Care for kin: within group relatedness and allomaternal care are 1

positively correlated and conserved throughout mammalian 2

phylogeny 3

Electronic supplementary material 2: Materials & Methods 4

Michael Briga, Ido Pen, Jonathan Wright

5

1. Literature search and estimates of relatedness 6

We considered all studies of placental mammals living in the wild in known social 7

arrangements, which was defined as an aggregation of at least two adult females with at least 8

one of them having dependent young, for which there was an estimate of the mean relatedness 9

for adult females based on microsatellite marker data. We excluded kin structures inferred 10

from behavioural data or other marker data, because these are considered less accurate (e.g. 11

[1, 2]. We searched the literature on October 22nd

2011 using the Web of Science database of 12

Web of Knowledge (http://apps.webofknowledge.com/UA_GeneralSearch_input.do?product= 13

UA&SID=V1JOIaGjakmPKkOBhBF&search_mode=GeneralSearch). We checked all 14

citations of the following statistical methods to estimate relatedness: [3-11]. This is an 15

exhaustive list that includes the most commonly used estimators of relatedness [12]. Most 16

studies (41 out of 48) used the Queller & Goodnight [3] index. For three species, studies that 17

report the mean did not report the standard error. For these, we took the mean standard 18

deviation of all studies in our dataset and divided it by the square-root of the number of social 19

units estimated in that particular study. 20

21

2. The social unit 22

In most species in the dataset, social units were readily identifiable based upon their spatial 23

segregation. However, some species live in flexible fission-fusion societies with a hierarchical 24

structure (e.g. delphinids [13] and elephants [14]). In these cases, we used the most prevalent 25

social unit (see S1 p.1). Average group sizes and their standard errors were taken from the 26

same study population as relatedness estimates are based on and if possible in the same study 27

years. For four species, studies that report the means did not report the standard error. For 28

these, we took the mean standard deviation of all studies in our dataset and divided it by the 29

square-root of the number of social units estimated in that particular study. 30

3. Allomaternal care 31

In this study we focus on allomaternal care only and did not investigate paternal care. This is 32

because females provide care in all mammal species. Male care is rather rare: only 9% of 33

mammal species exhibit biparental care [15]. We only used observations of allomaternal care 34

in the wild. That is because observations from captive animals may not be representative for a 35

species’ natural behaviour. Allomaternal care behaviours include allonursing, allofeeding, 36

allocarrying of young (e.g. in callitrichid primates), escorting and guarding or ‘babysitting’ of 37

young (e.g. in cetacea and probscidea). It is a common approach in comparative analyses to 38

categorize cooperative breeding as either ‘yes’ or ‘no’. Since allomaternal care includes such 39

a variety of behaviours then any quantitative data from the wild, if available (which is rare for 40

non-cooperative breeders), is often not comparable between species. 41

Data for allomaternal care is primarily based on reviews: [16-20]. Whenever a species was not 42

in these reviews we performed a search in the Web of Science database of Web of Knowledge 43

(http://apps.webofknowledge.com/UA_GeneralSearch_input.do?product=UA&SID=V1JOIa44

GjakmPKkOBhBF&search_mode=GeneralSearch) on October 22nd

2011 using as keywords 45

species name (scientific or common name) with (allo)nursing, (allo)lactation, (allo)maternal 46

care, (allo)feeding young, (allo)parental care, infant care or ‘cooperat*’. 47

4. Phylogeny and statistical analyses 48

We constructed the phylogeny of the 44 species of placental mammals (supplementary fig. 1) 49

using Mesquite ver. 2.71 [21] based upon previously published supertrees. Supertrees 50

combine existing phylogenetic tree topologies (based on morphological and molecular data) 51

that share some taxa in common. At the family level we used the supertree of Bininda-52

Emonds et al [22]. Whenever species-specific relationships were required, we used the 53

supertrees of Purvis [23] for the primates, of Jones et al [24] for the Chiroptera, of Price et al 54

[25] for Cetariodactyla, and of Bininda-Emonds et al [26] for the Carnivora. Since we lacked 55

data on several branch lengths in the phylogeny, we used arbitrary branch lengths following 56

the method of Grafen [27], which estimates branch lengths by setting the height of each node 57

equal to the number of taxa minus one. 58

One method to ascertain whether data exhibit phylogenetic dependence is to quantify the size 59

of the phylogenetic signal in traits or models using the parameter lambda [28, 29]. In a least 60

squares regression equation, this parameter is a multiplier of the off-diagonal elements of the 61

phylogenetic covariance matrix. Lambda commonly ranges between 0 and 1 (although values 62

larger than 1 are theoretically possible [28]): a value of 0 indicates that no phylogenetic 63

correction is needed. A value of 1 indicates that covariance in trait values among species fits a 64

Brownian motion model along the given tree. We estimated values of lambda using the 65

functions ‘fitContinuous’ or ‘fitDiscrete’ from the package geiger 1.3-1 [30] and ‘phylosig’ 66

from the package phytools 0.1-5 [31]. Both packages gave the same results. For these 67

analyses we inverse square-root transformed the group size data to fit the assumption of 68

normality [32]. 69

All statistical analyses were carried out in the statistical language R, v. 2.14.1 [33]. We 70

performed comparative analyses based on two methods. First, we had a generalized least 71

squares approach using the ‘gls’ function in the package nlme 3.1-102 [34]. Second, we used 72

Bayesian phylogenetic mixed models [35] with the function ‘MCMCglmm’ in the package 73

MCMCglmm [36]. In both analyses, we included standard errors of relatedness estimates and 74

we squarroot transformed group size to fit the assumption of linearity. Results, with and 75

without phylogenetic correction, were consistent (Results table1 and S2 supplementary table 76

1). 77

For model selection we used likelihood ratio (LR) tests and the second order Akaike 78

Information Criterion (AICc, [37]). Smaller values of AIC indicate a better fitting model and, 79

as a rule of thumb, models within two AIC-units of each other are considered equally well 80

supported (Burnham & Anderson [37], p. 70).81

Supplementary table 1: The association between mean relatedness among adult females and 82

allomaternal care for mammals in the dataset as analyzed using a Bayesian phylogenetic 83

mixed model (MCMCglmm, [36]). Results are shown (i) without phylogenetic correction, and 84

(ii) with phylogenetic correction. We used non-informative priors in all analyses (V=1, 85

nu=0.002), which are commonly used in the literature [38]. We ran two parallel MCMC 86

chains of 5,000,000 iterations, retaining every 5th

and an initial burning of 1,000,000 87

iterations. This fulfils the conservative requirements suggested by the Raftery & Lewis 88

diagnostic [39]. We used the Gelman-Rubin diagnostic to check for the convergence of model 89

parameters [40]. Potential scale reduction, PSR, factors for all chains was at the most 1.07, 90

which is less than the maximum of 1.1, meaning model convergences are appropriate. 91

Geweke [41] diagnostic test showed that the means of the first 10% and last part of a Markov 92

50% are drawn from the same distribution (Z-scores between -2 and 2). Trace plots, density 93

plots and autocorrelation run lengths showed that all chains had mixed properly. 94

Coefficient

Lower 95% CI

Upper 95% CI

p DIC

(i) Without phylogeny -117.2

Intercept 0.04 -0.09 0.17

Allomaternal care 0.49 0.22 0.76 0.0005

Sqrt(Number of females) -0.002 -0.03 0.03 0.869

AllocarexSqrt(Number of females) -0.10 -0.20 0.001 0.052

(ii) With phylogeny

-123.0

Intercept 0.04 -0.13 0.20

Allomaternal care 0.47 0.19 0.76 0.002

Sqrt(Number of females) 0.001 -0.03 0.03 0.950

AllocarexSqrt(Number of females) -0.10 -0.20 0.009 0.073

95

Supplementary figure 1: Phylogenetic tree used in the analyses. 96

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