1
Data S1
2
3
Methods for house sparrow case study
4
Data selection for house sparrow case study
5
Many morphological traits change between- and within-ages, but some are stable
6
after birds mature (e.g. tarsus length). To test for the stability of measurements, we
7
used all measurements of every adult male (≥ 1 year old) from 2000 to 2012 to
8
calculate the within- and between-year repeatability values (intra-class correlations,
9
or ICC; Nakagawa & Schielzeth 2010) of the seven morphological traits (five body-
10
size indicators and two ornaments). The observer error was accounted for when
11
estimating the within-year repeatability, but not in the between-year repeatability,
12
because in the latter case only the annual mean could be used. The within-year
13
repeatability values of all the morphological traits were higher than 0.56 (Table S1).
14
Moreover, when we accounted for the monthly differences in tail length and wing
15
length (note that the length of feathers changes through time within a year), the
16
within-year repeatability values of these two traits increased from 0.66 to 0.74, and
17
from 0.77 to 0.83, respectively (Table S1). The between-year repeatability values of
18
tarsus length, beak length and wing length were greater than 0.62, but tail length
19
was not (0.45; Table S1). We note that, when calculating the between-year
20
repeatability, we averaged all measurements within one year, so we could not
21
account for monthly differences, which might have influenced the wing and tail length.
22
The relatively low between-year repeatability of tail length, which is particularly
23
subject to wear between moults, might be a result of this limitation, because it was
24
averaged across months.
1
25
26
27
28
29
Table S1. The within- and between-year repeatability of phenotypic traits in the house sparrow population on Lundy Island from
2000 to 2012. The number of years recorded (Ny), number of individuals (Ni) and the number of records (Nr) for males are used in
calculating the mean values, and within- and between-year repeatability. The within-year repeatability was the mean value over 13
(7 for mask) years.
Male
30
31
Female
Repeatability (Male)
Trait
Ny
Ni
Nr
Mean ± sd
Ny
Ni
Nr
Mean ± sd
Within year
Within year*
Between year
Tarsus length
13 (2000-2012)
358
959
18.58 ± 0.86
13 (2000-2012)
533
1261
18.37 ± 0.87
0.84
-
0.83
Beak length
10 (2003-2012)
291
757
13.06 ± 0.75
10 (2003-2012)
421
984
12.92 ± 0.93
0.62
-
0.62
Tail length
10 (2003-2012)
286
741
58.58 ± 2.37
10 (2003-2012)
371
861
56.59 ± 2.31
0.66
0.74
0.45
Wing length
13 (2000-2012)
367
1018
78.52 ± 2.21
13 (2000-2012)
551
1349
75.58 ± 2.45
0.77
0.83
0.71
Mass
13 (2000-2012)
369
995
28.05 ± 1.98
13 (2000-2012)
561
1365
27.65 ± 2.33
0.62
0.62
0.62
Badge size
13 (2000-2012)
316
2841
35.51 ± 4.37
-
-
-
-
0.56
0.66
0.40
Mask area
7 (2006-2012)
179
967
15.12 ± 3.20
-
-
-
-
0.75
0.76
0.37
*within-year repeatability after accounting for monthly differences
2
Where we had multiple measurements of a male, we included the measurements of
body-size indicators temporally closest ± two years to a focal mating event thus making
measurements as relevant as possible to any given event. We also extracted another
dataset that included only the measurements of body-size indicators taken in the year in
which a particular mating event occurred, and we ran the same statistical analyses
using this reduced dataset. The exploratory analyses showed that the results based on
this reduced dataset were similar to the results based on the two-year-tolerance dataset.
Hereafter, we present only results based on the two-year-tolerance dataset for bodysize indicators.
Statistical analysis for house sparrows case study
We note that we did not have measurements of every trait for every individual in our
dataset, so there were missing values for the response variable in some of the models.
Deleting these missing values might lead to biased estimates (Nakagawa & Freckleton
2008). MCMCglmm uses a data augmentation procedure to treat missing values in the
response under the assumption of ‘missing at random’ (Hadfield 2010). Therefore, we
kept the missing values in our dataset in most analyses (see below for an exception).
The proportion of missing values in each dataset is listed in Table S3.
We used the MCMCglmm default priors for fixed effects. We specified an inverse
Wishart prior for all random effects and residuals as V = 1 and nu = 0.05, where V
defined variance, and nu defined the degree of belief in V. The only exception is the
random slope, where we specified V = diag(2) and nu = 0.05. For each model, we ran
three parallel chains and used Gelman–Rubin diagnostics to check for convergence
(Gelman & Rubin 1992). Also, we checked the within-chain independence by calculating
the autocorrelation between successive samples for fixed and random effects,
separately, in each chain.
3
Table S3. The sample size of the comparisons between extra-pair and cuckolded male
house sparrows for each trait, including the number of broods (N[Broods]), number of adult
males (N[Males]), and the number of trios (N[Unique trios] and N[Trios], see the following
explanation). A trio includes a female, her cuckolded male and her focal extra-pair male.
The N[Unique trios] indicates the number of unique trios in the dataset, and the N[Trios]
indicates the number of trios used in the comparisons. The N[Trios] is usually larger than
N[Unique trios] because some trios occurred in more than one year. The missing value (%)
is the percentage of missing values in the record entry. rQG is the genetic similarity
measurements following Queller and Goodnight’s method (Queller & Goodnight 1989),
and rLR is the measurements following Lynch and Ritland’s method (Lynch & Ritland
1999).
N[Broods] N[Males] N[Unique trios]
N[Trios]
N [Records entry]
rQG
387
274
445
461
922
0.3
rLR
387
274
445
461
922
0.3
Tarsus length
356
237
400
414
828
2.2
Beak length
356
237
400
414
828
15.2
Mass
356
237
400
414
828
5.4
Wing length
356
237
400
414
828
0.6
Tail length
356
237
400
414
828
15.6
Badge size
247
163
225
231
1524
1.6
Mask area
234
161
223
229
649
48.3
423
274
445
461
922
0
Trait
Missing value (%)
Genetic similarity
Body-size indicator
Ornaments
Age
Age
4
Specific statistical models
In the models for genetic similarity, we ran random-slope generalized linear mixed
models, GLMMs, with the variable combination described in the main text. In the models
for the body-size indicators, we included the following four extra random effects:
observers who measured the traits (to account for measurement bias), male age at
capture (because body size may change with age), the year when the males were
captured (because body sizes may change between years), and also male identity.
Among the models for the body-size indicators, we included capture month from the end
of the breeding season (Oct = 0, Nov = 1, Dec = 2, Jan = 3, and so on) as a fixed effect,
instead of a random effect, for tail length and wing length, because sparrows undergo a
complete prebasic moult each year and in our population sparrows usually finish this
moult in October and the length of feathers may gradually decline after this point due to
abrasion.
In the models for the ornaments, we included all the random effects in the models
analysing body-size indicator, except the year of capture. In addition, we included
capture event as another random effect because we measured each ornament three
times once a male was caught. To improve the MCMC model convergence, we used a
subset of data for these analyses, where we removed trios in which both extra-pair and
cuckolded males had no capture record in the year of mating. For mask size, the
models with the predictive variable combination listed above did not converge with the
subset of data, potentially due to the high proportion of missing values (~48%).
Therefore, to help the model to converge, we reduced the number of random effects by
taking out less important effects (according to the magnitude of the variance
components). Consequently, we included only observers, sire identity and the capture
event as random effects in the final model. Results from the model with fewer random
effects were quantitatively similar with results from the full model. Thus, we only report
the results from the reduced model.
5
In the models for male mating age, we included female mating age as an extra fixed
effect (because there could be assortative mating on age; Potti 2000; Auld et al. 2013)
and female identity and the year of mating as random effects.
Meta-analyses
Data collection
Article collection
We screened through references included in previous meta-analytic studies,
comparative studies or reviews (i.e., Arnqvist & Kirkpatrick 2005; Akçay & Roughgarden
2007; Kempenaers 2007; Cleasby & Nakagawa 2012). We also conducted a keyword
search, using “extra-pair / extrapair / extra pair”, “paternity” and “polyandry” to search on
the Web of Science and Google Scholar from 1987 to 2013. We screened titles and/or
abstracts of all the articles in the search results and only examined the texts in detail for
the studies whose titles and abstracts seemed relevant. For the database, we only
included articles in which the authors conducted pairwise comparisons between extrapair and cuckolded males on at least one of the four trait categories.
Estimating Zr for each comparison
To acquire Zr from each comparison, we first calculated the standardized mean
differences (d) between the measurements of extra-pair males and those of cuckolded
males. When the mean (m) and standard deviations (s) of the measurements of extrapair and cuckolded males (mE, mW and sE, sW, respectively) were provided, we used
these values to calculate d using the equations below (cf. Nakagawa & Cuthill 2007):
d=
mE - mW
spooled ,
eqn 1
6
spooled 
(n  1)(sW  sE )
2n  2
,
eqn 2
where n is the number of pairs of extra-pair and cuckolded males. The proportions of
effect sizes calculated from m and s are 58% in the dataset of genetic similarity, 66% in
body size, 36% in secondary sexual traits, and 39% in age; we note that, when
available, we always used m and s to obtain effect sizes. For articles without m and s,
we used the reported test statistics (e.g. paired t or its non-parametric equivalent, z,
from matched-pair tests) to estimate d using the following equation:
d = t paired
2(1- rWE )
n
,
eqn 3
where rWE is Pearson’s correlation coefficient between the measurements of extra-pair
males and those of cuckolded males.
However, only very few articles provided the actual rWE values, which are required for d
calculations; when rWE was provided (the number of effect sizes with provided actual rWE:
n[Genetic similarity] = 3, n[Body size] = 7, n[Secondary sexual trait] = 6, and n[Age] = 6), the values were
distributed mostly between 0 and 0.8. We note that a high proportion of the effect sizes
in the dataset of each trait category (37% in genetic similarity, 33% in body size, 54% in
secondary sexual traits and 46% in age) required this calculation using Equation 3, but
we did not have the actual rWE to conduct such a calculation. Therefore, we prepared
three different datasets for each trait category: (1) assuming the rWE value of 0 for all the
effect sizes, (2) assuming the rWE value of 0.8, and (3) using an rWE representative value
for each trait category. For articles with actual rWE, the d values in each of these
datasets are the values estimated from the actual rWE. In order to obtain a
representative rWE value for each trait category for comparisons without actual rWE, we
conducted a meta-analysis in each trait category to obtain meta-analytic means for rWE.
In each of these meta-analyses, we used the Zr-transformed rWE values as the response,
weighted with their corresponding sampling variance, 1/(n – 3). The meta-analytic mean
rWE value for genetic similarity is 0.2262, body size 0.0482, secondary sexual traits
7
0.5367, and age 0.1394 (note that these meta-analytic means were obtained by using
random effect models with the R package ‘metafor’; Viechtbauer 2010). These metaanalytic means of rWE were used as representative values of rWE in further calculations.
Once we calculated all the d values in each of the three datasets for each trait category,
we transformed d into a correlation coefficient, r, using the formula,
r
d
d2  4
eqn 4
Then, we converted r into Zr using the following equation,
æ 1+ r ö
Zr = 0.5 ln ç
è 1- r ÷ø
eqn 5
We also obtained the sampling variance for each Zr using 1/(n – 3). In our analyses, a
positive Zr indicates that extra-pair males have larger measurements on a particular trait
than the cuckolded males; that is, extra-pair males are genetically more similar to focal
females, have larger body size, more exaggerated secondary sexual traits, or are older.
In addition, we note that the r-values of 0.1, 0.3 and 0.5 are considered to be small,
moderate and large, respectively (sensu Cohen 1988); these r-values translate into the
Zr values of 0.10, 0.31 and 0.55, respectively.
Meta-analyses and meta-regression
For each meta-analysis and meta-regression models, we conducted all analyses for
each of the three datasets (rWE = 0, 0.8, or representative values). The exploratory
results from each of the three datasets (differing in the setting of rWE) were similar within
the same trait category, so we only present results based on the dataset of rWE
representative values using the tree with Hackett’s backbone for the publication bias
tests.
8
For each of the meta-analytic models in MCMCglmm, we ran all models for 5,000,000
burn-in iterations, followed by 5,000,000 iterations and a thinning interval of 500, which
resulted in 10,000 samples for each parameter’s posterior distribution. We specified an
inverse Wishart prior for all random effects and residuals as V = 1 and nu = 0.002. For
all models, we ran three parallel chains and used Gelman–Rubin diagnostics to check
for convergence (Gelman & Rubin 1992). We also calculated the autocorrelation
between successive samples for fixed and random effects, separately, in each chain to
check the within-chain independence. For each meta-analytic model, we report the
means of the posterior distributions and their 95% credible intervals (95% CIs) as our
parameter estimates.
We conducted a phylogenetic meta-analysis and a meta-regression in each of the four
trait categories using the method described by Hadfield & Nakagawa (2010). For each
meta-analysis, we used the topology of two phylogenetic trees from Jetz et al. (2012):
the one based on Hackett’s backbone and the other on Ericson’s backbone (Ericson et
al. 2006; Hackett et al. 2008). The exploratory results from these two phylogenetic trees
are similar to each other; this is expected because parameter estimates in phylogenetic
comparative analyses are known to be robust to tree misspecification to a certain
degree (Rohlf 2006; Stone 2011).
We calculated a heterogeneity statistic I2 for multilevel meta-analytic models, described
by Nakagawa & Santos (2012), which is modified from Higgins and Thompson’s I2
(Higgins & Thompson 2002). Low, moderate and high heterogeneities refer to I2 of 25%,
50% and 75%, respectively (Higgins et al. 2003). We also calculated the phylogenetic
heritability, H2, as the proportion of total variance in Zr that can be explained by the
variance of additive genetic values (i.e. phylogenetic variance; Lynch 1991) equivalent
to Pagel’s λ (Pagel 1999; Hansen & Orzack 2005; Hadfield & Nakagawa 2010). To test
for potential publication bias, we conducted Egger’s regression on meta-analytic
residuals (sensu Nakagawa & Santos 2012) to test for evidence of publication bias in
our datasets (Egger et al. 1997). Significant intercepts away from zero indicate a
possibility of publication bias. To quantify the potential publication bias, we performed
the trim-and-fill tests on the meta-analytic residuals with the R0 estimator (Duval &
9
Tweedie 2000a, b). We obtained the required adjustment by estimating the difference
between zero and the intercept after applying the trim-and-fill procedure. Also, to
visualize the distribution of the data points for potential publication bias, we plotted
funnel plots with both the raw data (original effect sizes) and the meta-analytic residuals,
respectively.
Results
Publication bias for meta-analyses
Egger’s regression tests showed that there was only weak, if any, evidence for
publication bias in any of our datasets (genetic similarity: the intercept, b0 = -0.30, 95%
CI = -0.73 to 0.13; body size: b0 = -0.10, 95% CI = -0.35 to 0.16; secondary sexual traits:
b0 = 0.30, 95% CI = -0.15 to 0.75; age: b0 = 0.50, 95% CI = -0.13 to 1.21). The trim-andfill tests did not identify any missing studies in any trait category apart from secondary
sexual traits (8 missing studies, p = 0.002). The meta-analytic mean for the residuals in
the secondary sexual trait dataset incorporating ‘filled data points’ (or missing data
points) was -0.037; this indicates that the original meta-analytic mean might be slightly
overestimated. The funnel plots also showed little sign of publication bias for both the
raw data and the meta-analytic residuals (Figure S3).
10
Figure S3. Funnel plots of Zr against its precision (1/standard error for Zr) and residual
against the precision in each of the four trait categories. The dashed grey lines in the
figures of original Zr indicate the meta-analytic means; the dotted grey lines in the
figures of residual Zr indicate the adjusted means according to the results of trim-and-fill
tests. Solid circles represent the collected data points, whereas the empty circles are
data points filled by the trim-and-fill method.
11
1
Data S2: Details of paternity assignments and genetic
2
pedigree
3
We assigned paternity and constructed the genetic pedigree using the genotypes at
4
13 microsatellite loci (Dawson et al. 2012; Schroeder et al. 2012). We assigned the
5
genetic fathers with 95% confidence for approximately 90% of all offspring (Table S2)
6
in software CERVUS 3.0 (Marshall et al. 1998; Hadfield et al. 2006; Kalinowski et al.
7
2006; Schroeder et al. 2012). We genotyped at least two different DNA samples for
8
the great majority of adult birds.
9
Where we obtained two mismatching genotypes from two separate tissue samples
10
from a single individual, the respective samples were genotyped repeatedly. This
11
allowed for precise genotyping and detection of any sample mix-ups. After
12
confirming the genetic maternity of the observed social mothers, we allowed all
13
potentially-alive males to be assigned as sires. We carefully checked each offspring–
14
sire combination where the assigned sire was not the female’s pair-bonded mate.
15
We took an iterative approach and compared the assigned sire with the next-best
16
matching sire. If both sires mismatched at ≤1 locus then we assigned the social mate
17
if it was among the two best sires. If the social mate was not one of these two
18
matching sires then we compared the observation records of both individuals and
19
assigned paternity to the one that was seen or caught closest in time to the
20
respecitve breeding season (in years). This cleared up all ambiguities, and allowed
21
us to distinguish between brothers where both were assigned.
22
In cases where two or more loci mismatched, if the social sire was not assigned by
23
the software, we took the conservative approach and refrained from assigning a sire
12
24
or the extra-pair status. This is the reason we did not assign complete parentage for
25
all sampled chicks. Among those individuals that could not be assigned parentage
26
with fewer than two mismatches, 77% of the DNA samples were extracted from very
27
small tissue or blood samples, dead embryos in rotten eggs, or similarly
28
compromised samples. In these cases, the DNA may have been severely degraded,
29
or present in very low concentration, such that fewer than six loci amplified and we
30
did not assign parentage. This also implies that a larger proportion of unassigned
31
individuals died early in life (Table S2), which should be considered when
32
interpretating these results. However, we currently have no reason to believe that
33
early-life mortality is linked with extra-pair status (Hsu et al. 2014). A more detailed
34
description of the pedigree construction, including information on the probability of
35
sample mix-ups and genotyping error, is available in Schroeder et al. (In revision).
36
37
13
Data S3: Tables and figures with supporting information
*Note: Table S1, S3 and Figure S3 are embedded in corresponding places in Data S1.
Table S2. Sample size of offspring in house sparrow case study.
*complete pedigree means that we identified all social and genetic parents for that individual.
S2a. Sample collection of all offspring including unhatched eggs and chicks
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
N[Egg laid]
N[Offspring sampled]
244
259
385
515
862
1041
499
409
136
241
291
593
155
219
323
459
761
857
430
356
117
222
213
550
Offspring
sampled (%)
63.5
84.6
83.9
89.1
88.3
82.3
86.2
87
86
92.1
73.2
92.7
N[Offspring with genetic paternity
assignment]
143
202
300
403
736
844
391
312
104
165
168
478
Sampled offspring with genetic
paternity assignment (%)
92.3
92.2
92.9
87.8
96.7
98.5
90.9
87.6
88.9
74.3
78.9
86.9
N[Offspring with
complete pedigree]
138
200
278
393
733
844
323
257
71
156
155
391
Sampled offspring with
complete pedigree (%)
89.0
91.3
86.1
85.6
96.3
98.5
75.1
72.2
60.7
70.3
72.3
71.1
S2b. Sample collection of unhatched eggs
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
N[Egg
N[Egg
N[Sampled
hatched]
unhatched]
unhatched eggs]
166
225
317
373
664
776
328
254
93
184
180
474
78
34
68
142
198
265
171
155
43
57
111
119
0
14
40
75
145
144
113
128
32
50
36
76
Sampled unhatched
eggs (%)
0.0
41.2
58.5
52.8
73.2
54.3
66.1
82.6
74.4
87.7
32.4
63.9
N[Unhatched eggs with
genetic paternity assignment]
0
6
32
58
134
135
81
92
20
0
3
25
Sampled eggs with
genetic paternity
assignment (%)
0.0
42.9
80.0
77.3
92.4
93.8
71.7
71.9
62.5
0
8.3
32.9
N[unhatched eggs with
*complete pedigree]
0
5
25
52
132
135
47
66
8
0
3
20
Sampled eggs with
*complete pedigree
0.0
35.7
62.5
69.3
91.0
93.8
41.6
51.6
25.0
0.0
8.3
26.3
14
S2c. Sample collection of chicks that died before fledging
Year
N[Chicks died
before fledging]
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
70
63
139
154
436
436
169
110
25
69
50
112
Chicks died
before
fledging (%)
42.2
28.0
43.8
41.3
65.7
56.2
51.5
43.3
26.9
37.5
27.8
23.6
N[Sampled
Dead chicks
sampled (%)
dead chicks]
59
43
105
130
388
373
158
84
17
57
47
112
N[Dead chicks with genetic
paternity assignment]
84.3
68.3
75.5
84.4
89.0
85.6
93.5
76.4
68.0
82.6
94.0
100.0
47
39
96
129
377
369
151
78
16
52
37
107
Sampled dead chicks
with genetic paternity
assignment (%)
79.7
90.7
91.4
99.2
97.2
98.9
95.6
92.9
94.1
91.2
78.7
95.5
N[Dead chicks with
*complete pedigree]
45
38
87
127
376
369
124
70
13
47
31
83
Sampled dead chicks with
*complete pedigree (%)
76.3
88.4
82.9
97.7
96.9
98.9
78.5
83.3
76.5
82.5
66.0
74.1
S2d. Sample collection of fledglings
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
N[fledglings]
96
162
178
219
228
340
159
144
68
115
130
362
Chicks fledged
(%)
57.8
72.0
56.2
58.7
34.3
43.8
48.5
56.7
73.1
62.5
72.2
76.4
N[Sampled
fledgling]
96
162
178
216
228
340
159
144
68
115
130
362
Sampled
fledgling (%)
100.0
100.0
100.0
98.6
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
N[Fledgling with genetic
paternity assignment]
96
157
172
216
225
340
159
142
68
113
128
346
Sampled fledgling with genetic
paternity assignment (%)
100.0
96.9
96.6
100.0
98.7
100.0
100.0
98.6
100.0
98.3
98.5
95.6
N[Fledgling with
*complete pedigree]
93
157
166
214
225
340
152
121
50
109
121
288
Sampled fledgling with
*complete pedigree
96.9
96.9
93.3
99.1
98.7
100.0
95.6
84.0
73.5
94.8
93.1
79.6
15
Table S4. Results from the random slope GLMMs, explaining variation in each male house sparrow genotypic or
phenotypic trait in the Lundy population. Male status is the male mating status with extra-pair male = 1 and cuckolded
male = 0 (the baseline). Posterior means and 95% credible intervals (95% CIs) are presented. rQG is the genetic similarity
measurements following Queller and Goodnight’s method, and rLR is the measurements following Lynch and Ritland’s
method.
Characteristics
Fixed effects
(Intercept)
Mean
(95%CI)
Genetic similarity
rQG
rLR
Body-size indicators
Tarsus
Beak length
-0.04
(-0.13 to
0.06)
0.09
(-0.02 to
0.21)
-
-0.01
(-0.10 to 0.08)
-
0
(-0.37 to
0.36)
0.01
(-0.05 to
0.08)
-
Ornaments
Badge size
Mask area
0.53
(-0.24 to
1.28)
0
(-0.06 to
0.06)
-0.09
(-0.11 to 0.07)
-
-0.61
(-2.01 to
0.89)
0
(-0.04 to
0.03)
-
0.22
(-0.93 to
1.47)
0
(-0.06 to
0.05)
-
-0.5
(-0.82 to -0.2)
-
-
0.19
(0.13 to 0.25)
0
(0 to 0)
0
(0 to 0)
0
(0 to 0.01)
0
(0 to 0)
0.31
(0.19 to 0.43)
-0.46
(-0.6 to -0.33)
0
(0 to 0)
0
(0 to 0)
-0.46
(-0.6 to -0.33)
0
(0 to 0.01)
0.01
(0 to 0.01)
1.5
(1.21 to 1.78)
Mass
Wing length
Tail length
-0.1
(-0.52 to
0.33)
-0.01
(-0.05 to
0.02)
-
-0.17
(-0.88 to
0.54)
0.04
(-0.02 to 0.1)
-0.11
(-0.69 to
0.47)
-0.02
(-0.05 to
0.01)
-0.04
(-0.05 to 0.03)
-
Male age
♂ status
Mean
(95%CI)
Month for
feather#
Mean
(95%CI)
♀ age
Mean
(95%CI)
-
-
-
-
-
Random effects
(Intercept) :
(Intercept).trio
♂ status :
(Intercept).trio
Mean
(95%CI)
Mean
(95%CI)
♂ status : ♂
status.trio
Mean
(95%CI)
0.02
(0.01 to 0.03)
0.01
(0 to 0.02)
-0.01
(-0.02 to
0.01)
-0.01
(-0.02 to
0.01)
0.06
(0.02 to 0.1)
0.02
(0.01 to 0.03)
0.01
(0 to 0.03)
0
(-0.02 to
0.01)
0
(-0.02 to
0.01)
0.04
(0.01 to 0.08)
Observer
Mean
(95%CI)
Mean
(95%CI)
-
-
0.19
(0.01 to 0.49)
0.03
(0 to 0.09)
0.58
(0.07 to 1.48)
0.05
(0 to 0.14)
0.39
(0.05 to 0.97)
0.17
(0.03 to 0.39)
0.49
(0.04 to 1.45)
0.44
(0.08 to 1.04)
3.62
(0.65 to 8.88)
0.04*
(0 to 0.13)*
2.16
(0.24 to 5.86)
-
-
-
♂ capture Year
Mean
(95%CI)
-
-
0.13
(0.03 to 0.28)
0.23
(0.04 to 0.54)
0.13
(0.02 to 0.28)
0.06
(0.01 to 0.15)
-
-
-
♂ identity
Mean
(95%CI)
-
-
1.16
(0.95 to 1.39)
0.66
(0.52 to 0.81)
0.94
(0.77 to 1.13)
0.56
(0.45 to 0.7)
0.07
(0 to 0.16)
0.13
(0 to 0.37)
-
♂ capture
event
♂ capture
month
Mean
(95%CI)
Mean
(95%CI)
-
-
0.01
(0 to 0.02)
0
(-0.02 to
0.01)
0
(-0.02 to
0.01)
0.04
(0.01 to
0.08)
0.1
(0.01 to 0.3)
0.06
(0.01 to
0.14)
0.11
(0.03 to
0.23)
0.8
(0.64 to
0.97)
-
0.01
(0 to 0.01)
-0.01
(-0.01 to 0)
Mean
(95%CI)
1.01
(0.88 to 1.14)
-0.74
(-0.89 to 0.61)
-0.74
(-0.89 to 0.61)
1.50
(1.30 to 1.70)
0.01
(0 to 0.01)
0
(-0.01 to 0)
(Intercept) : ♂
status.trio
1
(0.83 to 1.08)
-0.72
(-0.85 to 0.59)
-0.72
(-0.85 to 0.59)
1.53
(1.34 to 1.74)
-
-
-
-
-
-
-
-
-
-
0.41
(0.15 to 0.63)
-
-
-
0.33
(0.23 to 0.43)
0.06
(0 to 0.15)
♂ capture age
0.03
(-0.08 to 0.14)
0
(-0.01 to 0)
-
-0.01
(-0.01 to 0)
0.22
(0.09 to 0.33)
-
-
-
16
Mating year
♀ identity
Dispersion
Male
(95%CI)
Male
(95%CI)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Mean
(95%CI)
0
(0 to 0)
0
(0 to 0)
0.03
(0.02 to
0.03)
0.11
(0.09 to 0.13)
0.07
(0.06 to 0.09)
0.02
(0.02 to 0.03)
0.09
(0.07 to 0.11)
0.03
(0.03 to 0.03)
0.01
(0.01 to 0.01)
0.21
(0.04 to 0.44)
0.26
(0.17 to 0.35)
0.11
(0.04 to 0.2)
For ornaments, the male capture age is the male mating age.
17
Table S5. Results from the meta-analyses, explaining the pairwise difference of male genotypic or phenotypic traits
between extra-pair and cuckolded males. Positive values indicates that extra-pair males are genetically more similar to
focal females, have larger body size, more exaggerated secondary sexual traits or are older than cuckolded males who
mated with the same female(s). Here we present results based on Zr with the estimated correlation between extra-pair
and cuckolded males (rEW) with Hackett’s phylogenetic tree (see Method). Results from two models were presented in
each trait category. The meta-analyses with intercept and no fixed effects show the overall effect size in that trait category.
The meta-regression has no intercept but fixed effects (Trait type), showing the trait-specific effect sizes. In the analysis of
genetic similarity, trait type indicates the genetic markers used to estimate genetic similarity. In the analyses of body size
and secondary sexual trait, trait type indicates which phenotypes were measured. In cases where the original author did
not specify which phenotype they measured, we classified such comparisons as (general) body size. In age, the trait type
indicates how the original authors classify male mating age, either by age class (first year or older), known specific age, or
that the authors did not provide such information.
Characteristics
Fixed effects
(Intercept)
Mean
(95%CI)
Trait type
Genetic similarity
MetaMeta-regression
analysis
Body size
Metaanalysis
-0.03
(-0.15 to
0.09)
0.05
(-0.05 to
0.14)
Mean
(95%CI)
DNA
fingerprinting
MHC
Mean
(95%CI)
Mean
(95%CI)
Microsatellite
-0.02
(-0.27 to
0.26)
-0.07
(-0.30 to
0.15)
-0.03
(-0.16 to
0.10)
Meta-regression
Beak
Body
size
Tarsus
Mean
(95%CI)
Weight
Mean
(95%CI)
Wing
length
Random effects
Phylogeny
Mean
(95%CI)
Species
Mean
(95%CI)
Study
Mean
(95%CI)
0.01
(0 to
0.02)
0.01
(0 to
0.02)
0.004
(0 to
0.01)
0.003
(0 to
0.01)
0.003
(0 to
0.01)
Secondary sexual trait
MetaMeta-regression
analysis
Age
Metaanalysis
0.10
(-0.02 to
0.21)
0.09
(-0.01 to
0.20)
0.03
(-0.11 to
0.17)
0.04
(-0.10 to
0.17)
0.06
(-0.05 to
0.18)
0.03
(-0.09 to
0.16)
0.05
(-0.06 to
0.17)
0.004
(0 to 0.01)
0.003
(0 to 0.01)
0.003
(0 to 0.01)
Ornament
Song
0.07
(-0.04 to
0.18)
0.25
(0.07 to
0.42)
Meta-regression
Age
class
Known
age
Unknown
0.01
(0 to
0.02)
0.01
(0 to
0.02)
0.01
(0 to
0.03)
0
(0 to
0.02)
0
(0 to
0.01)
0.01
(0 to
0.02)
0.01
(0 to
0.02)
0.06
(-0.10 to
0.22)
0.11
(-0.02 to
0.23)
-0.05
(-0.57 to
0.49)
0.01
(0 to 0.02)
18
Dispersion
Mean
(95%CI)
0.003
(0 to
0.01)
0.003
(0 to
0.01)
0.002
(0 to
0.004)
0.002
(0 to 0.01)
0.01
(0 to
0.02)
0.01
(0 to
0.02)
0.01
(0 to
0.02)
0.01
(0 to 0.02)
19
Table S6. The heterogeneity (I2 %) explained by random components of meta-analytic models in each of the four trait
categories. Each I2 was shown in the form of a posterior mean with 95% credible intervals, 95% CIs, in parentheses. I2%
of 25%, 50% and 75% are referred to as low, moderate and high heterogeneity, respectively. The H2 is the phylogenetic
heritability, which is equivalent to Pagel’s λ (Pagel 1999; Hansen & Orzack 2005; Hadfield & Nakagawa 2010)
Trait category
I2[Article]
I2[Species]
I2[Phylogeny]
I2[Residual]
I2[Total]
H2
Genetic similarity
-
-
17.30
(0.68 to
47.31)
10.50
(0.68 to 27.72)
27.79
(5.51 to 56.38)
58.01
(13.09 to
97.95)
Body size
8.24
(0.66 to
22.06)
8.42
(0.48 to
22.98)
11.80
(0.70 to
33.60)
4.78
(0.51 to 11.91)
33.25
(13.12 to
56.69)
33.25
(16.04 to
72.83)
Secondary sexual
trait
11.08
(0.28 to
32.49)
7.16
(0.29 to
20.37)
7.86
(0.25 to
24.24)
8.64
(0.30 to 25.42)
34.74
(12.26 to
58.26)
22.60
(0.63 to 61.35)
Age
-
-
16.38
(0.47 to
47.17)
21.38
(0.65 to 49.57)
37.76
(8.93 to 66.11)
43.03
(1.99 to 92.61)
20
Figure S1. Heterozygosities in each cohort year based on the 13 microsatellite loci that we used for paternity analysis. In
each cohort year, we included only individuals born or first caught in that year, and excluded the known immigrants, to
estimate the heterozygosities. The numbers in parentheses, represent sample sizes in each cohort year. The means and
standard errors of the heterozygosities are presented. The solid line represents the observed heterozygosity values and
the dashed line represents the expected heterozygosity values.
21
Figure S2. The proportion of extra-pair offspring among all offspring (EPP %) per cohort in Lundy Island house sparrows.
The sample sizes (n) represent the total number of offspring with known social and genetic parents in each year.
22
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