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Journal of Anthropological Archaeology 18, 251–281 (1999)Article ID jaar.1999.0342, available online at http://www.idealibrary.com on

Fitness and Reproductive Trade-Offs in Uncertain Environments:Explaining the Evolution of Cultural Elaboration

Mark Madsen

InterNAP Network Services, 601 Union Street, Suite 1000, Seattle, Washington 98101

E-mail: [email protected]

and

Carl Lipo and Michael Cannon

Department of Anthropology, University of Washington, Seattle, Washington 98105

E-mail: [email protected], [email protected]

Received August 26, 1998; revision received December 9, 1998; accepted April 15, 1999

Dunnell (1989) proposed that cultural elaboration is likely a consequence of selection withinuncertain environments. He developed the theory to the extent that it performs well in explain-ing the distribution of elaboration within eastern North America at regional scales. Moredetailed studies require development of the theory so that additional hypotheses and implica-tions can be deduced. We draw upon theories of selection in fluctuating environments andtheories about reproductive strategies to propose a simple model of selection for culturalelaboration in uncertain environments. The simple model has several general implications forthe relationship between fecundity, elaboration, and other archaeological observables, includ-ing population age structure, spatial variation and mobility, and the character of environmentalvariability. © 1999 Academic Press

INTRODUCTION burials flourished for a time on the coast

Theory provides the maps that turn an unco-ordinated set of experiments or computer sim-ulations into a cumulative exploration.

Booker et al. (1989) Artificial Intelligence40:235–282

Cultural elaboration, particularly in itsmost spectacular expressions in burialceremonialism and monumental architec-ture, is a natural source of curiosity forarchaeologists whenever and wherever itoccurs. Archaeologists have given signifi-cant attention, for example, to explainingwhy Hopewell burials contain immensequantities of obsidian, copper, and otherdifficult-to-acquire materials and whyMoche monumental architecture and

251

of Peru and then vanished. Indeed, theearliest archaeological work in many re-gions of the world has focused on culturalelaborations. Despite these efforts, nogeneral explanation for elaboration hasemerged. The explanations that do existare theoretically deficient, as they charac-teristically contain a common threadtraceable to the vitalistic foundations ofnineteenth-century cultural evolution(Dunnell 1989). Until recently, however,there has been little effort aimed at ex-plaining elaboration in light of scientificprinciples of human cultural evolution.Lacking a falsifiable, scientific frameworkfor building explanations, archaeologists

0278-4165/99 $30.00Copyright © 1999 by Academic PressAll rights of reproduction in any form reserved.

are still faced with a critical question: why

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252 MADSEN, LIPO, AND CANNON

would people expend such enormousamounts of energy on tasks and objectsseemingly unrelated to their survival or toreproduction?

If we accept the proposition that humancultural behavior evolves by the sameDarwinian principles as the rest of theorganic world, explanations for elabora-tion must be built using natural selection,cultural transmission, and drift (Dunnell1980, 1989; O’Brien and Holland 1990). Ex-ploring the outlines of such an explana-tion is the purpose of this article, not de-bating the wisdom or efficacy of aDarwinian approach to archaeology. Evenif one assumes a Darwinian perspectivefor building explanations of cultural elab-oration, no single explanation can be ex-

ected. Many possible explanations cane constructed within a Darwinian frame-ork for any particular class of phenom-

na, of which all may be equally robust inerms of theory. Alternative hypotheses

ust be evaluated based on their ability toccount for the empirical world in partic-lar cases. Thus, our analysis in theresent context is also not a complete ex-lanation of cultural elaboration in all its

orms and conceptions. A general expla-ation cannot exist because evolution isn endless interplay of general principlese.g., natural selection, physiology, andonstraints and rules for behavior) withhe specific and contingent history of par-icular populations [Mayr 1959(1976):317].he best one can do toward providing ageneral” explanation for a phenomenons to build increasingly comprehensive

odels that show how a set of invariantrinciples interact with variability tohape historical phenomena in consistentays. General theories about a class ofhenomena such as cultural elaborationan be sufficient for explaining the materialorld, but never necessary, since these the-ries cannot specify how the contingentistory of a situation interacts with gen-

lanations for specific instances of elabo-ation take the form of a narrative,howing how general principles interactith the history of a population to pro-uce the archaeological record (O’Hara988).Within the umbrella of Darwinian evo-

ution, several investigators have begun toormulate and champion theories of cul-ural elaboration (Boone 1998; Dunnell989; Neiman 1998). Our purpose in thishapter is to explore and deepen our un-erstanding of one particular theory, thewaste” explanation that was proposed byunnell (1989) in his discussion of elabo-

ation in the archaeological record of east-rn North America. In particular, we worko provide a quantitative model of Dun-ell’s “waste” explanation and to evaluatehether this model is sufficient for pro-ucing populations in which elaborationan be fixed by natural selection. Evaluat-ng whether the theory used to constructur models is necessary and sufficient isutside the scope of this article. Such anvaluation requires attempts to apply andalsify hypotheses generated from the the-ry in the context of a particular evolu-ionary narrative. For a beginning to thisask, we refer readers to the accompany-ng articles in this issue. After examiningunnell’s (1989) “waste” explanation in

ome detail, we examine “bet-hedging”odels of reproduction in uncertain envi-

onments in order to provide a quantita-ive understanding of his model. We con-lude our discussion by presenting detailsf our attempts to deduce some conse-uences of the model for common classesf archaeological evidence.

EVOLUTION AND CULTURALELABORATION

In an attempt to demonstrate the powerf evolutionary theory, Dunnell (1989) ex-mined the distribution of cultural elabo-

ration in eastern North America at the

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253REPRODUCTIVE TRADE-OFFS AND CULTURAL ELABORATION

regional scale. Dunnell assumed that allorganisms use, to some degree, energy inbehaviors unrelated to their immediatewelfare or reproduction. This assertionseems unremarkable to us, at least for ver-tebrates. Such expenditures of energy,termed “waste” by Dunnell, are present inall individuals at some level. That suchexpenditures are, in fact, unrelated to cur-rent survival or reproduction may seemcontroversial to some. Certainly, such ex-penditures of energy appear to provide aonundrum for an adaptationist argumentf we had to determine the precise adap-ive function that “wasteful” uses of en-rgy performed. Rather than determinehe function of waste, Dunnell attackedhe problem from a different angle. Hesked: Are there conditions under whichxpenditure of energy on elaboration oraste could be favored by selection and

hus increase the level of investmentithin certain populations? The latteruestion simply seeks to assess whetherelective environments exist in whichaste could be a positive contributor totness. This is a very different kind ofuestion than simply looking for thefunction” of waste.Dunnell’s answer was that at least one

et of conditions exist under which selec-ion can favor waste within a population.f individuals (or families, corporateroups, production units, etc.) vary in themount of energy they expend in “waste-ul” activities, environments with unpre-ictable variance in resources could favoraste because these individuals would

end to have lower reproductive rates. Inimes of unpredictable resource availabil-ty, such individuals are able to better pro-ide for themselves and their offspringhrough the cessation of the “wasteful”ehavior (Fig. 1). Dunnell further rea-oned that cultural elaboration should oc-ur in those regions where resourcesould be unpredictable, rather than re-

e either rich or poor.Dunnell’s examination of “waste” in the

rchaeological record was motivated byonsideration of the large-scale patterningf elaboration in eastern North AmericaDunnell 1999, this issue). Within the Laterchaic and Woodland archaeological

ecord of the eastern United States, cul-ural elaboration in the form of burial cer-monialism is frequent though not ubiq-itous, either in space or in time. Burialeremonialism can be traced to two sepa-ate lineages in the eastern half of Northmerica. Elaboration in burial appears in

he Maritime Archaic of southern Canadae.g., Tuck 1984), apparently unrelated toevelopments further south. Extensiveortuary activity also occurs in the areas

outh of the Great Lakes within the phase-ike entities called Glacial Kame and Red

chre. Evidence is strong that these unitsventually became the Adena andopewell cultural units (Caldwell 1958;unningham 1948; Dragoo 1963; Griffin948; Railey 1990; Ritzenthaler 1957; Webbnd Snow 1945). Thus, in eastern Northmerica, we have evidence of elaborationecoming prevalent within a historical

ineage, eventually disappearing from theopulation with the rise of the so-calledLate Woodland” (see Dunnell andreenlee 1999, this issue).Geographically, burial ceremonialism

rst appears along the western and north-rn margins of the deciduous forest zoneather than in the biotically richer centralr southern oak-hickory forest (Fig. 2).his pattern is not what one would expect

f elaboration is the product of surplusesr leisure time. The pattern is, however,recisely what we would expect givenunnell’s explanation. Elaboration occurs

arliest in those parts of the eastern foresthere mast-producing species occur in

ow densities compared to forests furtherast or south and where resource levelsould be the most variable (Buikstra 1981;


Chapman 1975; Charles and Buikstra1983).

Dunnell’s “waste” explanation per-forms well when evaluated against thetasks it set out to accomplish. First, themodel accounts for the temporal and spa-

FIG. 1. Simplified model of the selection of “ized waste as a behavior not involved in reproduof environmental shortfall. Here, mean “carryinmental trends and no change or difference in suin time is highly variable. Three horizontal barsdifferent sizes. All populations can persist throdrastic shortfalls (B) and/or repetitive shortfallsrun, larger populations are more fit but, in enfluctuations in “carrying capacity,” populationswill be at an advantage not only because of thement of waste provides a reservoir of time to a

tial pattern of cultural elaboration in pre-historic eastern North America, at least atthe regional scales for which data are mostreadily available. Second, the explanationis a demonstration of how Darwiniananalysis can be applied to an important

ste” from Dunnell (1989). Dunnell conceptual-on and that can act as an energy buffer in timesapacity” (—) is held constant (i.e., no environ-stence) while the carrying capacity at any pointpresent different populations in equilibrium at

minor shortfalls in productivity(A); however,will cause extinction or emigration. In the shortnments which experience large unpredictablebilized at smaller sizes by waste-type behavioraller size but also because temporary abandon-

“intensification” (D).

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archaeological problem that, at firstglance, appears to provide a conundrumfor explanation via natural selection. Al-though Dunnell’s model is potentially ap-plicable to parts of the archaeologicalrecord in other parts of the world, Dunnelldid not set out to create a quantitative

odel of “waste” or to examine the evo-ution of waste within any specific popu-ation in his 1989 paper (Dunnell 1999, thisssue).

The need for further theoretical devel-pment stems from the desire to use thexplanation at finer scales of analysis, as

FIG. 2. Distribution of early cultural elaboratHopewell/Adena and the Red Ochre/Glacial Kanorthern, marginal, and energetically unpredearliest evidence occurring in the most norther

videnced by the other articles in thisolume. The original theory, however, isast in terms too general to specify theuantitative relationship between re-roduction, energy use, and environ-ental uncertainty for individuals, sinceunnell’s focus was on the distributionf phenomena at regional scales. Oururpose here is to work within the high

evel structure of Dunnell’s explanationnd formulate a theory of the evolutionf elaboration suitable for use in draw-

ng hypotheses about individuals andopulations.

in eastern North America. The distribution ofmortuary complexes corresponds closely to theble edge of the oak-hickory forests with thend marginal environments.

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FITNESS AND SELECTION IN ferent proximate causes (e.g., Boone 1998).


TEMPORALLY VARIABLEENVIRONMENTS

The key to expanding and developingDunnell’s explanation for cultural elabo-ration lies in understanding the effectsthat variation in resources has on fitnessand the historical trajectories that selec-tion can create for these traits. Environ-mental uncertainty plays an importantrole in evolution because traits take onadaptive value only in the context of par-ticular environments. When environ-ments vary over time, the fitnesses oftraits necessarily fluctuate, even if the setof traits that any individual possesseshave not changed. When environmentsvary slowly with respect to the speed withwhich replication of the traits occur, selec-tion may “track” the changes effectivelyby slowly changing the frequencies of thetraits within the population. When envi-ronments vary quickly with respect to therate of replication, however, individualsmay encounter many environmental cir-cumstances that are more or less optimalfor the traits they possess. Selection, insuch circumstances, may yield a morecomplex trait history, including the possi-bility of apparently “suboptimal” traits in-creasing in frequency (Seger and Brock-mann 1987). It is the scenario in which“suboptimal” traits succeed over more ap-parently “optimal” traits that we poten-tially find the conditions in which “waste”may persist in populations.

In this context, Dunnell’s explanationfor cultural elaboration can be seen as aspecific case of a more general phenome-non—of selection acting on heritable vari-ation in temporally uncertain environ-ments. The argument is supported byregional patterns of cultural elaboration ineastern North America. Other investiga-tors, following independent lines of rea-soning, have produced models that areformally equivalent even if based on dif-

The theory, however, predicts somethingthat may be seen by some as counter tostrict Darwinian principles: individualswith the highest reproductive output donot necessarily have the highest fitness. Atfirst glance this statement would seem tobe false, since traditionally fitness is de-fined as reproductive success. To under-stand how lower reproductive rates canactually result in higher fitness values re-quires examining the nature of fitness.

What Is “Fitness?”

At a common sense level, fitness ismeant to convey a quantitative sense ofhow well individuals are designed for sur-vival or reproduction in their current en-vironment. Beyond this vague notion,however, there are many uses of the term“fitness” in the literature of evolutionarybiology (e.g., Dawkins 1982; Endler 1986;Michod 1999). For our purposes, the mostimportant distinction between modern fit-ness concepts is the difference betweenassessing fitness at the level of individualsand measuring it as a property of classesof traits (Madsen and Lipo 1999). The goalof our discussion of fitness is to examineeach fitness concept with respect to itsutility in explaining the evolution of heri-table traits. Thus, what drives our explo-ration is the pursuit of dynamic suffi-ciency in our understanding of fitness(Lewontin 1974).

Perhaps the most influential fitness con-cept is the notion that fitness is equivalentto the reproductive success of individuals.Often referred to as “individual fitness,”this concept is the most common technicaldefinition. Within evolutionary ecologyespecially, fitness is typically treated asdesign for individual survival and repro-ductive success, measured through prox-ies or “currencies.” Despite its ubiquity,this notion of individual fitness is prob-lematic. Hamilton (1964a, 1964b), for ex-

ample, noted the fact that natural selec- fitness of traits is a summary measure ofhepmac

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tion will favor traits that cause anindividual’s genes to be passed on, re-gardless of whether the individual is, it-self, successful at producing offspring.The classic example is, of course, sterilecastes within social insects. If we hold thatfitness is defined strictly as reproductivesuccess then we must conclude that sterileworkers have zero fitness because theyproduce no offspring. Hamilton’s answerto this fallacy was to argue that individualfitness was too narrow a concept, since itignored the effects on the transmission oftraits that accrued by virtue of kinship.The broader concept of “inclusive fitness”is the way Hamilton and others solvedproblems with individual fitness, thoughthe general problem remains. It is nowgenerally appreciated among evolution-ary biologists that individual and inclu-sive fitness simply may not capture allkinds of phenomena that can create evo-lution by selection within a population(Michod 1999).

Implicit in population biology models isanother concept of fitness, equally impor-tant and in many ways more useful. Inpopulation genetics, fitness is a technicalterm that denotes the rate of increase of atype within a population (also known asthe Malthusian parameter or Fisherian fit-ness of a type). This conception of fitnessis due to the writings of Fisher and Hal-dane, who were worked along withWright for formalizing the linkage be-tween Mendelian genetics and Darwiniannatural selection. Fitness, in this sense, isa statistical property of a class of individ-uals within a population, not a “capacity”of any particular individual. Fitness, inthis sense, is not determined entirely bythe heritable capacities of individuals. Be-cause fitness is being measured as the rateof increase of a type, many factors beyondheritability can affect the value we mea-sure, including frequency dependenceand variability in the environment. The

ow heritable capacities interact with thenvironment and with other traits in theopulation (Michod 1999). As such, fitnesseasured solely at the level of traits is

nother way to solve the problems of theoncept of fitness as reproductive success.

How do we relate the preceding defini-ions of fitness? Ideally, we would findhat they are equivalent but distinct waysf looking at the heritable capacities of

ndividuals. Sadly, this does not appear toe the case. At the level of traits, orFisherian” fitness, the most commonlysed measure of fitness is the intrinsic (orgeometric”) rate of increase of a traithereafter symbolized as “l”). The intrin-

sic rate of increase of a trait is equivalentto the average lifetime of reproductivesuccess by individuals carrying the trait.This equivalence is only valid, however, ata constant population density, withoutage structuring in the population andwithout frequency dependent effects.These and other conditions, however, areunlikely to be common. Consequently,under normal circumstances, lifetime re-productive success may not be a goodgeneral predictor for how heritable traitsspread within a population (Charlesworth1990; Murray 1997).

If the fitness of traits and the reproduc-tive success of organisms are not typicallyinterchangeable, we must determine theproper relationship of these concepts.Which conception of fitness is fundamen-tal to evolutionary explanation? Althoughboth uses of fitnesses have places in evo-lutionary studies, we believe that fitnessshould be considered a statistical propertyof traits, not as individual reproductivesuccess, for several reasons. First, from astrategic standpoint most research ques-tions focus on the history of traits orgroups of traits, not on individuals. Wemust be able to express our models, there-fore, in terms of the frequencies of traits.We do not claim, of course, that the indi-

vidual is irrelevant and that evolutionary

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theory can be reduced to a sterile “artifactphysics.” On the contrary, individuality isstill critical in evolutionary models sinceindividuals are the locus of behavior andthus form the interaction between traitsand the environment in which they makea difference. Rather than reject the notionof individual reproductive success, we aremerely saying that the statistical summaryof these real-world interactions—fitness—should occur at the level of the traits weare trying to explain.

Additionally, while individual repro-ductive success is certainly a major reasonwhy traits can outreplicate one another(especially for genetically transmittedtraits), reproduction at the level of the in-dividual is only a contributing factor. Fre-quency dependence and the environmentwithin which traits are expressed mayhave equal or greater effects on the actualrates at which traits propagate within apopulation (Charlesworth 1990; Michod1999; Seger and Brockmann 1987). Finally,reproductive effort itself is a complex out-come both of heritable capacities (bothcultural and genetic) and selection oper-ating within a context of trade-offs occur-ring throughout an individual’s lifespan(Roff 1992; Stearns 1992). Fundamentally,reproductive effort and reproductive suc-cess are traits that contribute to but do notonstitute the replication of all of an indi-idual’s genetically heritable capacities.eproductive effort and reproductive suc-ess are traits that must explained inerms of the spread of heritable informa-ion.

Moreover, reproductive success is onlymeasure of biological reproduction and

hus genetic replication. Fitness, in theense of reproductive success, has dimin-shed explanatory value when individualapabilities are inherited through a com-ination of genetics and culture. Only atness concept that operates at the level of

raits offers us the ability to disentangle

on trait frequencies as these effects aremanifested through dual systems of in-heritance. In the case of traits such as re-productive effort and reproductive suc-cess that are inherited through bothcultural and genetic replication, it is clearthat a concept of fitness that considersfrequencies of traits rather than individu-als is necessary to achieve our goal of dy-namic sufficiency.

It is with the concept of fitness operat-ing at the level of traits that we now areable to tackle the explanation of culturalelaboration. In our study of “waste,” wecan now build a model for cultural elabo-ration that links the fitness of a culturallytransmitted trait with optimal reproduc-tive effort in a temporally variable envi-ronment. Building this model requiresseveral elements. These elements includean understanding of the dynamics of se-lection in variable environments, a theoryof reproductive effort in variable environ-ments, and a general argument linkingthe effects of a cultural trait (e.g., burialceremonialism) to potential reproductiveeffort.

Selection in Temporally VariableEnvironments

Although few real environments areconstant in productivity and structure, ba-sic population genetics (and more re-cently, cultural transmission) models areconstructed using an implicit assumptionthat selection pressures don’t change. Inother words, it is commonly assumed thatthe fitness of a trait is constant. Early ex-ceptions included analysis of frequency-dependent effects by Wright, Haldane,and others, but systematic treatment ofthe dynamics of selection with stochasticfitness coefficients is a relatively recentendeavor. Dempster (1955) noted that intemporally variable environments, the fit-ness of a trait was best measured by the


geometric mean of its fitnesses in eachenvironmental state. Like the well-knownarithmetic mean, the geometric mean is ameasure of central tendency. The geomet-ric mean of a series of numbers (of lengthn) is merely the nth root of the product ofthe numbers and thus is multiplicativerather than additive. Dempster recog-nized that since reproduction is inherentlymultiplicative, the best measure of fitnesswould therefore be a statistic that paral-leled the behavior of reproduction.Gillespie (1977, 1991) and others havetaken this fundamental observation anddeveloped a theory of selection in stochas-tic environments (e.g., Tuljapurkar 1990).

Several predictions of the theory arequite general. First, stochastic variation inthe fitness of a trait is often a sufficientcondition for the maintenance of severaldifferent expressions of traits within apopulation. Second, the effects of spatialvariation in the environment are quite dif-

FIG. 3. Bet-hedging: a demonstration of the gstrategies are shown: one with high birth ratefecundity (squares). These strategies are placed“good” years, both kinds of strategies succeed, bchild mortality proportional to the number of chthe high risk, high-fecundity strategy since the lthe high-fecundity type. During bad years, the plow, since child mortality will preferentially affeof good and bad years the high-fecundity strawhich it spreads in the population. The geomethat the low-fecundity strategy has the higher r

ferent than temporal variability. Spatialvariation, coupled with mobility, leads tofitness values that are the arithmetic meanof fitnesses in each environment, so longas the time required to move between dif-ferent areas is small, relatively speaking.In such situations, few of the effects notedbelow are important (Seger and Brock-mann 1987). Finally, due to the multipli-cative nature of replication, selection in astochastic environment will tend to favorthose traits that display the lowest vari-ance in fitness across environmentalstates (Gillespie 1977; Slatkin 1974). Thelatter result is quite general and gives riseto a “bet-hedging” quality to evolution intemporally variable environments as wellas to trade-offs in life-history traits such asreproductive effort.

A simple example illustrates the bet-hedging effect (Fig. 3). Take two reproduc-tive strategies, one with high birth rate, or“fecundity” (shown in Fig. 3 as circles),

etric and arithmetic means. Two reproductive“fecundity” (circles) and the other with lowerto a series of “good” and “bad” years. Duringuring the “bad” years resource shortages causeen a parent needs to feed. Good years select for-fecundity “type” increases at a lower rate thanff for the high-fecundity strategy is particularlyhose with larger family sizes. In a random mix

experiences a greater variance in the rate atmean of payoffs in each kind of period showsof increase.

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and the other with lower fecundity and risk minimization in behavioral ecol-


(shown in Fig. 3 as squares). In a constantenvironment and if the transmission ofthe “strategy” is reliably transmitted todescendants (whether genetic or cultural),we would naturally expect that the strat-egy with higher innate fecundity wouldcome to dominate the population. Theoutcome in variable environments, how-ever, is very different. Assume an envi-ronment partitioned into “good” and“bad” years. During “good” years, re-sources are assumed to be plentifulenough to allow parents of both kinds ofbirth rates to supply and care for theiroffspring. “Bad” years, on the other hand,are characterized by resource shortages inwhich parents may have difficulty feedingtheir offspring, with child mortality pro-portional to the number of children a par-ent needs to feed.

Good years, obviously, will select forthe high-risk, high-fecundity strategy.During good years, the low-fecundity“type” continues to increase, but at alower rate than the high fecundity type.During bad years, the situation is re-versed. The payoff for the high-fecunditystrategy is particularly low, since childmortality will preferentially affect thosewith larger family sizes. When one exam-ines a random mix of good and bad years,it is easy to see that the high-fecunditystrategy experiences a greater variance inthe rate at which it spreads in the popu-lation. If we calculate the geometric meanof payoffs in each kind of period, we cansee that the low-fecundity strategy has thehigher rate of increase.

Variability in the Allocation of ReproductiveEffort

The simple “bet-hedging” effect justdescribed is quite general. One can usethe mathematics of variance minimizationto explain features of life insurance, strat-egies for purchasing and selling stocks,

ogy as well as trade-offs concerning re-productive effort. In our analyses, we areconcerned with how the simple mechan-ics of bet hedging and the geometric meanfitness effect may create evolutionarytrade-offs in the allocation of energy toreproduction as opposed to survival oreven cultural elaboration.

An important problem in the evolutionof reproductive strategies is the optimalallocation of energy to reproductive effortover the whole lifespan, taking into ac-count the “costs” of reproduction (Stearns1992). In particular, models derived fromreproductive effort theory that focus onclutch size are relevant to our concerns.All of these models have their roots in thework of David Lack who, in 1947, pointedout that birds should produce the numberof eggs (“clutch size”) which fledges themost offspring, even if the clutch size isbelow the maximum possible for a spe-cies.

In an environment where there is vari-ation in the juvenile mortality rate that iscorrelated to the family size a parent mustprovision (due, for example, to variationin resources), individuals with largernumbers of dependent offspring shouldexperience greater variation in bringingoffspring to adulthood. At the level oftraits, many individual traits can affect“clutch size,” including rules for birthspacing and age at first reproduction. In atemporally variable environment, selec-tion should manifest itself as an increasein the frequency of those traits that yieldlower variance in reproductive success,due to the effects of the geometric meanprinciple discussed above. In a nicely de-signed experiment, Boyce and Perrins(1987) found exactly this effect in birdsstudied over a period of 22 years. We nowturn to the expansion of this model inways that potentially will allow us to linkreduction of variance in reproductive suc-

cess with traits related to cultural elabo-

mti

tive fecundity,” a measure of the ability to


ration.A simple model of reproductive effort in a

temporally variable environment. For asimple model of reproductive effort invariable environments, we begin withSchaffer’s (1974) analysis of the effects ofsurvival variation on optimal reproductiveeffort. Although the results are known tobe much more complex in age-structuredpopulations, Goodman (1984) has shownthat Schaffer’s model has the same quali-tative behavior as more complicated mod-els that incorporate increased demo-graphic sophistication (e.g., Charlesworth1990). Importantly, the Schaffer model,because of the importance of the linkagewith population growth, is written interms of “absolute” fitness (i.e., growthrates) rather than the relative selection co-efficients of population genetics (Michod1999). This feature of the model makes itparticular applicable in our study of traitsrelated to reproductive rates that aretransmitted both genetically and cultur-ally.

In our simple model, the rate at which aset of traits contributes to populationgrowth (i.e., the geometric rate of in-crease) is determined by three factors: fe-cundity, numbers of offspring, and adultsurvival. Equation 1 describes the rela-tionship between these factors contribut-ing to the rate of increase

l i 5 misi 1 Si, (1)

where m is fecundity for the trait group,easured in offspring per unit time, s is

he proportion of those offspring surviv-ng infancy; and S is the “adult” survival

probability thereafter. The subscripts in-dicate that the rate is on a per-trait orper-trait group basis, not for the popula-tion as a whole. For simplicity, Schaffer(1974) combined fecundity and juvenilesurvival into a single value called “effec-

produce offspring and raise them to inde-pendence. In what follows, therefore, E 5ms.

For a particular phenotype, there arelikely to be changing values of each ofthese parameters (effective fecundity andadult survival) in an environment that isvarying unpredictably. Therefore, withthe simplification that the environmentmay be represented by “good” or “bad”periods and that over the long run bothoccur in equal proportions, the mean rateof increase of a single phenotype is givenby

l# 2 5 lglb, (2)

where the subscripts g and b stand for“good” and “bad” periods, respectively.The second set of subscripts for the traitgroup involved has been left off for clarity.

Environmental variability can be repre-sented in Eq. 1 by introducing a parame-ter that equals the departure (d) from anoverall “average” fecundity

lg 5 E~1 1 d! 1 S

lb 5 E~1 2 d! 1 S

l# 2 5 @E~1 1 d! 1 S#@E~1 2 d! 1 S#

l# 2 5 ~E 1 S! 2 2 d 2E 2.

(3)

Across a mix of good and bad periods,there is a value for reproductive effort thatmaximizes the rate of increase of the phe-notype within the population. To deter-mine this value, we first calculate eachphenotype’s maximal rate of increase andthen explore the relationship that existsbetween phenotypes with differing valuesof effective fecundity as measured by d.

The reproductive effort (F) that maxi-mizes each phenotype’s rate of increase isfound by differentiating Eq. 3 with respect

As


to F and finding the value of F at whichthe differential is equal to 0.

l 2

F 5 2~E 1 S!EF 2 2Ed 2

EF

1 2~E 1 S!SF .

(4)

fter some algebraic rearranging, Eq. 4 iset equal to 0 when

FIG. 4. The effect of adult survival and effectitop panel, we show that probabilities of adult seffort and effective fecundity (E) increases withreproductive effort likely means decreased paderivatives of the functions (bottom panel), threproductive effort for a given trait group. Notebottom panel) actually results in a greater probaalthough this strategy will yield smaller than m

EF S1 2

Ed 2

E 1 SD 5 2SF . (5)

If both adult survival and effective fecun-dity are concave functions of energy de-voted to reproduction, the highest rate ofincrease will be achieved at an intermedi-ate level of reproductive effort (Fig. 4). Asshown in the top of Fig. 4, it is reasonableto assume that probabilities of adult sur-vival will decrease with increasing repro-

fecundity on optimal reproductive effort. In theival (S) decreases with increasing reproductivereasing reproductive effort because increasingtal investment per offspring. Taking the firsttersection of the two functions is the optimalt the decreased reproductive effort (dashed line,ity of adult survival (F 2) than greater effort (F 1)mum numbers of offspring at any one time.

veurvinc

rene inthabilaxi

ductive effort, simply because of the risks ple, although based on models of r- and


and costs associated with reproduction.Similarly, it is reasonable to assume thateffective fecundity will increase with in-creasing reproductive effort, but will beconcave instead of convex. The reason forthis is that fecundity itself is only one as-pect of the composite parameter “effectivefecundity.” The other component is juve-nile survival, and it is reasonable to sup-pose that there is an inverse relationshipbetween juvenile survival and reproduc-tive effort, since increasing reproductiveeffort likely means decreased parental in-vestment per offspring.

Thus, if we graph the first derivatives ofthe functions (following Eq. 5), the inter-section of the two functions is the optimalreproductive effort for a given trait group(Fig. 4, bottom panel). The graph illus-trates what Boyce and Perrins (1987)showed empirically: in temporally vari-able environments the geometric meanfitness effect will lead to smaller-than-maximum numbers of offspring at anyone time.

Since it is clear that the environmenthas an important impact on determiningoptimal reproductive effort, in order tolink the reproductive effort model to evo-lutionary dynamics our next step is to ex-amine the effects of changing environ-mental structure. First, we can ask aboutthe effects of increased variability in theenvironment. Within our model, the mag-nitude of the difference between good andbad years is measured by d, the departurefrom the overall average effective fecun-dity. As depicted in the bottom panel ofFig. 4, the effects of increasing d lead toshifting the fecundity curve to the left.Thus, increasing environmental variabil-ity will lead to selection for decreased re-productive effort in our simple model.This is an important conclusion of thesimple model presented here, though theresult is hardly novel. Boone’s (1998)model of cultural elaboration, for exam-

K-selection, describes the same selectionpressure for intermediate levels of repro-ductive effort in uncertain environments.What differentiates the bet-hedgingmodel from Boone’s explanation is thatwe postulate no other causes for elabora-tion other than an energetic link betweenreproductive effort and elaboration. Noproximate mechanisms such as costly sig-naling or conspicuous consumption arerequired.

The model presented here does require,however, an understanding of how cul-tural transmission interacts with the bet-hedging effect described earlier. Withmultiple-trait groups present in the pop-ulation that vary in allocation of energy toreproductive effort, we can work back-ward from Eq. 3 to determine the rate ofincrease of each trait group. Obviously,the trait group whose reproductive effortis closest to the optimum for a given valueof d will have the highest rate of increase.Thus, the square root of Eq. 2 representsthe rate of increase for each set of traits.By scaling the l-value of one trait group tothat of another, we can examine the likelyeffects of linking reproductive effort to aculturally transmitted trait, since mostcultural transmission models, like those inpopulation genetics, are written in termsof relative fitness coefficients, not the ab-solute fitness described by l.

Cultural transmission and the simple modelof reproductive effort. The hallmark of cul-tural transmission is the fact that replica-tion of cultural traits is not linked to bio-logical generations, but is continuousthroughout one’s lifetime (Boyd and Rich-erson 1985; Cavalli-Sforza and Feldman1981). Although a full analysis of dual-transmission systems would necessitatebeginning with models that explicitly rep-resent both genetics and culture, we be-lieve that a simpler model is a good start-ing point for making deductions about thedynamics of reproductive effort in cultural

populations. To approximate the effects of where W is the relative fitness of pheno-


continuous transmission through life his-tory, we begin with Seger and Brock-mann’s (1987:194) analysis of a haploidmodel with overlapping generations anditeroparity. Although this model providesan excellent starting point to exploretransmission and reproduction, it is notmeant to represent our view of how bet-hedging and reproductive effort will beincorporated into theories of culturaltransmission. Because the details of fit-ness measures depend critically on thenature of “mating” systems, future workwill be aimed at incorporating stochasticvariation in fitness within more detailedtransmission models of the kind proposedby Boyd and Richerson (1985). The Segerand Brockmann model, however, providesa reasonable place to begin our discus-sion.

In our simplified model, the continuousnature of cultural transmission is approx-imated by overlapping “generations” andallowing all individuals “alive” at eachtime period in the model to continuetransmitting. Overlapping generations arerepresented by allowing a proportion (s)of the current time slice’s individuals tosurvive and replicate during the next in-terval. Since the fraction of individuals isassumed to be a simple random sample,some individuals will replicate manytimes during their lifetime, others only afew or once. Thus, each period of time isrepresented by a population with a pro-portion of existing individuals and a num-ber of “new” individuals, interpretable asbiological children and “naı̈ve” in a cul-tural sense. The latter exist in the propor-tion 1 2 s. If we consider a populationwith two phenotypes, one representinglow allocation in reproductive effort ( A),and the other high allocation (B), the fre-quency of phenotype A in the population( p) is

pt11 5 pt@s 1 ~1 2 s!Wt/Vt#, (6)

t

type A in generation t (since fitness isvariable over time) and V t measures thepopulation mean fitness in generation t as

Vt 5 1 1 pt~Wt 2 1!. (7)

In addition to measuring the degree ofoverlap between transmitting genera-tions, the parameter s is proportional tothe “amount” of environmental variabilityindividuals tend to experience over theirlifetimes in a changing environment.When s is near 0, individuals tend to ex-perience only a few swings between envi-ronmental states. When s is near 1 and theoverlap of generations nearly complete,however, nearly all individuals survive in-definitely relative to the model and live toexperience many environmental states.We recognize that the method represent-ing cultural transmission as overlappinggenerations in a lottery contest is hardlyfaithful to the kinds of complex environ-ments we envision providing the selectiveenvironment for cultural elaboration. Thissimple model, however, allows us to ex-amine the effects of temporal variabilitythat occurs quickly or slowly with respectto an individual’s lifetime.

To introduce environmental variabilityinto our simple model, we again assume,as with Schaffer’s analysis earlier, thatvariation is partitioned into “good” and“bad” periods, which occur in a stationaryrandom distribution in approximatelyequal proportions. In such an environ-ment, the equilibrium proportion of phe-notype A is the frequency ( p) that maxi-mizes

f~p! 5 s ÎVg~p!Vb~p! 1 ~1 2 s!

3 @p ÎWgWb 1 ~1 2 p!#,(8)

where V i( p) are the population mean fit-nesses in good and bad periods (Eq. 7)

and W are the individual fitnesses in productive effort alongside high-fecun-


i

good and bad periods (in fact, the W i aremerely the l values in Eq. 3, scaled tofrequencies).

Equation 8 is composed of a weightedaverage of two geometric means, with thepopulation geometric mean fitness in thefirst term and the individual geometricmean in the second. When the parameters is near 0, individuals experience few ep-isodes of environmental variation and theright hand term of Eq. 8 contributes themost weight to the frequency of pheno-type A in the population. In this scenario,the factor that matters is the geometricmean fitness of each phenotype acrossgood and bad periods. Thus, when there islittle overlap in transmission becausetraits are not transmitted culturally, onlythe fitnesses of each trait averaged acrossenvironments play a role in the dynamicsof selection.

When s is large, however, more weightis given to the first term in the equation.The first term emphasizes the effects ofthe population’s geometric mean fitness.Population mean fitness averages the fit-ness of all phenotypes across environ-mental states. In this scenario, both indi-vidual and population geometric meansfavor reduced reproductive effort in vari-able environments (and thus linked“wasteful” traits). The population’s geo-metric mean fitness may be maximized,however, when there is a polymorphismof the two phenotypes rather than a purepopulation of high-fecundity or low-fe-cundity individuals (with associatedlinked cultural traits). The parameter s islarge whenever there is strong overlap be-tween generations, the condition usedhere to indicate a high degree of continu-ous cultural transmission. Thus, we pre-dict that whenever the relevant traits arebeing transmitted culturally, selection in avariable environment could easily supportthe maintenance of a polymorphism of“wasteful” traits in linkage with lower re-

dity traits with no associations to elabora-tion. Of course, outside the context of oursimple model, all of these variables arecontinuous, and we would expect to see acontinuous distribution of traits main-tained in the population, if our argumentholds despite the simplifications madehere.

Limitations of the simple model. Apartfrom the obvious simplifications made inthe formal model described above, thereare deeper limitations to the model. Themodel is inadequate whenever there isage structure in the population or, in otherwords, whenever age-specific fecundities,adult survival probabilities, or probabili-ties of cultural transmission differ. Char-lesworth (1990) and others (e.g., Mc-Namara 1997) have outlined a theory ofselection in variable environments forage-structured populations. Although themathematics are complex compared tothose used here, there is little evidencethat the major qualitative conclusions arecontradicted by these developments(Goodman 1984).

A more serious problem with the modeldescribed above lies in the simplificationof the environment into “good” and “bad”classes in equal proportions. The simpli-fication is made to make calculation of thegeometric means simple for purposes ofthe formal model. Although seeminglyharmless, we need to be sure that the sim-plification does not obscure details thatmight mitigate the utility of the theory forarchaeological purposes. Gillespie’s (1991)discussion of selection in variable envi-ronments is quite a bit more general thanthe model described above, but the math-ematics are often analytically intractable.Gillespie uses diffusion approximations toexplore the theory, and his conclusionssupport the general qualitative picture de-scribed here. Since we are particularly in-terested in exploring the dynamic proper-ties of the model not easily expressed

through equations, we use a simulation

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approach here to validate the dynamicsufficiency of our model and to deducefrom it implications that might be ar-chaeologically relevant.

ARCHAEOLOGICAL EXPECTATIONSOF THE BET-HEDGING MODEL

he Linkage between Reproductive Effortand Cultural Elaboration

Dunnell’s (1989) explanation of culturallaboration can now be cast as a form ofelection for variance reduction. Individ-als that practice behaviors related tolaboration, in his model, tend to succeedn variable and marginal environmentsince on average they have lower fecun-ity due to energy that is channeled fromeproduction into other uses. Those indi-iduals with lower fecundity necessarilyend to have lower variance between goodnd bad periods than individuals withigher fecundity (and lower investment inlaboration). Therefore, selection favorshe suite of traits that link lower fecundityith investment in cultural elaboration, as

ong as lower fecundity and elaborationend to occur together. In terms of our

odel of reproductive effort in a tempo-ally variable environments, this general-zation can be explained as a consequencef variable environments in which selec-ion favors those traits that have the low-st variance in their rate of increase acrossnvironmental states. When examiningraits that determine reproductive effort,he geometric mean principle applies—arait may increase within a population be-ause it has the lowest variance in successven if it does not result in the highesteproductive effort and success. This con-lusion runs counter to the common viewhat fitness is defined as individual repro-uctive success. This view is widely sup-orted, however, both in mathematicalodels of fitness (Charlesworth 1990;

nd through consideration of the nature oftness itself (Dawkins 1982; Michod 1999).hat bet-hedging is a feature of real pop-lations in variable environments has alsoeen observed in animal populations

Boyce and Perrins 1987; Bulmer 1984,985; Cohen 1966; Nilsson et al. 1996).A final step in developing a formal the-

ry that underlies Dunnell’s (1989) expla-ation of cultural elaboration, then, is topecify the connection between elabora-ion and the evolution of reproductive ef-ort in variable environments. Since theseraits potentially have independent trans-

ission histories, it is clear that there is noecessary connection between reproduc-ive effort and elaboration. Under partic-lar circumstances, however, there can ben evolved linkage between them. Thisinkage is becomes clear by examining theossibilities afforded by separate cultural

ransmission of traits related to elabora-ion and traits related to reproductive ef-ort. If we suppose that each trait has twotates (high and low elaboration invest-ent and high and low reproductive ef-

ort), four trait groups are formed by theombination of traits. Given the relation-hip between environmental variability,eproductive effort, and survival de-cribed above, we can see immediatelyhat the phenotype investing largemounts of energy into elaboration andigh reproductive effort should be se-

ected against quickly in all conceivablenvironments. The other “pure” combina-ion, low investment in elaboration andow reproductive effort, can be expectedo exist in most populations and in mostnvironments, though it is unclear at whatevels.

Remaining are the two intermediatehenotypes. It is important to notice that

here is no “mechanical” linkage betweenhe two traits, only an evolutionary asso-iation in phenotypes. That is, these traitsre free to vary in frequency within a pop-

ulation as a function of transmission and

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selection. What requires explanation iswhy the association might be preferen-tially successful, and thus evolve into astable set of traits whereby the two traitsare transmitted to others almost as a pack-age.1,* In some individuals, the balancebetween traits in the tradeoff may not besuccessful. For example, individuals whoattempt both high investment into elabo-ation and high reproductive effort areikely to fall victim to severe environmen-al perturbations when they occur. Overime, we expect that selection will yield aeries of associations between traits in-olved in energetic tradeoffs and themergence of stable phenotypes withell-defined trait values for both invest-ent in elaboration and reproductive ef-

ort. It is in this evolutionary sense that weink traits for cultural elaboration withraits affecting reproductive effort. In theroximate sense, however, the traits have

ittle to do with one another during theirransmission and expression as behavior.

Finally, evolutionary models are silentith respect to the forms that traits gov-

rning elaboration or reproductive effortake. Within the class of traits related tolaboration, for example, all we can say ishat from the perspective of evolutionaryheory, the traits must be costly and notontribute to reproductive effort and suc-ess. The form that the traits take is aistorical matter, defined by innovationnd novelty at some point in the past,assed down by cultural transmissionithin and between lineages, and modi-ed enroute by the cultural analogs ofutation and “recombination.” Similarly,

raits governing reproductive effort mayffect any number of biological variables.or example, birth spacing above the min-

mum, age at first reproduction followingaturity, and reproductive lifespan each

re likely to have a culturally transmitted

* See Note section at end of article for footnote.

ikely to be complex, since selection for theultural trait will likely result in selectionf underlying biological parameters. Thus,hen we consider the role of cultural

ransmission it is particularly clear thathe linkage between elaboration and re-roductive effort is an evolved, not me-hanical, association.

he Relationship between Theory andSimulation Modeling in EvolutionaryArchaeology

The next step in transforming this gen-ral discussion about variability in envi-onments, reproductive behavior, and cul-ural transmission into a set of potentialest implications is to expand and explorehe sufficiency of the model in detail. It isne thing to argue that selection mightroduce change in the frequency of a par-

icular trait; it is quite another to under-tand how those frequencies dynamicallyary in particular environmental and phe-otypic conditions. In this regard, simula-

ion is a useful tool for developing specificxpectations that investigators can use toevelop hypotheses for empirical situa-

ions.Simulation modeling, however, has a

ad reputation in archaeology, primarilyecause many using it have not recog-ized that simulation plays a limited role

n science. Simulation modeling shouldot be used to build “digital replicas” of arehistoric system or society. Givennough lines of program code, the pro-rammer can replicate virtually any be-avior desired in their simulation model—ut have we learned anything new byprogramming in” all of the behaviorsnd effects we already knew existed?While replicating the past is a poor use

f simulation, it is entirely appropriate forxploring the sufficiency of a theoreticalodel or set of equations when solving

he equations directly is difficult or impos-

sible. One can also use simulation for de- their “Sugarscape” model and is the ap-


riving test implications from a mathemat-ically complex model for testing againstempirical data. Simulation is also an ex-cellent means for studying the complexinteractions of the components of a theoryprior to performing expensive and possi-ble destructive analysis. Finally, as Dun-nell (this issue) notes, Darwinian evolu-tion is fundamentally a stochastic theory;and in such theories no single test case isadequate to falsify a particular hypothesis.Instead, the test implications deducedfrom our models need to be balancedagainst a distribution of cases to determinethe utility of particular model or hypoth-esis. Simulation has a part to play in suchhypothesis tests and will help investiga-tors develop expectations for how fre-quently, given chance and necessity, par-ticular evolutionary trajectories might beexpected.

In our minds, the best use of simulationin science is to explore the complex inter-actions of a set of simple assumptions in astatistically significant manner. For exam-ple, if one postulates that natural selectionis responsible for the success of a giventrait, a simulation that includes an explicit“selection” step will not tell the researcheranything new. Selection, in this case, hasbeen “programmed in” from the verystart. In contrast, if we begin with a modelwhere agents inhabit a simple environ-ment and obey simple rules for reproduc-tion, foraging, and other behaviors, it isentirely appropriate to use the simulationto study the dynamics of selection amongthe agents and their environment. Such amodel can be used to determine what en-vironmental and demographic circum-stances might create the observed trend ingenotypes or cultural replicators, and thusthe observed trend in phenotypes. Thelatter approach, termed “agent-based” or“individual-based” modeling, has beenfollowed by Epstein and Axtell (1996) in

proach we follow here.Individual-based modeling is a relatively

new paradigm in the simulation of systemswith many interacting parts (Judson 1994;Kohler and Carr 1996; Langton and Hie-beler n.d.). Traditional approaches to simu-lation tended to represent the behavior ofsystems of individuals through differentialequations representing the modal behaviorof individuals taken as a group. Modelingselection in such simulations is unsatisfac-tory for our purposes, since one is com-pletely specifying the nature and intensityof selection through the equations. Individ-ual-based modeling offers a different ap-proach. It allows the dynamics of selectionto emerge through the natural interactionsbetween individuals and objects represent-ing their environment. In many ways indi-vidual-based simulation models, a philo-sophical outgrowth of object-orientedprogramming methods, represent a power-ful technique for building and exploring theimplications of selection models.

The change in perspective is significant.Researchers have come to appreciate thatmany of the complex phenomena we seearound us are simply the global conse-quences of local behavior. Such studieshave begun to revolutionize many aspectsof economics and political sciences. Ingeneral, individual-based approacheshave led to the development of theory thatcan better account for the stochastic na-ture of historical change. Agent-basedmodels allow us to develop theories andexplanations however necessary, but forceus to state these explanations in quantita-tive terms. Because evolutionary theory isfundamentally quantitative, this feature ofsimulation modeling is enormously bene-ficial. In addition, agent-based simula-tions permit anthropologists to examinetheir assumptions, such as those posed byevolutionary ecologists, about behavior incomplex scenarios and test whether (andunder what conditions) these assumptions

can generate the classes of phenomena

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that they predict.Simulations cannot, and will never be

able to, generate explanations for a partic-lar empirical case or class of phenomena.

n contrast to what we call the “digitaleplica” approach to simulation, we be-ieve that simulations are not producers ofheory. The simulations we discuss below

erely allow us to explore the theory de-eloped in the simple model describedbove in situations that are more realistic.he purposes of such explorations are toeduce additional test implications or to

udge the sufficiency of the explanationor the phenomena in question.

We based our simulations on a program-ing architecture known as SWARM.

WARM is an emerging standard for agentased modeling that has been under devel-pment at the Santa Fe Institute for the pasteveral years (see http://www.santafe.edu/rojects/swarm/). SWARM is unique in that

t permits scientists to create very compli-ated models and to explore aspects of mul-idimensional interaction (requiring sophis-icated programming) with minimal effortn the programmatic “mechanics” of thectual application (e.g., memory manage-ent, display management, etc.) For this

eason, SWARM is serving as a central fo-us to a wide range of researchers in fieldsuch as anthropology, economics, biology,hysics, and archaeology. A number of ar-haeologists have begun using SWARM toxamine issues such as the formation of vil-ages and the effects of environment on ag-iculture (e.g., Kohler and Carr 1996).

lements of a Simulation Model for Wasteas Reproductive Trade-Off

To model life-history trade-off predic-ions in a variety of environmental condi-ions and to examine whether (and underhat conditions) life history models can

ctually generate the classes of “wasteful”henomena that they predict, we built an

esses. The basic components of our wasteimulation consist of a population ofgents with variable phenotypes and aariable environment that consists of aingle food resource, arbitrarily calledsugar,” following Epstein and Axtell’sSugarScape” model. Agent phenotypesre created with the ability to move, toorage for food to meet metabolic needs,nd a set of rules for interacting with oth-rs and reproducing new agents through-ut their lifetimes. The features of theimulation include biological reproduc-ion, realistically uncertain environments,nd phenotypes composed of “genetical-y” and “culturally” transmitted traits.

To examine the effects of unpredictablenvironments on reproductive success,he rules of reproduction are an importantomponent of our model. When agentseach a tunable minimum age for repro-uction, they can reproduce provided

hey meet several biological and culturalonditions or thresholds. In order to re-roduce, both females and males mustossess a biologically determined mini-um amount of energy as well as a sur-

lus that is determined by a culturallynherited preference. Each of these traits

aps to biological and cultural forms ofnergy storage. Females also have a bio-ogically and culturally determinedmount of time they must wait betweenirths (i.e., birth spacing). If an agent that

s ready to reproduce meets an agent ofhe opposite sex who is also ready to re-roduce, a new agent is born. This newgent inherits biological parameters fromts parents in a simple Mendelian mannerwithout crossover) and inherits an initialandom sample of its parent’s culturalepertoire. Juvenile agents are born with-ut fully developed movement or foragingapabilities; normal development yieldsdult capabilities according a linear func-ion throughout “adolescence.” Duringevelopment, parents actively invest en-

ergy into child rearing by providing chil- units and have no “reality” as types (Dun-


dren sugar resources to make up for anyforaging shortfalls children may encoun-ter due to partially developed subsistenceskills.

A second key feature to our simulationis cultural transmission. The phenotypesof agents were modeled to be composedof traits that were transmitted both cultur-ally and genetically. Cultural traits aretransmitted as follows. As agents movearound the landscape, they encounter oneanother opportunistically. When encoun-ters occur, there is a probability that theagents will “talk” to each other and ex-change cultural traits. In the simulation,cultural traits are modeled as “tokens”that can be one of three types. The firsttype can be taken without cost to an agent;such tokens represent “memes” that areselectively neutral. The second type in-vokes a cost in energy to the receivingagent. “Costly” tokens model the codesfor phenotypic traits that use energy thatcan be put into reproduction but are in-stead “wasted” on activities or phenotypicelaboration that has no short-term fitnessbenefit (i.e., does not increase the intrinsicrate of growth, l). Agents are not requiredto take these tokens but are given a cul-tural rule that determines the maximumtoken cost that an agent is willing to pay.The third kind of tokens are ones whichcode for cultural preferences for time be-tween births, the amount of energy sur-plus required before having a child, andthe maximum token cost the agent is will-ing to pay. These tokens have no cost andresult in the replacement of the receiver’spreference by the preference of the trans-mitter.

Because tokens flow culturally and ge-netically through the population indepen-dent of one another, persistent pheno-types are emergent properties of tokencombinations that individuals possess atany given moment in time or, in otherwords, phenotypes are statistical counting

nell 1971). To account for the effect ofagents with constantly changing pheno-types, the simulation tracks the reproduc-tive success of phenotypic classes ratherthan individual agents. The analogousprocedure in population genetics is totrack the success of genotypes rather thanindividuals (Dawkins 1982; Roff 1992).Within our simulation, we do not modelthe norm of reaction or complex develop-ment; possession of the codes for a phe-notype means that the phenotype is ex-pressed, regardless of environment. Werealize that lack of phenotypic plasticityand “meme”/environment interactionswill be seen by some as a fundamentalflaw but we believe that models shouldbegin simply and expand in complexityonly when warranted.

We have defined “wasteful” traits as be-havior or structures that have a cost in theshort run but are a benefit in reproductivesuccess over the long run by lowering thevariance of fitness. The “traits” that arepassed via inheritance in our model, how-ever, refer to propensities, not behavior.Thus, we need to track both the “codes”that agents possess and their actual ex-pressed behavior, since the latter involvesan element of chance. In our simulation,we examined the distribution of valuesacross three variables of interest: theagent’s interbirth interval, the amount ofsugar stored, and the energy spent on cul-tural tokens. Phenotypes for tracking theamount of “wasteful” behavior were cre-ated by treating each variable as a dimen-sion and dividing each dimension into aseries of modes and by creating a paradig-matic classification. Though selection isnot explicitly programmed into the simu-lation, we expect that the frequencies ofphenotypes in the population will changeas a consequence of differential reproduc-tion and cultural transmission.

In order to examine the effect of selec-tion on the frequency of these pheno-

types, agents were subjected to a suite of runs in two different environments—pre-


environmental conditions in which therate of sugar growth was varied. The kindsof environments we studied included con-stant, cyclical, and chaotic growth and en-vironments with periodic failures. The ef-fect of spatial variability and mobility wasexamined by allowing agents to movegreater or lesser distances to search forresources. Tracking the number of chil-dren each individual produced and theirlifetime expression of “wasteful” behav-iors permitted us to calculate the geomet-ric and arithmetic mean fitnesses for phe-notypes. In addition, we tracked changingpatterns of age structure of the popula-tion, population size, and variances overtime as well as the distribution of wastefulbehaviors in the population.

Discussion of Archaeological Expectations

Though the SWARM simulation weconstructed contains relatively few di-mensions along which individuals canvary, the parameter space of “possible”simulation runs is still enormous. In addi-tion to the large parameter space, theneed to examine evolution in stochasticenvironments across a large number ofsimulation runs means that the resultsdiscussed below are necessarily prelimi-nary, even though they are the results ofobserving many runs over a wide set ofparameters sampled from the availablespace. Nevertheless, the simulation runsshed light on the relationship between“wasteful” behavior and environmentaleffects, mobility of agents, age structure,and the distribution of wasteful pheno-types across populations.

The effect of environmental uncertainty.The most general result of the model isthat marked unpredictability in the envi-ronment is indeed capable of creating se-lection for “wasteful” behavior within thesimulation populations. Figure 5 depictsthe results from four different simulation

dictable (left) and unpredictable (right)with two different populations. One pop-ulation was composed of only wastefulphenotypes while the other populationwas made up of only nonwasteful pheno-types. In a constant environment, both thearithmetic and geometric mean fitnessesof nonwasteful phenotypes were uni-formly higher than those of the wastefulphenotypes. In other words, in constantenvironments, selection did favor thosetrait complexes that maximized the repro-ductive effort of individuals. In unpredict-able environments, however, “wasteful”phenotypes tended to have higher geo-metric mean fitnesses than nonwastefulvariants, all other things being equal, andconsequently increased in frequencywithin the population. Thus, as the bet-hedging hypothesis predicts, the generalpremise of the “waste” model appears tohold true. Additionally, we believe thatthe model is correctly constituted, sincerarely were populations driven to fix ei-ther “wasteful” or nonwasteful pheno-types; under all reasonable circumstancesthe population was composed of a mixtureof different levels of investment in“waste,” as one would expect when indi-viduals experience many environmentalfluctuations during their lives.

Mobility. Unlike our simple formalmodel of bet-hedging, agent-based simu-lation allowed us to examine more com-plicated implications of the model such asthe effects of spatial variation and migra-tion. Understanding the effects of mobilityare critical to real-world applications ofevolutionary models, since settlementpatterns are directly linked to subsistenceand thus to fitness. Additionally, settle-ment patterns are relatively easy to studyfrom regional archaeological data, thusforming a natural way to begin applyingevolutionary models to the record. From apurely theoretical perspective, mobilityand migration act as a form of income

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averaging, so long as the fitnesses of a distribution of the simulated populations


single phenotype are not spatially auto-correlated (Levene 1953; Seger and Brock-mann 1987). Migration tends to have anameliorating effect on the tradeoff be-tween the total number of children andthe number of surviving children. That is,individuals can lessen the effects of uncer-tainty by moving from an area of low pro-ductivity to one of high productivity. Fig-ure 6 summarizes a set of runs designed toexamine the effects of mobility. In two setsof simulation runs, we systematically var-ied the “search radius” within which in-dividual agents were able to search forand move toward energy resources, indi-cated pictorially in Fig. 6 by the length ofarrows linked to agents.

The simulation runs on average demon-strated that populations of agents that aregiven the ability to see and move overlarger distances evolve lower levels of“waste” than populations that are morerestricted in their movement. This findingis consistent with what evolutionary biol-ogists have observed with respect to thebet-hedging effect in other species (seeSeger and Brockmann 1987; Charlesworth1990; Roff 1992). It also potentially informson the relationship between cultural elab-oration and sedentariness. It has oftenbeen argued that cultural elaboration re-sults from resource intensification andpermanent settlement (see discussion inSterling, this issue). In our simulation ofbet-hedging effects, however, levels ofwasteful behavior became fixed within thepopulation despite the fact that none ofthe agents were immobile and dependentupon a single location in the environmentfor subsistence. This effect demonstratesthat sedentariness, as it is usually thoughtof, is not required for selection to favor“waste.” Sedentariness merely increasesthe strength of selection for waste in un-predictable environments.

Demographic structure. Selection forwaste was also linked to the average age

(Fig. 7). During each simulation, we re-corded the age at death of each individual,allowing us to study the probable effectsof bet-hedging on skeletal populations.We also took periodic “censuses” of theliving population in order to examine thedemography of our simulated popula-tions. Across our simulation runs, popula-tions with higher frequencies of “waste-ful” behavior tended to have a equal ratioof adults to juveniles within the popula-tion and in death assemblages. Runs inwhich waste was selected against tendedto yield populations with higher juvenilemortality as well as a large proportion ofjuveniles to adults in the living populationderived from higher birth rates. Thus, thetradeoff effect acts not only to increase thegeometric mean fitness of the population,but also to alter the age distribution of thepopulation through increased survival aswell as the mechanical effects of lowerbirth rates on the age structure of a pop-ulation.

Phenotypic polymorphism. Finally, wefound that we could measure the degreeto which a “wasteful” phenotype can co-exist with other phenotypes in a stablepolymorphism (Fig. 8). To do this, wescaled phenotypic dimensions such asculturally transmitted birth spacing inter-vals, accumulation of sugar, and averageexpenditure of energy on “expensive” cul-turally transmitted traits along an index of“wastefulness.” Placing the populationsinto predictable and unpredictable envi-ronments, we examined the populationdistribution across this index. As Fig. 8shows, while the mean value of this“wastefulness” index is not affected byselection, markedly unpredictable envi-ronments yield phenotypic distributionsthat are strongly right-skewed, or skewedin the direction of having more “wasteful”phenotypes. This finding has significantpotential for archaeologists seeking tomeasure degrees of “wastefulness” in the

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archaeological record. Given the difficultyof measuring the “wasteful” behavior ofindividuals in archaeological circum-stances, these results show that the overalldistribution of elaboration within a popu-lation, even scaled at ordinal levels, mightbe sufficient to examine bet-hedging ef-fects in real archaeological data.

Consequences for empirical research. Al-though selection can favor costly artifactclasses in variable environments due tothe bet-hedging effect, the model does notspecify the form that such artifacts cantake. Waste will follow historically contin-gent trajectories within each cultural tra-dition. Determining the form that any par-ticular instance of “waste” takes is amatter of historical analysis that requiresexamining a particular dataset in a partic-ular ecological setting. Additionally, theform that “wasteful” artifacts take poten-tially provides the variability for otherkinds of selective processes. For example,artifacts involved in trade-offs in repro-ductive effort and success may also berelated to costly signaling, functional spe-cialization, and redistribution. It is impor-

FIG. 7. The effect of “wasteful” behaviors on awas selected against (left panel), populations tenlarge proportion of juveniles to adults in the lquencies of “wasteful” behavior (right panel), aadults to juveniles within the population.

tant to recognize that because of dimin-ishing returns for any one kind of energyexpenditure, there are often multiple evo-lutionary solutions for reducing varianceand creating the life history trade-off ef-fect. The fixation of any particular traitmay require additional fitness conse-quences resulting from food redistribu-tion and other kinds of functional organi-zations.

In such cases, these proximate mecha-nisms can act to intensify selection forcostly artifact classes. Increased invest-ment in mound building, for example,may be driven by the bet-hedging effect.However, the fixation of mound buildingwithin the population may be due to itsrole in creating a large-scale food sharingsystem. An important lesson that archae-ologists can learn from these results is thatthey should pay close attention to the fre-quency of wasteful traits within popula-tions, which may be the result of a suite ofvaried and complex evolutionary forces.

In addition to examining the historicaltrajectories for artifact classes, archaeolo-gists must also be aware of the role that

istributions. In simulation runs in which wasted to have higher juvenile mortality as well as ag population. In populations with higher fre-distributions tended to have an equal ratio of

ge dde

ivinge

subsistence systems play in creating the on how the effects discussed above would


selective environment for “wasteful”traits. The ability to store resources andbuffer shortfalls with multiple sources offood, for example, potentially decreasesthe bet-hedging effect and thus selectionfor “wasteful” traits. On the other hand,populations that depend upon a singlefood staple or live in sedentary, dispersedsettlements may provide particularlystrong selective environments for “waste-ful” traits since small changes in produc-tivity have large impacts on these kinds ofsettlement systems. Also, as we men-tioned earlier, one clear result of themodel is that “wasteful” traits will in-crease as mobility decreases within an un-certain environment due to geographic re-strictions, population in-filling, or changesin settlement patterns. Thus, there shouldbe a clear relationship between the levelof “wastefulness” seen in populations andthe details of settlement strategies.

Like the study of subsistence systems,skeletal data may also play a role in ex-amining how the bet-hedging effect is ex-pressed within a particular population. Ashas been discussed, life history trade-offsmanifest themselves in biological vari-ables, such as population age distributionand birth spacing intervals (e.g., Katzen-berg 1996; Skinner 1997). Some of thesevariables should be measurable in care-fully controlled skeletal samples throughestimates of age at first birth and age atdeath, though considerable additionalsimulation work needs to be done to focus

FIG. 8. Polymorphic population compositionUsing a scaled measure of “wastefulness” comptransmitted birth-spacing intervals, accumulatio“expensive” culturally transmitted traits and pldictable environments, we examined the populavalue of the “wastefulness” index between thdifferent, the skewness values for the two populis, unpredictable environments yield phenotypihaving more “wasteful” phenotypes (upper righon the other hand, are relatively evenly distribu

be manifested, if at all, through the tapho-nomic and analytic filters imposed bymost skeletal death assemblages.

Finally, fine-grained studies of environ-mental conditions will provide one of thestrongest avenues of information forstudying the bet-hedging effect in the ar-chaeological record. New high-resolutionstudies of past climatic conditions pro-vided by ice cores, deep sea drilling, treerings, and coral growth records will un-doubtedly serve as a rich source of datafor archaeologists examining the selectiveconditions for “wasteful” phenotypes(e.g., Meeker et al. 1997; Melice and Rou-cou 1998). These new, yearly and decadallevel records of past rainfall and temper-ature can easily generate informationabout the amplitude, frequency, and mag-nitude of environmental failures. It is im-portant to recognize that single or isolatedenvironmental downturns are not suffi-cient to create the bet-hedging effect. Inorder for there to be selective pressure forwasteful behavior, individuals must expe-rience at least several environmental per-turbations. It is the transition betweengood and bad periods of environmentalproductivity, and thus fitness, that createsvariance in success for wasteful vs non-wasteful phenotypes. Studies of environ-mental variability should focus on the ex-amination of the variability using suchstatistics as the coefficient of variance,which consider the effect of differences inmeans on the absolute amount of vari-

predictable and unpredictable environments.d of phenotypic dimensions such as culturallyf sugar, and average expenditure of energy ong the populations into predictable and unpre-distribution across this index. While the mean

wo kinds of environments was not markedlyns are markedly different (bottom graph). Thatistributions that are skewed in the direction ofPopulations in more predictable environments,

(upper left graph).

s inosen o

acintione tatioc dt).ted

ance. In addition, there cannot be an ab- Moreover, the form of “wasteful” behav-

be

uaeFpfdmpdatfcvtaeb1Pm


solute requirement for the minimumamount of variability that populationsmust experience for there to be selectionfor wasteful “phenotypes.” The amount ofvariability necessary to generate the bet-hedging effect is always a product of pop-ulation densities, subsistence systems,settlement strategies, and the overall pro-ductivity of the environment.

CONCLUSIONS

In this article we have attempted to usea simple mathematical model and agent-based simulation to understand the con-ditions under which selection would favorthe life history trade-off that may be ex-pressed in “wasteful” phenotypes. It isimportant to recognize that the explana-tion provided here is sufficient but not nec-essary for any particular case of culturalelaboration. First, given any particularcase, only some of the many evolutionarysolutions to coping with unpredictable en-vironments result in the expression ofwasteful behaviors. No individual mustengage in wasteful behaviors in order tocope evolutionarily with variability in theenvironment. Second, cultural elaborationmay be favored by selection for reasonsother than unpredictable environments.These selective environments potentiallyinclude selection for costly signaling,functional specialization, and functionalintegration. Understanding if the bet-hedging effect is responsible for increas-ing investment in wasteful behavior is anempirical matter that can be solved bylooking at empirical effects deduced fromthe model, such as skeletal age distribu-tions.

That explanations of cultural phenom-ena are sufficient but not necessary alsomeans that it will never be possible toexamine the characteristics of a given en-vironment and predict the equilibriumfrequency of “wasteful” phenotypes.

ior or artifacts is historically contingent.Rather than being predictive, the life-his-tory trade-off hypothesis is a relativelysimple null model for the expected distri-

ution of traits related to the bet-hedgingffect in the archaeological record.Increasing the sophistication of the sim-

lation may well enhance the model’sbility to account for variability in culturallaboration in space and time, however.or example, although there may be com-licated rules for translating inherited in-

ormation into behavior (in other words,ecision making algorithms), this initialodel was purposely built to be very sim-

le. That is, we were simply seeking toetermine if the actions of transmissionnd selection are adequate for generatinghe conditions necessary to favor “waste-ul” kinds of phenotypes. More sophisti-ated models for translating phenotypicariables into behavior along the lines ofhose built by Boyd and Richersen (1985)nd Cavalli-Sforza and Feldman (1981) orven the newer work on “meme” theoryy Gabora (1997) and others (e.g., Lynch996; Lynch and Baker 1986, 1993, 1994;ayne 1996; Pocklington and Best 1997)ay increase the sufficiency of the theory.

ACKNOWLEDGMENTS

First and foremost, we gratefully acknowledge theinspiration, comments, and corrections given to usby R. C. Dunnell. Obviously, this work is an out-growth of his earlier research, so in a very real sensethis article would not exist without his help. We arealso thankful for comments on the original manu-script by Deborah Schechter as well as discussion byEric A. Smith and his students. Kim Kornbacherassisted the authors by editing the final manuscript.Portions of the original research for this article wereperformed by Madsen with support from the Na-tional Science Foundation Graduate Fellowship pro-gram and with assistance from Sigma Xi.

NOTE

1 From the point of view of an organism, the rela-tionship between the traits for investment in elabo-

ration and reproductive effort is the “somatic bud- Charles, D. K., and J. E. Buikstra


get,” which is the notion that there is a finite amountof energy that an organism can expend. From thissomatic budget individuals must allocate energy tometabolism, extraction of further energy from theenvironment, and reproduction as well as social in-teraction and cultural replication. Trade-offs in theallocation of this energy are inevitable; energy usedfor one purpose may not be used for another. Fromour discussion of reproductive effort, we can expecttrade-offs between the number and survival of off-spring in variable environments. Similarly, we canexpect other trade-offs to exist, even between formsof social interaction (e.g., burial ceremonialism) andreproductive effort.

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