1 Online Supplementary Information: Full methods, and supplemental tables and figures
2
1
3
4
10
11
8
9
12
5
6
7
Primers for seven loci were originally developed for the alpine accentor Prunella collaris
[Pco2, Pco3, Pco5, Pco6, Pco9, Pco10 and Pco36] (Saito et al. 2001), and a further 11 loci were originally characterized for zebra finch Taeniopygia guttata [TG01_077, TG01_148,
TG02_078, TG02_088, TG02_120, TG03_002, TG03_035, TG04_012, TG04_041, TG05_046 and TG05_053] (Dawson et al. 2010), and have been successfully used across a wide range of bird species (see the passerine microsatellite cross-utility database on the
BIRDMARKER website at http://www.shef.ac.uk/nbaf-s/databases/birdmarker). We used the following PCR cycling program for our multiplex reactions (Table S2): 15 min
13
14
15 of denaturation at 95° C, 8 cycles of 30 s at 94° C, 1.5 min at 60° C, and 1 min at 72° C.
This was followed by 25 cycles of 30 s at 94° C, 1.5 min at 52° C, and 1 min at 72° C, with a final extension period of 30 min at 60° C.
16
17
18
19
We estimated the BMM model coefficients from a sample of 1,000 iterations. In order to obtain this sample for each model, we used the following range of model parameters: number of iterations = 1,000,000-2,000,000; burn-in = 900,000-1,000,000; and thinning
20 of 100 or 1,000. We used an Inverse Gamma prior for all models.

2
21
22
23
24
25
Do females gain direct benefits from multiple paternity?
We fitted a mixed effects model with the proportion of hatched eggs as the response term to indicate the hatching success of a clutch. We fitted social group composition
(polyandrous or monogamous), the paternity of the clutch (0 = single paternity; 1 = multiple paternity), and the mean relatedness of the breeding adults of the group as
26
27
28
29 predictors. We included the social group ID as a random effect to account for repeated clutches from the same groups. We also fit a model with the same structure to the response ‘proportion of fledged young’ to assess the effects of social mating system and paternity on fledging success.
30 Do females have increased extra-group paternity when paired to a low
31
32
33
34 heterozygosity/genetically similar social partner?
We fitted a model with extra-group mating as a binary response term to indicate if a clutch contained young sired by extra-group males. We fitted the social male’s heterozygosity, relatedness to the female and the social group composition(polyandrous
35
36 or monogamous) as predictors. We included the female ID as a random effect to account for repeated clutches from the same female.
37
38
39
Are extra-group sires more heterozygous/genetically dissimilar than social males?
We fitted a model with paternity as a binary response term, when extra-group sires obtained paternity we scored a ‘1’ and all other males were scored as ‘0’. We fitted the
40
41
42 male’s heterozygosity and relatedness to the female as predictors. We included the female ID and nest ID as random effects to account for repeated clutches from the same female.

3
43
44
45
46
47
Furthermore, we tested whether extra-group mating led females to gain access to males that had higher quality than their social partners. This allowed us to compare the heterozygosity and relatedness of the social male with that of extra-group sires in order to investigate if females were seeking copulations with extra-group males of higher quality. Following recommendations (Wetzel & Westneat 2009; Harrison et al. 2013) we
48
49
50 used a paired randomization test to compare the traits of the cuckolded male with those of the extra-group sire. Permutation was conducted within pair, and we performed
10,000 permutations.
51
52
Are extra-group young more heterozygous than within-group young?
We fitted a mixed effects model with offspring heterozygosity as a response term. We
53
54
55 fitted each chick’s paternity status (within-group or extra-group) and social group composition (polyandrous or monogamous) of the brood as predictors. We included the nest ID as a random effect to account for offspring from the same brood and female.
56 Is chick survival influenced by heterozygosity?
57
58
59
60
Finally, we fitted a mixed effects model with fledging success as a binary response term, when a chick fledged we scored a ‘1’ and when a chick failed to fledge we scored a ‘0’.
We included the chick’s heterozygosity as a predictor, and the nest ID as a random effect to account for repeated chicks from the same brood.
61 Do males benefit from breeding in socially polyandrous groups?
62
63
64
To test whether loss of paternity through extra-group paternity differed between social group composition, we fitted a model with the presence of extra-group young as a binary response term and included social group composition (polyandrous or

4
65
66 monogamous) as a predictor. Group identity was included as a random effect to account for repeated breeding attempt by the same group.
67
68
69
After taking into account all paternity lost and gained through extra- and within-group paternity, we tested whether the number of young produced by each male differed according to their status (i.e. whether the male was socially monogamous, or cobreeding
70
71
72
73
74 in a socially polyandrous group [here males were further divided into alpha and beta males]). We fitted a mixed effects model with ‘number of young’ as the response term and social group composition as the predictor. Sire identity was included as a random effect to account for males that bred both in monogamy and in polyandry. We built a similar model to test whether the number of young that fledged by each male differed
75 according to their status.
76
77
78 Dawson DA, Horsburgh GJ, Küpper C, et al. (2010) New methods to identify conserved
79
80
81
82
83 microsatellite loci and develop primer sets of high cross-species utility – as demonstrated for birds. Molecular Ecology Resources, 10, 475–494.
Harrison XA, York JE, Cram DL, Young AJ (2013) Extra-Group Mating Increases
Inbreeding Risk in A Cooperatively Breeding Bird. Molecular Ecology, doi:
10.1111/mec.12505.
84
85
86
Saito D, Nishiumi I, Nakamura M (2001) Characterization of nine polymorphic microsatellite loci from the alpine accentor Prunella collaris. Molecular Ecology
Notes, 1, 258–259.

87
88
89
90
91
Wang J (2010) Do marker-based paternity assignments favour heterozygous and unrelated males? Molecular Ecology, 19, 1898–1913.
Wetzel DP, Westneat DF (2009) Heterozygosity and extra-pair paternity: biased tests result from the use of shared markers. Molecular Ecology, 18, 2010–2021.
5

92
93
94
95
96
97
Summary characteristics and parameters of the 18 microsatellite loci used in the paternity analysis. N
A
, number of alleles detected; H
O
, observed heterozygosity; H
E
, expected heterozygosity; NE
1
, nonexclusion probability for the first parent; NE
2
,
98
99
100
101 nonexclusion probability for the second parent when the first has been assigned.
Observed and expected heterozygosities, and exclusion probabilities were estimated using the genotypes of all adults. The Pco loci were developed by Saito et al. (2001), while the TG loci were developed by Dawson et al. (2010).
Locus N
A
Pco10*
Pco2
Pco3
Pco36*
Pco5*
Pco6
Pco9
TG01_077 4
TG01_148 3
8
6
TG02_078 2
2
2
7
14
10
H
O
H
E
NE
1
NE
2
P
HW
0.681 0.456 0.897 0.824 1.00
0.336 0.335 0.944 0.861 0.58
0.504 0.533 0.837 0.663 0.03
0.509 0.854 0.460 0.297 <0.001
0.500 0.852 0.469 0.303 <0.001
0.784 0.748 0.647 0.470 0.80
0.690 0.677 0.735 0.560 0.68
0.422 0.455 0.891 0.740 0.08
0.371 0.423 0.911 0.780 0.09
0.095 0.136 0.991 0.937 0.01
6

TG02_088 5
TG02_120 4
TG03_002 3
TG03_035 4
TG04_012 3
TG04_041 2
TG05_046 3
TG05_053 8
0.443
0.470
0.730
0.444
0.499
0.756
0.900
0.876
0.640
0.774
0.800
0.461
102 *Significant deviation from Hardy-Weinberg equilibrium
0.10
0.25
0.491 0.525 0.864 0.722 0.16
0.457 0.422 0.912 0.819 0.93
0.362 0.340 0.943 0.831 0.90
0.034 0.034 0.999 0.983 1.00
0.259 0.278 0.962 0.864 0.01
0.41
103
7

104
105 Multiplex reaction details.
M13 label Locus
FAM (blue) Pco5
FAM (blue) TG01-077
FAM (blue) TG04-041
FAM (blue) Pco9
FAM (blue) TG03-035
VIC (green) TG03-002
VIC (green) Pco3
VIC (green) TG05-053
VIC (green) TG02-120
VIC (green) TG02-088
NED (black) TG04-012
NED (black) TG01-148
NED (black) TG02-078
NED (black) Pco36
NED (black) TG05-046
PET (red)
PET (red)
Pco2
Pco10
0.8
0.1
0.1
0.4
0.8
0.4
0.4
0.4
0.2
0.4
0.4
0.2
0.4
0.4
0.4
Forward (μl) Reverse (μl)
0.2
0.4
0.8
1.6
1.6
0.8
1.6
1.6
0.8
1.6
1.6
1.6
3.2
0.4
0.4
1.6
3.2
1.6
1.6
8

106
PET (red)
PET (red)
107
Pco6 0.4
P2=Fwd/P8=Rev 1.2
1.6
4.8
9

108
109 Number of mothers and chicks in each year.
Year
2009-2010
2010-2011
110
2011-2012
111
Number of mothers
19
24
20
Number of chicks
67
136
106
10

11
112
113
114
Quantification of assignment bias towards more heterozygous males following Wang
(2010).
115
116
117
118
For each locus, we calculated ‘hH’, the ratio of the mean heterozygosity of the assigned sires (‘All assigned sire H
O
’) to the expected heterozygosity at the locus (‘Pop. H
E
’, see
Table S1). A ratio of 1 suggests the assigned males have a heterozygosity equal to the expected heterozygosity, and that there is no assignment bias towards more (or less)
119
120 heterozygous males (Wang 2010). The mean hH for our 16 loci was 1.019, suggesting no assignment bias when all 16 markers were used for paternity assignment.
Locus
Pco10*
Pco2
Pco3
Pco6
Pco9
TG01_077
TG01_148
TG02_078
TG02_088
TG02_120
TG03_002
TG03_035
Pop. mean Het. Pop. H
E
All assigned sire H
O
All assigned sire hH
0.681
0.336
0.456
0.335
0.725
0.314
1.590
0.936
0.504
0.784
0.690
0.422
0.371
0.095
0.443
0.470
0.491
0.457
0.533 0.510
0.748 0.824
0.677 0.654
0.455 0.365
0.423
0.136 0.100
0.444 0.500
0.499 0.500
0.525 0.367
0.422
0.420
0.481
0.957
1.100
0.965
0.803
0.992
0.735
1.126
1.002
0.699
1.139

121
TG04_012
TG04_041
TG05_046
TG05_053
Average across loci
0.362
0.034
0.259
0.730
122
0.340 0.400
0.034 0.038
0.278 0.260
0.756 0.776
1.176
1.131
0.935
1.025
1.019
12

123
124 Relationship between hatching success (proportion of hatched eggs), and multiple
125 paternity (presence of multiple paternity) in socially polyandrous dunnock groups.
Fixed term
126
Intercept (no multiple paternity)
Multiple paternity (extra-group)
Multiple paternity (intra-group)
127
Estimate ( β )
1.017
0.495
1.564
95% CI
0.024 to 2.162
-1.110 to 2.229
0.011 to 3.244
13

128
14
129
130
131
132
133
Decision flow diagram depicting how we decided whether a particular chick would be maintained in the final results of the paternity assignment analysis or not. Decision process started with a sample of 340 chicks/embryos, and finished with 288
134 chicks/embryos being maintained in the final paternity analysis.
135
136 Hatching success of dunnock clutches from socially monogamous and polyandrous
137
138
139
140 females. Point estimates represent mean hatching success of clutches with no multiple paternity (circles), with multiple paternity due to extra-group paternity (triangles), and multiple paternity due to intra-group paternity from cobreeding males of socially polyandrous groups (squares). Vertical bars depict ± 1 S.E.
141

142
143
15
144
145
146

147
0.9
0.8
●
0.7
148
0.6
Monogamous
●
Polyandrous
Multiple paternity
●
No
Y es − Extra−group
Y es − Intra−group
16