Supplementary material
I.
Methods
II. Tables S1 and S2
III. Figure S1 legend
Methods
Reproductive success and genetic sampling
Reproductive success is ideally measured as the number of offspring which an
individual contributes to the next generation (Charlesworth 1994). In lekking species and
those with similar non-resource-based mating systems, males’ contributions to offspring
rearing ends after copulation, and so the number of copulations (Gibson & Bradbury
1985; Höglund & Alatalo 1995; Reynolds et al. 2007) or number of offspring sired
(DuVal & Kempenaers 2008; Semple et al. 2001) are frequently used as proxies for
reproductive success. Note that this approach necessarily neglects possible effects of
mate quality or influences of stochastic processes (e.g. nest predation) on realized genetic
representation in the next generation.
Nests were located by systematic and continuous search of the undergrowth, and
monitored every other day until chicks fledged, or the nest was depredated. Clutches
consist of a maximum of two eggs and males provide no paternal care. Chicks were
banded and a blood sample was collected before fledging, and the mother’s identity was
determined by direct observation of the bands of the female feeding nestlings. Genetic
samples from chicks that did not survive are also included in analyses. Starting in 2005,
one egg from each nest with an identified female attending it was placed in an incubator
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(Lyons Turn-X) and maintained at 98-100 degrees F and ca. 70% humidity until
hatching. If the egg remaining in the nest was depredated, incubated eggs were sacrificed
before hatching and embryonic tissue preserved in ethanol for genetic testing [25]. If
chicks died before the mother was identified, parentage was determined using parental
pair assessment in CERVUS 3.0 (below). When nests survived until hatching, incubatorhatched chicks were genetically sampled and returned to their nests within three daylight
hours.
Genetic techniques and paternity assignment criteria
Blood was preserved in lysis buffer (0.01 M Tris, 0.01 M NaCl, 0.01 M NaEDTA, 1% n-Lauroylsarcosine; adjusted to pH 8.0), and DNA extracted using DNeasy
Blood and Tissue kits (QIAGEN). Alleles were amplified by PCR from twenty
microsatellite loci, described elsewhere (DuVal and Nutt 2005; DuVal 2007a; DuVal et
al. 2007). Allele sizes were scored in the program Genemapper (Applied Biosystems),
and genotypes analyzed in the maximum likelihood program CERVUS 3.0 to identify
paternity (Marshall et al. 1998; Kalinowski et al. 2007). These loci had a combined
second-parent non-exclusion probability of 0.000014 in the study population.
Candidate fathers were all adult-plumaged males present in each year of the
study. Because of the large number of potential sires, chicks were only assigned to a sire
if they matched that sire with 95% or higher confidence, and perfectly matched no more
than one sire at all loci. Chicks sometimes matched several possible sires when paternity
was analyzed without maternal information (e.g. when nests of incubated eggs failed
before hatching). These chicks were nevertheless assigned paternity if they matched one
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male with high (95%) confidence. Tests of this approach revealed it to be a reliable
indicator of paternity, though lack of maternal information decreased assignment success
(DuVal and Kempenaers 2008). Assignment confidence represents the difference in loglikelihood scores of the two most likely candidate fathers, based on 10,000 simulation
cycles given the number of candidates in each year and locus-specific population allele
frequencies.
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Supplementary tables
Table S1. The full set of generalized linear mixed models considered when assessing the
effects of identified life history variables on annual reproductive success of alpha males.
Model
Rank
1
2
3†
4
5†
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
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Model
-logLik
k
AICc
ΔAICc
wi
I+A+A2+F
T+A+A2
A+A2+F+I+T
A*T+F
A+A2+T+I†
A*T
A*T+I+F
T+I+F
A*I+A*F+A2+T
T+I
T+F
I+F
A+T+F
T*F
T
A+T
A+F+F
T+A2
A+I
A*I
A+A2
A*F
A
A+F
I
I*F
F
-104.89
-106.58
-104.38
-105.91
-106.22
-107.62
-105.87
-108.19
-104.08
-110.88
-111.15
-111.15
-110.99
-111.15
-113.87
-113.65
-112.56
-113.83
-114.14
-113.89
-116.14
-117.2
-119.89
-118.83
-121.18
-119.769
-141.011
6
5
7
6
6
5
7
5
9
4
4
4
5
5
3
4
5
4
4
5
4
5
3
4
3
5
3
222.67
223.79
223.94
224.71
225.32
225.87
226.93
227.00
228.12
230.18
230.71
230.72
232.61
232.93
233.98
235.71
235.74
236.07
236.69
238.39
240.68
245.03
246.02
246.07
248.60
250.16
288.27
0
1.12
1.27
2.05
2.67
3.20
4.27
4.34
5.45
7.51
8.05
8.05
9.94
10.27
11.32
13.05
13.08
13.41
14.03
15.73
18.02
22.36
23.36
23.41
25.94
27.50
65.60
0.40†
0.23
--- †
0.14
--- †
0.08
0.05
0.05
0.03
0.009
0.007
0.007
0.003
0.002
0.001
0.001
0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
Generalized linear mixed models assessed the effect on annual reproductive success of
tenure as an alpha male (T), individual age (A), the quadratic term for age (A2), whether a
male was in his initial year of alpha status (I), and whether a male was in his final year as
alpha (F). All models considered individual identity as a random effect, interactions are
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indicated with an asterisk, and the global model is designated in bold (model 9).
Following notation in the program R, an interaction term also denotes inclusion of the
component variables as individual fixed effects. AICc is the Akaike’s Information
Criterion with small sample size correction, calculated from the negative log likelihood
of the model (-logLik) and k, where k is the number of parameters with one parameter
included for random effects. AICc weights (wi ) are an indicator of the relative support
for the model in the set of models considered.
†
Models 3 and 5 were excluded from the
calculation of wi values because their similarity in log likelihood values to models 1 and
2, respectively, from which they differ by only one parameter, suggests that these model
should not be treated as competitive (Anderson and Burnham 2002). In each of these
cases, the model with the lowest number of parameters was retained as a candidate model
under consideration.
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Table S2. Parameter estimates from the generalized linear mixed model receiving
comparable support to the model designated as “best fit”.
Model predictors
Estimates +
Z
p
S.E.
Mean
95% confidence
estimate
interval from bootstrap
from
lower
upper
bootstrap
Intercept
-5.88 + 1.60
-3.67
0. 0002
-8.09
-13.94
-3.74
Year of alpha
0.48 + 0.11
4.45
<0.0001
0.57
0.30
0.98
Age
1.29 + 0.35
-2.27
0.0003
1.76
0.84
3.03
Age2
-0.07 + 0.02
-3.69
0. 0002
-0.10
-0.18
-0.05
tenure
This model differed from the best fit model only in its exclusion of the binary term
indicating final year of alpha status, and parameter estimates were similar to those in the
best fit model. Individual identity was included as a random effect in this model, and
data were 102 observations on 43 individuals. Bootstrapped 95% confidence intervals
for the fixed effects were generated by sampling 10,000 times with replacement to create
datasets of 43 individuals’ reproductive histories as alpha, including all sampled years for
each selected individual.
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Supplementary figure legend
Figure S1. Annual reproductive success (ARS) predicted for males of different age
given their current year of alpha tenure. Model predictions were determined from the
best-fit model explaining ARS as a function of year of alpha tenure, individual age, the
quadratic effect of age, and final year of alpha status to ARS (Table 3). Solid black lines
represent the means of bootstrapped parameter estimates, grey lines are mean estimates
from the original model, and dashed lines indicate the 95% confidence limits from
bootstrapped model estimates. Effects of the binary variable final year as alpha received
weak support in the final model and are not shown graphically.
References for supplementary material
Anderson, D. R., and K. P. Burnham. 2002. Avoiding pitfalls when using
information-theoretic methods. The Journal of Wildlife Management 66:912-918.
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