Supplementary file 1 for “Experimental evidence that group size drives divergent benefits of cooperative breeding for male and female ostriches”

 

Julian Melgar1, Mads F. Schou1, Maud Bonato2, Zanell Brand3, Anel Engelbrecht3, Schalk Cloete4,3 & Charlie K. Cornwallis1

 

1 Department of Biology, Lund University, Lund, Sweden
2 Kynsna Elephant Park, Kynsna, South Africa
3 Directorate Animal Sciences, Western Cape Department of Agriculture, Elsenburg, South Africa
4 Department of Animal Sciences, University of Stellenbosch, Matieland, South Africa

 

*Corresponding authors:
Email: ,

This file includes Tables S1-S19

Supplementary Tables

A: The composition of breedinng groups of adults observed in the karoo national park

Year Date Group_size Females Males male_female Sex_ratio (M:F)
1 2018 17-Nov 3 2 1 1:2 2.0
2 2018 17-Nov 5 3 2 2:3 1.5
5 2018 17-Nov 8 3 5 5:3 0.6
7 2018 18-Nov 3 2 1 1:2 2.0
8 2018 18-Nov 11 6 5 5:6 1.2
9 2018 18-Nov 3 2 1 1:2 2.0
10 2018 18-Nov 3 1 2 2:1 0.5
17 2018 18-Nov 3 1 2 2:1 0.5
19 2018 18-Nov 2 1 1 1:1 1.0
20 2018 18-Nov 3 2 1 1:2 2.0
21 2018 18-Nov 5 1 4 4:1 0.2
22 2018 18-Nov 6 4 2 2:4 2.0
24 2018 18-Nov 4 2 2 2:2 1.0
25 2018 18-Nov 6 4 2 2:4 2.0
26 2018 18-Nov 4 3 1 1:3 3.0
27 2018 18-Nov 3 2 1 1:2 2.0
29 2018 18-Nov 6 3 3 3:3 1.0
30 2018 18-Nov 7 4 3 3:4 1.3
34 2018 19-Nov 5 2 3 3:2 0.7
39 2018 19-Nov 3 1 2 2:1 0.5
43 2018 19-Nov 2 1 1 1:1 1.0
45 2018 19-Nov 4 2 2 2:2 1.0
47 2018 19-Nov 3 2 1 1:2 2.0
49 2018 19-Nov 2 1 1 1:1 1.0
50 2018 19-Nov 3 1 2 2:1 0.5
51 2018 19-Nov 6 2 4 4:2 0.5
52 2018 19-Nov 17 5 12 12:5 0.4
53 2018 19-Nov 4 2 3 3:2 0.7
54 2018 19-Nov 18 12 6 6:12 2.0
55 2018 19-Nov 11 9 2 2:9 4.5
57 2018 19-Nov 8 6 2 2:6 3.0
58 2018 19-Nov 6 4 2 2:4 2.0
60 2018 19-Nov 5 3 2 2:3 1.5
61 2018 19-Nov 2 1 1 1:1 1.0
62 2018 19-Nov 4 1 3 3:1 0.3
64 2018 19-Nov 2 1 1 1:1 1.0
65 2018 19-Nov 2 1 1 1:1 1.0
66 2018 19-Nov 4 1 3 3:1 0.3
67 2014 08-Nov 2 1 1 1:1 1.0
68 2014 08-Nov 2 1 1 1:1 1.0
69 2014 08-Nov 2 1 1 1:1 1.0
72 2014 08-Nov 6 3 3 3:3 1.0
73 2014 08-Nov 6 1 5 5:1 0.2
74 2014 08-Nov 5 3 2 2:3 1.5
76 2014 08-Nov 2 1 1 1:1 1.0
78 2014 08-Nov 5 1 4 4:1 0.2
79 2014 08-Nov 4 2 2 2:2 1.0
80 2014 08-Nov 4 1 3 3:1 0.3
81 2014 08-Nov 6 3 3 3:3 1.0
82 2014 08-Nov 3 2 1 1:2 2.0
84 2014 08-Nov 15 12 3 3:12 4.0
85 2014 08-Nov 12 9 3 3:9 3.0
86 2014 08-Nov 2 1 1 1:1 1.0
87 2014 08-Nov 8 4 4 4:4 1.0
88 2014 08-Nov 2 1 1 1:1 1.0
89 2014 08-Nov 4 3 1 1:3 3.0
90 2014 08-Nov 3 1 2 2:1 0.5
94 2014 08-Nov 2 1 1 1:1 1.0
95 2014 09-Nov 2 1 1 1:1 1.0
96 2014 09-Nov 6 4 2 2:4 2.0
101 2014 09-Nov 4 2 2 2:2 1.0
103 2014 09-Nov 6 4 2 2:4 2.0
106 2014 09-Nov 2 1 1 1:1 1.0
107 2014 09-Nov 2 1 1 1:1 1.0
108 2014 09-Nov 7 1 6 6:1 0.2

B: Group size effects on the number of eggs produced by males

Fixed Effects Posterior Mode (CI) pMCMC
No_care : Nmales_3 0.46 (0.13, 0.65)
No_care : Nmales_1 1.65 (1.32, 1.84)
Care : Nmales_3 0.11 (-0.17, 0.38)
Care : Nmales_1 1.05 (0.81, 1.39)
No_care : Nfemales 0.55 (0.38, 0.73) 0.001
Care : Nfemales 0.38 (0.24, 0.54) 0.001
No_care : Nfemales^2 -0.21 (-0.37, -0.03) 0.012
Care : Nfemales^2 0.11 (-0.06, 0.26) 0.252
No_care : Nfemales : Nmales_3 0.5 (0.28, 0.83) 0.001
No_care : Nfemales : Nmales_1 0.56 (0.32, 0.79) 0.001
Care : Nfemales : Nmales_3 0.34 (0.13, 0.55) 0.002
Care : Nfemales : Nmales_1 0.38 (0.22, 0.66) 0.001
No_care : Nfemales^2 : Nmales_3 -0.19 (-0.46, 0.05) 0.14
No_care : Nfemales^2 : Nmales_1 -0.25 (-0.45, -0.01) 0.03
Care : Nfemales^2 : Nmales_3 0 (-0.18, 0.28) 0.654
Care : Nfemales^2 : Nmales_1 0.16 (-0.1, 0.37) 0.29
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Nmales_3 vs No_care : Nmales_1 -1.14 (-1.49, -0.96) 0.001
Care : Nmales_3 vs Care : Nmales_1 -1 (-1.24, -0.67) 0.001
No_care : Nfemales vs Care : Nfemales 0.14 (-0.04, 0.41) 0.146
No_care : Nfemales^2 vs Care : Nfemales^2 -0.28 (-0.5, -0.07) 0.004
No_care : Nfemales : Nmales_3 vs No_care : Nfemales : Nmales_1 -0.03 (-0.38, 0.33) 0.918
No_care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_3 0.14 (-0.14, 0.54) 0.248
No_care : Nfemales : Nmales_1 vs Care : Nfemales : Nmales_1 0.17 (-0.18, 0.44) 0.414
Care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_1 -0.02 (-0.38, 0.22) 0.566
No_care : Nfemales^2 : Nmales_3 vs No_care : Nfemales^2 : Nmales_1 0.03 (-0.27, 0.38) 0.736
No_care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_3 -0.23 (-0.56, 0.12) 0.172
No_care : Nfemales^2 : Nmales_1 vs Care : Nfemales^2 : Nmales_1 -0.25 (-0.68, -0.07) 0.018
Care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_1 -0.12 (-0.41, 0.22) 0.66
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.05) 41.69 (2.34, 90.34)
Camp 0 (0, 0.02) 33.85 (0.36, 79.74)
Residual 0 (0, 0.01) 24.45 (0.58, 68.73)

C: Group size effects on the number of eggs produced by females

Fixed Effects Posterior Mode (CI) pMCMC
No_care : Nmales_3 1.56 (1.41, 1.73)
No_care : Nmales_1 1.62 (1.4, 1.83)
Care : Nmales_3 1.3 (1.13, 1.48)
Care : Nmales_1 1.21 (0.94, 1.4)
No_care : Nfemales -0.08 (-0.18, 0) 0.03
Care : Nfemales -0.2 (-0.28, -0.11) 0.001
No_care : Nfemales^2 0.01 (-0.1, 0.09) 0.898
Care : Nfemales^2 0.22 (0.12, 0.32) 0.001
No_care : Nfemales : Nmales_3 -0.12 (-0.22, 0.01) 0.088
No_care : Nfemales : Nmales_1 -0.08 (-0.25, 0.07) 0.308
Care : Nfemales : Nmales_3 -0.2 (-0.31, -0.1) 0.002
Care : Nfemales : Nmales_1 -0.19 (-0.34, -0.05) 0.012
No_care : Nfemales^2 : Nmales_3 0.01 (-0.09, 0.13) 0.798
No_care : Nfemales^2 : Nmales_1 -0.12 (-0.22, 0.11) 0.492
Care : Nfemales^2 : Nmales_3 0.2 (0.08, 0.3) 0.001
Care : Nfemales^2 : Nmales_1 0.26 (0.1, 0.49) 0.002
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Nmales_3 vs No_care : Nmales_1 -0.07 (-0.25, 0.16) 0.686
Care : Nmales_3 vs Care : Nmales_1 0.13 (-0.11, 0.31) 0.306
No_care : Nfemales vs Care : Nfemales 0.1 (-0.03, 0.21) 0.112
No_care : Nfemales^2 vs Care : Nfemales^2 -0.22 (-0.36, -0.1) 0.001
No_care : Nfemales : Nmales_3 vs No_care : Nfemales : Nmales_1 -0.04 (-0.21, 0.17) 0.822
No_care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_3 0.13 (-0.03, 0.25) 0.172
No_care : Nfemales : Nmales_1 vs Care : Nfemales : Nmales_1 0.11 (-0.1, 0.3) 0.318
Care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_1 0.02 (-0.19, 0.17) 0.844
No_care : Nfemales^2 : Nmales_3 vs No_care : Nfemales^2 : Nmales_1 0.02 (-0.13, 0.28) 0.45
No_care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_3 -0.18 (-0.34, -0.02) 0.03
No_care : Nfemales^2 : Nmales_1 vs Care : Nfemales^2 : Nmales_1 -0.34 (-0.61, -0.11) 0.006
Care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_1 -0.13 (-0.33, 0.13) 0.328
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.02) 33.91 (1.59, 79.02)
Camp 0 (0, 0.02) 40.26 (2.27, 81.64)
Residual 0 (0, 0.01) 25.83 (1.07, 65.2)

D: Group size effects on the number of chicks produced by males

Fixed Effects Posterior Mode (CI) pMCMC
No_care : Nmales_3 -0.12 (-0.58, 0.22)
No_care : Nmales_1 1.08 (0.69, 1.52)
Care : Nmales_3 -0.95 (-1.45, -0.43)
Care : Nmales_1 -0.18 (-0.79, 0.33)
No_care : Nfemales 0.54 (0.26, 0.79) 0.001
Care : Nfemales 0.64 (0.34, 1.14) 0.001
No_care : Nfemales^2 -0.32 (-0.51, -0.04) 0.026
Care : Nfemales^2 -0.14 (-0.49, 0.21) 0.462
No_care : Nfemales : Nmales_3 0.68 (0.22, 1.02) 0.001
No_care : Nfemales : Nmales_1 0.47 (0.17, 0.86) 0.004
Care : Nfemales : Nmales_3 0.52 (0.11, 0.9) 0.006
Care : Nfemales : Nmales_1 2.23 (0.72, 4.49) 0.001
No_care : Nfemales^2 : Nmales_3 -0.34 (-0.63, 0.09) 0.148
No_care : Nfemales^2 : Nmales_1 -0.41 (-0.6, 0.01) 0.022
Care : Nfemales^2 : Nmales_3 0.19 (-0.32, 0.52) 0.542
Care : Nfemales^2 : Nmales_1 -1.58 (-2.91, -0.33) 0.004
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Nmales_3 vs No_care : Nmales_1 -1.24 (-1.7, -0.86) 0.001
Care : Nmales_3 vs Care : Nmales_1 -0.53 (-1.13, -0.06) 0.016
No_care : Nfemales vs Care : Nfemales -0.19 (-0.7, 0.18) 0.352
No_care : Nfemales^2 vs Care : Nfemales^2 -0.18 (-0.56, 0.24) 0.448
No_care : Nfemales : Nmales_3 vs No_care : Nfemales : Nmales_1 0.16 (-0.36, 0.65) 0.608
No_care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_3 0.04 (-0.39, 0.63) 0.686
No_care : Nfemales : Nmales_1 vs Care : Nfemales : Nmales_1 -1.74 (-4.1, -0.22) 0.008
Care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_1 -2.12 (-4.05, -0.12) 0.008
No_care : Nfemales^2 : Nmales_3 vs No_care : Nfemales^2 : Nmales_1 0.2 (-0.4, 0.51) 0.802
No_care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_3 -0.24 (-0.95, 0.1) 0.122
No_care : Nfemales^2 : Nmales_1 vs Care : Nfemales^2 : Nmales_1 0.93 (-0.15, 2.46) 0.058
Care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_1 1.4 (0.24, 2.95) 0.008
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.08) 9.35 (0.07, 32.26)
Camp 0.13 (0, 0.34) 60.03 (13.92, 99.13)
Residual 0 (0, 0.26) 30.62 (0.1, 79.01)

E: Group size effects on the number of chicks produced by females

Fixed Effects Posterior Mode (CI) pMCMC
No_care : Nmales_3 1.06 (0.74, 1.39)
No_care : Nmales_1 1.05 (0.69, 1.5)
Care : Nmales_3 0.26 (-0.17, 0.61)
Care : Nmales_1 -0.47 (-0.94, 0.08)
No_care : Nfemales -0.1 (-0.28, 0.04) 0.13
Care : Nfemales 0.02 (-0.18, 0.21) 0.942
No_care : Nfemales^2 -0.01 (-0.13, 0.19) 0.84
Care : Nfemales^2 0.16 (-0.01, 0.41) 0.06
No_care : Nfemales : Nmales_3 -0.07 (-0.28, 0.08) 0.3
No_care : Nfemales : Nmales_1 -0.13 (-0.45, 0.1) 0.21
Care : Nfemales : Nmales_3 -0.12 (-0.29, 0.11) 0.394
Care : Nfemales : Nmales_1 0.55 (0.04, 1.74) 0.008
No_care : Nfemales^2 : Nmales_3 0.06 (-0.09, 0.28) 0.4
No_care : Nfemales^2 : Nmales_1 -0.16 (-0.41, 0.14) 0.456
Care : Nfemales^2 : Nmales_3 0.34 (0.08, 0.53) 0.014
Care : Nfemales^2 : Nmales_1 -0.57 (-1.34, 0.03) 0.04
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Nmales_3 vs No_care : Nmales_1 -0.1 (-0.39, 0.35) 0.856
Care : Nmales_3 vs Care : Nmales_1 0.65 (0.18, 1.11) 0.008
No_care : Nfemales vs Care : Nfemales -0.13 (-0.37, 0.09) 0.246
No_care : Nfemales^2 vs Care : Nfemales^2 -0.09 (-0.41, 0.08) 0.178
No_care : Nfemales : Nmales_3 vs No_care : Nfemales : Nmales_1 0.05 (-0.25, 0.37) 0.712
No_care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_3 0.01 (-0.25, 0.26) 0.966
No_care : Nfemales : Nmales_1 vs Care : Nfemales : Nmales_1 -1.08 (-2.03, -0.25) 0.001
Care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_1 -0.81 (-1.9, -0.13) 0.006
No_care : Nfemales^2 : Nmales_3 vs No_care : Nfemales^2 : Nmales_1 0.27 (-0.14, 0.49) 0.258
No_care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_3 -0.23 (-0.5, 0.05) 0.118
No_care : Nfemales^2 : Nmales_1 vs Care : Nfemales^2 : Nmales_1 0.55 (-0.19, 1.28) 0.15
Care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_1 1.01 (0.2, 1.68) 0.004
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.06) 3.75 (0.05, 15.39)
Camp 0.12 (0.02, 0.31) 35.93 (7.11, 63.09)
Residual 0.2 (0.07, 0.39) 60.32 (30.63, 87.5)

F: Group size effects on the time nests were incubated

Fixed Effects Posterior Mode (CI) pMCMC
Nmales_3 0.35 (-0.51, 1.03)
Nmales_1 -1.24 (-1.91, 0.13)
Number nests 0.23 (-0.15, 0.62) 0.19
Nfemales 0.94 (0.56, 1.34) 0.001
Nfemales^2 -0.26 (-0.8, 0.06) 0.092
Nmales_3 : Nfemales 0.78 (0.32, 1.11) 0.001
Nmales_1 : Nfemales 1.56 (1.02, 2.28) 0.001
Nmales_3 : Nfemales^2 -0.09 (-0.54, 0.36) 0.64
Nmales_1 : Nfemales^2 -0.78 (-1.64, -0.26) 0.014
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
Nmales_3 vs Nmales_1 1.27 (0.29, 2.06) 0.006
Nmales_3 : Nfemales vs Nmales_1 : Nfemales -0.94 (-1.67, -0.14) 0.024
Nmales_3 : Nfemales^2 vs Nmales_1 : Nfemales^2 0.62 (-0.01, 1.59) 0.04
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0.01 (0, 1.71) 5.99 (0.01, 21.46)
Camp 0.01 (0, 0.64) 2.2 (0, 9.06)
Residual 2.82 (1.98, 3.89) 42.69 (29.12, 54.01)

G: The effect of nest incubation on hatching success

Fixed Effects Posterior Mode (CI) pMCMC
Nmales_3 -2.31 (-3.12, -1.53)
Nmales_1 -2.75 (-3.66, -1.44)
Nest incubation (% time) 0.35 (0.03, 0.7) 0.034
Time monitored (days Z) 0.02 (-0.53, 0.61) 0.994
Nnests 0.12 (-0.3, 0.46) 0.696
Nfemales 0.01 (-0.36, 0.58) 0.622
Nfemales^2 -0.07 (-0.45, 0.52) 0.956
Nmales_3 : Nfemales -0.1 (-0.45, 0.55) 0.88
Nmales_1 : Nfemales 1.21 (-0.11, 2.27) 0.064
Nmales_3 : Nfemales^2 0.27 (-0.23, 0.76) 0.27
Nmales_1 : Nfemales^2 -1.07 (-2.13, -0.03) 0.052
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0.01 (0, 1.08) 3.74 (0, 16.53)
Camp 0 (0, 1.21) 5.44 (0.01, 18.05)
Residual 1.91 (1, 3.36) 34.41 (20, 50.56)

H: Group size effects on the amount of time males spent incubating

Fixed Effects Posterior Mode (CI) pMCMC
Nmales_3 -7.67 (-8.83, -6.03)
Nmales_1 -4.6 (-6.77, -2.1)
Nfemales 0.09 (-0.62, 1.05) 0.57
Nfemales^2 -0.34 (-1.09, 0.46) 0.502
Nmales_3 : Nfemales -0.22 (-0.96, 0.9) 0.918
Nmales_1 : Nfemales 1.97 (-0.35, 3.81) 0.102
Nmales_3 : Nfemales^2 -0.37 (-1.06, 0.63) 0.618
Nmales_1 : Nfemales^2 -1.28 (-3.16, 1.05) 0.33
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
Nmales_3 vs Nmales_1 -3.07 (-5.28, -0.76) 0.004
Nmales_3 : Nfemales vs Nmales_1 : Nfemales -2.04 (-3.92, 0.57) 0.126
Nmales_3 : Nfemales^2 vs Nmales_1 : Nfemales^2 1.26 (-1.5, 2.95) 0.5
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 1.04) 0.58 (0, 3.04)
Camp 0 (0, 0.83) 0.5 (0, 2.41)
Group 0 (0, 0.83) 0.5 (0, 2.41)
ID 0.02 (0, 6.07) 3.72 (0, 16.93)
Residual 27.56 (19.9, 39.7) 85.15 (71.44, 93.11)

I: Group size effects on the amount of time females spent incubating

Fixed Effects Posterior Mode (CI) pMCMC
Nmales_3 -4.06 (-4.96, -3.06)
Nmales_1 -4.64 (-6.1, -3.66)
Nfemales -0.3 (-0.77, 0.18) 0.212
Nfemales^2 -0.14 (-0.68, 0.44) 0.776
Nmales_3 : Nfemales -0.46 (-1.03, 0.01) 0.07
Nmales_1 : Nfemales 0.15 (-0.69, 1.05) 0.634
Nmales_3 : Nfemales^2 0.24 (-0.48, 0.7) 0.732
Nmales_1 : Nfemales^2 -0.38 (-1.53, 0.34) 0.22
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
Nmales_3 vs Nmales_1 1.02 (-0.04, 1.85) 0.04
Nmales_3 : Nfemales vs Nmales_1 : Nfemales -0.8 (-1.66, 0.17) 0.134
Nmales_3 : Nfemales^2 vs Nmales_1 : Nfemales^2 0.61 (-0.33, 1.67) 0.174
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0.06 (0, 1.77) 2.73 (0, 10.55)
Camp 0.01 (0, 1.88) 3.45 (0, 11.1)
Group 0.01 (0, 1.45) 2.08 (0, 8.81)
ID 2.86 (0.86, 5.26) 17.31 (5.33, 30.28)
Residual 8.51 (6.28, 11.07) 53.74 (39.69, 67.38)

J: Group size effects on the interruptions to incubation

Fixed Effects Posterior Mode (CI) pMCMC
Nmales_3 1.59 (0.78, 2.4)
Nmales_1 -0.14 (-1, 1.25)
Nfemales 0.52 (-0.06, 0.95) 0.06
Nfemales^2 -0.67 (-1.13, -0.16) 0.018
Nmales_3 : Nfemales 0.44 (-0.11, 0.88) 0.15
Nmales_1 : Nfemales 1.71 (-0.03, 5.47) 0.034
Nmales_3 : Nfemales^2 -0.55 (-1.1, 0) 0.03
Nmales_1 : Nfemales^2 -1.3 (-4.47, 0.17) 0.048
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
Nmales_3 vs Nmales_1 1.5 (0.5, 2.73) 0.002
Nmales_3 : Nfemales vs Nmales_1 : Nfemales -1.64 (-5.13, 0.5) 0.106
Nmales_3 : Nfemales^2 vs Nmales_1 : Nfemales^2 1.23 (-0.55, 4.09) 0.224
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0.01 (0, 0.78) 4.73 (0.01, 19.29)
Camp 0.01 (0, 1.01) 5.81 (0.01, 25.69)
Residual 2.89 (1.72, 4.97) 89.47 (63.25, 99.95)

K: The effect of the disparity in incubation on the number of interruptions

Fixed Effects Posterior Mode (CI) pMCMC
Nmales_3 : Difference in incubation -1.43 (-2.36, -0.26) 0.024
Nmales_1 : Difference in incubation 0.18 (-1.4, 1.33) 0.994
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0.01 (0, 1.8) 9.75 (0.01, 32.67)
Camp 0.01 (0, 3.03) 25.1 (0.01, 52.24)
Residual 2.13 (1.29, 4.88) 65.15 (32.8, 99.84)

L: The effect of the disparity in incubation between males and females on % of eggs broken

Fixed Effects Posterior Mode (CI) pMCMC
Nmales_3 : Difference in incubation -0.64 (-1.23, -0.06) 0.026
Nmales_1 : Difference in incubation 0 (-0.73, 0.67) 0.936
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.57) 3.94 (0.01, 11.73)
Camp 0.01 (0, 0.39) 2.6 (0.01, 8.48)
Residual 0.87 (0.51, 1.39) 20.19 (12.04, 28.72)

M: The effect of the % of eggs broken on hatching success

Fixed Effects Posterior Mode (CI) pMCMC
Intercept -2.49 (-2.86, -2.02)
Broken eggs (%) -0.82 (-1.2, -0.58) 0.001
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.26) 1.21 (0.01, 5.46)
Camp 0.01 (0, 0.49) 2.9 (0, 10.15)
Residual 0.85 (0.53, 1.76) 24.05 (12.96, 34.28)

N: Group size effects on the number of eggs produced by groups

Fixed Effects Posterior Mode (CI) pMCMC
No_care : Nmales_3 4.45 (3.76, 4.85)
No_care : Nmales_1 4.79 (4.13, 5.51)
Care : Nmales_3 3.23 (2.62, 3.74)
Care : Nmales_1 2.93 (2.05, 3.39)
No_care : Nfemales 1.89 (1.53, 2.13) 0.001
Care : Nfemales 1.51 (1.18, 1.78) 0.001
No_care : Nfemales^2 -0.19 (-0.45, 0.13) 0.304
Care : Nfemales^2 0.35 (0.13, 0.7) 0.01
No_care : Nfemales : Nmales_3 1.77 (1.51, 2.15) 0.001
No_care : Nfemales : Nmales_1 1.99 (1.46, 2.47) 0.001
Care : Nfemales : Nmales_3 1.53 (1.17, 1.86) 0.001
Care : Nfemales : Nmales_1 1.53 (0.99, 1.97) 0.001
No_care : Nfemales^2 : Nmales_3 -0.07 (-0.44, 0.26) 0.612
No_care : Nfemales^2 : Nmales_1 -0.37 (-0.94, 0.18) 0.198
Care : Nfemales^2 : Nmales_3 0.3 (-0.03, 0.65) 0.064
Care : Nfemales^2 : Nmales_1 0.5 (0.07, 1.17) 0.034
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Nmales_3 vs No_care : Nmales_1 -0.41 (-1.16, 0.15) 0.138
Care : Nmales_3 vs Care : Nmales_1 0.48 (-0.2, 1.05) 0.186
No_care : Nfemales vs Care : Nfemales 0.38 (-0.04, 0.72) 0.09
No_care : Nfemales^2 vs Care : Nfemales^2 -0.55 (-0.98, -0.18) 0.008
No_care : Nfemales : Nmales_3 vs No_care : Nfemales : Nmales_1 -0.04 (-0.74, 0.47) 0.586
No_care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_3 0.35 (-0.13, 0.76) 0.188
No_care : Nfemales : Nmales_1 vs Care : Nfemales : Nmales_1 0.56 (-0.15, 1.09) 0.126
Care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_1 -0.11 (-0.55, 0.65) 0.914
No_care : Nfemales^2 : Nmales_3 vs No_care : Nfemales^2 : Nmales_1 0.53 (-0.35, 0.91) 0.42
No_care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_3 -0.31 (-0.86, 0.08) 0.094
No_care : Nfemales^2 : Nmales_1 vs Care : Nfemales^2 : Nmales_1 -0.85 (-1.72, -0.24) 0.012
Care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_1 -0.27 (-0.87, 0.44) 0.376
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.19) 2.08 (0.01, 8.24)
Camp 0.14 (0, 0.55) 10.27 (0.02, 22.94)
Residual 2 (1.54, 2.39) 87.65 (73.69, 99.92)

O: Group size effects on the number of chicks produced by groups

Fixed Effects Posterior Mode (CI) pMCMC
No_care : Nmales_3 2.79 (2.19, 3.57)
No_care : Nmales_1 3.15 (2.27, 3.93)
Care : Nmales_3 1.32 (0.72, 2.03)
Care : Nmales_1 0.74 (-0.11, 1.57)
No_care : Nfemales 1.07 (0.73, 1.47) 0.001
Care : Nfemales 0.8 (0.41, 1.13) 0.001
No_care : Nfemales^2 -0.24 (-0.59, 0.13) 0.272
Care : Nfemales^2 0.2 (-0.17, 0.58) 0.286
No_care : Nfemales : Nmales_3 1.15 (0.71, 1.57) 0.001
No_care : Nfemales : Nmales_1 0.95 (0.41, 1.58) 0.001
Care : Nfemales : Nmales_3 0.73 (0.4, 1.28) 0.001
Care : Nfemales : Nmales_1 0.74 (0.08, 1.28) 0.034
No_care : Nfemales^2 : Nmales_3 0.08 (-0.49, 0.35) 0.918
No_care : Nfemales^2 : Nmales_1 -0.81 (-1.31, -0.02) 0.04
Care : Nfemales^2 : Nmales_3 0.35 (-0.16, 0.76) 0.158
Care : Nfemales^2 : Nmales_1 -0.05 (-0.75, 0.57) 0.816
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Nmales_3 vs No_care : Nmales_1 -0.46 (-1.04, 0.62) 0.558
Care : Nmales_3 vs Care : Nmales_1 0.6 (-0.13, 1.47) 0.124
No_care : Nfemales vs Care : Nfemales 0.44 (-0.1, 0.81) 0.15
No_care : Nfemales^2 vs Care : Nfemales^2 -0.27 (-0.94, 0.04) 0.092
No_care : Nfemales : Nmales_3 vs No_care : Nfemales : Nmales_1 0.27 (-0.56, 0.9) 0.64
No_care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_3 0.27 (-0.23, 0.91) 0.22
No_care : Nfemales : Nmales_1 vs Care : Nfemales : Nmales_1 0.24 (-0.48, 1.2) 0.448
Care : Nfemales : Nmales_3 vs Care : Nfemales : Nmales_1 0.17 (-0.64, 0.8) 0.69
No_care : Nfemales^2 : Nmales_3 vs No_care : Nfemales^2 : Nmales_1 0.57 (-0.19, 1.33) 0.102
No_care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_3 -0.4 (-0.94, 0.26) 0.258
No_care : Nfemales^2 : Nmales_1 vs Care : Nfemales^2 : Nmales_1 -0.42 (-1.45, 0.32) 0.198
Care : Nfemales^2 : Nmales_3 vs Care : Nfemales^2 : Nmales_1 0.43 (-0.41, 1.19) 0.342
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0.01 (0, 0.19) 1.29 (0.01, 5.23)
Camp 0.41 (0, 1.09) 14.62 (0.52, 27.84)
Residual 3.07 (2.32, 3.66) 84.09 (69.83, 98.91)

P: The effect of average within-group relatedness on the number of chicks produced by males

Fixed Effects Posterior Mode (CI) pMCMC
Male relatedness -0.27 (-0.65, 0.21) 0.3
No_care -0.42 (-2.08, 0.37)
Care -1.66 (-3, -0.32)
No_care : Nfemales 0.56 (0.25, 1.06)
Care : Nfemales 0.54 (0.17, 0.97)
No_care : Nfemales^2 -0.25 (-0.61, 0.08)
Care : Nfemales^2 0.11 (-0.26, 0.52)
No_care : Male relatedness 0.01 (-0.57, 0.44) 0.788
Care : Male relatedness -0.19 (-1.16, 0.32) 0.212
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Male relatedness vs Care : Male relatedness 0.33 (-0.48, 1.31) 0.352
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.09) 18.09 (0.07, 68.46)
Camp 0 (0, 0.46) 63.74 (5.62, 99.68)
Residual 0 (0, 0.07) 18.17 (0.09, 70.59)

Q: The effect of average within-group relatedness on the number of chicks produced by females

Fixed Effects Posterior Mode (CI) pMCMC
Female relatedness -0.24 (-0.5, 0.08) 0.122
No_care : Nmales_3 0.45 (-0.39, 1.32)
No_care : Nmales_1 0.66 (-0.27, 1.51)
Care : Nmales_3 -0.45 (-1.25, 0.43)
Care : Nmales_1 -0.83 (-1.62, 0.24)
No_care : Nfemales 0.48 (-0.37, 1.07)
Care : Nfemales 0.33 (-0.74, 1.39)
No_care : Nfemales^2 -0.36 (-0.95, 0.17)
Care : Nfemales^2 0.07 (-0.77, 0.92)
No_care : Female relatedness -0.36 (-0.62, 0.09) 0.11
Care : Female relatedness 0.04 (-0.52, 0.56) 0.952
Fixed Effect Comparisons Posterior Mode (CI) pMCMC
No_care : Female relatedness vs Care : Female relatedness -0.2 (-0.91, 0.32) 0.33
Random Effects Posterior Mode (CI) I2 % (CI)
Year 0 (0, 0.06) 6.48 (0.05, 26.22)
Camp 0.1 (0.03, 0.36) 70.85 (31.52, 98.98)
Residual 0 (0, 0.18) 22.67 (0.23, 62.04)

R: Sample size of experiment and summary statistics of reproductive success and incubation

2012 (N=11) 2013 (N=11) 2014 (N=12) 2015 (N=14) 2016 (N=17) 2017 (N=15) 2018 (N=16) Total (N=96)
Number of females
1 2 (18.2%) 2 (18.2%) 2 (16.7%) 4 (28.6%) 4 (23.5%) 4 (26.7%) 4 (25.0%) 22 (22.9%)
3 4 (36.4%) 4 (36.4%) 4 (33.3%) 4 (28.6%) 5 (29.4%) 4 (26.7%) 4 (25.0%) 29 (30.2%)
4 5 (45.5%) 5 (45.5%) 6 (50.0%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 16 (16.7%)
6 0 (0.0%) 0 (0.0%) 0 (0.0%) 6 (42.9%) 8 (47.1%) 7 (46.7%) 8 (50.0%) 29 (30.2%)
Number of males
1 6 (54.5%) 6 (54.5%) 6 (50.0%) 2 (14.3%) 3 (17.6%) 3 (20.0%) 4 (25.0%) 30 (31.2%)
3 5 (45.5%) 5 (45.5%) 6 (50.0%) 12 (85.7%) 14 (82.4%) 12 (80.0%) 12 (75.0%) 66 (68.8%)
Group composition (No.Males No.females)
1 1 2 (18.2%) 2 (18.2%) 2 (16.7%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 6 (6.2%)
1 3 2 (18.2%) 2 (18.2%) 2 (16.7%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 6 (6.2%)
1 4 2 (18.2%) 2 (18.2%) 2 (16.7%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 6 (6.2%)
1 6 0 (0.0%) 0 (0.0%) 0 (0.0%) 2 (14.3%) 3 (17.6%) 3 (20.0%) 4 (25.0%) 12 (12.5%)
3 1 0 (0.0%) 0 (0.0%) 0 (0.0%) 4 (28.6%) 4 (23.5%) 4 (26.7%) 4 (25.0%) 16 (16.7%)
3 3 2 (18.2%) 2 (18.2%) 2 (16.7%) 4 (28.6%) 5 (29.4%) 4 (26.7%) 4 (25.0%) 23 (24.0%)
3 4 3 (27.3%) 3 (27.3%) 4 (33.3%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 0 (0.0%) 10 (10.4%)
3 6 0 (0.0%) 0 (0.0%) 0 (0.0%) 4 (28.6%) 5 (29.4%) 4 (26.7%) 4 (25.0%) 17 (17.7%)
Number of eggs laid during period without care
Mean (SD) 79.27 (36.32) 110.09 (67.75) 122.42 (46.99) 114.57 (68.91) 130.76 (69.94) 140.60 (95.47) 150.69 (80.44) 123.95 (71.80)
Range 21.00 - 121.00 9.00 - 188.00 49.00 - 217.00 16.00 - 222.00 31.00 - 266.00 16.00 - 282.00 29.00 - 302.00 9.00 - 302.00
Number of eggs laid during period with care
Mean (SD) 22.45 (12.67) 27.36 (11.21) 20.50 (9.25) 24.29 (14.78) 21.18 (11.76) 24.87 (15.92) 15.56 (7.64) 22.04 (12.35)
Range 0.00 - 42.00 8.00 - 43.00 9.00 - 37.00 8.00 - 63.00 0.00 - 43.00 8.00 - 61.00 5.00 - 29.00 0.00 - 63.00
Number of chicks hatched during period without care
Mean (SD) 35.27 (24.42) 46.82 (40.90) 69.08 (42.67) 42.00 (31.23) 53.65 (34.81) 68.53 (64.25) 55.69 (50.95) 53.66 (44.00)
Range 1.00 - 74.00 0.00 - 102.00 9.00 - 161.00 7.00 - 106.00 0.00 - 144.00 3.00 - 197.00 1.00 - 214.00 0.00 - 214.00
Number of chicks hatched during period with care
Mean (SD) 3.00 (3.35) 2.09 (2.81) 2.58 (4.19) 5.93 (6.38) 3.41 (2.67) 3.53 (4.47) 2.00 (2.99) 3.26 (4.09)
Range 0.00 - 9.00 0.00 - 7.00 0.00 - 10.00 0.00 - 23.00 0.00 - 10.00 0.00 - 12.00 0.00 - 12.00 0.00 - 23.00
Number of broken eggs
Mean (SD) 12.36 (10.40) 15.09 (8.28) 13.17 (9.57) 8.29 (4.71) 10.12 (9.07) 12.47 (7.31) 6.25 (5.87) 10.78 (8.21)
Range 0.00 - 30.00 1.00 - 30.00 4.00 - 35.00 4.00 - 19.00 0.00 - 32.00 1.00 - 24.00 1.00 - 21.00 0.00 - 35.00
Proportion of time incubating
Mean (SD) 0.30 (0.30) 0.36 (0.30) 0.48 (0.24) 0.47 (0.26) 0.49 (0.26) 0.45 (0.32) 0.63 (0.23) 0.47 (0.28)
Range 0.00 - 0.83 0.00 - 0.83 0.09 - 0.82 0.06 - 0.72 0.00 - 0.93 0.01 - 0.88 0.16 - 0.96 0.00 - 0.96

S: Overview of replacements and removals of individuals in experimental groups

Before replacement/removal
After replacement/removal
Year Group ID Date Sex of removed no. males no. females no. males no. females
Replacements
2013 108 2013-09-26 Male 1 3 1 3
2014 58 2014-05-20 Female 1 4 1 4
2014 63 2014-08-09 Male 3 3 3 3
2015 58 2015-06-23 Male 3 1 3 1
2016 20 2016-07-28 Female 1 6 1 6
2016 60 2016-09-29 Female 3 3 3 3
2016 70 2016-05-17 Male 3 3 3 3
Removals
2014 58 2014-08-28 Female 1 4 1 3
2015 25 2015-12-01 Male 3 6 2 6
2015 27 2015-10-29 Male 3 6 2 6
2015 60 2015-10-30 Male 3 3 2 3
2015 64 2015-07-21 Female 1 6 1 5
2016 25 2016-08-07 Female 3 6 3 5
2016 27 2016-11-14 Female 3 6 3 5
2016 70 2016-12-02 Male 3 3 2 3
2017 22 2017-10-27 Female 3 3 3 2
2017 29 2017-11-13 Female 3 1 3 0
2017 62 2017-09-16 Male 3 6 2 6
2018 25 2018-11-18 Female 3 6 3 5

R Session Information

## R version 4.1.1 (2021-08-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur 10.16
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggpubr_0.4.0               magick_2.7.3              
##  [3] devtools_2.4.3             usethis_2.1.5             
##  [5] arsenal_3.6.3              ggsci_2.9                 
##  [7] data.table_1.14.2          kableExtra_1.3.4          
##  [9] stringdist_0.9.8           openxlsx_4.2.5            
## [11] wesanderson_0.3.6          arm_1.12-2                
## [13] lme4_1.1-28                PerformanceAnalytics_2.0.4
## [15] xts_0.12.1                 zoo_1.8-9                 
## [17] sciplot_1.2-0              gplots_3.1.1              
## [19] car_3.0-12                 carData_3.0-5             
## [21] reshape_0.8.8              Hmisc_4.7-0               
## [23] Formula_1.2-4              survival_3.3-1            
## [25] QuantPsyc_1.5              MASS_7.3-56               
## [27] boot_1.3-28                languageR_1.5.0           
## [29] doBy_4.6.12                MCMCglmm_2.33             
## [31] coda_0.19-4                Matrix_1.4-1              
## [33] cowplot_1.1.1              ape_5.6-2                 
## [35] forcats_0.5.1              stringr_1.4.0             
## [37] purrr_0.3.4                readr_2.1.2               
## [39] tidyr_1.2.0                tibble_3.1.6              
## [41] ggplot2_3.3.5              tidyverse_1.3.1           
## [43] dplyr_1.0.8                Rmisc_1.5                 
## [45] plyr_1.8.7                 lattice_0.20-45           
## [47] knitr_1.38                
## 
## loaded via a namespace (and not attached):
##   [1] readxl_1.4.0         backports_1.4.1      systemfonts_1.0.4   
##   [4] splines_4.1.1        digest_0.6.29        htmltools_0.5.2     
##   [7] fansi_1.0.3          magrittr_2.0.3       checkmate_2.0.0     
##  [10] memoise_2.0.1        cluster_2.1.3        remotes_2.4.2       
##  [13] tzdb_0.3.0           modelr_0.1.8         svglite_2.1.0       
##  [16] askpass_1.1          prettyunits_1.1.1    jpeg_0.1-9          
##  [19] colorspace_2.0-3     rvest_1.0.2          haven_2.4.3         
##  [22] xfun_0.30            callr_3.7.0          crayon_1.5.1        
##  [25] microbenchmark_1.4.9 jsonlite_1.8.0       glue_1.6.2          
##  [28] gtable_0.3.0         webshot_0.5.2        pkgbuild_1.3.1      
##  [31] abind_1.4-5          scales_1.1.1         qpdf_1.1            
##  [34] DBI_1.1.2            rstatix_0.7.0        Rcpp_1.0.8.3        
##  [37] viridisLite_0.4.0    htmlTable_2.4.0      foreign_0.8-82      
##  [40] pdftools_3.1.1       htmlwidgets_1.5.4    httr_1.4.2          
##  [43] RColorBrewer_1.1-2   ellipsis_0.3.2       farver_2.1.0        
##  [46] pkgconfig_2.0.3      nnet_7.3-17          sass_0.4.1          
##  [49] dbplyr_2.1.1         utf8_1.2.2           labeling_0.4.2      
##  [52] tidyselect_1.1.2     rlang_1.0.2          munsell_0.5.0       
##  [55] cellranger_1.1.0     tools_4.1.1          cachem_1.0.6        
##  [58] cli_3.2.0            generics_0.1.2       pacman_0.5.1        
##  [61] broom_0.7.12         evaluate_0.15        fastmap_1.1.0       
##  [64] yaml_2.3.5           processx_3.5.3       fs_1.5.2            
##  [67] zip_2.2.0            caTools_1.18.2       nlme_3.1-157        
##  [70] xml2_1.3.3           brio_1.1.3           compiler_4.1.1      
##  [73] rstudioapi_0.13      curl_4.3.2           png_0.1-7           
##  [76] ggsignif_0.6.3       testthat_3.1.3       reprex_2.0.1        
##  [79] bslib_0.3.1          stringi_1.7.6        highr_0.9           
##  [82] ps_1.6.0             desc_1.4.1           cubature_2.0.4.4    
##  [85] nloptr_2.0.0         tensorA_0.36.2       vctrs_0.4.0         
##  [88] pillar_1.7.0         lifecycle_1.0.1      jquerylib_0.1.4     
##  [91] bitops_1.0-7         corpcor_1.6.10       R6_2.5.1            
##  [94] latticeExtra_0.6-29  KernSmooth_2.23-20   gridExtra_2.3       
##  [97] sessioninfo_1.2.2    pkgload_1.2.4        gtools_3.9.2        
## [100] assertthat_0.2.1     rprojroot_2.0.2      withr_2.5.0         
## [103] Deriv_4.1.3          mgcv_1.8-40          parallel_4.1.1      
## [106] hms_1.1.1            quadprog_1.5-8       grid_4.1.1          
## [109] rpart_4.1.16         minqa_1.2.4          rmarkdown_2.13      
## [112] lubridate_1.8.0      base64enc_0.1-3