Of Cast Net and Caste Identity - Hum. Ecol.

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HumanEcology,Vol. 24, No. 1, 1996

Of Cast Net and Caste Identity:MemeticDifferentiationBetween Two Fishing

Communitiesof KarnatakaDebal Deb'

Twofishing castes,Ambigaand Harikantra, f Kamatakaemploydifferenttechniquesor throwingast nets in the samehabitat.Ambigas hrow he netfrom above the head, as opposedto the far easier Harikantramethodofthrowing t the waist level. Thesedifferentechniques re describedhere asmemes, transmittedthroughlearning.A logico-deductivehypothesis is

developed ere oexplainheorigin nd maintenancef the memeticdifferencebetween the castes, with the help of circumstantial semiotic andanthropologicalvidence.

KEY WORDS: caste; caste marker; fishing; India; Karnataka, meme; social learning.

INTRODUCTION

Endogamous,occupational astesin Indiaare uniquein socialhistory

in that they seem to be analogousto reproductivelysolated populationsof biologicalspeciesoccupyingdifferentecologicalniches. Likethe speciespopulations oexisting n a habitatby diversifyinghe nichespace,the castegroupspertaining o any particularhereditaryoccupationdisplaycertaindifferences n the manner and extent of commonresourceuse. The term"nichespace"is used here in a descriptive ense, and is restricted o thespace of resource use as means of subsistence.Thus the niche space of acaste is composedof the multipledimensionsof the resourcebase, equip-ment for exploitingthe resource,methods of employing he gear, and soforth. While there exist largeoverlapsbetween the occupationalniches of

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109

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110 Deb

the sympatriccaste populations, he differencesin resource use patternsallow the caste groupsto avoidcompetitiveexclusion.Thus, two castes ofbasketweavers of western Maharashtra xclusivelyuse different raw ma-terialsfor their craft(GadgilandGuha, 1992). GadgilandIyer (1988)havealso shown that HalakkiVakkal,Naik,andHoleyaof Karnatakause threedifferentplant species for weavingmats, thus avoidingoverlapwith eachother in raw materialrequirements.The divisionof the resourcespectrumin suchcasesmighthave resulted romattempts o avoidoccupational om-petitionbetweenthe castes(Gadgiland Malhotra,1983;Gadgiland Guha,

1992).Castes were originallydefined by their distinct categories of occu-pations (Datta, 1944; Klass, 1980). However, numerous castes have un-dergone occupational shifts over the past few centuries through thedisintegrationof traditionalvillage crafts and services (Beteilles, 1965;Owens and Nandy, 1977). Modernizationhas caused the disappearanceof numerous traditional caste occupations, such as toddy-tapping, pal-anquin bearing, and shellac handicrafts. The growth of the techno-in-dustrial sectors has also expandedthe range of alternativeoccupationsfor different caste guilds. This in turn has resulted in extensive overlap

of resourceuse patternsand occupations.However,in general the oblit-eration of traditional culturalbarriersto caste exogamyhas not yet oc-curred. Thus, the Bestha of Andhra Pradesh, who originally werepalanquinbearers (Thurstonand Rangachari, 1909), have now adoptedfishing as a primaryoccupation, yet maintain their cultural distinctionfrom other fishingcastes. Likewise,in the Sunderbansarea of West Ben-gal, the cultivator castes Pod and Bagdi have invaded the occupationalniche of the fishingcaste Kaibarta,while retainingtheir own traditionalcaste identities. In particular, n the regionswhere the pace of industri-

alization is relatively slow, rules of caste endogamyare rigorouslyob-served, and the traditional patterns of niche diversification betweencastes are still apparent.

The questionof originand maintenanceof the differences n the tra-ditional modes of resourceuse is of intrinsic nterestfor an understandingof the differentiationof the niche space between castes. In this paper, Ipresent a probabilisticmodel describing he originand persistenceof thedifference between two traditionalfishing castes of Karnataka n theirmethods of throwingcast nets. I present an exampleof how traditionalcastes sharinga particularniche spacemaintaina differencebetween eachother on semiotic evels.However,I do not intend here to mountany func-tionalistargument o explainthe originof the caste systemin terms of re-source use norms.



Cast Net and Caste Memes 111

RESEARCH ETTING

This study,conducted n sixmaritimevillagesof KumtaTaluk,UttaraKannadadistrict,KarnatakaFig. 1) concernstwo fishing castes-Ambigaand Harikantra-who observeendogamy,clan exogamy,and preferentialcross-cousinmarriage.Both castes are distributedmainly n estuarineandcoastalregionsof Karnataka, nd in largesettlements n UttaraKannada

3 5

RIVER20*N AGHANASHINI

UTTARAKANNADA

ghnhini

Gudk t T4E0- E30'Kagat odkan

03 Hollonagadde

Manki

Kumta

14 25' -

? 1 2 3 4 5L I I I - I I

KM

7 4?25' 30'

Fig. 1. Map showing he fishingvillagesat the Aghanashini stuary,KumtaTaluk,UttaraKannadadistrict,Karnataka.



112 Deb

district.The Ambigacaste namerefers to "water" Sanskrit mbu and am-bha). The Ambiga people identify themselves as the "Water Children"(Gangemakkalu)nd their traditionalmode of subsistencehas alwaysbeenassociatedwith riverineand maritimehabitats(as reflectedby their por-trayal n folkloreas ferrymenandfishermen).The wide range of traditionalfishing equipmentand techniquesemployedby the Ambigaattest to theirlong specializationn fishing.

The Harikantramploya similarrangeof fishingcraftsand gear. How-ever, they use considerablyewer traditional ishingitems and techniquesthan the Ambiga.Their name is probablyderived from an older name,"Hurikartaru," mplying that originally they were "coir rope-makers"(Campbell,1883). In contrastto the Ambiga,Harikantras re generalistsinsofar as a large segmentof the populationhas numeroussecondaryoc-cupations,such as farming,smallbusiness,sailoring,school teaching,andother services.

In recentyears,consequentuponthe introduction f mechanizedcraftsand correspondinglymodernized echniques, he frequencyof individualaswell as groupownershipof modernfishingequipmenthas increasedamongthe wealthier section of the fishingcommunities.Even non-fishingcastes

have begun investing n the fishingbusiness.Thus, castes hitherto tradi-tionallyseparatedby occupationalniche are apparently ndergoinga proc-ess of social homogenizationbased on resourceuse. Therefore,this studyfocuses on the traditional rafts, gear, and techniquesstill in use, as wellas those obsolescentthroughmodernization.

In termsof these fishing techniquesand equipment, he overall nichespace occupiedby Ambigas s thus inclusiveof, andlargerthan that of theHarikantraFig. 2). The old-fashioned ingle-man anoe,pati, the sail boatwith rudder,pongai,the enclosurenet, chachu-bale6,he drag net, elu-bale,and a largevarietyof hooks and lines are used exclusivelyby Ambigafish-

ermen. Except for the drag net, goru-bale,and the stake net, bubsi-bale,whichin principle s a largervariationof the Ambiga'sbag net gandi-baleh,all kinds of fishing gearused by the Harikantra re also traditionally sedby the Ambiga.Even the stake net, which is now a prerogativeof Hari-kantras,seems to have been used earlierby Ambigas (Campbell,1883).How its use was taken over by Harikantrass, however,unknown.

THE CAST-NET THROWING MEMES

In addition o these differences, here is also a considerabledifferencebetween the AmbigaandHarikantramethods of throwing he circularcastnet, bisu-bale,commonlyused by both the castes. The Harikantra like




tlo

10 - / ,g~~~~~~~~~~~1

o-

0 S6015 2

r llr ika b-a

7~~~~~~~~~~~~~

No. of nets

Fig. 2. A portionof the nichespace composedof fishingequipmentassharedby Ambigaand Harikantra.

other fishingcastes in the district-Bhoi, Kharvi,and Gabit)throwthe netfrom the waist level, swinging romthe left side,whereas the Ambigaem-ploy an apparentlymore difficult method of shooting it from above thehead.The techniquesare invariantandcaste-specific, ndone can identifya fisherman's aste merely by observinghis mannerof throwing he net.

While a Harikantra ishermancan throw a cast net most efficientlywhile standingin shallow waters (<0.6 m), an Ambigacan throw it effi-cientlyalso in deeper waters(ca. 1.2 m). When it is used from aboard acanoe,the efficiency n catching ishbecomesequalfor both the techniques.However,the bisu-bale s used more often for artisinal ishing by the fish-ermen while standingin shallow river water than from aboard a canoe,and the net is used more frequently by Ambiga than Harikantra.Thegreater dependenceof the Ambigaon the cast net is related to their in-ferior economicstatus(Fig. 3). Whereas a largesection of the Harikantrapopulationowns modern craft (including rawlersand purseseine boats),most Ambigacannot afford craftbiggerthan a pati or great costlier thanhooks andbisu-ba'leISST, 1986, personalobservation).Almost all Ambiga

households ownBisu-ba'16ets (Fig. 3).Bisu-badlenets are used in beppu,a fishingmethod in whichfish arescared into bisu-ba'16y glisteningtendercoconut leaves fastened to linesleading to the gape of the net. Relatively recently, the Harikantrahave



114 Deb

0~e j8 I

75 75

Rmbiga Harikantra

25 ~-25

R B C

Fig.3. Comparison etweenpercentages f Ambigaand Harikan-tra householdsn termsof fishingas primary ccupation A), pos-session of bisu-bale B), and ownership f cultivableands(C).

introducedanotherkindof beppu, n which the cast net is replacedby thedragnet, goru-balek.he differentuses of the nets maybe seen as distinct,caste-specificmemes. I use the term "meme" n Dawkins' 1990) sense of

a "unit of cultural nheritance" r "unit of imitation."The evidence discussedabove seems to indicate that the Harikantra

came to the fishingprofession ater than the Ambiga,andthereforehad tolearnmanyof the latter's ishing techniques. n what follows I attempttotrace,with the helpof BoydandRicherson 1985)models, a) the earlyproc-ess of the origin,and(b) subsequent stablishment f the Harikantrameme.

ORIGIN OF THE VARIANT MEME

Since the differenthereditaryoccupationsof castes served to reducecompetitionfor a given resource (Gadgil and Malhotra, 1983), any en-croachment nto the occupationalniche of a caste would be undesirablefrom the point of view of the original occupant.It is thereforeunlikelythat the Ambigawouldwillingly each theirfishingtechniques o any groupencroachingnto their niche.Therefore he only plausiblewayfor the Hari-kantrato learn the cast net throwing echniquewould be by imitating heAmbigause of the net. In otherwords,the meme can onlybe transmittedvia imitativeor observationalearning,whichinvolves some cognitive op-

erations and covert repetitions, regardless of reinforcements(Bandura,1977). In the absence of any help or instructions rom the Ambiga, suchimitativelearning requiresthat the learningindividualsmust supplementobservationwith trial-and-erroro acquirethe skill.



Cast Net and CasteMemes 115

It is realistichere to presumethe existence of n > 1 models for imi-tation by each Harikantra ndividual. f Aj is the performance throwingthe net overhead) by the jth Ambiga model, andXj is the learner'sper-formance,then

Xi=A 1+ej

whereej are normallydistributed andomvariableswith mean 0 andvari-ance

Ej.The learner'sestimatemay diverge rom the model'sperformance

Aj becauseof randomvariations n the models'performance,and/or cog-nitive errors,and/orerrors n his performancewhile imitating.The intro-ductionof the finite errorvalue,ej, is basedon the fact that it is possibleto throw the net from a continuumof heights ranging rom overheadtoknee level,and thereforeerrors n imitating he overhead echniquewouldrangeover that continuum.

Althoughthe net can be thrown rom a continuumof throwingposi-tions fromoverhead o knee level, most of the errorvariantsare likelytobe useless and subsequently liminated.At this point, it is reasonable o

supposethat at least one of the errorvariantsprovedto be almostas effi-cient in terms of coveringthe water area, capturing ish, etc., in shallowwatersas the model Ambigameme (MA,while its efficiencydecreased ndeeperwaters.Oncethisparticularrrorvariant, ayMH,proves o be nearlyas efficient as MA n the shallowerwaters, t is likelyto become fixed as anovelmeme by instructionalearningn subsequent enerationsof learners,if and only if the variantMHrequires ess skillthanMAto perform.

This importantprovisogives an opportunity o test the model: afterits invention,the error variantMH,that is, the Harikantra echnique ofthrowing he net fromwaistlevel, mighthavebeen maintainedf it proved

to be somewhateasier to perform, n addition o beingefficacious n shal-lower waters. If MH s no less difficult hanMA,then it should not be fa-vored as an alternative o MA; he more so because it is inefficacious ndeeperwaters.Thus,the meme would be subject o selection on the basisof its relativeoperational acility.

DIFFERENTIAL DIFFICULTY:AN EMPIRICAL TEST

Student volunteers from non-fishingcastes were selected based ontheir inexperience n throwingnets, and divided nto two groups,and as-signedto either an Ambigaor to a Harikantraisherman.Eachgroup wasgiventen demonstrations f cast-netthrowing,and was then asked to imi-



116 Deb

tate theirrespectivemodel. The numberof trialsmadeby each individualwas scored. In order to keep the variance of error (Ej narrow,the indi-vidualswithin each groupwere allowed to verballyaid each other to elimi-nate mistakesin imitatingthe model. The procedurewas repeated oversuccessivedaysuntil the membersof each groupwere certifiedby expertsto have satisfactorilyearned the technique.

The groupswere now reversedand the experiment epeateduntileachgroup had learned both techniques.The mean scores of each group forlearningthe first and the second techniquewere calculated,and the sig-

nificanceof the differencewas ascertainedby a t-test. The resultsgiven inTableI clearlyshow thatwhileexperienceor skill in employingeithertech-nique facilitateslearningthe other, the Ambigatechniqueis about fourtimes more difficultto learn than the Harikantraechnique.

SELECTION AND SPREAD OF THE NEW MEME IN THEPOPULATION

Once a groupof Harikantrandividuals ave learnedeithertechnique,theywould transmit hemthrough nstruction o newlearners. nstructionallearning s likelyto buildup a preference or the HarikantraechniqueMH

based on the ease of its learningandemployment.Thus,a Harikantra ar-ent who has adoptedMA is likelyto teach his "cultural ffspring"he Am-biga technique,but nonethelesswould show a bias (B) toward the easierHarikantraechnique.If the weightof the ith parentteachingMA is wi,sothat Ewi = 1, his bias towardMH can be measuredas the productwij BFollowingthe rules of linear transmissionof culturaltraits illustrated nBoyd and Richerson(1985, pp. 145-146),the frequencyof learningMH by

the culturaloffspringafter the biasedtransmissionwill be

TableI. DifferenceBetween the Numberof TrialsRequired or Untrained ndividualsoSuccessfullyLearn the Ambiga MA) and HarikantraMH) Waysof Throwingbisu-bale

Net throwing Mean No.technique N of trials SD t p

Learning MA 12 130.0 41.80the 1st 6.39 <0.001technique MH 9 34.0 18.59

Learning MA 12 57.4 18.58the 2nd 5.28 <0.001technique MH 9 22.0 12.23

Σ




p'=p + B (1 -p)

wherep is the frequencyof the memeMH n the population,andB is thebias toward hat meme.Therefore, he frequencyof adopting he preferredmeme will increase in each (cultural)generationas long as B > 0, and n> 1. The results also shows that the frequencywill increaseregardlessofwhetherthe respectiveweights (wi) of the parentsare equal or not (seeAppendixA). With an initialfrequency as low as 0.01 andB = 0.1, thefrequencyof learningMHwill exceed the 50%mark in the

populationbyonlyseven generations.The entirepopulation s expectedto have adoptedthe meme in just nine generations f eitherB or p is a little higher (seeFig. 4a). This indicatesthat even an insignificant mount of bias can leadto rapidchangesin the frequencyof differentvariants n the population.

THE MEMEAS A MARKEROF GROUPIDENTITY

Manyobjectsof functionalutilitytend to be transformedhrough ra-dition into objectsof socio-religious onventionality,ften to the extent ofprejudices cf. Rappaport1971). Conventionalitymay also take the formof a group marker,such that the item of behavior n conventiondistin-guishesthe communitypracticing t, and the behaviorassumes a semanticvalue for the group(s) n question.Examplesof suchmarkers f group den-tity are found in all societies:the sacredthreadof Brahmins, he sandal-wood markon the Vaishnava'sorehead,the crown of the monarch,thewhite robe of clergymen, he horse and the hat of Westerncowboys,the

a 1.0 b 1.0

p/ p'/

0.2 0.2-

10 20 30 40 50 10 20 30 40 50

Generation Generation

Fig.4. (a) Biasedtransmission f the memeMH fromthreeparentswithdifferentamplitudesof the preferenceB, (b) Conformist ransmission f the meme fromthree andfourparentswithfrequencydependentbiasF = 0.1.



118 Deb

judge'swig,the policeandmilitaryuniforms,andso on all serve as markersto identifythe specialtyof the respectivecommunities.

Differentiationby groupmarkers s likelyto occur between differentcastes occupyingdifferentoccupationalniches. When a caste-specificnicheis invadedby othercastes,the caste originallyoccupying he niche is likelyto distinguish ts specialtyfrom others by certain markersrelated to itsresourceuse behavioror norm. The more difficulta behavior s, the morelikely is it to be preferredas a markerfor the original occupantof theniche, because that behaviorwould be the least likely to be usurped by

outsiders.Typically, he overhead net techniqueis extremelydifficultforany new learner(Table I). Hence, this particular echniqueseems to havebeen chosen as a markerof specializationby the oldest fishingcastes inat least five States of India(TableII), where the traditional ishermen n-variablyuse the overheadtechnique,while newcomers o the occupation(including immigrantpeople who took to fishing relatively recently) arefound to have adopted only the waist-level echnique.

The data in TableII also indicate hat the bias for the waist-levelnettechniquehas not been sufficient or the discontinuation f the overheadtechniqueamongspecialistisherfolk.One reasoncouldbe that theadvantageof the overhead echnique n deeperwatersoverrides he trade-offof diffi-culty. However,since the advantageies only in the facilityof fishingwhilestandingin deeper water, and not in terms of catchingmore fish (Bhat-tachaiyya,1993;personalobservation),t seems morereasonable o surmisethat the drivefor group dentityhas been strongenoughfor the "overhead"meme to survive he invasionby the "waist-level"meme. In this case, the

TableII. Cast Net ThrowingTechniquesUsed by FishingCommunitiesn DifferentStates

Cast net throwing echnique

State Overhead Waist level

Karnataka Ambiga Bhoi, Harikantra,aaladheer,aMoghaveeraa

Assam Jaloi-keot Kurmi, Oraon, SadgopPOrissa Keuto Gokha, Kartia,Bhuiya,a

MahishyabAndhraPradesh Vadde,Jalari Bestha,aMala,a

Vadapalija,PallaeWestBengal Kaibarta Kaibarta,Malo, Pod,a

Bagdia

aOriginally on-fishing ommunitywhich has now invaded he fishingniche.bNon-fishing ommunitymigrated romneighboring tates, practicing ishingas a secondaryoccupation.




retention,or survival f the Ambiga echniques betterexplainedby culturalmechanisms hanby standard conomicor fitnessmodels.

In Kamataka,wherecasteexogamys relativelytrong, xamples f such"castemarkers"Bhattacharyya,993)are numerous.Differences etween heAmbigaand Harikantraisherfolkn the repertoire f caste-specific se ofcraftsand nets have been describedn Fig. 2. Anotherexample s providedby a community f Muslinfishermen, aladheer locallyknown as Jaldi inKumta)who live in severalmaritimevillagesof Kumtaand other parts ofKarnataka. hese fishermendisplayyet anothervariantof cast-net hrowing

technique,which s the mirrormageof thememeforHarikantraechnique-throwing t the waist level from the right-handide insteadof the left-handside. Jaladheerswere earlierrenownedn Maharashtraor theirskill n navalwarfare,but in the eighteenth entury heylost theirgloryunderBritishruleandmigratedo Karnatakao takeupfishingandtrade orlivelihood.Clearly,they adopted he Harikantraechnique f throwing isu-balM,et distinguishedthemselves rom the Hindu isherfolk yreversinghe direction f the throw.

The bias (B) toward he waist-level echniquediscussedabove is likelyto get transformed nto a caste marker,after it has been spreadover aconsiderable ection of the population.A similarbias (say B') towardthe

overhead technique (against the waist-level technique) would operateamongthe Ambigafor the purelyculturalreason of distinguishinghem-selves from the othergroups(the Harikantra ndJaladheer).The biasmaynow take many forms,and its spreadwouldbe determinedby the propor-tion of the populationadoptingit. Thus, when the meme is adopted bythe majority-whetherfor its ease of use or its symbolicvalue-it is likelyto become a markerof group identity.Boyd and Richerson(1985) illus-tratedthe rules for such "conformistransmission"f a meme with a fre-quency-dependentbias F, which will operate only when the numberof

culturalparentstransmittingt i > n/2, and is governedby the conditionsF < I| O < i < n/2

for for n >2F > I| n > i > n/2

and F = 0 otherwise.

Assuming hateach set of parents ransmittinghe meme is a randomsample of the population,and that all parentshave equal weights (wi =

1/n),the frequencyof the culturaloffspringadopting he meme after trans-mission(see AppendixB) will be:

n* E nC pi t -_ n-t X F

.

!i/n)Σ



120 Deb

wherenC1is the binomialcoefficientfor the combinationof i parents, andp is the initial frequencyof the meme within the population. (The primeof the resultant requency s differentfrom that in the previous equation,merelyto show the difference n their derivations.)Since this model pre-supposesan equal weightof all parents,onlythe number > n/2 is impor-tant, regardless of which parent can teach the meme. The pattern oftransmissionwith three parents s elaborated n AppendixB.

Obviously,once the frequencyof culturalparentstransmittinghe fa-vored meme even slightlyexceeds the valuep = 0.5 as describedabove,

p" will progressivelyncreaseover generations.Figure 4b illustrates thatwhen n = 3 and F = 0.1, the whole populationwill adopt the favoredmeme in 40 generationswhich, in the context of continuous and activesociallearning,especiallywith horizontal omponentof transmission,wouldspan a fairlybriefperiodof time.

Thus,withincreasing alueofp", the rule of conformitywouldensurethat no Harikantra ndividual s likely to employMA and conversely,noAmbigaindividualwouldemployMH. The outgroupmeme would now beconsideredwithineithergroupas an unwantedvariantof the conventional,ingroupmeme. While the Harikantrawould find no reason for adopting

the difficult meme MA,the Ambiga are likely to retain the meme as amarkerof their distinctionas the specialistcaste. In either case, the castemarkerwouldreinforceconformity o the group'snorm.

CONCLUSION

The specialist/generalist ichotomybetween the Ambigaand Harikan-tra whichgives rise to differences n economic and social achievements salso likelyto strengthen he caste distinctions.The economicallybetter-off

generalistcaste Harikantraoday considers the Ambigainferior in socialstatus.Thus,even the modern echnologiesof purseseine and trawl ishing,whichrequiregroup enterprises,are ownedby separatecaste cooperativesin the district.The caste memes will possiblycontinue to remaindistinctas long as thereis no pressureon the castes to coordinate ishingactivities.

The fact thatthe Bhoi fishermen,who originallywere palanquinbear-ers (Campbell, 1883), like the Bestha of AndhraPradesh(ThurstonandRangachari,1909),or otheroriginallynon-fishing asteswho have invadedthe fishingniche (Table II), also throw the cast net from the waist levellendssupport o the hypothesis f memeticdifferentiation f group dentity.It is probablethat the meme MHwas not inventedby Harikantras,butlearned instead from some othergroupof fisherfolk,e.g., Bhoi, or Kharvi,who employ the same technique. However,this alternativescenario does




not preclude the conjecture that this meme originated through efforts (of

whichever group) to imitate the overhead technique of a specialist fishing

caste, nor that the two memes evolved into caste-specific characteristics

reinforcing the distinction between the castes.

ACKNOWLEDGMENTS

This work was accomplished during my visit in 1990 to the Centres

for Ecological Sciences and Theoretical Studies, Indian Institute of Science,Bangalore. I am grateful to M. Gadgil, N. V. Joshi, and Mrinal Ghosh fortheir helpful suggestions, to R. B. Harikant for his assistance, and to twounknown referees for their most perceptive criticisms.

APPENDIX A

Biased Transmission

For any number of cultural parents transmitting the favored meme,the amount of bias toward the meme shown by any parent is wr.B,where

wi is the weight of the ith meme such that Ewi = 1, and B is the biastoward the favored meme. Even when none of the parents are using thefavored meme, they would nonetheless show a bias toward it while teach-ing the offspring (Boyd and Richerson, 1985, pp. 145-146). Thus, whenMH is favored, the transmission of the memes will follow the patternshown in Table Al for n = 2. Regardless of the weights of the parents,the frequency of the favored meme in the next generation will be (in my

notation)

Table Al. The Patternof BiasedTransmission f the Two Memes from Two CulturalParents,EachShowinga BiasTowardMH

No. of parents Probabilityhat a naivetransmitting individual cquires

MA MH MA MH

2 0 1-B B1 1 w1(1-B)+w2(1-B) w1(l+B)+w2(1+B)

0 2 0 1

Σ

Σ



122 Deb

p' =p2+p (1 -p) (1 +B) (w1+ W2)+B (1 _p) 2

i.e., p' =p +B (1 -p)

This result obtains for any number n > 1 of cultural parents.

APPENDIX B

Frequency-Dependent Transmission

The minimum number of cultural parents required for a frequencydependent transmission of a meme is n = 3, in which case the pattern oftransmission of the memes under consideration is shown in Table BI fol-

lowing Boyd and Richerson (1985).

When all parents have equal weights, i.e.,wi

=1/3,

thefrequency

ofthe meme H in the subsequent generations will be

p"=p+3Fp(1-p)(2p-1)

where p is the initial frequency of individuals adopting MH, and F is the

frequency dependent bias factor (see text) which assumes a positive value

as soon as the number of parents transmitting the biased meme exceeds

n/2, or p > 0.5.With larger n, the frequency will increase, following the formula

TableBL.The Patternof Frequency-Dependentransmission f theMemeMH fromThreeCulturalParentsof Equal Weights

No. of parents Probabilityhat a naivetransmitting individual cquires

MA MH MA MH

3 0 1 0

2 1 3(2/3 + F) 3(1/3 - F)1 2 3(1/3 -F) 3(2/3 + F)0 3 0 1




p"=EnC,pi (1 -p) ni. F+ i/n

where nCi s the binomialcoefficient or the combination f i parents roma set of n parents,and the sign of F depends on i, as discussed above.Thus p" increasesfaster for n = 4 thanwith n = 3, for the same initialfrequency p = 0.51, and F = 0.1 (Fig. 4b).

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