Emergent matriliny in a matrifocal, patrilineal population: a male coalitionary perspective

Abstract

Daughter-biased parental investment and limited paternal care promote matrifocality and matrilineal descent, both of which are forms of matricentric social organization. However, matrifocality can occur under patrilineal descent. We hypothesize that matrilineal descent could emergently organize social relationships if a society were normatively patrilineal but matrifocal. Furthermore, in matrifocal environments, male and female social lives are envisioned as sex-specific adaptive strategies. Males purportedly form large, flexible social support networks that conflict with conjugal partnership investment owing to a tradeoff in the allocation of effort associated with either investing in male social support or provisioning the conjugal household. However, no quantitative analyses exist about the effect of conjugal partnership formation on male social relations in matrifocal communities. Here we examine whether matrilineal kinship organizes male same-sex social relationships and the effect of conjugal partnerships on male social support in a normatively patrilineal, but matrifocal village. We find that matrilineal kinship influences male social support networks, but not labour cooperation. Consistent with a tradeoff associated with investing in male social support or a conjugal union, we find that labouring with a conjugal partner, but not conjugal partnership itself, reduces male labour and social support outcomes. Our results suggest new insights into men's roles in matricentric social organization: (1) matriliny can emerge in patrilineal systems when household economics shift toward matrifocality in which matrilineal descent is used to organize male social support, and (2) the degree to which this shift occurs depends on the proportion of men who invest in same-sex social networks as opposed to a conjugal partner and offspring.

This article is part of the theme issue ‘The evolution of female-biased kinship in humans and other mammals’.

1. Introduction

Matrifocality refers to a cultural complex where women, in their roles as mothers, are the focus of relationships within households [1–5]. These female-headed households typically consist of a mother, her adult daughters and their children [2–4]. The mother–daughter–sister bond forms the core of affective social life and the senior woman controls economic decision-making domestically. Although men may be present, they appear peripheral to the domestic unit, resulting in ‘male marginality’ [4,5]. Together, matrifocality and male marginality are associated with a number of social and reproductive outcomes, including flexible sexual unions, minimal paternal investment and inter-sexual conflict [4–10].

While originally characterized as pathological [11], a remnant of West African matrilineal social organization and family structure [12,13], or a consequence of plantation slavery that promoted promiscuity through marriage prohibitions between enslaved peoples [14], over the last 40 years ethnographers and evolutionary social scientists have recognized the adaptive nature of matrifocality [4–10], with males and females pursuing sex-specific strategies for navigating social life [8]. Factors such as poverty, paternity uncertainty or stochastic male presence promote women (but not men) to invest more heavily in daughters relative to sons, causing females to form same-sex social relationships with genetic kin [5,8]. Males, on the other hand, compete with natal and lineal kin for access to scarce resources owing to resource dilution [15,16] and therefore have an incentive to form large, flexible networks, creating a marketplace for male social relationships [10,17–24].

The conditions that promote matrifocality—female control of resources and limited paternal care—also have been hypothesized to promote matrilineal descent [25,26]. However, matrifocality exists in a range of descent systems, including patriliny [5,19], suggesting that matricentric social organization is not precluded by patriliny. We suspect that matriliny could emergently organize social relationships within a patrilineal descent system if it were sufficiently matrifocal. Matrifocal systems clearly involve tight social bonds between kinswomen (e.g. grandmothers, mothers, sisters, daughters, aunts and nieces); however, males are often characterized as having loose social organization. Matrilineal kinship may be useful for organizing male alliances in matrifocal contexts with normative patrilineal descent, because male matrilineal kin do not compete over access to shared patrilineal resources [15,16]. Furthermore, men who are related through matrilineal kinship likely have a history of interaction through shared kindreds in matrifocal households, thereby reducing transaction costs associated with cooperative partnerships. Here we seek to determine whether males from a matrifocal community, which is normatively patrilineal, use matrilineal descent to organize same-sex social relationships.

The social brain hypothesis argues that personal social relationships consist of a series of layers that differ in terms of their quality and quantity (e.g. close support clique, sympathy group, affinity group) [27–29]. At each successive layer, the number of people to whom an individual is connected increases; however, this comes with a concomitant decrease in levels of intimacy [30,31]. As such, social relationships are envisioned as experiencing opportunity costs, where time and energy spent in one relationship cannot be spent on other relationships. The tradeoff in the allocation of effort in human social relationships is most notably recognized when individuals engage in long-term romantic partnerships [32,33]. Labelled the ‘dyadic withdrawal hypothesis' [32–36], research on the formation of long-term romantic partnerships suggests that as individuals become romantically involved, their friendship networks shrink and they become less involved with those friends who remain in the network [32,33,37]. While sexual unions in matrifocal contexts are generally fluid, men sometimes form long-term conjugal bonds with females and invest in offspring and the conjugal household [4,10,38–42]. The dyadic withdrawal hypothesis suggests that these men should experience a contraction in the quantity and quality of their same-sex social relationships (sensu [43]).

Here, we examine the strategies males employ for navigating social support and reproductive opportunities in a normatively patrilineal, matrifocal, Afro-Caribbean community. First, we examine whether matrilineal descent influences male social support and labour cooperation. Second, we examine how conjugal partnership formation affects male labour and social support outcomes. Analyses demonstrate that matrilineal kinship does promote male–male cooperation in social support networks, but not labour cooperation. Furthermore, analyses demonstrate a quantity–quality tradeoff in close social relationships—males who work with a conjugal partner, but not conjugal partnership per se, is associated with a reduction in both labour and social support.

2. Study site

Dominica is an independent nation located in the Caribbean Lesser Antilles between the French Departments of Martinique and Guadalupe [44]. Colloquially known as ‘the Nature Isle,’ it is underdeveloped and has one of the highest poverty rates in the Caribbean [45]. Bwa Mawego (pseudonym) is a rural, poor smallholder village located along the eastern coast in St David parish [45,46]. The village contains approximately 400 residents living within 12 hamlets [18,47]. The village has a male-biased adult sex ratio owing to female emigration (128 men, 97 women in 2018) related to female-biased parental investment [5,16,39]. Villagers descend from a mix of West African, native Carib and European stock [46]. Kinship and family are important aspects of social life. Nearly everyone in the village is related through consanguineal links or affinal ties that emanate largely through mating relationships (as opposed to marriage or long-term unions) [15]. Formal marriage as an institution is rare [46]; however, couples still forge durable conjugal unions. While the community has a matrifocal orientation, a variety of residential arrangements exist, including conjugal households and singletons [15,45]. Although the people of Bwa Mawego engage in a number of economic enterprises, including slash-and-burn horticulture, fishing and minor craft production, the focus of economic activity is small-scale commercial agriculture related to the production of essential oil of bay [20,21,23,24,48]. Bay oil is a distillate of the native Caribbean bay tree (Pimenta racemosa [Miller] J. W. Moore), the leaves of which are harvested and steam distilled every 10 months [20,24]. The nation's lone essential oil cooperative purchases raw oil from smallholders and refines it for sale on the international commodities market [23]. Land dedicated to bay tree production is owned in common by patrilineages; however, lineage members have usufruct land rights. When a person seeks to convert their tree leaves into oil, they may either contract another to labour for them (whereby the patrilineage member with usufruct land rights and the worker split the cash proceeds, two-thirds to one-third, respectively) or they may work the land themselves (whereby the individual receives all cash proceeds) [21,23]. Female heads of households often own bay trees and employ men (including close relatives) to collect and process the bay leaves. Men who organize more labour events (either through labour contracting or through their own initiative) have better labour competency reputations, which cause them to receive more labour contracts [21]. Bay oil production is arduous, sometimes dangerous, and requires assistance. Individuals may receive help from those who have been given assistance in the past, from others who seek to create a new labour partnership, or from conjugal partners and children. Farmers seeking to generate a labour force from the first two applicant pools incentivize assistance through the purchase and provisioning of food, alcohol and cigarettes, which can be a substantial cash investment. However, those working with conjugal partners and children generally do not require such purchases. Men who labour for a greater number of people have better prosocial reputations, which result in them receiving greater labour assistance [20,21,48]. Receiving a labour contract or working one's own land guarantees a male access to cash; however, males who provide labour assistance only receive the possibility of labour assistance in the future (if they organize a labour event) or the possibility of social support in a time of need [20,21,23,24,48]. Labouring in bay oil production is a primary mechanism for generating male social support [23]. Males who labour together are more likely to assist one another in a time of need and males who assist fewer farmers overall have reduced social support relative to those who assist more [23]. Here we seek to assess how latent matrilineal kinship and conjugal partnership formation affect social support and labour relationships.

3. Material and methods

(a). Labour

Bay oil production data were collected over a 10-month period between July 2007 and April 2008 [19,22]. Although bay oil can be produced year-round, 10 months corresponds to a full cycle of bay oil production, during which all individuals would presumably have an opportunity to organize a labour event or assist another in labour. The lead author and one village resident performed daily instantaneous scan sampling of the village's eight distilleries whereby we recorded the individual responsible for organizing the labour event, as well as all helpers, including their age, sex, conjugal status and hamlet of residence. Two hundred and forty-one distillation events were recorded involving 115 people (17 females; 98 males), of whom 63 organized a labour event (5 females; 58 males), 101 assisted (17 females; 84 males), and 49 organized labour and assisted another (2 females; 47 males). Labour organizers received, on average, assistance from two individuals (range: 0–9). Of the 58 males who organized a labour event (average age: 42; min/max: 16/68), 31 were in a conjugal relationship, and 14 men worked with their conjugal partner at least once. Of the 10 labour events organized by the five females, nine included a male who was her conjugal partner, including two males who never organized a labour event themselves.

(b). Social support

Following the 10 months of labour, 48 of the 98 males engaged in labour were selected for assessing social support outcomes [22]. Two village residents, a male and a female, rated pairs of labourers as having a positive, neutral or negative relationship, using the following prompt: ‘if person X was in a time of need, would person Y provide assistance?’ Positive ratings indicated the man would always assist the other, neutral ratings indicated the man might provide assistance under particular conditions, and negative ratings indicated he would never support the other. While not a direct measure of social support, the village's small population size, in conjunction with the highly conspicuous nature of male social life, made peer assessment a possibility [49,50]. Furthermore, during the data collection process, we were interested in the extent to which antagonistic relationships existed between individuals, requiring the use of peer assessments owing to the delicate nature of such relationships and the high likelihood of under-reporting by respondents themselves [50]. Raters had moderate agreement (r = 0.41; p < 0.001; n = 2256) (assessed via a QAP correlation in Ucinet version 6.523 [51]) and social support network data were averaged, resulting in five ordinal categories (positive = 205, moderately positive = 331, neutral = 1156, moderately negative = 561 and negative = 3). The social support data showed evidence of successive layers of relationship quality that significantly differed in terms of the average number of alters at each level of intimacy for both support received and support given (figure 1).

Figure 1.

Relationship type as a function of relationship quality for male social support given and received.

(c). Kinship

Genetic and social kinship (i.e. patrilineal membership and latent matrilineal descent) were obtained via a series of genealogical interviews occurring between 1987 and 2004 [15,52]. The database contained information for 1288 individuals born between 1835 and 2004. Data were analysed using Descent [52,53]. The 48 males who laboured in bay oil and had their social support and reputations measured represented 25 patrilineages and 23 latent matrilineages, and had an average coefficient of relatedness of 0.029.

The datasets supporting this article are accessible via the electronic supplementary material.

4. Results

(a). Does matrilineal kinship promote labour cooperation?

If socio-ecological factors that give rise to matrifocality also promote matrilineal descent, then males might use matrilineal kinship for organizing cooperative action, even in societies that are normatively patrilineal. In the context of labour exchange, matrilineal kinship could translate into either greater labour given or a higher probability of labour reciprocation among maternally related males. We modelled labour given as the number of days an individual provided labour to another over the 10-month time period. The 241 labour events resulted in 249 unique labour exchange dyads between a person who organized a labour event and someone who provided labour. Because we are only interested in male–male cooperation, we removed those cases involving a female, as well as those whose lineal kinship was not known, resulting in a dataset containing 182 labour exchange dyads. A generalized estimating equation Poisson regression (run in STATA/IC 15.1 [54]) shows that neither shared matrilineal nor patrilineal kinship promoted an increase in labour given (Wald χ² = 1.2; p < 0.5; N observations = 362; N groups = 181) (table 1).

Table 1.

Generalized estimating equation (GEE) regression coefficients associated with labour cooperation. IRR, incident rate ratio; OR, odds ratio; RSE, robust standard error.

labour given	IRR (s.e.)	z	p
same matriline (0 = no; 1 = yes)	1.04 (0.2)	0.2	0.83
same patriline (0 = no; 1 = yes)	0.85 (0.1)	−0.9	0.35
labour reciprocation	OR (RSE)	z	p
days labour given	2.4 (0.4)	5.6	<0.0001
same matriline (0 = no; 1 = yes)	2.04 (1.4)	1.1	0.29
same patriline (0 = no; 1 = yes)	0.4 (0.3)	−1.1	0.29

We modelled reciprocal partnership formation as a dummy-coded contingency variable (dyad reciprocated = 1; dyad did not reciprocate = 0). Of the original 249 unique labour exchange dyads, only 159 were capable of reciprocating as both individuals organized labour events. Of these dyads, 50 provided labour reciprocally (31%). Because we are only interested in male–male reciprocity, we further removed those cases involving a female, resulting in dataset containing 148 unique labour dyads, 48 of which showed evidence of reciprocity (32%). After removing those cases where a male's lineal kinship was not known (n = 19) and controlling for the number of days of labour a man provided to another, a generalized estimating equation (run in STATA/IC 15.1 [54]) shows that neither shared matrilineal nor patrilineal kinship promoted labour reciprocity (Wald χ² = 32.6; p < 0.0001; N observations = 258; N groups = 129); however, the number of days labour given did predict an increase in reciprocity (table 1).

(b). Does matrilineal kinship organize Afro-Caribbean male social support networks?

To test this proposition, ego level data on matrilineal kinship were transformed into a relational matrix (table 2). We control for a number of covariates that Afro-Caribbean ethnographers, evolutionary biologists and social scientists suggest could affect social support outcomes, including genetic and social kinship, age-based homophily, residential proximity and labour exchange [7,8,10,16,17,38,55–62]. Matrix regression (employing a quadratic assignment procedure and Double Dekker semi-partialling method to control for multi-collinearity and structurally auto-correlated data [63]) in Ucinet version 6.523 [51] demonstrates that male social support networks were predicated on a number of factors, including latent matrilineal kinship, labour exchange, genetic kinship and hamlet-based homophily (R² = 0.17; p < 0.001; n = 2162) (table 3). By contrast, neither patrilineal membership nor age-based homophily had any effect on social support outcomes. Of all pairs of men that had any positive social relationship, 44% experienced reciprocated social support ties.

Table 2.

Matrix-level descriptive statistics associated with the factors affecting male social support.

	N	mean (s.d.)	min./max.	yes	no
social support	2256	0.03 (0.4)	−1/1	—	—
genetic kinship	2162	0.03 (0.08)	0/0.531	—	—
absolute age difference	2256	15 (11)	0/51	—	—
days exchanging labour	2256	0.1 (0.6)	0/9	—	—
same patrilineage	2256	—	—	106	2150
same latent matrilineage	2256	—	—	142	2114
same hamlet	2256	—	—	514	1742

Table 3.

MRQAP regression coefficients associated with male Afro-Caribbean social support.

	β	p
days exchanging labour	0.26	0.0005
genetic kinship	0.20	0.0005
live in same hamlet (0 = no; 1 = yes)	0.12	0.003
same latent matrilineage (0 = no; 1 = yes)	0.09	0.01
from same patrilineage (0 = no; 1 = yes)	−0.02	0.29
absolute age difference	−0.014	0.36

(c). Do conjugal partnerships affect male labour relationships?

The dyadic withdrawal hypothesis suggests that conjugal partnership formation may cause males to withdraw investments of time and energy from same-sex social relationships [32,33]. Males could signal their intent to withdraw from the same-sex social marketplace by simply being in a conjugal union or by labouring conspicuously with their conjugal partner. Labouring with a conjugal partner maximizes household income, while labouring with friends dilutes household wealth through labour incentives (e.g. alcohol, food, cigarettes). To determine whether conjugal partnership formation itself or labouring with a conjugal partner affects labour support, we first examine the factors affecting labour assistance. The outcome variable is the number of people who assisted a farmer at each labour event. We employ a generalized estimating equation in STATA/IC 15.1 [54] to account for those individuals who organized multiple labour events. After controlling for age, we find that working with a conjugal partner decreased the amount of assistance a male received (Wald χ² = 13.3; n observations = 238; n individuals = 55; p = 0.001) (table 4); however, simply having a conjugal partner did not (Wald χ² = 5.2; n observations = 242; n individuals = 55; p = 0.08).

Table 4.

Regression coefficients associated with labouring with a conjugal partner and labour assistance received and given. IRR, incident rate ratio; RSE, robust standard error.

	IRR ± (RSE)	z	p
labour assistance received
age	0.98 (0.005)	−2.5	0.013
laboured with conjugal partner (0 = no; 1 = yes)	0.79 (0.08)	−2.4	0.017
labour assistance given
age	0.98 (0.009)	−1.9	0.061
per cent labour events working with a conjugal partner	0.45 (0.17)	−2.1	0.039

Next, we examine the factors influencing the amount of labour males give to others. We analyse those males who organized a labour event plus two additional males who never organized a labour event but worked for their conjugal partner. The outcome variable is the number of days of labour a man gave to others in bay oil production over the 10-month data collection period. To account for the presence of a number of men who did not provide any labour to others, we employ a zero-inflated Poisson regression using STATA/IC 15.1 [54]. After controlling for age, we find that males who spent a greater percentage of labour events working with a conjugal partner provided fewer days assistance to others (Wald χ² = 7.9; p = 0.019; n = 56) (table 4). However, simply being in a conjugal union was not associated with the amount of labour they gave (Wald χ² = 3.4; p = 0.18; n = 56).

(d). Do males who labour with a conjugal partner give and receive less social support?

The social brain hypothesis suggests that personal social relationships consist of a series of layers where each successive layer includes more people but at lower levels of trust and intimacy [29,31]. When time, energy and resources are invested into a conjugal partner, this leaves less opportunity for investing in same-sex social support relationships. Because men who work with a conjugal partner give and receive less labour to and from other men, we expect this to negatively influence their same-sex social support networks. Specifically, we expect it to reduce the number of close personal relationships they maintain. To determine whether this is the case, we examine those men who organized a labour event and had their social support network assessed (n = 37). The outcome variables are (1) the number of alters to whom ego gives positive social support (i.e. both raters agreed ego and alter had a positive relationship) and (2) the number of alters from whom ego receives positive social support (i.e. both raters agreed alter and ego had a positive relationship). After controlling for age, a Poisson regression (run in STATA/IC 15.1 [54]) shows that men who spent a greater percentage of labour events working with a conjugal partner had fewer positive social relationships in terms of whom they assisted (pseudo R² = 0.29; p < 0.001; n = 37) and from whom they received assistance (pseudo R² = 0.21; p < 0.001; n = 37) (table 5) (figure 2).

Table 5.

Regression coefficients associated with labouring with a conjugal partner and social support received and given. IRR, incident rate ratio; RSE, robust standard error.

	IRR ± (RSE)	z	p
positive social support given
age	0.95 (0.01)	−4.9	<0.001
per cent labour events working with a conjugal partner	0.28 (0.1)	−3.1	0.002
positive social support received
age	0.96 (0.009)	−4.4	<0.001
per cent labour events working with a conjugal partner	0.41 (0.1)	−2.9	0.003

Figure 2.

The effect of labouring with a conjugal partner on positive social support given and received by males. Data are jittered to show mass. Black circles indicate observed values, hollow triangles indicate predicted values.

5. Discussion

This study was performed to (1) assess whether matrilineal descent organizes male–male cooperation in a normatively patrilineal, but matrifocal community and (2) reveal how conjugal partnership formation affects the quantity and quality of male social support. Our analyses suggest that matrilineal kinship organizes male social support networks, but not male labour cooperation. Furthermore, our analyses suggest that simply being in a conjugal union does not negatively impact labour and social relationships; however, labouring with a conjugal partner does negatively impact both labour and social support.

Scholars have long debated the origins and adaptive functions of matrilineal descent [25,26,64–67]. The ‘expendable male hypothesis' argues that matriliny emerges from environments that favour female control of resources and limited male investment in offspring [26]. These conditions also promote matrifocality. Because matrifocality can occur in patrilineal systems, this opens the possibility that matrilineal descent could emerge within a patrilineal descent system if it was sufficiently matrifocal, as matricentric social organization would be beneficial for the family. However, for matriliny to be institutionalized beyond matrifocality, the matriline must be recognized as an organizing principle of social life. Male marginality associated with local resource competition causes men to enter into a competitive marketplace for forming same-sex social relations. In matrifocal populations that are normatively patrilineal, men are in active competition with patrilineal kinsmen, making them poor options for social partners. In such a context, men may have substantial incentives to recognize matrilineally related kinsmen for organizing social relationships. First, men do not compete with matrilineal kin for access to limited descent-based resources. Second, costs associated with forming relationships are lowered for male matrilineal kinsmen as they likely have histories of repeated interactions based on common female kindred who serve as focal points for organizing cooperation. Our analyses reveal that latent matrilineal kinship is associated with men's social support but not labour cooperation. Why? Jaeggi & Van Schaik [68] demonstrate that male–male coalitions are a necessary condition for male–male food sharing to evolve in primates; however, the converse is not true. If this relationship extends to contexts other than food sharing in humans, it may be that our analyses are capturing a single point in a dynamic process where male-coalitionary behaviour will eventually give rise to cooperation in other dimensions of male economic life. Thus, we propose in the transition to matriliny proper, latent matrilineal kinship may be crucial for organizing men's mutual economic aid, which then facilitates the development of matrilineal descent as it becomes beneficial for women and men. The rarity of matriliny proper [26] might suggest that socio-ecological factors leading to ‘expendable males’ may be insufficiently stable to support the long-term development of recognized matrilineages. Hence, we suspect that matrifocality and other forms of incipient matriliny, which may be difficult to assess in cross-cultural analyses, are comparatively common.

The dyadic withdrawal hypothesis suggests that conjugal partnership formation may be incompatible with maintaining a robust same-sex social support network owing to a tradeoff between investing in either friends or a conjugal partner [29–37]. In Dominica, one way to invest in the conjugal household is to labour in bay oil production with one's spouse. Working with a spouse increases household income, as scarce resources are not diverted to incentivizing male labour. However, pursuing such a strategy may cause a contraction of one's friendship network. In fact, our analyses demonstrate that when men work with their conjugal partner, they experience a reduction in the amount of labour support given and received. Because labour and social support are interlinked, men who work more frequently with a conjugal partner have fewer close coalitionary ties, in terms of what they give and receive from others. Some men have a conjugal partner, but do not work with her. These men may dilute household resources for the benefit of male alliances. It would be worthwhile to know why some men pursue this strategy, and the specific costs and benefits of doing so. We suspect the degree to which the shift from matrifocality to matriliny occurs depends on the proportion of men in a population who invest in same-sex social networks as opposed to a conjugal partner and offspring. In populations where a greater proportion of males invest in conjugal partners rather than same-sex social relationships, we hypothesize that matriliny proper will be less likely to emerge.

Owing to the male-biased sex ratio, a number of bachelors exist and these men pose a threat to conjugal stability. Community interviews demonstrate that many men with a conjugal partner worry she will leave him for another suitor in the future. If a man has invested in his conjugal partner at the expense of his social support network and later his conjugal partner abandons him, he is in a most unfortunate position—without a romantic partner or friends. Evolutionary biologists have argued that in mammalian species with modular social organization, like humans, a tension exists between all-male bachelor units and males with female partners [69]. When human bachelors can usurp male mating opportunities, those who occupy mating relationships are incentivized to create institutions for managing these bachelor threats [69]. Under conditions of matrifocality where normative patrilineal descent exists but local resource competition causes men to seek social relationships outside of the patriline, men may have an incentive to use matrilineal kinship as a way of neutralizing bachelor threats and increasing the scope of cooperation.

In conclusion, our analyses support the view that emergent matriliny can organize social relationships within a patrilineal descent system that is matrifocal, and male-coalitionary dynamics play an important role. The dynamics of coalitionary behaviour is affected by nested levels of social relationships where each successive level includes more people but at reduced trust and intimacy. Opportunity costs do not permit people to simultaneously invest in both a conjugal partner and other alliances. The extent to which males support either a conjugal partner or their alliance partners in matrifocal contexts impacts how matriliny emerges within patriliny.

Ethics

The research was approved by the Institutional Review Boards of Washington State University: IRB no. 09673 and IRB no. 09673-003.

Data accessibility

The datasets supporting this article are accessible via the electronic supplementary material.

Authors' contributions

S.J.M. conceived of and designed the research. S.J.M., R.J.Q. and E.P. collected the data. S.J.M. analysed the data. S.J.M., R.J.Q. and E.P. wrote the paper.

Competing interests

The authors declare they have no competing interests.