg a q þ gqa Þ >0 ¼ gq @a

(14)

implying LX  Xa > 0: ecological feedbacks increase the incentives for encephalization. The sign of Ln is also positive, as a larger equilibrium group size increases productivity when there is greater encephalization. Given expression (7), this means Lnna > 0 in expression (10): economic feedbacks increase the incentives for encephalization. This is not yet the joint complementarity result mentioned earlier, in which increased encephalization leads to larger group sizes that drive further encephalization. Rather, the feedback arises because the reduction in a stimulates increases in group size. If the net effect of (i)–(iii) is increased encephalization, however, the joint complementarities come into play, as we describe below. When expressions (7) and (11)–(14) are plugged back into expression (10), we can verify all the negative terms in La are cancelled out by terms in LX  Xa , so dð½@F=@ejX¼X  Þ=da > 0 and there is an increased demand for encephalization. The ecological feedbacks more than compensate for the effects of reduced productivity. The economic feedbacks further increase the incentives for encephalization. This result is reminiscent of Agee and Crocker’s (1998) results on parental choices, though in reverse. Agee and Crocker consider parents’ choices for investing in own consumption and in the development of their children’s hominin capital. They show how an exogenous increase in geneticbased intelligence causes economic and ecological outcomes to become ‘‘behaviorally and reciprocally linked’’ (p. 267). They illustrate how accounting for these feedback processes can generate results contrary to a model that does not address these processes. Here we show the opposite: an exogenous ecological shock (i.e., a reduction in resource density) generates ecological and economic feedback processes that impact upon nature’s demand for encephalization. This expands the scope of endogenous risk (Shogren and Crocker 1999; Crocker and Tschirhart, 1992) to the evolutionary level—only truly exogenous shocks (e.g., climate change; though today even that is endogenous) are unaffected by economic and ecological interactions. Moreover, this

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expands the scope of ecosystem externalities (see Crocker and Tschirhart, 1992) to include evolutionary impacts, as the hominins’ impacts on the resource stock affect evolutionary changes.15 We have shown the increase in a increases ½@F=@ejX¼X  relative to S, resulting in increased encephalization (e˙ > 0). Additional economic and ecological feedbacks arise in response to this initial increase in e, influencing further changes in e. The marginal affect of e on ½@F=@ejX¼X  is: dð½@F=@ejX¼X  Þ ¼ Le þ LX  Xe þ Ln ne de

(15)

It can be verified that Le < 0, given diminishing returns to encephalization in production. Consider the second term on the right hand side (RHS) of (15), LX  Xe . The sign of this term is the same as the sign of Xe . We derive:

@X  he Se ð1 þ bh Þ ¼  þ  @e hX hX ðT  SbÞ

(16)

where h ¼ ð1  cÞgqX  (so that he ¼ ½ce gq þ ð1  cÞgqe X  > 0 and hX ¼ ð1  cÞgq > 0). Recognizing that T  Sb ¼ T=ð1 þ bh Þ > 0 and ½@F=@ejX¼X  ¼ T he =½1 þ bh  (so that he ¼ ð½1 þ bh ½@F=@ejX¼X  Þ=T), expression (16) becomes: " #    2 @X  ð1 þ bh Þ2 @F  ð1 þ bh Þ S Se   ¼ e˙ (17) ¼  @e hX T @e X¼X  hX T me N  r where the final equality comes from Eq. (9). Expression (17) says the impact of greater encephalization on the conditional steady state resource stock is inversely related to the intertemporal change in e. On the one hand, subsistence requirements increase with greater encephalization, creating a need for a larger resource stock, ceteris paribus. On the other hand, greater encephalization increases productivity for any given level of resource stock, and so less of the stock is required to maintain subsistence requirements. After the increase in a spurs an initial increase in e, so that e˙ > 0, the sign of (17) is initially negative: increases in e result in a smaller X*, which reduces the incentives for further encephalization in (15). This mitigating ecological effect eventually vanishes as e approaches its new equilibrium value. Expressions (8) and (13) indicate Lnne > 0: economic feedbacks further increase the marginal incentives for encephalization. Along with expression (8), this means encephalization and group size are joint complements, with investments in one reinforcing investments in the other. These reinforcing investments could produce runaway selection (at least to a point, since eventually encephalization costs (Se > 0) will be a mitigating factor) if Lnne is large enough to result in dð½@F=@ejX¼X  Þ=de > 0. Eventually, dð½@F=@ejX¼X  Þ=de will be positive if Lnne > jLej (i.e., the economic feedback effect dominates the effect of diminishing returns to encephalization when group size is held constant). This is because Xe ! 0 as e converges to its new equilibrium value (which we indicate below will be larger than the pre-savannah value). But even if dð½@F=@ejX¼X  Þ=de < 0, the value of dð½@F=@ejX¼X  Þ=de will be greater than if there were no economic feedback effects. The long-run equilibrium effect of the increase in a is increased encephalization. To illustrate this last result, we note that the evolutionary equilibrium value of e is implicitly defined by the condition ½@F=@ejX¼X  ¼ @S=@e. From this relation, and recalling that Xe ¼ 0 in an evolutionary equilibrium, we can derive: de La þ Ln na þ LX Xa >0 ¼ da See  ½Le þ Ln ne 

(18)

15 Ecosystem externalities arise when individuals’ choices affect, via ecosystem interactions, ecological state variables unrelated to the initial decision that impact on future economic welfare (Crocker and Tschirhart, 1992). In addition, our theory leads one to contemplate the idea that perhaps there could be ‘‘cycles’’ in encephalization. Evolutionary pressures could work towards greater or smaller levels of encephalization, depending on the distribution of resources across the landscape. The distribution would vary with exogenous (e.g., climate) and endogenous factors (e.g., hunting technologies). For instance, a would increase as hominins entered an ice age and it would decrease afterwards. It is unclear at this stage, however, whether the ice ages really would last long enough for significant changes in the brain.

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The numerator in expression (18) is the same as expression (10), which is positive. The denominator 2 2 equals ðS2 =rÞ½@ G=@e2 jX¼X  , which is positive because ½@ G=@e2 jX¼X  is negative in an evolutionary stable equilibrium (Rice, 2004). The encephalization process we describe echoes the results of Becker and Murphy (1992). They find knowledge and specialization (coordination in our case) to be jointly determined when specialization is limited by coordination costs and many specialists provide mainly the same skills (as in our model). But Becker and Murphy’s finding that specialization, and in turn knowledge, is limited by coordination costs is incomplete in the present context—physiological costs via impacts on subsistence requirements and ecological feedbacks also work to temper the encephalization process. According to this theory, encephalization among Australopithecus is not the result of social interactions independent of ecological interactions. This result contrasts with the social intelligence theories that either passively disregard ecological interactions or, as in the Ecological DominanceSocial Competition (EDSC) theory, assert these interactions were unimportant because hominins were dominant over their ecosystem. Also in our model, encephalization was not the result of ecological interactions independent of social interactions, as with ecological intelligence theories. Though hominin choices (movement into the savanna and increased coordination) led to increased marginal gains from encephalization, these choices were driven by ecological processes (climate change). Further, the encephalization process was either reinforced or mediated by ecological interactions—not the result of human dominance over the ecosystem. The systems were jointly determined. 3. Trade and evolution: Homo sapiens We now investigate how the incentives for encephalization change as hominin behaviors change. Specifically, we focus on the impact of specialization and trade. Trade is the key hominin behavioral advancement, and involves significantly more specialization than what was modeled in our Australopithecus foraging model.16 We therefore take a quantum leap forwards in time—from one hominin species to another. Debate remains about when trade began; evidence exists suggesting trading networks among early modern humans (Homo sapiens) existed by at least 130,000 B.P. (Holden, 1998), and trading had taken off by about 40,000 years ago (Horan et al., 2005). Interestingly, encephalization has ceased or even declined during this same time frame (Ruff et al., 1997). Here we consider a case to illustrate how these two events may be linked. Early markets would have initially been extremely thin, with few products being exchanged. Becker and Murphy (1992) argue investments in human capital lead to a thickening of markets, as human capital allows for increased specialization and less reliance on self-provisioning. Agee and Crocker (1998) suggest research is needed on the role of ecosystem interactions in this trading process. We now apply their ideas at the evolutionary level. Investments in hominin capital eventually led to less time spent foraging and more time spent in other activities such as tool production. At some point, the number of tools and activities that Homo engaged in would have been too large for any individual to manage. Specialization and exchange by individuals engaged in highly differentiated tasks would have been the inevitable result. How do specialization and exchange influence encephalization? We address this question by departing somewhat from our previous model, which was already complex and would become more so if we attempted to incorporate exchange. We focus on a simpler construction to illustrate the main points, which intuitively should carry over to more complex specifications. We do not focus on coordination costs, though coordination is to some extent required when trading.17 Rather, we focus on specialization in two distinct tasks, which contrasts with our earlier model in which specialization involved similar activities spread across the landscape. The model we adopt comes from Horan et al. (2005). Trade arises to exploit differences in skill, and so we introduce heterogeneity among Homo. Assume individuals are in one of two subgroups: (i) skilled hunters (indexed by j = s) and (ii) unskilled hunters (indexed by j = u). Members of each group 16 In addition, Isaac (1983) and Ofek (2001) claim exchange began from the home base. People brought food back and exchanged, and they also specialized in tool production. 17 Horan et al. (2008) describe how speech could have co-evolved with trade to reduce the coordination costs associated with trade.

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derive utility from consuming meat and a possibly broad set of other goods (e.g., clothes and shelter). These other goods were not modeled previously, but they would have become increasingly important as Homo substituted man-made adaptations for physiological ones. Utility is a Cobb–Douglas function of meat (m) and other goods (a): b 1b

U j ¼ mj aj

; j ¼ s; u

(19)

where b is a parameter assumed not to vary by skill-class. The indices are represented as subscripts for meat and other goods to distinguish the indices from the exponents; elsewhere they are represented as superscripts. Individuals maximize (19) subject to a time constraint: T j ¼ T jm þ T ja jm

(20) ja

ja

where T is hunting effort and T is effort directed at producing other goods. Let a = T for simplicity. We ignore processing; rather we define harvesting of meat by the standard Schaefer production function (Clark, 1990): m j ¼ q j T jm X

(21)

where X represents the extant population (biomass) of wildlife. Catchability is an increasing function of encephalization, qj(e), with qs > qu and qse > que for a given e. Though individuals share the same level of encephalization, skilled hunters can make better use of this trait. This does not mean skilled hunters are more intelligent. Rather, the increased efficiency among skilled hunters could reflect some other traits used in conjunction with intelligence (e.g., eyesight, sense of smell) to influence hunting productivity. Encephalization does not affect production of other goods, e.g., e has crossed a threshold such that the marginal impact of e on the production of a is now zero. We could have just as easily assumed encephalization was more important to produce other goods than for hunting. The key element is that some activities require more intelligence than others, though everyone has the same level of e in our model.18 Finally, we modify Homo population growth relative to (2) to account for the heterogeneous, interacting sub-populations. The offspring of skilled hunters can be either skilled or unskilled; similarly, unskilled hunters can have either skilled or unskilled offspring. Denote the proportion of skilled hunters’ offspring who are skilled by ms; and the proportion of unskilled hunters’ offspring who are unskilled by mu. Heredity is likely to bias the distribution of offspring’s skills along the lines of parentage, such that ms > 0.5, mu > 0.5. Sub-population j grows according to: ! ! m j mj ð1  mi Þmi j  1 Nj þ r (22) N˙ ¼ r Ni for j 6¼ i S S The first RHS term in (22) is equivalent to our population growth specification in (2), except that subpopulation j’s fertility rate, rmj =S, is weighed by the proportion of offspring being contributed to this sub-population, mj. The second RHS term represents sub-population i’s reproductive contribution to sub-population j. Note population growth is a function of meat and not other goods. Though individuals require other goods in their consumption bundle, food remains the limiting resource for Homo population growth. Finally, the proportion of skilled individuals is given by & = Ns/N, which changes endogenously over time due to natural selection. 18 It is common to model changes in a continuously defined trait by assuming the trait is homogeneous throughout the population (Rice, 2004). We implicitly assume that interbreeding results in a uniform value of e across the population, but simultaneously allow for a distribution of skill levels across individuals (presumably based on variation in some other trait). This is not inconsistent, as some traits may invade a population more completely than others. In reality, of course, there will be some variability in EQ levels within a population (in which case encephalization might refer to the average value of e). But this variation is much less than that for other traits influencing skill levels (e.g., eyesight and strength; one’s vision may be half as clear as the average without significant disability arising, whereas a value of e that is half of the average implies the evolutionary equivalent of late Australopithecus). Our assumption that everyone has the same e simplifies the analysis, but would not fundamentally alter our main results.

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Horan et al. (2005) derive the equilibrium consumption levels and equilibrium proportion of skilled hunters arising under self-sufficiency and under exchange, where exchange involves skilled hunters specializing in hunting and unskilled hunters specializing in producing other goods.19 Given their results and setting Ts = Tu = T, average per capita consumption under self-sufficiency is: F ss ¼ & ss bqs TX þ ð1  & ss Þbqu TX ¼ ½& ss ðqs  qu Þ þ qu bTX where &

ss

(23)

solves:

ð1  ms Þqs

&ss 1  & ss  ð1  mu Þqu ¼ ms qs  mu qu ; or & ss ¼ 1 ss 1& & ss

(24)

Average per capita consumption under exchange is: F e ¼ & e bTqs X þ & e ð1  bÞTqs X ¼ & e Tqs X

(25)

where:

&e ¼ 1  ð1  ms Þb  ð1  bÞmu < 1

(26)

Note & ss depends on e in an interior solution, while & e is independent of e. This means that, under selfsufficiency but not under trade, the marginal incentives for encephalization will partly depend on how encephalization affects the proportion of skilled hunters. Horan et al. also show & ss > & e : more skilled hunters arise under self-sufficiency due to the greater ecological pressures faced by unskilled hunters relative to skilled hunters in this scenario. In contrast, trade allows unskilled individuals to consume as a function of skilled hunters’ productivity, and so they face fewer ecological pressures relative to skilled hunters. Given these results, the marginal incentives for encephalization under self-sufficiency and exchange, evaluated at their respective steady states, are:   ss  @F ss  @& s u ss s ss u ¼ ðq  q Þ þ & q þ ð1  & Þq bTX ss (27) e e 

@e

X¼X 

@e



@F e  ¼ & e qse TX e @e X¼X 

(28)

where the equilibrium condition Fi* = S (i = e,ss) can be used to derive the steady state values of the resource stocks X ss ¼

X e ¼

S ½& ss ðqs  qu Þ þ qu bT S

& e Tqs

(29)

(30)

For a given value of e, the marginal incentives for encephalization are larger under trade if ½@F e =@ejX¼X  > ½@F ss =@ejX¼X  , or if ½@ðDFÞ=@ejX¼X  > 0, where DF = Fe  Fss. The marginal incentives for encephalization are smaller under trade if ½@ðDFÞ=@e < 0jX¼X  . We investigate this by using (27)–(30) to obtain:  @DF  ðq =eÞð1  & ss Þ½vs  vu   ð@& ss =@eÞðqs  qu Þ S (31) ¼ u  ½& ss ðqs  qu Þ þ qu  @e X¼X  where v j ¼ qej e=q j . The denominator of the RHS of (31) is positive, so the sign of (31) depends on the numerator. The first term in the numerator accounts for the marginal effect of increased 19 Other possibilities could emerge in this Ricardian trade model, depending on the proportion of skilled hunters. If the proportion is low, unskilled hunters engage in both activities while skilled hunters specialize. If the proportion is high, skilled hunters engage in both activities while unskilled hunters specialize. The conditions required for complete specialization are b > &e and qs/qu > ((1  &e )/& e )b/(1  b), which we assume holds.

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encephalization on the gains from trade. The last term in the numerator reflects how increased encephalization alters the natural selection of skill levels under the two scenarios. The sign of the first numerator term in (31) is positive if vs > vu. With trade, skilled hunters produce meat for everyone, and so everyone benefits from the more skilled hunters having more intelligence. If increased intelligence generates a sufficiently larger proportional increase in qs than in qu, the gains are further enhanced: individuals have greater incentives to specialize, and nature has even greater incentives to invest in encephalization in the trade scenario. In contrast, if vu > vs, the increase in encephalization is less under trade. Now trade insulates unskilled hunters from ecological pressures associated with their own encephalization. The sign of the second numerator term in (31) is of the same sign as:

@& ss ðqs =eÞ½vs  vu ½ms  & ss =1  & ss  ¼ @e ð1  ms Þqs =ð1  & ss Þ2 þ ð1  mu Þqu =ð& ss Þ2

(32)

which is derived from relation (25). The sign of this expression is ambiguous. If & ss + ms > 1, which might be expected since skilled hunters consume more meat than unskilled hunters and since ms > 0.5, then we can show ms > & ss .20 This means the sign of (32) is positive when vs > vu, negative when vu > vs, and zero when vu = vs. Greater natural selection of skilled hunters in the self-sufficiency scenario places more weight on meat consumption by skilled hunters, whereas the proportion of unskilled hunters is comparatively larger under trading. If increased intelligence generates a larger proportional increase in qs than in qu, average consumption increases in the self-sufficiency case due to a comparatively larger proportion of skilled hunters under self-sufficiency. This would increase the incentives for encephalization under self-sufficiency. In contrast, the comparatively larger proportion of unskilled hunters under trade are insulated from ecological pressures due to trade, and therefore experience smaller incentives for encephalization. When vu > vs, the level of natural selection of skilled hunters falls under self-sufficiency relative to trade, and the marginal incentives for encephalization become comparatively larger under the trade scenario. These results suggest a tradeoff between the effects of encephalization on the gains from trade and on natural selection, with the dominant effect being ambiguous without greater specification of the model and its parameters. This result expands and enriches the Agee and Crocker (1998) conjectures: increased human capital leads to a thickening of markets, which reduces externalities and in turn should increase human capital. Here, we find a thicker market may strengthen or diminish evolutionary externalities. Moreover, the relative magnitudes of the marginal incentives for encephalization under the two programs could change over time. If specialization and trade diminish the incentives for encephalization, this supports Smith’s (1965) notion that specialization reduces intelligence—at the evolutionary level. But our reasoning differs. Smith’s notion was specialists have fewer incentives to invest in general knowledge. In our case, encephalization would diminish because trade diversifies against ecological risks, thereby helping to insulate individuals from ecological pressures. 4. Conclusion Ecologically-based (including behavioral ecology) theories of encephalization tend to discount feedbacks from human choices, whereas theories based on social interactions tend to overlook feedbacks from ecological interactions. Herein we argue that both feedbacks matter. Encephalization occurred because hominins were a fundamental part of the ecosystem, and so economic and ecological feedbacks jointly influenced the evolutionary incentives for encephalization. Some feedbacks were reinforcing and spurred increased encephalization. Other feedbacks would have created opposing evolutionary incentives, putting the brakes on encephalization. This suggests no single event existed that triggered runaway encephalization. Rather, a series of exogenous events (e.g., climate changes; we only model one here, but we look at others involving Homo in a companion paper) could have spurred behavioral innovations that supported greater 20

This condition holds true in each of Horan et al.’s (2005) simulations.

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encephalization. Initially these behaviors involved cooperation and specialization, but they eventually spread to encompass institutions such as complex exchange networks. At first the behavioral adaptations increased the marginal benefits of encephalization, though these were eventually mitigated by ecological responses. Later, the behavioral adaptations may have diversified ecological risks so as to diminish the marginal benefits of encephalization. If this is the case, simple early behavioral adaptations could have led to significant increases in encephalization, while much more complex adaptations were later required to achieve smaller increases. Encephalization would be a process characterized by diminishing returns to behavioral advances. This result yields insights into the long-running debate in economics over whether specialization increases or decreases intelligence. 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