Research The influence of social niche on cultural niche...

Research The influence of social niche on cultural niche construction: modelling changes in belief about marriage form in Taiwan Mikhail Lipatov 2,3,4, , Melissa J. Brown 1,3, * , and Marcus W. Feldman 2,4 1 Department of Anthropology, 2 Department of Biology, 3 Institute for Research in the Social Sciences, and 4 Morrison Institute for Population and Resource Studies, Stanford University, Stanford, CA 94305, USA With introduction of social niche effects into a model of cultural change, the frequency of a practice cannot predict the frequency of its underlying belief. The combination of a general model with empirical data from a specific case illustrates the importance of collaboration between modellers and field researchers, and identifies the type of quantitative data necessary for analysing case studies. Demographic data from colonial-period household registers in Taiwan document a shift in marriage form within 40 years, from a mixture of uxorilocal marriages and virilocal marriages to the latter’s dominance. Ethnographic data indicate marriage-related beliefs, costs, ethnic effects and colonial policies as well as the importance of horizontal cultural transmission. We present a formal model for the effects of moral beliefs about mar- riage and a population economic index on the decline of uxorilocal marriage. We integrate empirical marriage rates and an estimated economic index to produce five projections of the historical frequencies of one belief. These projections demonstrate how economic development may affect a cultural niche. They also indicate the need for future research on the relationship between wealth and cultural variability, the motivational force of cultural versus social factors, and the process of cultural niche construction. Keywords: horizontal cultural transmission; economic index; uxorilocal marriage; virilocal marriage; colonial household registers; cultural change 1. INTRODUCTION Humans are inextricably social and cultural animals. We are, each of us, born into a particular society with its specific structure and a particular culture with its specific languages and beliefs. For humans, then, society and culture constitute niches at least as much as the eco- logical environment. Other scholars of this issue discuss ways in which aspects of human societies and cultures have constructed the ecological niches in which people live. Here, we view the theory of niche construction within the realm of human society and culture in order to explore how these niches—which can power- fully influence the ecological environment and genetic evolution (e.g. [1,2])—are themselves constructed and passed on by humans who live within them. We view the social niche of a population as the sum of all the social selection pressures to which the population is exposed and the cultural niche of a population as the sum of all the cultural selection pressures to which the population is exposed (modifying the definition of an ecological niche from Odling-Smee et al.[1]; see also Ihara & Feldman [3] for a mathematical formulation of cultural niche construction). Social selection pressures derive from the fact that all human societies have an organization, or order, constituted by a series of overlap- ping, hierarchical role-structures [4 6] (see also Runciman [7] for a different but compatible view of social selection). These structures are defined by expec- tations of behaviour for role holders, expectations that are socially negotiated in a process we consider social selection [8]. Cultural selection pressures derive from the fact that human culture is a series of overlapping, nested sets of meaningful ideas [9] often referred to as symbolic or meaning systems. Note that ‘meaningful ideas’ is used as an anthropological technical term, refer- ring to information that is shared, abstract, public (i.e. external to individuals) and either believed as truth by some percentage of the referent population or else closely associated with other ideas so believed [8,10] (see also [9,11 13]). Such ideas are expressed and learned behav- iourally, yet internalized in individual minds [14,15]. Under cultural selection, ideas that an individual already has internalized influence his/her broadcasting, reception or internalization of subsequent ideas to which she/he is exposed [8] (see also [16 21]). Thus, human social niche construction occurs when social precedents feed- back to change shared expectations of roles [8]. Human cultural niche construction occurs when belief *Author for correspondence ([email protected]). M.J.B. and M.L. contributed equally to this manuscript. One contribution of 13 to a Theme Issue ‘Human niche construction’. Phil. Trans. R. Soc. B (2011) 366, 901–917 doi:10.1098/rstb.2010.0303 901 This journal is q 2011 The Royal Society on June 12, 2018 Downloaded from

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Phil. Trans. R. Soc. B (2011) 366, 901–917




One coconstruc

The influence of social niche on culturalniche construction: modelling changes in

belief about marriage form in TaiwanMikhail Lipatov2,3,4,†, Melissa J. Brown1,3,*,†

and Marcus W. Feldman2,4

1Department of Anthropology, 2Department of Biology, 3Institute for Research in the Social Sciences,and 4Morrison Institute for Population and Resource Studies, Stanford University,

Stanford, CA 94305, USA

With introduction of social niche effects into a model of cultural change, the frequencyof a practice cannotpredict the frequency of its underlying belief. The combination of a general model with empirical datafrom a specific case illustrates the importance of collaboration between modellers and field researchers,and identifies the type of quantitative data necessary for analysing case studies. Demographic datafrom colonial-period household registers in Taiwan document a shift in marriage form within 40 years,from a mixture of uxorilocal marriages and virilocal marriages to the latter’s dominance. Ethnographicdata indicate marriage-related beliefs, costs, ethnic effects and colonial policies as well as the importanceof horizontal cultural transmission. We present a formal model for the effects of moral beliefs about mar-riage and a population economic index on the decline of uxorilocal marriage. We integrate empiricalmarriage rates and an estimated economic index to produce five projections of the historical frequenciesof one belief. These projections demonstrate how economic development may affect a cultural niche.They also indicate the need for future research on the relationship between wealth and cultural variability,the motivational force of cultural versus social factors, and the process of cultural niche construction.

Keywords: horizontal cultural transmission; economic index; uxorilocal marriage;virilocal marriage; colonial household registers; cultural change

1. INTRODUCTIONHumans are inextricably social and cultural animals. Weare, each of us, born into a particular society withits specific structure and a particular culture with itsspecific languages and beliefs. For humans, then, societyand culture constitute niches at least as much as the eco-logical environment. Other scholars of this issue discussways in which aspects of human societies and cultureshave constructed the ecological niches in which peoplelive. Here, we view the theory of niche constructionwithin the realm of human society and culture inorder to explore how these niches—which can power-fully influence the ecological environment and geneticevolution (e.g. [1,2])—are themselves constructed andpassed on by humans who live within them.

We view the social niche of a population as the sum ofall the social selection pressures to which the populationis exposed and the cultural niche of a population as thesum of all the cultural selection pressures to which thepopulation is exposed (modifying the definition of anecological niche from Odling-Smee et al. [1]; see also

for correspondence ([email protected]).and M.L. contributed equally to this manuscript.

ntribution of 13 to a Theme Issue ‘Human nichetion’.


Ihara & Feldman [3] for a mathematical formulation ofcultural niche construction). Social selection pressuresderive from the fact that all human societies have anorganization, or order, constituted by a series of overlap-ping, hierarchical role-structures [4–6] (see alsoRunciman [7] for a different but compatible view ofsocial selection). These structures are defined by expec-tations of behaviour for role holders, expectations thatare socially negotiated in a process we consider socialselection [8]. Cultural selection pressures derive fromthe fact that human culture is a series of overlapping,nested sets of meaningful ideas [9] often referred to assymbolic or meaning systems. Note that ‘meaningfulideas’ is used as an anthropological technical term, refer-ring to information that is shared, abstract, public (i.e.external to individuals) and either believed as truth bysome percentage of the referent population or else closelyassociated with other ideas so believed [8,10] (see also[9,11–13]). Such ideas are expressed and learned behav-iourally, yet internalized in individual minds [14,15].Under cultural selection, ideas that an individual alreadyhas internalized influence his/her broadcasting, receptionor internalization of subsequent ideas to which she/he isexposed [8] (see also [16–21]). Thus, human socialniche construction occurs when social precedents feed-back to change shared expectations of roles [8].Human cultural niche construction occurs when belief

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or disbelief influences whether particular ideas areaccepted as meaningful (believed or associated withbelief ) in a population [8] (see also [1,3,22]).

We focus on the interaction of society (role-struc-tures) and culture (ideas) and the potential for theirdistinct dynamics to reshape the cultural niche (seealso [3,8,23–25]). Demographic and ethnographicdata document a change in marriage practices inTaiwan during the early twentieth century, from aplurality of ways to select a mate to dominance ofone form. Here, we present a formal model exploringthe interaction of cultural ideas (represented bymoral beliefs about marriage) and social structure(represented by an ability to pay brideprice), the phe-notypic expression of this interaction in matepreferences (as represented by the actual marriageform practised), and the niche-constructing feedbackto the content of the population ideational pool or cul-tural niche. Unlike Lansing & Fox’s discussion [26] ofthe complex set of ideas in the Balinese water temples’ritual calendar, we focus on two specific cultural ideasin order to explore some of the nuanced interactionsbetween cultural ideas and social structure.

2. DATA ON MARRIAGE CHANGE IN TAIWAN,1906–1945(a) Marriage forms

In rural Danei Township and Jibeishua village (inDongshan Township) in Taiwan’s southwesterncounty of Tainan (figure 1), frequencies of marriageforms changed between 1906 and 1945, both amongthe ethnic Han (Chinese) majority and the plains Abor-igine (Austronesian) minority [27–29]. Although Hanin Taiwan practised a range of marriage forms[27,30,31], there were primarily two forms of marriagein Danei and Jibeishua at the beginning of the twentiethcentury [28,32]. Virilocal ‘major’ marriage ( , lit.for a woman to leave her natal household as a man’swife)—where a young woman, after puberty, was trans-ferred from her father’s household to her husband’s—was the Han cultural ideal, and it was commonamong both Han and plains Aborigines [27–29]. Thecost of such a marriage—brideprice, feasting and feesfor the go-between—was significant for the groom’sfamily and was not offset by the dowry provided bythe bride’s family. The brideprice alone was oftenequivalent to a year’s income for a farm family andcould require 10–15 years of saving to accumulate[30]. (Note: In China and Taiwan studies, unlike Afri-can studies, ‘brideprice’ is the standard andappropriate translation for , not ‘bridewealth’,because the cash and gifts included in brideprice wereculturally viewed as buying a woman and all rights toher labour and children [30,33–35]. Additionally, viri-local major marriages and uxorilocal marriages aregenerally referred to as ‘marriage forms’ rather thanjust post-marital residence because the terms encom-pass related rituals and jural rights and duties as wellas residence; moreover, they are frequently comparedwith other forms of marriage which are also virilocal).

Uxorilocal marriage ( or , lit. bringingin a son-in-law)—where an adult man moved into hiswife’s household—was a persistent minority of

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marriages, of variable frequency [27,28,30,32]. Uxor-ilocal marriage required no brideprice, feasting, fees ordowry, for Han or plains Aborigines. Moreover, theconcept of uxorilocal marriage in Taiwan included arange of practices that elsewhere in the world wouldbe treated as distinct marriage forms. According toWolf & Huang [30], the most common version ofuxorilocal marriage among the Han was where a son-in-law would agree to give his father-in-law’s surnameto one or more of his sons, and only those boys wouldhave rights of property inheritance of their maternalgrandfather’s property. Ethnographic evidencesuggests that the most common form of uxorilocalmarriage among plains Aborigines in the villages ofToushe (in Danei Township), Jibeishua (in DongshanTownship) and Longtian (in Guantian City) wasessentially a form of brideservice, where no surnamechanges would be made, no property inheritancerights would be granted, and after 10 years or so ofworking for his father-in-law, a son-in-law wouldmove his wife and children out and establish his ownhousehold [28]. Such variation fits within a largerHan acceptance of a wide range of marital forms.Unlike Christian Europe, where there was a largelyuniform marriage type (serial monogamy) but widevariation in form of inheritance, in Han China andHan diasporas, there was a largely uniform inheritanceform (all brothers inherited equally) but families couldcontract virtually any form of marriage mutuallyagreed upon [28,30,33,36–38].

One of the best predictors of uxorilocal marriage wassibling composition [30,39–41]. Han women whoreached age 15 with no brothers or only very youngbrothers living in their household were much morelikely to marry uxorilocally than women with at leastone living older brother. Generally, these women’snatal families had at least minimal property or tenancyrights, which could be used to entice a Han man into anuxorilocal marriage. These trends also appear to holdfor plains Aborigines, but plains Aborigine womenwith older living brothers might also marry uxorilocally[27–29]. Poverty affected mortality rates, and thus sib-ling composition, but so too did stochastic effects.Elderly women Brown interviewed frequently reportedhaving lost a brother or a husband when an oxcartflipped over on him. Whether such accidents left ahousehold without male labour was a stochastic effect,for it depended on the existing sibling composition asdetermined by the prior history of the household.Pandemics, war and natural disasters also yielded sto-chastic effects. For Han men, conditions of poverty,which meant they could not pay a brideprice, caused,for example, by having five or more living brothers, orone or more parents deceased by the time a manreached marriageable age, best predicted whether hewould marry uxorilocally. Among plains Aboriginemen, the correlation with poverty appears to be lessstrong. (Note: Wolf used quantitative data to assessthese correlations for a northern Taiwanese Han town-ship; Brown used qualitative data from in-depthinterviews in three southwestern plains Aboriginesvillages, discussed further below.)

Han viewed uxorilocal marriage as shameful; thusHan men who resorted to this form of marriage were







distance (km)


0 20 40 60 80 100

30 50 70 90


Cengwen river

Figure 1. Map of Tainan County, Taiwan.

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often viewed with suspicion by their in-laws and thelocal community [29,30,40]. By contrast, becauseuxorilocal marriage among plains Aborigines in theearly twentieth century has generally been viewed asa holdover from seventeenth century matriliny (e.g.[27,28,42]), its ‘traditional status’ for Aborigines hasled to the expectation ‘that the factors that weakenuxorilocal marriage among the Han, especially thedenigrated status of the in-marrying son-in-law andeven the lack of trust in the relations of son-in-law toparents-in-law would be diminished among theplains [A]borigines’ [29]. Further expectations thatdivorce rates for the uxorilocally married would belower among plains Aborigines than among Hanwere not realized [29]. However, late nineteenth cen-tury European missionary reports that marriage waslax among plains Aborigines and divorce common—presumably also derived from matriliny—precludethe conclusion that uxorilocal marriages were not‘culturally honoured’ [29].

Ethnographic research in the plains Aboriginevillages of Toushe (Danei Township), Jibeishua

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(Dongshan Township) and Longtian (Guantian City),all in Tainan County, suggests that plains Aborigineresidents there may have viewed uxorilocal marriagemore neutrally than the Han. Some 79 elderly villagers(surviving, mentally capable villagers, aged 60 andolder, interviewed in 1991–1992) who had been con-sidered plains Aborigines in their youth reported on atotal of 85 marriages in their parents’ and grandparents’generation (which occurred roughly 1900–1920): 40per cent of the 18 Longtian marriages were uxorilocal,44 per cent of the 44 Jibeishua marriages and 70 percent of the Toushe marriages [28]. These same villagersreported lower rates of uxorilocal marriage for their owngeneration (which occurred roughly 1925–1940): 35per cent of the 20 Longtian marriages were uxorilocal,31 per cent of the 35 Jibeishua marriages and 23 percent of the 44 Toushe marriages [28]. Brown foundthat these ‘plains Aborigine’ villagers demonstrated noshame or reluctance in speaking of their own, theirparents’ or their grandparents’ uxorilocal marriages.Nor did their reports describe maltreatment of uxorilo-cally married men within their community. The only

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uxorilocally married Han man who spoke ill of his plainsAborigine in-laws (who did not give him any property)confessed to not having honoured the terms of the mar-riage agreement by refusing to give any of his sons hisfather-in-law’s surname. Given the sharp contrast ofshame, reluctance and reports of discrimination aboutuxorilocal marriages in the ethnographic interviews inHan areas of Taiwan and China by Brown (duringfield research in 1991–1992, 1994, 1996, 2002 and2009) and other anthropologists (e.g. [40]), the consist-ently neutral tenor of these responses provides strong,qualitative evidence that, in the early twentieth century,uxorilocal marriages did not hold the same stigma forplains Aborigines in these villages as they did for Han.

(b) Ethnic relations

The Hoklo variety of Han were the ethnic majority ofTaiwan and Danei Township, but plains Aboriginesconstituted a numerical majority of Toushe village(in Danei Township) and Jibeishua village (in nearbyDongshan township) [28,32]. By the beginning of Japa-nese colonial rule (1895), ethnic relations betweenHan and plains Aborigines were peaceful, and plainsAborigines had adopted (Hoklo) Han language andmany Han customs [28]. Plains Aborigines were stig-matized and identified primarily because they did notbind their daughters’ feet, in contrast to the Hanwho lived in Danei and Jibeishua.

The ethnic border also served as a marital border.Some Han and plains Aborigines did marry, butsuch marriages were mostly regarded as shameful—poor Han men marrying uxorilocally to plains Aboriginewomen, or poor Han widows remarrying virilocally toplains Aborigine men. According to one elderlyJibeishua man, interviewed in 1992,

Phil. T

The women [of his parents’ and grandparents’ gener-

ation] were all fierce. The men of surrounding

villages [who were Han] did not want to marry

them; they [the Han men] called them [Jibeishua

women] hoan-a-pho [savage biddies], so the

[Jibeishua] village men had to marry them [28].

In other words, Han would not arrange virilocal mar-riages for their sons with women stigmatized as‘savages’. Similarly, Han would generally not marrytheir daughters to plains Aborigine men as first-timebrides (i.e. young women marrying for the firsttime). (Note that multiple marriages occurred via thepractice of women remarrying following widowhoodor divorce, which was common among both Han andplains Aborigines despite Han disapprobation (see[29,30]). Polygyny was accepted but relatively rare inChina and Taiwan, as documented by the low fre-quency of concubine marriages in our database; seealso [43].)

Plains Aborigines were poorer on average than Hanin Tainan County [28,44]. However, plains Aborigineswere economically better off in Jibeishua than Danei,owing to agricultural conditions. Danei was partlyrich flood plains with paddy agriculture, dominatedby Han, and partly foothills with limited irrigation,where most of the plains Aborigine minority lived.Jibeishua was on the Jianan plain, surrounded bypaddy fields.

rans. R. Soc. B (2011)

(c) Economic development

The Japanese colonial government (which ruledTaiwan 1895–1945) invested heavily in developingTaiwan between 1895 and 1930 [28,45] (see also[46,47]), constructing roads, bridges, a railroadsystem, hospitals, schools, sewage systems, dams, fac-tories, sugar mills and more. Irrigation systemsexpanded the number of rice crops possible per year;in Jibeishua after 1925, when the Jianan irrigationsystem was in place, people could plant three ricecrops per year. Public health measures effectively con-trolled plague, malaria and tuberculosis, reducingmortality rates across the board [48,49]. Although uni-versal compulsory education was never achieved, mostpeople, even in rural areas, had at least 2 years of pri-mary education in Japanese. Many Taiwanese had theopportunity to attend middle school, making themsuitable for entry-level employment in Japanese-runfactories, businesses, government offices and banks.This economic and educational development resultedin non-elite Taiwanese (both Han and plains Abori-gines) having more money. Thus, poor men wereincreasingly able to accumulate sufficient cash to paya brideprice.

Such development produced fundamental changesin Taiwan’s social niche. As defined above, a socialniche is the sum of all social selection pressures, andsocial selection is the social negotiation process overexpectations in the behaviour of role holders in hier-archically organized and networked role-structures.Economic development created new roles and newstructures, for example, in factories, railroad systemsand public health organizations. It also allowed manychanges in continuing role-structures, such as the kin-ship system (for which marriage is an important meansof recruitment). For example, Wolf [39] has documen-ted quantitatively that the ‘minor’ form of virilocalmarriage (where a family would adopt a young girland raise her to be the wife of one of their sons) wascommon among Han in northern Taiwan at the begin-ning of the Japanese period but declined in frequencyby 1925. Wolf uses qualitative, ethnographic evidenceto attribute this decline to the ability of young peopleto buy themselves out of such marriages owing to theincreased economic opportunities that came with colo-nial development (cf. Lim case study in Brown [45]).Here, young people used the resources available frommodifications in the social niche to renegotiate theexpected behaviour of sons and adopted daughters-in-law to such an extreme that they actually did awaywith the latter role entirely.

Also related to economic development, the Japanesecolonial government, beginning in 1915, enforced aban on the practice of footbinding. Elderly Han inter-viewed in 1991–1992 in Danei and Dongshantownships reported that Japanese police who super-vised the unbinding of their mother’s (or in onewoman’s case, her own feet) said the unbinding wasfor women to be able to work in the paddy fields.The footbinding ban was intended to expand femaleparticipation in agricultural labour, but it also unin-tentionally removed the ethnic boundary betweenplains Aborigines and Han and drove the subsequentassimilation of plains Aborigines in Toushe and

1906–1915 1916–1925 1926–1935 1936–1945

u / (

u +


marriage date

Figure 2. Proportion of uxorilocal marriages for Aborigineand Han women from Danei and Aborigine women fromJibeishua, by 10 year marriage cohorts. Green bars, Jibeishua

Aborigines; violet bars, Toushe Aborigines; blue bars, DaneiAborigines; red bars, Danei Han. Note: Toushe Aboriginesare a subset of the Danei Aborigine population.

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Jibeishua to a Han identity [28,45]. This removalshifted marriage patterns in Danei and Jibeishua byincreasing the rates at which Han allowed their daugh-ters to marry plains Aborigine men (as first-timebrides) and at which Han brought in plains Aboriginebrides for their sons [28]. In other words, the foot-binding ban coincides with an overall decrease inuxorilocal marriage rates, both for plains Aboriginesin relation to Han and for everyone overall (figure 2).

The resulting change in ethnic identity also hadconsequences for villagers’ customs (practices) andcultural ideas [23,28,50]. By 1991, people practisedcustoms largely indistinguishable from neighbouringvillages that had always been considered Han (exceptfor one part of their religious practices). Toushe andJibeishua villagers whose identities changed fromplains Aborigine to Hoklo Han also believed manymore Han cultural ideas over time, although a lag inthe adoption of ideas was still apparent [28,50].Such evidence that the spread of cultural ideas in apopulation can follow the spread of an associated prac-tice suggests that behaviour itself (phenotype) may bean important factor in cultural niche construction(i.e. changes in whether particular ideas are acceptedas meaningful; cf. [8,23]).

The frequency of cultural ideas in the early-twentieth-century plains Aborigine population in these villagesis unknown. The only evidence available is from retro-spective ethnographic interviews from a survivingsample (e.g. [28]) or occasional historical claims, oftenby Western missionaries, about the cultural ideas ofan entire village, county or even ethnic group (e.g.[29,51–53]). There is debate among Taiwan scholarsabout the degree to which southwestern plains Abori-gines had adopted Han cultural ideas by 1900 (e.g.[28,29,42,50,54,55]).

(d) Demographic data

To monitor Taiwan’s population, the colonial govern-ment developed a household registration system, inwhich every person had to register with the police asa member of one, and only one, household [30]. Infor-mation registered included name, age, sex, relation tothe head of the household, marital status, and, in theearly part of the Japanese period, ‘class,’ ‘race’ asinherited from one’s biological father and (for females)whether feet were bound. Japanese-period registers formany localities have been computerized and archived.Some information in the original registers is not avail-able in the public-use database, affecting somepotential analyses. For example, all names have beenreplaced by identification numbers, which meansthat quantitative assessment of surname changes isnot possible. Each locality database contains theabove information for every single person alivebetween 1906 and 1945 who resided in that localityfor at least 1 day. In other words, the people rep-resented in the database for each locality (village,township, small city and urban neighbourhood) arethe entire population for that 40 year period, notmerely a sample.

The entire population, so defined, includes migranthouseholds as well as long-term residents. Taiwan’s

Phil. Trans. R. Soc. B (2011)

population during the colonial period was extremelymobile, but the Japanese colonial government tookmeasures to reduce the impact of such mobility onthe household registers. Most importantly for our pur-poses, household registers reflect Taiwanese conceptsof family ( ), not merely residence. Individualscould be registered in their family’s household butphysically resident elsewhere. If individuals reportedthat they would be gone from the locality for aperiod of time, for example, for work, the localpolice merely added a pasted-on rice-paper strip tothe comments section of their permanent householdregister indicating the sojourn. (They also had to reg-ister with the police in the locality to which they weregoing, but registered as sojourners, not as permanentresidents.) Any marriages or other events that occurredduring this period would be recorded on the perma-nent household register page in their home locality.There were relatively few sojourners in Danei and Jibe-shua, since these localities include no major urbancentres. In our analyses, we have excluded sojournersfrom consideration. Thus, only migrations thatincluded the entire household are included in oureffective populations.

The Danei and Jibeishua databases (recordinginformation on 21 151 and 3268 people, respectively)provide the following information for every marriagethat occurred between 1906 and 1945: date, form(uxorilocal or virilocal), first- or high-order marriage(indicating serial remarriage), community address ofpost-marital household (which allows us to identifyresidence in Toushe village within the larger DaneiTownship database). The databases also providedetailed information on spouses including, in manycases, their natal households.

In our analyses, we only examine first marriages fortwo reasons. First, we want to be able to compare ourresults to previously published studies of the Taiwanhousehold registers, which focus on first marriages(e.g. [27,29–31,38,39,40,56]). Second, remarriagesoccurred with different social expectations, underdifferent economic conditions, and with differentcultural views from first marriages. Moreover, firstmarriage form does not necessarily predict remarriage





1906–1915 1916–1925 1926–1935 1936–1945

u / (

u +


marriage date

Figure 3. Rates of uxorilocal marriage for all women fromDanei, by 10 year marriage cohorts.

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form. Wolf & Huang [30] suggest that remarriageshave a higher frequency of uxorilocal marriages thanfirst marriages. For example, a virilocally marriedwoman whose husband died young (especially if heleft young sons and no brothers) was highly likely tomarry uxorilocally, either arranged by her parents-in-law or herself, since there was likely to be bothproperty and need of adult male labour.

We also focused on uxorilocal and virilocal majorforms of marriage because other forms of marriagewere relatively rare in these particular sites. For localwomen married from their natal homes in first mar-riages, occurring any time between 1906 and 1945,there were 2003 virilocal major marriages in allDanei Township, 374 uxorilocal marriages, 166minor marriages (only nine of which included plainsAborigines) and 27 concubine marriages. In Jibeishuavillage, there were 342 virilocal major marriages, 99uxorilocal marriages, 17 minor marriages (eight ofwhich included plains Aborigines) and six concubinemarriages. (Note: Concubine marriages were alwaysto virilocally married men).

Here, we present uxorilocal marriage rates forwomen from the township of Danei and the villagesof Toushe and Jibeishua between 1906 and 1945.We define the uxorilocal marriage rate, U, as theratio u/(u þ v), where u is the number of first uxorilo-cal marriages among all the women from a particularvillage or township during a particular period oftime, and v is the corresponding number of first virilo-cal (major) marriages. These data count women whowere living in households in Danei or Jibeishua atthe time when the woman either left her householdto marry (virilocally) or had a husband brought infor her. Thus, we are counting the marriages ofwomen from that locality at the time of marriage.Those whose first marriages contributed to theToushe rate are women who were living in householdsin Toushe on their 15th birthday, generally the earliestage at which first marriages occurred (e.g. [30]),although plains Aborigine women tended to marry atlater ages than Han women [29]. (Note: This qualifi-cation reduces the number of women in migranthouseholds included in the Toushe figures.)

We calculate the marriage frequencies in terms ofmarital cohorts (e.g. figure 2) because this calculationcaptures period effects—larger historical factors thataffected all marriages at a particular time, such asthe 1915 footbinding ban. Note that no error rangeis indicated because the data are not a sample;rather, they represent the entire population of specifiedwomen. The first cohort shows the plains Aborigineswith a clearly higher rate of uxorilocal marriage thanHan. We do not know how these frequencies of thepractice of uxorilocal marriage relate to culturalideas. There follow two cohorts where the Aboriginerates drop and approach the Han rates, and finally acohort that shows no significant difference betweenthe Han and Aborigine rates. (A two-sample test ofequality of proportions with continuity correction indi-cated that the Danei Aborigine and the Danei Hanuxorilocal marriage proportions in the fourth cohortare the same.) There is a more-or-less steady declinein uxorilocal marriage in all groups over the colonial

Phil. Trans. R. Soc. B (2011)

period to a low of about 5 per cent in the finalcohort, but the decline in the Aborigine rates fromthe first to second cohort is strongest.

We primarily use the data in figure 3 from Daneionly, which combine the rates for Han and plainsAborigine women, to inform construction of a basicmodel of declining uxorilocal marriage rates, becausethis combination simplifies the mathematical calcu-lations. (The marital-cohort rates in figure 3 can beunderstood as weighted averages of the Danei Hanand Danei Aborigine rates presented in figure 2.)However, in the analysis, we do use data onDanei Han only (UH1) from figure 2 to calculate thehistorical projections of changing beliefs.

3. MATHEMATICAL MODELBased on the qualitative and quantitative evidencesummarized above, we identified the following key fac-tors that might have affected uxorilocal marriage ratesin Taiwan: a set of cultural ideas about the shameful-ness of uxorilocal marriage (including associationwith son preferences), economic conditions affectingthe cost of a virilocal marriage (especially the bride-price), and sibling composition (which is affected byboth economic and stochastic effects on mortalityrates). As discussed above, it is unknown—and unli-kely to ever be known—what the frequency ofcultural ideas regarding marriage was at the beginningof the Japanese colonial period in Taiwan. It is, how-ever, clear that economic and public healthconditions improved dramatically over the course ofthe colonial period, resulting in greater wealth in thepopulation and lower mortality rates.

Given the importance of poverty and sibling com-position in predicting the probability of uxorilocalmarriages (e.g. [27,30]), and given evidence that prac-tices can and do change before cultural ideas [28,50],the influence of cultural niche construction is notclear. In other words, it is not clear whether or howcultural ideas about marriage form must have changedbefore, during or even after the decline in uxorilocalmarriage rates. Thus, we turn to a mathematicalmodel to indicate the possible dynamics of culturalideas, given the known changes in the social niche.In constructing the model, we allow for direct influ-ence of cultural ideas and a population economicindex. We also include an indirect representation ofstochastic influences on sibling composition.

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(a) Transmission of cultural ideas

We suppose that every person in the locality has a cul-tural idea about the morality of virilocal and uxorilocalmarriages, which affects the relative desirability of eachform. Each person either has an idea (s1) that uxorilo-cal marriages are immoral and thus undesirable or anidea (s0) that uxorilocal and virilocal marriages areequally moral and desirable. In other words, peoplewith s0 are neutral; they have no clear preferencebetween the two forms of marriage. An interestingconsequence of the empirically based conceptuali-zation of these cultural ideas as a preference andneutral idea is that under certain conditions, discussedbelow in ‘calculating the uxorilocal marriage rate’, s1

is dominant over s0. (For any individual, s is assumedto be independent of monetary wealth.) We define xas the proportion of people who have s ¼ s0 at agiven time in a particular population, and 12x is theproportion of people with s ¼ s1.

Our model includes horizontal transmission of s

[16]. We allow for the possibility that the empiricaldecline in uxorilocal marriage was driven by achange in beliefs. The rapidity of this decline (lessthan a generation), especially for plains Aborigines,means that cultural influence must have come horizon-tally rather than vertically. Moreover, once marriageform was already changing, individuals may wellhave been influenced in their opinion of marriageforms practised by their own and adjacent cohorts.Consequently, our model assumes that vertical trans-mission does not produce a change in the value of xbetween the parental and offspring generations (it isunbiased) and also that whether a person believesuxorilocal marriages are immoral (s1) or neutral (s0)is affected by the beliefs of others within the same bio-logical generation. (Note: The model assumes thatcultural selection operates by ideas directly influencingeach other, but empirically we would expect individ-uals’ ideas to be influenced both by the expressedideas of their peers and observations of the outcomes(e.g. divorce) of actual marriages (phenotype) in theadjacent cohorts—siblings, cousins, neighbours andclassmates.) For simplicity, we assume that bothvertical and horizontal transmissions of ideas aregender-blind, so that the system quickly reaches astate where x is the same in both genders.

(b) Population economic index

We introduce W, a population-level economic index.Given that colonial Taiwan was economically highlystratified, we conceptualize W not as wealth in generalbut as the proportion of individuals in the populationthat had sufficient wealth to pay a brideprice. Thisview of W makes the model slightly more realisticbecause the range of variation in brideprice was con-siderably less than the range of variation in overallwealth in the population [30].

W ranges between 0 and 1. When W ¼ 0, poverty isso great that no one can afford to pay brideprice andeveryone marries uxorilocally. When W ¼ 1, societalwealth is sufficiently high that everyone has enoughmoney to pay a brideprice and, thus, everyone canmarry according to his/her cultural beliefs. Since one

Phil. Trans. R. Soc. B (2011)

of the two beliefs in the model is neutral, havingenough money for a brideprice will not automaticallymake a person with s0 marry virilocally. Taiwan’s over-all wealth increased during the colonial period, sowe would say that W increased. Thus, in contrast toShennan [57], we consider an industrializing contextin which access to resources increases over time andfor a larger percentage of the population.

We recognize that using a population-level econ-omic index is not ideal. We use a population-levelindex because, first, although we do not have village-or township-wide, individual-level data on wealth, wedo have reliable qualitative evidence of the popu-lation-wide increase in wealth. Second, the poor,rural character of Danei Township and Jibeishua Vil-lage suggests that the within-population variation inthe ability to pay brideprice can be approximatedby the proportion W. We are not assuming thatthe level of brideprice in this poor rural area ofTaiwan would not itself increase with increasingpopulation wealth. Rather, based on Brown’s ethno-graphic interviewing about the arrangement ofmarriage in different generations and Wolf ’s [39] eth-nographic evidence discussed above about youngpeople buying themselves out of minor marriages,we assume that, with economic development, morepoor men in Danei and Jibeishua had the option ofsojourning in an industrial centre and therebyaccumulating the needed wealth to return to theirrural homes with enough cash for a brideprice. Asmore men tapped into the industrializing economyoutside of Danei, W, the proportion able to pay abrideprice, increased.

(c) Indirect effects on s1

The model includes a constant parameter, s, whichranges between 0 and 1, and measures the degree towhich the cultural belief s1 influences a person’s mar-riage practice. We include this parameter in the modelbecause empirical evidence suggests that, despite view-ing uxorilocal marriage as shameful, Han arrangeduxorilocal marriages for their daughters if they hadno sons. When s is low, the influence of s1 is lowbecause the cultural idea is swamped by mitigatingeffects. As discussed above, sibling composition is areliable predictor of uxorilocal marriages, and siblingcomposition is strongly correlated with mortalityrates, which are in turn affected by both poverty andstochastic occurrences. The parameter s is intendedto capture the stochastic effects on sibling compo-sition, such as farm accidents. Stochastic events thatcould affect sibling composition and make s lowinclude the 1918 influenza pandemic and colonialconscription of men as coolie labour for the JapaneseImperial Army during World War II (table 1). (PlainsAborigines and Han in Danei and Jibeishua wereaffected by both of these events.) Decreasing sincreases the proportions of uxorilocal marriages forpeople with s1 (rows 2 and 3 in table 2). When s ishigh, the cultural idea has a strong influence on prac-tice because mitigating effects have little significance(they are minor events, or fewer in number). Forexample, although hurricanes occur in Taiwan, there

Table 2. The probability of uxorilocal marriage by pairing


marriagepairing type

frequency ofthese marriagepairings


1. s0 � s0 x2 1 2 12


2. s0 � s1 2x(1 2 x) 1 2 12

W (1 þ s)

3. s1 � s1 (1 2 x)2 1 2 12

W [22(1 2 s)2]

Table 1. List of variables and symbols.

name definition

s cultural idea held by individual regarding morality of uxorilocal and virilocal marriage forms, which affects therelative desirability of each form. Takes one of two values.

s0 idea that uxorilocal and viriilocal marriages are equally moral and desirable.s1 idea that uxorilocal marriages are immoral and undesirable.x proportion of individuals in the population with s ¼ s0 at a given time.W a population-level economic index. The proportion of individuals in the population having sufficient wealth

to pay a brideprice. Varies between 0 and 1.

s degree of influence of s1 on a person’s marriage practice, due to stochastic mitigating effects. Variesbetween 0 and 1.

U total effective proportion of uxorilocal marriages in the population.U ¼ x2ð1� 1

2W Þ þ 2 xð1� xÞð1� 1

2W ½1þ s�Þ þ ð1� xÞ2ð1� 1

2W ½2� ð1� sÞ2�Þ

H horizontal transmission. The difference between the proportion of people switching to s0 and the proportion ofpeople switching to s1. H ; H10 2 H01. Ranges between –1 and 1.

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was no mention of hurricane-related deaths in ethno-graphic interviews.

Because s is a constant—it is the same for everyone inthe population—we operationalize it as saying thatpeople are subject to the same risk of stochastic eventsthat might affect their sibling composition. Forexample, people were at the same risk that a male intheir household would die from the flu pandemic,would die because an oxcart laden with sugarcanewould overturn or would be pressed into labour servicefor the army. This assumption, entailed in making s aconstant, does not take into account the influence ofpoverty or household occupation in the probabilitythat such events affect any particular household. Wemake this simplification for tractability of the model,but we also suggest that economic influences on theimpacts of these events can be conceptualized asbeing incorporated into the economic index, W.

(d) Calculating the uxorilocal marriage rate

In table 2, we present the probabilities that hypothe-tical couples with specified cultural ideas (s0 or s1)will marry uxorilocally, assuming pairing is randomwith regard to s in order to keep the model assimple as possible. In row 1, we see that the frequencyof couples both having s0 is x2. Empirically, mating isprobably not entirely random with regard to s. How-ever, the ethnographic evidence discussed above ofthe potential effects of poverty and sibling compositionon marriage forms does suggest some randomness ofmating with respect to s, since poverty or sibling com-position could lead people with a strong personal beliefin the cultural idea s1, that uxorilocal marriages are

Phil. Trans. R. Soc. B (2011)

shameful, to marry uxorilocally. If everyone in thepopulation is wealthy enough to afford bridepriceand thus to marry as they like (i.e. W ¼ 1), then theprobability that a s0 � s0 couple will marry uxorilo-cally is 1

2, because both individuals are neutral about

marriage form. (Here, we ignore the possibility that adesire to save the brideprice for other uses might biasthe frequency towards uxorilocal marriages.) Hence,from the third column of table 2, Pr[uxorilocalmarriage j s0 � s0] ¼ 12 1


In row 3 of table 2, the probability that a s1 � s1

couple will nevertheless marry uxorilocally is stronglyinfluenced by the direct effects of wealth (the pro-portion of people who can afford a brideprice) andthe indirect effects of s on s1: Pr[uxorilocal marriagej s1 � s1] ¼ 121

2W [22(12s)2]. If the population

is so poor that no one can afford a brideprice (i.e.W ¼ 0), then 100 per cent of these couples willmarry uxorilocally, despite their cultural belief s1. If,at the other extreme, the population is wealthyenough that everyone can marry according to prefer-ence (i.e. W ¼ 1), then the rate at which they marryuxorilocally will be determined by s, which affectsboth individuals in the couple. If the effect of s1 is neg-ligible (s ¼ 0) and if everyone can afford brideprice(W ¼ 1), uxorilocal marriage occurs randomly (Pr[ux-orilocal marriage j s1 � s1 and W ¼ 1 and s ¼ 0] ¼ 1


There is no influence from s1, leaving s0 as the onlycultural belief, and since s0 is neutral with regard tomarriage form, its influence is to push the frequencyof uxorilocal marriages towards neutrality (i.e. 1

2). If

the effect of s1 is maximized (s ¼ 1) and if everyonecan afford brideprice (W ¼ 1), the probability ofuxorilocal marriage is 0 because couples are able tofollow their beliefs and s1 � s1 couples have a strongpreference against uxorilocal marriage.

In row 2, the probability that a s0 � s1 couple willmarry uxorilocally is directly affected by societalwealth (W ) and also indirectly affected by s. If thepopulation is so poor that no one can afford a bride-price (i.e. W ¼ 0), then 100 per cent of these coupleswill marry uxorilocally, despite the cultural belief s1

of one of the couple. If, at the other extreme, the popu-lation is wealthy enough that everyone can marryaccording to preference (i.e. W ¼ 1), then the rate atwhich they marry uxorilocally will be determined by

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s, which affects only one individual in the couple (sinceonly one has s1). If the effect of s1 is negligible (s ¼ 0),then, even if everyone can afford brideprice (W ¼ 1),uxorilocal marriage occurs randomly (Pr[uxorilocalmarriage j s0 � s0 and W ¼ 1 and s ¼ 0] ¼ 1

2) because

the other member of the couple is neutral with respectto marriage form. If the effect of s1 is maximized (s ¼1) and if everyone can afford brideprice (W ¼ 1), theprobability of uxorilocal marriage is 0 because couplesare able to follow their beliefs and one member of thecouple has a strong preference against uxorilocal mar-riage while the other is neutral (hence the one with thestrong belief will hold sway). In other words, s1 isdominant over s0. When s ¼ 1, the proportion of uxor-ilocal marriages for s1 � s1 and s0 � s1 couples is atits lowest value of 12W.

We can use table 2 to calculate U, the totaleffective proportion of uxorilocal marriages in thepopulation:

U ¼ x2 1� 12W

� �þ 2xð1� xÞ 1� 1

2W ½1þ s�

� �

þ ð1� xÞ2 1� 12W ½2� ð1� sÞ2�

� �: ð3:1Þ

In other words, the number of expected uxorilocalmarriages in the population is the sum, for each ofthe random pairings, of the frequency of the pairingmultiplied by the probability that pairing will resultin an uxorilocal marriage.

(e) Horizontal transmission

Couples in cohort t match up, marry and transmitbeliefs to cohort t þ 1. We refer to couples in differentcohorts, rather than generations, because the passageof time between the cohorts is generally not sufficientfor biological reproduction and we have assumed thatvertical transmission is unbiased. Horizontal trans-mission of cultural ideas can occur in a variety ofways. For example, a person with idea s0 in cohortt þ 1 can receive a broadcast expression from aperson with idea s1 and change his/her idea to s1.Alternately, a person with belief s0 in cohort t þ 1can observe a marriage as practised by a couple incohort t and change his/her belief to s1. The prob-ability of a change from s0 to s1 is H01, and theprobability for a change from s1 to s0 is H10. Horizon-tal transmission influences cultural selection. It isviewed as different from the more subtle effects of cul-tural niche construction, where a person with idea s0

in cohort t þ 1 receives a broadcast expression froma person with idea s1 and this reception changes his/her perception of which idea is generally believedand thus meaningful in the larger population.

At the conclusion of this horizontal transmissionprocess, the proportion of people with belief s0 isequal to

xnext ¼ xþHxð1� xÞ; ð3:2Þ

where H is defined as the difference between the pro-portion of people switching to s0 and the proportionof people switching to s1 (H ; H102H01). H rangesbetween 21 and 1. When everyone is switching tos1 (H ¼ 21), the reduction in x is the greatest, andx decreases quadratically: xnext ¼ x2. When everyone

Phil. Trans. R. Soc. B (2011)

is switching to s0 (H ¼ 1), the increase in x is thegreatest: 2x2x2.

4. SOCIAL MEDIATION OF THE EXPRESSION OFCULTURAL IDEASAt the origins of cultural evolution modelling, Cavalli-Sforza & Feldman [58] made a simplification in thecultural transmission process for modelling facility(which did not interfere with their goal of counteringArthur Jensen’s racist claims by demonstrating thatnon-genetic effects could lead to the educationalinequalities he cited as support, see also [59]).Although culture was defined as learned information,transmission was modelled more simply as the imita-tion of behaviour (the effects of parental phenotypedirectly on children’s phenotype). The precedent ofthis simplification established an expectation for mod-elling cultural transmission that became standard inthe field (e.g. [1,16,17].) (Note: Durham [60] didnot make this simplification, but because he did notmathematically model the alternative cultural trans-mission process he proposed, modelling practices didnot shift.)

This simplification implies a one-to-one correspon-dence between cultural information and humanbehaviour—in other words, an implication that onceindividuals acquire information they act on it. Thishighly unrealistic implication has contributed towider social science scepticism of cultural evolutionmodelling, for anthropologists, sociologists, historiansand other scholars have long recognized that individ-uals often have ideas in their heads that they are notinterested in or able to implement in practice(cf. [10,14,18,23,60,61]; e.g. [30,39,40,62]). Thegeneral model we present here moves away from thatsimplification towards realism by treating culturalideas (which are learned information stored in themind) as analogous to genotype: mediated by external,‘environmental’ factors—here, factors in the socialniche—which affect the expression of these ideas inbehaviour (phenotype).

Two sample theoretical scenarios explore how thefrequency of cultural ideas (x) can be environmentallymediated by societal wealth (W ) and stochastic events(s) to affect the frequency of uxorilocal marriage in prac-tice (U). (In §5, we apply this general model to theDanei data.) In both scenarios, x0 ¼ 0.3, s ¼ 0.7 andH ¼ 21. We set the initial frequency of s0 in the popu-lation at x0 ¼ 0.3, which is approximately the frequencyof uxorilocal marriage (U) in the overall Danei popu-lation at the beginning of the Japanese period(figure 3). In other words, we assume that any disjunc-ture between behaviour and belief prior to cohort 1(married between 1906 and 1915) was accounted forby s—for example, among Han who viewed uxorilocalmarriage as shameful but arranged uxorilocal marriageswhen they had no sons—but that cultural ideas havesince come into one-to-one correspondence with be-haviour (cf. [28,50]). We set the initial values of beliefand behaviour roughly equal to show that incorporatingrelatively simple economic (W ) and stochastic (s)effects yields the more realistic result of a disjunctureof belief and behaviour, even with initial values working

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against this outcome. We choose a negative value for Hbecause, based on ethnographic research [28,50], weexpect x to decrease over time, albeit after the changein practice. We set the influence of cultural belief s1 asmitigated by stochastic events, s, at an intermediatevalue in its empirically derived range (see appendixand table 3).

W, the population economic index, differs betweenthe two scenarios. In scenario 1, W is held constantat 0.8, a relatively wealthy level at which 80 per centof people can afford brideprice. In scenario 2, weallow W to change over time (W ¼ 1 2 ke2at, a stan-dard way of expressing exponential decay, where k ¼0.3 and a ¼ 0.5), in order to introduce more realisminto the model as we know that economic developmentincreased the wealth of Taiwanese society over thecourse of the colonial period. Thus, in scenario 2,W starts at 0.7 and increases exponentially up to 1,yielding an average value of W close to 0.8 (veryclose to the value in scenario 1).

We use equations (3.1) and (3.2) to calculate theproportion of s0 in cohort t þ 1, given the proportionin cohort t. Since H � 0 in both scenarios, x decreasestowards 0, and U tends to the proportion of uxorilocalmarriage among s1 � s1 couples. (If we were to set Hgreater than zero, x would increase towards 1, andU would tend to the proportion of uxorilocal marriageamong s0 � s0 couples.) In figure 4, we plot x and Ufor cohorts 1 through 4 in these two theoretical scen-arios. In both scenarios, x (plotted in purple) is thesame (since H is the same). In scenario 1, U (plottedin green) tends to 121

2W [22(12s)2] ¼ 0.236. In

scenario 2, U (plotted in blue) tends asymptoticallyto 1

2(12s)2 ¼ 0.045, and it spans a greater range of

values than in scenario 1.Figure 4 shows the disjuncture between the fre-

quency of a custom, in this case uxorilocal marriage(U), and the frequency (x) of an associated belief(s0) when economic (W ) and indirect, stochasticeffects (s) are introduced. In scenario 1, where U(plotted in green) and x (plotted in purple) are initiallyequal and W is constant at a relatively wealthy level,the divergence is clear. Moreover, the divergence isstable, since U approaches 24 per cent. In scenario 2,where W changes over time, U tracks the decline inx over time, but there is a significant time lag. Evenat the (unrealistic) extreme of x ¼ 0 and W ¼ 1 inthe fourth cohort, U is still over 10 per cent. Thus,marriage form frequency gives little guidance onunderlying cultural beliefs about marriage (matingpreferences). The results of these theoretical scen-arios—which are in agreement with the observedpersistence of uxorilocal marriages even in the appar-ent absence of supporting beliefs—suggest thepresence of an additional crucial factor to theconstruction of human cultural niches. We identifythis factor as society, in which we include politicaleconomy (cf. [7,8]).

5. PROJECTIONS OF THE CULTURAL NICHEBy linking our general mathematical model (from theprevious section) to the empirical data from Danei,here, we estimate the model’s parameters and produce

Phil. Trans. R. Soc. B (2011)

five possible projections of the historical changesbehind the decline in uxorilocal marriage rates.These projections allow us to assess the relative effectsof each of the parameters (x, s and W ) on the uxorilo-cal marriage rate (U) and also to explore how thecultural niche is constructed—in other words, whetherand how the content of the population ideational poolchanges.

(a) Linking the model and the empirical data

We denote marriage cohorts in the time periods1906–1915, 1916–1925, 1926–1935 and 1936–1945 by subscripts 1 through 4, respectively. Accord-ingly, U1 through U4 refer to the empirical Danei-wideuxorilocal marriage rates during these four timeperiods, as documented in figure 3. (Thus, U4 hasthe lowest value.) Similarly, UH1 refers to the uxorilo-cal marriage rate between 1906 and 1915 for a sub-section of the Danei population: Danei Han womenwho lived and married outside of Toushe. (This rateis documented in figure 2 by the red column in the1906–1915 range.) These rates are the empiricaldata incorporated into the model. We denote thepopulation economic indices in the time periods1906–1915, 1916–1925, 1926–1935 and 1936–1945 by W1 to W4, the prevalence of s0 for thesame time periods by x1 to x4, and the prevalence ofs0 in 1906–1915 for the Danei Han outside ofToushe by xH1.

We make several assumptions to simplify the model.The first two are empirically derived. First, we assumethat xH1 ¼ 0, given ethnographic accounts of Hanmoral disapproval of uxorilocal marriage (discussedabove [30,40]). (Note: we do not make assumptionsabout the value of x for the plains Aborigine popu-lation because of the existing debate, discussedabove, over whether Aborigine cultural ideas hadchanged (e.g. [28,29,42,44,54,55]). Second, weassume that, for the 1936–1945 period, any remainings0 � s0 couples marry uxorilocally about as often asthey marry virilocally. In other words, given historicalevidence of Taiwan’s increasing economic develop-ment over the colonial period, we assume that intime period 4, there is no economic pressure tomarry in either fashion (i.e. W4 ¼ 1, the maximumpossible value of the population economic index).This assumption parallels Wolf ’s [39] findings, dis-cussed above, that young people were able to buythemselves out of minor marriages by the end of thecolonial period. Furthermore, we assume that s andH remain constant between 1906 and 1945, that Wis constant for each cohort (since it represents theproportion of people in the cohort who can affordbrideprice) but variable between time periods, andthat U and x can vary between time periods of thepopulation.

Finally, we assume that equation (3.1) holds acrosssubsections of the population and across time, despitethe evidence that before 1915 the marriage market wassegregated in the township of Danei. Demographicdata do show that, before 1915, uxorilocal marriagerates were different for the Aborigine and Han popu-lations (figure 2) and each ethnic group was largely

Table 3. Five projections of the historical events behind the empirical values of U1, U2, U3, U4 and UH1 in figures 2 and 3.

projection 1 2 3 4 5

s 0.673 0.755 0.837 0.918 1.000H 20.872 20.157 0.00337 0.0636 0.0691

W1 0.833 0.813 0.799 0.791 0.788W2 0.865 0.866 0.857 0.851 0.849W3 0.926 0.929 0.925 0.921 0.920W4 1.000 1.000 1.000 1.000 1.000

x1 0.150 0.168 0.195 0.233 0.284x2 0.0390 0.146 0.195 0.244 0.298

x3 0.00634 0.126 0.196 0.256 0.313x4 0.000848 0.109 0.196 0.268 0.328

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endogamous (i.e. most Han married other Han, andmost Aborigines married other Aborigines; see [29]).Moreover, ethnographic reports about the social treat-ment of uxorilocally married men also suggest thatHan individuals were more likely than Aborigine indi-viduals to have s ¼ s1. However, in order to simplifythe model, we suppose that the marriage market wasrandom with respect to s, so that equation (3.1)holds for the Danei population between 1906 and 1915.

(b) Calculating the projections

In order to calculate the historical projections, webegin by obtaining the range of s. Given a particularvalue of s, we can calculate numerical values forH, xi and Wi that represent one projection behindthe empirical values of U1, U2, U3, U4 and UH1. Wefind that


p, s � 1: ð5:1Þ

Having found the range, we start with s just abovethe lower bound of its range, s ¼ 0.673, then computex4, W1 and x1 (see appendix equations (A 3), (A 4),(A 5), (A 6) and (A 7)):

x4 ¼ 1� 1�ffiffiffiffiffiffiffiffiffi2U4


s; ð5:2Þ

W1 ¼2ð1�UH1Þ1þ sð2� sÞ ð5:3Þ

and x1 ¼ 1� 1�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ðððU1 � 1Þ=W1Þ þ 1Þ


: ð5:4Þ

Now we consider how horizontal transmission (H )affects the frequency of cultural beliefs (x). Equation(3.2) describes the transitions between cohorts 1 and2, cohorts 2 and 3 and cohorts 3 and 4. Thus,we obtain the following identity (see appendixequation (A 10)):

x4 ¼ x1½1� 3Hð1� x1Þ þ 3H2ð1� x1Þð1� 2x1Þ

�H3ð1� x1Þð1� 9x1 � 9x21Þ þ 5H4x1ð1� x1Þ2

þH5x1ð1� x1Þ2ð1� 8x1 þ 8x21Þ þ 2H6x2


� ð1� 2x1Þð1� x1Þ3 þH7x31ð1� x1Þ4�: ð5:5Þ

This identity allows us to calculate H, given x1 and x4,which in turn allows us to use equation (3.2) to

Phil. Trans. R. Soc. B (2011)

calculate x2 and x3:

x2 ¼ x1 þH x1ð1� x1Þ ð5:6Þ


x3 ¼ x2 þH x2ð1� x2Þ: ð5:7Þ

Once we have x2 and x3, we can use equation (3.1) toobtain W2 and W3:

W2 ¼2ð1�U2Þ

1þ sð1� x2Þð2� s½1� x2�Þð5:8Þ


W3 ¼2ð1�U3Þ

1þ sð1� x3Þð2� s½1� x3�Þ: ð5:9Þ

In sum, given s ¼ 0.673, we have calculatednumerical values for H, x1, x2, x3, x4, W1, W2 andW3, which constitute projection 1 in table 3 andfigure 5.

To calculate the remaining projections in table 3,we use s ¼ 1, the upper limit of the parameter’s range(in column 5), and choose the three values of s thatdivide its range into four equal segments. We thencompute H, xi and Wi for each of these values, usingthe process described above for s ¼ 0.673. We incor-porate the empirical data for Ui from figures 2 and 3into the model. Using this method, equation (A 10)yields exactly one real value of H between 21 and 1in each of the four additional projections. Results ofthese computations are presented as projections 2 to5 in table 3 and figure 5.

(c) Discussion: relative effects on marriage form

and cultural belief

The projections in table 3 allow us to assess the relativecontributions of cultural and economic factors onmarriage form (phenotype) because the five projec-tions differ in the causal factors lowering theuxorilocal marriage rate (U). In projections 1 and 2,the drop is partly due to the increase in the proportionof people who can afford brideprice (W ) and partlydue to a decrease in the prevalence (x) of the culturalidea (s0) of neutrality towards uxorilocal marriage. Inprojection 3, the drop is caused chiefly by an increasein W, because the prevalence of s0 does not changevery much. In projections 4 and 5, a rise in W explains









1906–1915 1916–1925 1926–1935 1936–1945







y be


marriage cohort

Figure 5. The frequency (x) of cultural beliefs0 across cohorts

for projections 1–5. Dark blue diamonds, projection 1; pinksquares, projection 2; yellow triangles, projection 3; lightblue crosses, projection 4; purple asterisks, projection 5.

1 2cohort

3 4







Figure 4. x and U for two theoretical scenarios (x in purple,U in green for scenario 1 where W is constant, U in blue forscenario 2 where W increases exponentially).

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the decrease in U, even though the prevalence of s0

slightly increases.Figure 5 plots x1, x2, x3 and x4, the frequency (x) of

the cultural belief (s0) in marriage cohort 1 (1906–1915), 2 (1916–1925), 3 (1926–1935) and 4(1936–1945), respectively, for each of the five projec-tions in table 3. Figures 2 and 3 demonstrated that U,the rate of uxorilocal marriages, declines across thesame marriage cohorts depicted in figure 5. However,in figure 5, the frequency (x) of the cultural belief (s0)does not necessarily decline. In projections 4 and 5,the frequency of the belief (s0) in the neutrality ofuxorilocal marriage actually rises (x4 . x1), albeitmodestly. Projection 3 rises so imperceptibly that itcould easily be mistaken for stationary (x4 ¼ x3 ¼

0.196 . x2 ¼ x1¼0.195; table 3). Projections 1 and 2do show declines in the frequency of this culturalbelief, but they follow different trajectories. Projection2 declines linearly, still leaving a frequency (x) of thebelief (s0) of over 10 per cent in cohort 4, when theuxorilocal marriage rate (U) was already under 10per cent (data in figure 3). Only projection 1 showsan exponential decrease in the frequency (x) of thebelief (s0). However, this projection nears 0 incohort 3, when the rate of uxorilocal marriage (U)was still over 10 per cent (data in figure 3). The

Phil. Trans. R. Soc. B (2011)

clear conclusion is that there is no necessary cor-respondence between custom and belief, since it ispossible for custom to diverge from belief, sometimesquite widely.

We expect the prevalence (x) of cultural belief s0 tohave decreased over time because qualitative evidence(discussed above) suggests that, by the 1990s, manyHan cultural ideas had become dominant in theformer plains Aborigine communities of Toushe,Jibeishua and Longtian [28]. Consequently, the firsttwo projections, where x decreases with time, meetour expectations better than the latter two, where xincreases. That two of the projections lead to anincrease in x, however, suggests that in the absenceof quantitative empirical data on x, we cannot be cer-tain of its prevalence and thus we cannot resolve thedebate over the actual historical frequency of Han cul-tural ideas among plains Aborigines in Danei at thebeginning of the colonial period. The model suggeststhe possibility that the prevalence was 0—i.e. thatthere was no belief in neutrality at all—at the begin-ning of the colonial period. However, the qualitativeevidence, discussed above, regarding the lack ofshame and discrimination attached to uxorilocal mar-riage in Toushe, Jibeishua and Longtian suggests thatthe cultural idea of neutrality existed, even if at low fre-quency. In those projections that meet ourexpectations, there is still a range of possible frequen-cies of the cultural idea, from near 0 to over 10 percent. This range raises questions about the otherinfluences on U in the model: W and s.

Table 3 shows that, within a single projection, asmall change in the economic situation, representedby W, implies a larger change in culture (indicatedby x). In other words, within any single projection,influences of the frequency (x) of cultural ideas onchanges in the uxorilocal marriage rate (U) are sen-sitive to small changes in W. In considering theeffects of W and s, we must bear in mind that, to sim-plify the model, we assumed that economicdevelopment led to a general level of wealth sufficientfor everyone to afford a brideprice (i.e. W ¼ 1), andthus that cultural beliefs could potentially prevail indetermining marriage form. However, as the stochasticeffects mitigating the cultural effects of s1 weaken—forexample, as public health measures reduce mortality—and thus the cultural effects of s1 become stronger ( s goes to 1), the frequency (x) of s0 also increases.Thus, ironically, these assumptions mean that theincreasing importance of the idea s1 for the frequency(U) of the practice (an effect that might be thought ofas the increasing ‘strength’ of the belief in the popu-lation) allows a concurrent spread of the neutralbelief s0. This result of combining the general modelwith the Danei data runs directly counter to the pre-diction of the general model (discussed above) thatas s goes to 1, s1 should be dominant over s0. Thisunexpected result could be interpreted to mean thatthere is more cultural variability in the wealthier popu-lation. On the surface, this interpretation seemscompatible with current marriage practice in Taiwan,where ethnographic evidence suggests that ruralmarriages are overwhelmingly virilocal and urban mar-riages are increasingly neolocal (i.e. where bride and

Belief about marriage in Taiwan M. Lipatov et al. 913

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groom establish an independent household), perhapsthe ultimate expression of neutrality (cf. [63–67]).The result could also mean either that cultural ideasare less important in general than anticipated (andallowed for in the general model), or that culturalniche construction—changes in whether particularideas are accepted as meaningful (i.e. shared, abstract,public and truth to some percentage of thepopulation)—is more important and thus leads to aqualitatively different outcome from expectations.

The model also yields a lower bound for s (0.673)that is higher than we would expect based on empiricaldata of sibling composition as an effective predictor ofuxorilocal marriage. As discussed above, when s ishigh, the cultural idea strongly influences practice,and s ¼ 0.673 is a fairly high value for s. Recall thatsibling composition is one of the best predictors ofuxorilocal marriage [30,39–41]. This empiricallydocumented sensitivity suggests that we ought to finda low value for the lower bound of s, yet we do not.Several assumptions in the model could affect theempirical validity of this lower bound: randommating with regard to s, unbiased vertical trans-mission, gender neutrality with regard to s and s,and s constant. Changing any of these assumptionswould make the model substantially more cumber-some, but these may be valuable changes to considerin the future.

6. CONCLUSIONSThis model and its connections to the empirical case ofchanging marriage form in Taiwan yield several gen-eral conclusions about the construction of humancultural niches and the value of distinguishing betweensocial and cultural niches. They indicate the kind ofempirical data that would facilitate future models,and they suggest a potential for building bridges tothe social sciences.

(a) Culture is in constant flux

Table 3 and figure 5 together demonstrate that, in allprojections, the frequency (x) of the cultural idea s0

changes. Even in projection 3, x changes slightly(x4 ¼ x3 ¼ 0.196 . x2 ¼ x1¼0.195). In other words,human cultural niches—like ecological niches—are inconstant flux. This conclusion fits with our conceptionof a cultural niche as the sum of all cultural selectionpressures, which in turn derive from transmissionprocesses (including broadcasting, reception andinternalization of ideas) and interactions between cul-tural ideas. Shifts in belief by individuals constitutebits of change—constant flux—constructing thecultural niche. Such incremental change would onlybe noticeable at a population level when a signifi-cant number of people changed in the same way.Thus flux goes on constantly at the individual levelbut is only visible at the population level undercertain kinds of conditions, which suggests both thatwe should expect drift (i.e. stochastic effects insmall populations) to influence cultural change [16]and that cultural persistence (e.g. [7,68]) requiresexplanation.

Phil. Trans. R. Soc. B (2011)

(b) Phenotype is not a reliable indicator of


Figures 4 and 5 show that the frequency of a culturalunit—an idea or belief—need not correspond to thefrequency of the associated practice (phenotype).Consequently, we cannot determine the content ofthe ideational pool—the cultural niche—on the basisof the frequency of customs.

(c) Culture is sensitive to society

Table 3 indicates that even small society-wide changesin economic development may result in larger shifts incultural content, measured in the increasing frequency(x) of the belief s0, and the stronger influence (s) ofthe belief s1, providing further evidence of the impor-tance of including social factors in cultural evolutionmodels.

The results of linking the general model to theDanei data raise several possibilities for future explo-ration. Wealth may increase the cultural variability inthe population. Cultural ideas may be less importantmotivators of behaviour than social factors. Culturalniche construction may result in change that qualitat-ively departs from expectations based on culturalselection pressures alone. All of these possibilitieswould be best explored using models integrated withempirical data.

(d) Including culture and society yields more

realistic models

The introduction of even highly simplified social effectsleads to a more realistic model of cultural change. Themodelled sensitivity of the uxorilocal marriage form topopulation-level economic development agrees withWolf ’s [39] conclusions about the sensitivity of minormarriage to economic development in northernTaiwan. Moreover, when s is understood as mitigatingsocial effects, its inclusion can realistically result ina Han population with a high frequency of disap-probation of uxorilocal marriage (the idea s1) thatnevertheless maintains a noticeable frequency of uxori-local marriage (phenotype) owing to stochastic effectson sibling composition.

(e) Modifying the model requires quantitative

empirical data

This model is linked to one specific case study, whichhas allowed us to obtain specific estimates of the modelparameters and projections of changes in the economy(W ) and the frequency (x) of the culturally neutralidea (s0) that may underlie the changes in the uxorilo-cal marriage rate (U). However, the model can begeneralized to examine the contributions of culturaland economic factors in other case studies of changesin human customs, or further specialized to bemore realistic for a particular case study, if adequatequantitative data are available.

For example, fitting this model to a case study ofrapid change in a different time or place requiresreliable data on the changing frequency of the practiceover time as well as a general estimate of the economicpopulation index for at least one cohort in the timeperiod under consideration. To make our model

914 M. Lipatov et al. Belief about marriage in Taiwan

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more realistic, for example, to consider whether thecoefficient of horizontal transmission (H ) dependson the prevalence of uxorilocal marriage (U) or moredirectly on the prevalence (x) of cultural belief s0,would require reliable quantitative data not only onthe frequency of practices across individuals but alsoon the frequency of associated ideas. It would also bebeneficial to have an empirical understanding—andeven better, an estimate—of H, the influence of peerson ideas or beliefs. Thus, the model suggests theimportance of developing reliable methods for quanti-fying ideas independently of quantifying behaviours(see [10,50,61] for brief discussion of such methods).

(f) Realistic models promote social science


We suggest that the potential for increased specificityand realism generated by niche-construction modelsthat incorporate social as well as cultural effects onhuman culture can facilitate building bridges to thesocial sciences. We think that the implications of thefindings presented here move evolutionary models ofcultural change towards empirically based research inanthropology and sociology. Niche-constructionmodels have the potential to capture many realisticelements: separation of custom (phenotype) frombelief, influence of economics, social stratification,family composition and—perhaps most impor-tantly—the recognition that culture and society arecumulative and inherited, not reinvented in eachgeneration.

We thank Yang Wen-shan, current director of the Programmefor Historical Demography at the Academia Sinica inTaiwan, as well as Arthur Wolf and Chuang Ying-chang,for permission to use the Danei and Jibeishua demographicdatabases. M. J. Brown’s ethnographic research was fundedby the American Council of Learned Societies, the ChiangChing-Kuo Foundation, the Pacific Cultural Foundationand the Institute of Ethnology at the Academia Sinica inTaiwan. The collaborative modelling project was supportedby Stanford University’s Institute for Research in the SocialSciences, Freeman Spogli Institute for International Studies,Morrison Institute for Population and Resources Studiesand Center for East Asian Studies. The research wassupported in part by NIH GM28016 to M. W. Feldman.Contributions: M.J.B. conducted the empirical research;M.L. and M.J.B. analysed the demographic data; M.L.produced the model in collaboration with M.J.B. andM.W.F.; and all three authors wrote the paper. M.J.B. andM.L. contributed equally to this manuscript.

APPENDIXIn order to calculate the lower and upper bounds for s,shown in equation (5.1) in the text, we begin byre-writing equation (3.1) as

W ¼ 2ð1�UÞ1þ sð1� xÞð2� s½1� x�Þ : ðA 1Þ

We also solve equation (3.1) for x, keeping in mindthat, by definition, 0 � x � 1:

x ¼ 1� 1�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ð1� ð1�UÞ=W Þ


: ðA 2Þ

Phil. Trans. R. Soc. B (2011)

Solving for s, we can rewrite equation (A 2) as

s ¼ 1�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ð1� ð1�UÞ=W Þ

p1� x

: ðA 3Þ

To obtain the lower bound for s, we note that,because W4 ¼ 1 and U4 is lowest value of U, the numer-ator of the right-hand side of equation (A 3) will belowest for cohort 4 (1936–1945) as well. Moreover,horizontal transmission cannot reduce a non-zerovalue of x to zero. In other words, if we assume that xis non-zero in any of cohorts 1 to 3, then x4 canapproach, but may not equal 0 (i.e. x4 . 0). Finally,we substitute U ¼ U4, W ¼W4 ¼ 1 and x ¼ x4 ¼ 0into equation (A 3) to calculate the lower bound on s:

slow ¼ 1�ffiffiffiffiffiffiffiffiffi2U4

p: ðA 4Þ

From (A 4), since U4 ¼ 36/671 (data in figure 2), slow ¼

0.6724293.Because x4 is strictly greater than 0, we know that

s is strictly greater than slow. Moreover, since x4

may approach 1, and s � 1 by definition, a similaranalysis of equation (A 3) shows that s is boundedabove by 1. In sum, s could be anywhere within theinterval (slow, 1).

In order to calculate x4, shown in equation (5.2) inthe text, we substitute U ¼ U4, W ¼W4 ¼ 1 intoequation (A 2) and obtain x for time period 4(1936–1945) in terms of s and U4:

x4 ¼ 1� 1�ffiffiffiffiffiffiffiffiffi2U4


s¼ 1� slow

s: ðA 5Þ

To solve for x4, we must choose a value within thehalf-closed interval for s. We start with s just abovethe lower bound of its range, s ¼ 0.673. Given thisvalue, x4 ¼ 0.000847994.

In order to calculate W1, we remember that W isconstant for the entire population but variable betweentime periods. We focus on one subsection of the popu-lation for which we have U and an estimate of x in timeperiod 1 (1906–1915): the Danei Han who lived andmarried outside Toushe. Thus, we set U ¼ UH1 andx ¼ xH1 ¼ 0 in equation (A 1) to obtain W1 in termsof s and UH1:

W1 ¼2ð1�UH1Þ1þ sð2� sÞ : ðA 6Þ

For a given value of UH1, W1 is strictly less than thevalue obtained when s ¼ slow. If we substitute theempirical value of UH1 ¼ 69/326 (data in figure 2)and s ¼ 0.673 into equation (A 6) we obtain W1 ¼

0.8328727.In order to calculate x1, we modify equation (A 2)

to calculate the overall prevalence of s0 in timeperiod 1:

x1 ¼ 1� 1�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ð1� ð1�U1Þ=W1Þ


: ðA 7Þ

Entering the empirical values of U1 (103/423, data infigure 2), s ¼ 0.673, and W1 ¼ 0.8328727 intoequation (A 7), we obtain x1 ¼ 0.150437.

In order to calculate H, we begin by writing downequation (3.2) for the transitions between cohorts 1

Belief about marriage in Taiwan M. Lipatov et al. 915

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and 2, cohorts 2 and 3 and cohorts 3 and 4:

x2 ¼ x1 þH x1ð1� x1Þ; ðA 8aÞx3 ¼ x2 þH x2ð1� x2Þ ðA 8bÞ

and x4 ¼ x3 þH x3ð1� x3Þ: ðA 8cÞ

We substitute all instances of x2 in the right-hand sideof equation (A 8b) with the right-hand side of equation(A 8a). The result is a cubic polynomial in H:

x3 ¼ x1½1� 2Hð1� x1Þ þH2ð1� x1Þð1� 2x1ÞþH3x1ð1� x1Þ2�: ðA 9Þ

A similar substitution of equation (A 9) into theright-hand side of equation (A 8c) yields a 7th-degreepolynomial in H:

x4 ¼ x1½1� 3Hð1� x1Þ þ 3H2ð1� x1Þð1� 2x1Þ

�H3ð1� x1Þð1� 9x1 � 9x21Þ þ 5H4x1ð1� x1Þ2

þH5x1ð1� x1Þ2ð1� 8x1 þ 8x21Þ

þ 2H6x21ð1� 2x1Þð1� x1Þ3 þH7x3

1ð1� x1Þ4�:ðA 10Þ

In general, equation (A 10) will yield seven possiblevalues of H for any particular values of x1 and x4.However, up to six of these values may be complex.Any of the values that are real, greater than 21 andless than þ1, constitute a possible value for H thatsatisfies all the requirements for this parameterwithin our model.

For instance, we can substitute the values of x1

and x4 that correspond to s ¼ 0.673 (i.e. x1 ¼

0.150437 and x4 ¼ 0.000847994) into equation(A 10), obtaining:

0:000847994 ¼ 0:150437� ð1þ 2:54869H

þ 1:78185H2 � 0:127648H3

� 0:379552H4 þ 0:00243713H5

þ 0:0194036H6 � 0:00177356H7Þ:ðA 11Þ

Using MATHEMATICA, we solve this equation andobtain the following seven possible values forH, 23.06104, 21.16266 2 0.137671 i, 21.16266 þ0.137671 i, 20.871687, 3.11696, 6.41389 and7.66765. (Here, i equals the square root of 21.)Since only one of these is a real number between 21and 1 (H ¼ 20.871687), that is the value we use tocalculate x2 and x3.

Given H ¼ 20.871687 and x1 ¼ 0.150437, wecan solve equation (A 8a) to obtain x2 ¼ 0.03903042.Substituting this value of x2 and the same valueof H (20.871 687) into equation (A 8b) yieldsx3 ¼ 0.006 336 015.

Once we have x2, we can substitute U2 and x2 intoequation (A 1) to yield W2 in terms of these variablesand s:

W2 ¼2ð1�U2Þ

1þ sð1� x2Þð2� s½1� x2�Þ: ðA 12Þ

Phil. Trans. R. Soc. B (2011)

Once again, we can substitute the empirical valueU2 ¼ 92/488 (data in figure 2) along with s ¼ 0.673and x2 ¼ 0.03903042 into equation (A 12) to obtainW2 ¼ 0.8654805.

The method for calculating W3 is similar:

W3 ¼2ð1�U3Þ

1þ sð1� x3Þð2� s½1� x3�Þ: ðA 13Þ

Substituting U3 ¼ 93/744 (data in figure 2), x3 ¼

0.006336015 and s ¼ 0.673 into equation (A 13)yields W3 ¼ 0.9257966.

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