ESM B: SUPPLEMENTARY TABLES S1-S7
General information for supplementary tables S1-S7
Tables S1-S7 give details of analyses of deviance for generalised linear mixed models to make stepwise backward model selection procedures traceable. P values
always refer to the increase in deviance when respective terms are removed from the more complex models as assessed by likelihood ratio tests. Significant fixed
effects terms remaining in the resulting minimal adequate models are denoted in bold. See methods for further details. AIC: Akaike Information Criterion.
1
Table S1. Analysis of deviance tables for stepwise backward regressions of recruit lifespan on paternity status (paternity), sex, cohort, brood period within which
the recruits hatched (hatch period) and their two-way interactions with paternity. ((a) n = 168 recruits originating from 116 broods with mixed paternity and (b)
n = 242 recruits from all 168 genotyped broods. Generalised linear mixed models with Poisson error structure and log-link function were fitted (for −1transformed values to meet Poisson assumptions) and included brood of origin as a random effect to account for the non-independency of data measured for
recruits originating from the same brood.)
(a)
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:sex
−paternity:hatch period
−hatch period
−paternity:cohort
−cohort
−paternity
−sex
157
158
159
160
162
164
165
166
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:sex
−paternity:hatch period
−hatch period
−paternity:cohort
−cohort
−paternity
−sex
231
232
233
234
236
238
239
240
change in
df
―
1
1
1
2
2
1
1
residual
deviance
241.1
242.0
242.8
243.2
246.2
246.6
247.1
249.4
deviance
change (2)
―
0.8901
0.8211
0.3434
3.0542
0.3476
0.5148
2.2417
p
AIC
―
0.3454
0.3649
0.5579
0.2172
0.8404
0.4731
0.1343
263.14
262.03
260.85
259.19
258.25
254.59
253.11
253.35
change in
df
―
1
1
1
2
2
1
1
residual
deviance
361.6
361.8
362.1
362.1
365.1
366.6
367.3
370.9
deviance
change (2)
―
0.2317
0.2495
0.0110
3.0344
1.4865
0.7142
3.5440
p
AIC
―
0.6302
0.6175
0.9163
0.2193
0.4756
0.3980
0.0598
383.60
381.83
380.08
378.09
377.12
374.61
373.33
374.87
(b)
2
Table S2. Analysis of deviance tables for stepwise backward regressions of recruit lifetime breeding dispersal (i.e. the sequence of breeding dispersal distances
measured for an individual over its lifetime) on paternity status (paternity), sex, cohort, brood period within which the recruits hatched (hatch period) and their
two-way interactions with paternity. ((a) n = 108 dispersal events of 62 recruits originating from 57 broods with mixed paternity and (b) n = 157 dispersal events
of 93 recruits from 87 genotyped broods. Generalised linear mixed models with Gamma error structure and log-link function were fitted for y + 0.4 m
transformed dispersal distances to fit assumptions of the Gamma distribution (i.e. no zero values for Gamma variables possible). Individual nested within brood
of origin was included as random effects to account for the non-independency of data measured for the same recruit and for recruits originating from the same
brood.)
(a)
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:sex
−sex
−paternity:cohort
−cohort
−paternity:hatch period
−paternity
−hatch period
51
52
53
55
57
58
59
60
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:hatch period
−hatch period
−paternity:cohort
−cohort
−paternity:sex
−sex
−paternity
82
83
84
86
88
89
90
91
change in
df
―
1
1
2
2
1
1
1
residual
deviance
297.8
298.3
298.8
301.8
304.3
305.8
305.8
306.3
deviance
change (2)
―
0.4641
0.4677
3.0751
2.4253
1.5621
0.0134
0.4535
p
AIC
―
0.4957
0.4940
0.2149
0.2974
0.2114
0.9077
0.5007
321.83
320.29
318.76
317.84
316.26
315.82
313.84
312.29
change in
df
―
1
1
2
2
1
1
1
residual
deviance
444.6
444.8
445.1
446.9
448.0
448.7
448.7
449.1
deviance
change (2)
―
0.2382
0.2759
1.7783
1.1812
0.6638
0.0340
0.3662
p
AIC
―
0.6255
0.5994
0.4110
0.5540
0.4152
0.8536
0.5451
468.57
466.81
465.09
462.87
460.05
458.71
456.75
455.11
(b)
3
Table S3. Analysis of deviance tables for stepwise backward regression of recruit latency to first reproduction on paternity status (paternity), sex, cohort, brood
period within which the recruits hatched (hatch period) and their two-way interactions with paternity. ((a) n = 168 recruits originating from 116 broods with
mixed paternity and (b) n = 242 recruits from all 168 genotyped broods. Generalised linear mixed models with Poisson error structure and log-link function were
fitted and included brood of origin as a random effect to account for the non-independency of data measured for recruits originating from the same brood.)
(a)
step
simplification
residual df
maximal model
1
2
3
4
5
6a
6b
―
−paternity:hatch period
−paternity: sex
−paternity:cohort
−hatch period
−paternity
−cohort
−sex
157
158
159
161
162
163
165
164
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:sex
−paternity:hatch period
−paternity:cohort
−hatch period
−paternity
−cohort
−sex
231
232
233
235
236
237
239
240
change in
df
―
1
1
2
1
1
2
1
residual
deviance
125.1
126.7
126.7
126.9
127.4
129.7
135.7
137.1
deviance
change (2)
―
1.5557
<0.001
0.2119
0.5012
2.3104
6.0130
7.3499
p
AIC
―
0.2123
0.9999
0.8995
0.4790
0.1285
0.0495
0.0067
147.12
146.68
144.68
140.89
139.39
139.70
141.71
145.05
change in
df
―
1
1
2
1
1
2
1
residual
deviance
209.1
209.1
209.2
210.3
210.9
211.7
214.7
229.3
deviance
change (2)
―
0.0000
0.0438
1.1650
0.5557
0.8368
3.0050
14.592
p
AIC
―
1
0.8342
0.5585
0.456
0.3603
0.2226
0.0001
231.12
229.12
227.16
224.33
222.88
221.72
220.73
233.32
(b)
4
Table S4. Analysis of deviance tables for stepwise backward regressions of recruits' lifetime number of broods on paternity status (paternity), sex, cohort, brood
period within which the recruits hatched (hatch period) and their two-way interactions with paternity. ((a) n = 87 female recruits originating from 75 broods with
mixed paternity, (b) n = 121 female recruits from 105 genotyped broods, (c) n = 81 male recruits from 62 broods with mixed paternity and (d) n = 121 male
recruits from 91 genotyped broods. Generalised linear mixed models with Poisson error structure and log-link function were fitted (for −1-transformed values to
meet Poisson assumptions) and included brood of origin as a random effect to account for the non-independency of data measured for recruits originating from
the same brood.)
(a)
step
simplification
residual df
maximal model
1
2
3
4
5
―
−paternity:cohort
−paternity:hatch period
−paternity
−hatch period
−cohort
78
80
81
82
83
85
step
simplification
residual df
maximal model
1
2
3
4
5
―
−paternity:cohort
−paternity:hatch period
−paternity
−hatch period
−cohort
112
114
115
116
117
119
change in
df
―
2
1
1
1
2
residual
deviance
140.6
141.5
142.5
142.5
142.7
145.8
deviance
change (2)
―
0.8785
1.0093
0.0031
0.2244
3.0295
p
AIC
―
0.6445
0.3151
0.9555
0.6357
0.2199
158.63
155.50
154.51
152.52
150.74
149.77
change in
df
―
2
1
1
1
2
residual
deviance
193.2
194.1
194.3
195.2
195.9
201.2
deviance
change (2)
―
0.8183
0.2687
0.8485
0.7145
5.2860
p
AIC
―
0.6642
0.6042
0.3570
0.3980
0.0711
211.24
208.06
206.33
205.18
203.89
205.18
(b)
5
(c)
step
simplification
residual df
maximal model
1
2
3
4
5
―
−paternity:hatch period
−paternity:cohort
−cohort
−hatch period
−paternity
72
73
75
77
78
79
step
simplification
residual df
maximal model
1
2
3
―
−paternity:hatch period
−hatch period
−paternity:cohort
112
113
114
116
change in
df
―
1
2
2
1
1
residual
deviance
95.5
97.8
101.7
103.9
106.2
112.3
deviance
change (2)
―
2.3190
3.9042
2.2399
2.3327
6.0660
p
AIC
―
0.1278
0.1420
0.3263
0.1267
0.0138
113.44
113.76
113.66
111.90
112.24
116.30
change in
df
―
1
1
2
residual
deviance
156.1
156.1
156.3
163.0
deviance
change (2)
―
0.0262
0.2018
6.6995
p
AIC
―
0.8713
0.6533
0.0351
174.09
172.12
170.32
173.02
(d)
6
Table S5. Analysis of deviance tables for stepwise backward regressions of recruits' lifetime number of hatchlings on paternity status (paternity), sex, cohort,
brood period within which the recruits hatched (hatch period) and their two-way interactions with paternity. ((a) n = 87 female recruits originating from 75
broods with mixed paternity, (b) n = 121 female recruits from 105 genotyped broods, (c) n = 81 male recruits from 62 broods with mixed paternity and (d)
n = 121 male recruits from 91 genotyped broods. Generalised linear mixed models with Poisson error structure and log-link function were fitted and included
brood of origin as a random effect to account for the non-independency of data measured for recruits originating from the same brood.)
(a)
step
simplification
residual df
maximal model
1
2
3
4
5
―
−paternity:cohort
−paternity:hatch period
−hatch period
−paternity
−cohort
78
80
81
82
83
85
step
simplification
residual df
maximal model
1
2
3
4
5
―
−paternity:cohort
−paternity:hatch period
−paternity
−hatch period
−cohort
112
114
115
116
117
119
change in
df
―
2
1
1
1
2
residual
deviance
323.3
324.1
324.6
324.6
325.0
326.4
deviance
change (2)
―
0.7866
0.4772
0.0026
0.3829
1.4029
p
AIC
―
0.6748
0.4897
0.9596
0.5361
0.4959
341.32
338.10
336.58
334.58
332.97
330.37
change in
df
―
2
1
1
1
2
residual
deviance
419.1
419.9
420.3
420.4
420.7
424.6
deviance
change (2)
―
0.8072
0.4614
0.0804
0.3141
3.9138
p
AIC
―
0.6679
0.4970
0.7767
0.5752
0.1413
437.07
433.87
432.34
430.42
428.73
428.64
(b)
7
(c)
step
simplification
residual df
maximal model
1
2
3
4
5
―
−paternity:hatch period
−paternity:cohort
−hatch period
−cohort
−paternity
72
73
75
76
78
79
step
simplification
residual df
maximal model
1
2
3
4
5
―
−paternity:hatch period
−hatch period
−paternity:cohort
−cohort
−paternity
112
113
114
116
118
119
change in
df
―
1
2
1
2
1
residual
deviance
190.7
190.8
193.7
195.4
199.6
207.1
deviance
change (2)
―
0.0896
2.8554
1.7722
4.1442
7.4975
p
AIC
―
0.7647
0.2399
0.1831
0.1259
0.0062
208.71
206.80
205.66
205.43
205.57
211.07
change in
df
―
1
1
2
2
1
residual
deviance
291.0
291.4
291.5
297.5
301.9
311.1
deviance
change (2)
―
0.3886
0.1030
5.9431
4.4294
5.1578
p
AIC
―
0.5330
0.7483
0.0512
0.1092
0.0231
309.04
307.43
305.53
307.47
307.90
311.06
(d)
8
Table S6. Analysis of deviance tables for stepwise backward regressions of male recruits' paternity loss (proportion extra-pair offspring per brood) on paternity
status (paternity), sex, cohort, brood period within which the recruits hatched (hatch period), year and brood period when the respective broods were attended as
well as selected two-way interactions with paternity. ((a) n = 74 broods of 57 male recruits from 44 broods with mixed paternity and (b) n = 117 broods of 89
male recruits from 68 genotyped broods. Generalised linear mixed models with binomial error structure and logit-link function were fitted. Individual nested
within brood of origin was included as random effects to account for the non-independency of data measured for the same recruit and for recruits originating from
the same brood.)
(a)
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:cohort
−brood period
−paternity:hatch period
−hatch period
−paternity
−cohort
−year
64
65
66
67
68
69
70
71
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−brood period
−paternity:hatch period
−paternity:cohort
−paternity
−cohort
−hatch period
−year
107
108
109
110
112
112
113
114
change in
df
―
1
1
1
1
1
1
1
residual
deviance
164.0
164.0
164.0
164.8
165.0
165.3
166.5
171.1
deviance
change (2)
―
<0.001
0.0256
0.7387
0.2557
0.2414
1.2258
4.6434
p
AIC
―
1.0
0.8730
0.3901
0.6131
0.6232
0.2682
0.0312
184.01
182.01
180.04
178.78
177.03
175.27
174.50
177.14
change in
df
―
1
1
1
1
1
1
1
residual
deviance
270.3
270.3
270.5
271.0
271.2
271.9
273.2
275.3
deviance
change (2)
―
0.0391
0.1533
0.5010
0.1886
0.7630
1.3012
2.094
p
AIC
―
0.8433
0.6954
0.4790
0.6641
0.3824
0.2540
0.1479
290.28
288.32
286.47
284.97
283.16
281.93
281.23
281.32
(b)
9
Table S7. Analysis of deviance tables for stepwise backward regressions of male recruits' fertilisation success within the pair bond (number of within-pair
offspring sired per brood) on paternity status (paternity), sex, cohort, brood period within which the recruits hatched (hatch period), year and brood period when
the respective broods were attended as well as selected two-way interactions with paternity. ((a) n = 74 broods of 57 male recruits from 44 broods with mixed
paternity and (b) n = 117 broods of 89 male recruits from 68 genotyped broods. Generalised linear mixed models with Poisson error structure and log-link
function were fitted. Individual nested within brood of origin was included as random effects to account for the non-independency of data measured for the same
recruit and for recruits originating from the same brood.)
(a)
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:period
−year
−brood period
−paternity:cohort
−paternity
−cohort
−period
64
65
66
67
68
69
70
71
step
simplification
residual df
maximal model
1
2
3
4
5
6
7
―
−paternity:cohort
−paternity:period
−paternity
−period
−cohort
−year
−brood period
107
108
109
110
112
112
113
114
change in
df
―
1
1
1
1
1
1
1
residual
deviance
95.97
95.98
96.03
96.10
96.47
96.58
97.68
100.4
deviance
change (2)
―
0.0099
0.0571
0.0726
0.3621
0.1169
1.0938
2.7298
p
AIC
―
0.9206
0.8112
0.7875
0.5473
0.7324
0.2956
0.0985
115.96
113.97
112.03
110.10
108.46
106.58
105.67
106.40
change in
df
―
1
1
1
1
1
1
1
residual
deviance
146.2
146.3
146.6
147.3
148.5
150.1
151.2
155.2
deviance
change (2)
―
0.0243
0.3903
0.6505
1.2356
1.6136
1.0175
4.0085
p
AIC
―
0.8760
0.5321
0.4199
0.2663
0.2040
0.3131
0.0453
166.22
164.25
162.64
161.29
160.52
160.14
159.16
161.16
(b)
10