Appendix to Statistical Analyses
This appendix section contains descriptions of relevant test statistics and validation
of model assumptions used in the study “Phenology of sexual reproduction in the
common coral reef sponge, Carteriospongia foliascens”.
1) Pearson’s correlations
All correlations were done using the raw dataset in Statistica version 10.
Figure A1: Correlation scatterplot of mean monthly photoperiod (monthly mean daylight hours)
against mean monthly sea surface temperature (SST 2) at Little Pioneer Bay from March 2010 to
June 2012. There was a significant correlation of temperature and photoperiod during this period
(Pearson’s r = 0.768, p < 0.0001). Dashed lines represent upper and lower 95% confidence limits.
Corresponding text in the main article under headings: Results; Environmental parameters.
1
Figure A2: Correlation scatterplot of mean monthly sea surface temperature (SST) against
proportion of males that were reproductive at Little Pioneer Bay (L. Pioneer) from March 2010 to
June 2012. There was a significant correlation of temperature and proportion of males that were
reproductive over this period (Pearson’s r = 0.5.11, p < 0.05). Dashed lines represent upper and
lower 95% confidence limits. Corresponding text in the main article under headings: Results;
Patterns of reproduction.
2
Figure A3: Correlation scatterplot of mean monthly sea surface temperature (SST) against
proportion of females that were reproductive at Little Pioneer Bay (L. Pioneer) from March 2010 to
June 2012. There was no significant correlation of temperature and proportion of females that were
reproductive over this period (Pearson’s r = -0.306, p > 0.05). Dashed lines represent upper and
lower 95% confidence limits. Corresponding text in the main article under headings: Results;
Patterns of reproduction.
3
Figure A4: Correlation scatterplot of mean monthly sea surface temperature (temperature) against
total proportion of post-fertilized female propagules (i.e., embryos and larvae; %embryo + larvae)
at Little Pioneer bay from March 2010 to June 2012. There was a significant correlation of
temperature and total proportion post-fertilized female propagules over this period (Pearson’s r =
0.47, p < 0.05). Dashed lines represent upper and lower 95% confidence limits. Corresponding text in
the main article under headings: Results; Gametogenesis, embryogenesis and larval development.
4
Figure A5: Correlation scatterplot of low range mean monthly sea surface temperature
(temperature; July to September: 21.8°C to 25.9°C) against female reproductive output index (ROI)
at Little Pioneer Bay. There was a significant correlation of low range temperature and female ROI
(Pearson’s r = 0.38, p < 0.01). Note the non-linear relationship between female ROI and temperature
at this low range. Dashed lines represent upper and lower 95% confidence limits. Corresponding text
in the main article under headings: Results; Reproductive output (ROI).
5
Figure A6: Correlation scatterplot of low range mean monthly sea surface temperature
(temperature; July to September: 21.8°C to 25.9°C) against male reproductive output index (ROI) at
Little Pioneer Bay. There was a significant positive correlation of low range temperature and male
ROI (Pearson’s r = 0.39, p < 0.01). Note the non-linear relationship between male ROI and
temperature at this low range. Dashed lines represent upper and lower 95% confidence limits.
Corresponding text in the main article under headings: Results; Reproductive output (ROI).
6
Figure A7: Correlation scatterplot of high range mean monthly sea surface temperature
(temperature; October to December: 25.2°C to 28.9°C) against male reproductive output index
(ROI) at Little Pioneer Bay. There was a significant negative correlation of high range temperature
and male ROI (Pearson’s r = -0.54, p < 0.001). Dashed lines represent upper and lower 95%
confidence limits. Corresponding text in the main article under headings: Results; Reproductive
output (ROI).
7
Figure A8: Correlation scatterplot of increasing mean monthly sea surface temperature (SST2; July
to December) against population sexual productivity index (PoSPi) at Little Pioneer Bay from March
2010 to June 2012. There was a significant correlation of increasing temperature and PoSPi
(Pearson’s r = 0.78, p < 0.05). Dashed lines represent upper and lower 95% confidence limits.
Corresponding text in the main article under headings: Results; Population sexual productivity index
(PoSPi).
8
2) Periodic regressions: Validation of model assumptions and main tests
All residual plots and analyses were done using Statistica 10. Independent variables are
angular representation of time (θ, transformed) and raw data of the dependent variables
are used for all analyses. Numbering of tables herein follows the sequential order of tests
(i.e. starts at number 9) to highlight the specific group of analyses done.
For Durbin-Watson test statistics for temporal autocorrelation, please refer to table below
for interpretations (Savin and White 1977).
To test for positive autocorrelation
If d < dL = error terms positively autocorrelated
If d > dU = error terms not positively autocorrelated
If dL< d <dU = test inconclusive
To test for negative auto correlation
If (4-d) < dL = error terms are negatively correlated
If (4-d) > dU = error term not negatively autocorrelated
If dL < (4-d) < dL = test inconclusive
9. Photoperiod (dependent variable) across 2 reproductive cycles (time, θ)
Predicted v s. Residual Scores
Dependent v ariable: Monthly mean day light hours
Include cases: 1:24
0.04
0.03
0.02
Residuals
0.01
0.00
-0.01
-0.02
-0.03
-0.04
10.8
11.0
11.2
11.4
11.6
11.8
12.0
12.2
12.4
Predicted Values
12.6
12.8
13.0
13.2
13.4
0.95 Conf .Int.
Figure A9.1: Residual plot of photoperiod (dependent variable) over two reproductive cycles (time,
θ). Corresponding text in the main article under headings: Results; Environmental parameters.
9
Table A9.2: Summary statistics of forward stepwise regression of photoperiod (dependent variable)
over two reproductive cycles (time, θ). Red texts represent significant results. Corresponding text in
the main article under headings: Results; Environmental parameters.
Variable
cos θ
sin θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.907360
0.823301
0.823301
0.000000
2
0.996199
0.992412
0.169110
0.000000
Table A9.3: Summary statistics of multiple regression of photoperiod (dependent variable) over two
reproductive cycles (time, θ). Only the cos θ and sin θ variables were included in the model. Red
texts represent significant results. b represents the model coefficient of each variable. R2 = 0.99,
F(2,20) = 10751, p < 0.0000. Corresponding text in the main article under headings: Results;
Environmental parameters.
Variable
b
SE of b
t
Intercept 12.10320 0.005057 2393.224
0.97737 0.007233 135.129
cos θ
-0.43994 0.007070 -62.224
sin θ
p - value
0.000000
0.000000
0.000000
Table A9.4: Summary statistics of homogeneity of slope model (HSM) test of photoperiod
(dependent variable) in cycle 1 and cycle 2 (i.e. 2 years) over two reproductive cycles (time, θ). cos θ
and sin θ variables were included as the continuous variables (covariate) and cycle as the categorical
variable (treatment factor) in the model. Red texts represent significant results. Corresponding text
in the main article under headings: Results; Environmental parameters.
Effect
SS
Deg. Freedom
MS
F
p
3296.234
1
3296.234
5183498
0.000000
Intercept
0.000
1
0.000
0
0.583726
Cycle
10.403
1
10.403
16359
0.000000
cosθ
2.243
1
2.243
3527
0.000000
sinθ
0.000
1
0.000
0
0.720681
Cycle*cosθ
0.000
1
0.000
0
0.952592
Cycle*sin
0.002
1
0.002
3
0.112146
cosθ*sinθ
1
0.000
0
1.000000
Cycle*cosθ*sinθ 0.000
0.010
15
0.001
Error
10
10. Proportion of total reproductive sponges (males and females) over cycle 2 (time, θ)
Predicted vs. Residual Scores
Dependent variable: L. Pioneer
Include cases: 13:24
10
8
6
4
Residuals
2
0
-2
-4
-6
-8
-10
-12
-14
40
50
60
70
80
90
Predicted Values
100
110
0.95 Conf.Int.
Figure A10.1: Residual plot of proportion of total reproductive sponges, males and females
(dependent variable) over cycle 2 (time, θ). Corresponding text in the main article under headings:
Results; Patterns of reproduction.
Table A10.2: Summary statistics of forward stepwise regression of proportion of total reproductive
sponges, males and females (dependent variable) over cycle 2 (time, θ). Red texts represent
significant results. Corresponding text in the main article under headings: Results; Patterns of
reproduction.
Variable
cos θ
cos 2θ
sin θ
sin 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.732057
0.535907
0.535907
0.006792
2
0.862654
0.744171
0.208264
0.024124
3
0.949855
0.902225
0.158054
0.007022
4
0.956544
0.914976
0.012751
0.339656
11
Table A10.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
of total reproductive sponges, males and females (dependent variable) over cycle 2 (time, θ). No
evidence of temporal autocorrelation was detected. Refer to reference table above for
interpretations.
Sample size (n)
12
Number regressors (k)
3
dL
0.569
dU
1.274
d
2.49
4-d
1.51
Table A10.4: Summary statistics of multiple regression of proportion of total reproductive sponges,
males and females (dependent variable) over cycle 2 (time, θ). Only the cos θ, sin θ and cos 2θ
variables were included in the model. Red texts represent significant results. b represents the model
coefficient of each variable. R2 = 0.90, F(3,8) = 24.607, p < 0.0002. Corresponding text in the main
article under headings: Results; Patterns of reproduction.
Variable
Intercept
cos θ
sin θ
cos 2θ
b
SE of b
t
p - value
75.2778 1.998450 37.66809 0.000000
18.7147 2.826235
6.62179 0.000166
-10.1635 2.826235 -3.59611 0.007022
-11.6667 2.826235 -4.12799 0.003308
12
11. Proportion of total reproductive sponges (males and females) over cycle 1 (time, θ)
Predicted vs. Residual Scores
Dependent variable: L. Pioneer
Include cases: 1:12
40
30
Residuals
20
10
0
-10
-20
-30
20
30
40
50
60
70
80
90
Predicted Values
100
110
0.95 Conf.Int.
Figure A11.1: Residual plot of proportion of total reproductive sponges, males and females
(dependent variable) over cycle 1 (time, θ). Corresponding text in the main article under headings:
Results; Patterns of reproduction.
Table A11.2: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
of total reproductive sponges, males and females (dependent variable) over cycle 1 (time, θ). No
evidence of temporal autocorrelation was detected. Refer to reference table above for
interpretations.
Sample size (n)
12
Number regressors (k)
3
dL
0.569
dU
1.274
d
2.087179
4-d
1.912821
13
Table A11.3: Summary statistics of multiple regression of proportion of total reproductive sponges,
males and females (dependent variable) over cycle 1 (time, θ). Same predictor variables (cos θ, sin θ
and cos 2θ) used in cycle 2 were selected to allow comparison between the two cycles. Red texts
represent significant results. b represents the model coefficient of each variable. R2 = 0.64, F(3,8) =
4.714, p < 0.03. Corresponding text in the main article under headings: Results; Patterns of
reproduction.
Variable
b
SE of b
t
p - value
Intercept 57.9598 6.132126 9.45183 0.000013
1.9262 8.672136 0.22211 0.829793
cos θ
-30.6899 8.672136 -3.53891 0.007632
sin θ
cos 2θ -10.8645 8.672136 -1.25281 0.245654
Table A11.4: Summary statistics of homogeneity of slope model (HSM) test of proportion of total
reproductive sponges, males and females (dependent variable) between cycle 1 and cycle 2 (i.e. 2
years) over two reproductive cycles (time, θ). cos θ, sin θ and cos 2θ variables were included as the
continuous variables (covariate) and cycle as the categorical variable (treatment factor) in the
model. Red texts represent significant results. Corresponding text in the main article under headings:
Results; Environmental parameters.
Effect
Intercept
(1) Cycle
(2) cosθ
(3) sinθ
(4) cos2θ
1*2
1*3
2*3
1*4
2*4
3*4
1*2*3
1*2*4
1*3*4
2*3*4
1*2*3*4
Error
SS
Deg. Freedom
MS
F
p
106513.6
1
1799.5
1
1799.5
5.4484
0.047849
119.6
1
119.6
0.3620
0.564064
1959.5
1
1959.5
5.9329
0.040835
1523.0
1
1523.0
4.6112
0.064037
789.8
1
789.8
2.3913
0.160595
375.2
1
375.2
1.1361
0.317586
71.7
1
71.7
0.2171
0.653664
1.9
1
1.9
0.0058
0.940940
411.6
1
411.6
1.2462
0.296678
66.6
1
66.6
0.2015
0.665403
341.1
1
341.1
1.0327
0.339271
113.8
1
113.8
0.3444
0.573476
66.6
1
66.6
0.2015
0.665403
215.6
1
215.6
0.6527
0.442508
64.3
1
64.3
0.1945
0.670845
2642.2
8
330.3
106513.6 322.4984 0.000000
14
12. Proportion male reproductive across 2 reproductive cycles
Predicted vs. Residual Scores
Dependent variable: % repro
30
20
Residuals
10
0
-10
-20
-30
-40
10
20
30
40
Predicted Values
50
60
70
0.95 Conf.Int.
Figure A12.1: Residual plot of proportion of males (dependent variable) over two reproductive
cycles (time, θ). Corresponding text in the main article under headings: Results; Patterns of
reproduction.
Table A12.2: Summary statistics of forward stepwise regression of proportion of males over two
reproductive cycles (time, θ). Red texts represent significant results. Corresponding text in the main
article under headings: Results; Patterns of reproduction.
Variable
cos θ
sin θ
cos 2θ
sin 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.428908
0.183962
0.183962 0.036497
2
0.585104
0.342347
0.158385 0.035379
3
0.705250
0.497378
0.155031 0.021984
4
0.723027
0.522768
0.025390 0.327333
15
Table A12.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
of males (dependent variable) over two reproductive cycles (time, θ). No evidence of temporal
autocorrelation was detected. Refer to reference table above for interpretations.
Sample size (n)
24
Number regressors (k)
3
dL
0.881
dU
1.407
d
1.559297
4-d
2.440703
Table A12.4: Summary statistics of multiple regression of proportion of males (dependent variable)
over two reproductive cycles (time, θ). Only the cos θ, sin θ and cos 2θ variables were included in
the model. Red texts represent significant results. b represents the model coefficient of each
variable. R2 = 0.50, F(3,20) = 6.597, p < 0.003. Corresponding text in the main article under headings:
Results; Patterns of reproduction.
Variable
Intercept
cos θ
sin θ
cos 2θ
b
SE of b
t
p - value
38.1505 3.326324 11.46926 0.000000
12.7273 4.704133
2.70557 0.013611
-11.8095 4.704133 -2.51045 0.020765
-11.6838 4.704133 -2.48372 0.021984
16
13. Comparing proportion male reproductive between 2 cycles
Predicted vs. Residual Scores
Dependent variable: % repro
Include cases: 1:12
40
30
Residuals
20
10
0
-10
-20
0
20
10
40
30
70
60
50
Predicted Values
80
0.95 Conf.Int.
Figure A13.1: Residual plot of proportion of males (dependent variable) over cycle 1 (time, θ).
Corresponding text in the main article under headings: Results; Patterns of reproduction.
Table A13.2: Summary statistics of forward stepwise regression of proportion of males over cycle 1
(time, θ). Red texts represent significant results. Corresponding text in the main article under
headings: Results; Patterns of reproduction.
Variable
sin θ
cos 2θ
sin 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.578705
0.334899
0.334899
0.048677
2
0.675148
0.455825
0.120925
0.190951
3
0.755137
0.570232
0.114407
0.182595
Table A13.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
of males (dependent variable) over cycle 1 (time, θ). No evidence of temporal autocorrelation was
detected. Refer to reference table above for interpretations.
Sample size (n)
12
Number regressors (k)
1
dL
0.697
dU
1.023
d
2.061989
4-d
1.938011
17
Table A13.4: Summary statistics of multiple regression of proportion of males (dependent variable)
over cycle 1 (time, θ). Only the sin θ variable was included in the model. Red texts represent
significant results. b represents the model coefficient of each variable. R2 = 0.33, F(1,10) = 5.035, p <
0.05. Corresponding text in the main article under headings: Results; Patterns of reproduction.
Variable
b
SE of b
t
p - value
Intercept 35.1898 6.136026 5.73495 0.000189
-19.4722 8.677652 -2.24395 0.048677
sin θ
Predicted vs. Residual Scores
Dependent variable: % repro
Include cases: 1:12
40
30
Residuals
20
10
0
-10
-20
0
10
20
30
40
Predicted Values
50
60
70
80
0.95 Conf.Int.
Figure A13.5: Residual plot of proportion of males (dependent variable) over cycle 2 (time, θ).
Corresponding text in the main article under headings: Results; Patterns of reproduction.
18
Table A13.5: Summary statistics of forward stepwise regression of proportion of males over cycle 2
(time, θ). Red texts represent significant results. Corresponding text in the main article under
headings: Results; Patterns of reproduction.
Variable
cos θ
cos 2θ
sin θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.794658
0.631481
0.631481
0.002013
2
0.927734
0.860691
0.229210
0.003918
3
0.943211
0.889648
0.028957
0.185411
Table A13.6: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
of males (dependent variable) over cycle 2 (time, θ). No evidence of temporal autocorrelation was
detected. Refer to reference table above for interpretations.
Sample size (n)
12
Number regressors (k)
2
dL
0.569
dU
1.274
d
1.928115
4-d
2.071885
Table A13.7: Summary statistics of multiple regression of proportion of males (dependent variable)
over cycle 2 (time, θ). Only the cos θ and cos 2θ variables were included in the model. Red texts
represent significant results. b represents the model coefficient of each variable. R2 = 0.86, F(2,9) =
27.802, p < 0.00014. Corresponding text in the main article under headings: Results; Patterns of
reproduction.
Variable
b
SE of b
t
Intercept 41.1111 2.143797 19.17677
19.3647 3.031787 6.38721
cos θ
cos 2θ -11.6667 3.031787 -3.84812
p - value
0.000000
0.000127
0.003918
19
14. Proportion female reproductive across 2 cycles
Predicted vs. Residual Scores
Dependent variable: % repro
20
15
10
Residuals
5
0
-5
-10
-15
-20
18
20
22
24
26
28
30
32
34
36
Predicted Values
38
0.95 Conf.Int.
Figure A14.1: Residual plot of proportion of females (dependent variable) over two reproductive
cycles (time, θ). Corresponding text in the main article under headings: Results; Patterns of
reproduction.
Table A14.2: Summary statistics of forward stepwise regression of proportion of females over two
reproductive cycles (time, θ). Red texts represent significant results. Corresponding text in the main
article under headings: Results; Patterns of reproduction.
Variable
sin θ
Step
1
Multiple R Multiple R-square R-square change p-value
0.582566
0.339383
0.339383
0.002816
Table A14.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
of females (dependent variable) over two reproductive cycles (time, θ). No evidence of temporal
autocorrelation was detected. Refer to reference table above for interpretations.
Sample size (n)
24
Number regressors (k)
3
dL
0.881
dU
1.407
d
1.104271
4-d
2.895729
20
Table A14.4: Summary statistics of multiple regression of proportion of females (dependent
variable) over two reproductive cycles (time, θ). Same predictor variables (cos θ, sin θ and cos 2θ)
used in the analysis of proportion males over two reproductive cycles were selected to allow
comparison between the two sexes. Red texts represent significant results. b represents the model
coefficient of each variable. R2 = 0.37, F(3,20) = 3.859, p < 0.025. Corresponding text in the main article
under headings: Results; Patterns of reproduction.
Variable
b
SE of b
t
p - value
Intercept 28.46834 1.861271 15.29510 0.000000
-2.40688 2.632235 -0.91439 0.371406
cos θ
-8.61719 2.632235 -3.27372 0.003799
sin θ
0.41816 2.632235 0.15886 0.875372
cos 2θ
Table A14.5: Summary statistics of homogeneity of slope model (HSM) test of proportion
reproductive (dependent variable) between sex (i.e. males vs females) over two reproductive cycles
(time, θ). cos θ, sin θ and cos 2θ variables were included as the continuous variables (covariate) and
cycle as the categorical variable (treatment factor) in the model. Red texts represent significant
results. Corresponding text in the main article under headings: Results; Patterns of reproduction.
Effect
Intercept
(1) Sex
(2) cosθ
(3) sinθ
(4) cos2θ
1*2
1*3
2*3
1*4
2*4
3*4
1*2*3
1*2*4
1*3*4
2*3*4
1*2*3*4
Error
SS
53256.79
Deg. Freedom
MS
F
p
1 53256.79 311.0450 0.000000
1124.92
1
1124.92
6.5701 0.015274
59.78
1
59.78
0.3491 0.558758
979.74
1
979.74
5.7222 0.022797
761.48
1
761.48
4.4474 0.042871
109.61
1
109.61
0.6402 0.429543
50.15
1
50.15
0.2929 0.592116
35.86
1
35.86
0.2094 0.650320
878.74
1
878.74
5.1322 0.030389
205.80
1
205.80
1.2020 0.281110
33.28
1
33.28
0.1944 0.662269
295.01
1
295.01
1.7230 0.198643
495.73
1
495.73
2.8953 0.098538
318.07
1
318.07
1.8577 0.182409
107.79
1
107.79
0.6295 0.433377
0.0191 0.890878
3.27
1
3.27
5479.01
32
171.22
21
15. Mean oocytes sizes across 2 cycles
Predicted vs. Residual Scores
Dependent variable: Mean size
14000
12000
10000
8000
Residuals
6000
4000
2000
0
-2000
-4000
-6000
-8000
-10000
8000
12000
10000
16000
14000
20000
18000
24000
22000
28000
26000
Predicted Values
32000
30000
34000
0.95 Conf.Int.
Figure A15.1: Residual plot of mean oocyte size (dependent variable) over two reproductive cycles
(time, θ). Corresponding text in the main article under headings: Results; Gametogenesis,
embryogenesis and larval development.
Table A15.2: Summary statistics of forward stepwise regression of mean oocyte size over two
reproductive cycles (time, θ). Red texts represent significant results. Corresponding text in the main
article under headings: Results; Gametogenesis, embryogenesis and larval development.
Variable
sin θ
cos 2θ
cos θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.599092
0.358912
0.358912
0.001978
2
0.752936
0.566912
0.208001
0.004552
3
0.835403
0.697897
0.130985
0.008011
22
Table A15.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of mean oocyte
size (dependent variable) over two reproductive cycles (time, θ). No evidence of temporal
autocorrelation was detected. Refer to reference table above for interpretations.
Sample size (n)
24
Number regressors (k)
3
dL
0.881
dU
1.407
d
2.525024
4-d
1.474976
Table A15.4: Summary statistics of multiple regression of mean oocyte size (dependent variable)
over two reproductive cycles (time, θ). Only the cos θ, sin v and cos 2θ variables were included in
the model. Red texts represent significant results. b represents the model coefficient of each
variable. R2 = 0.70, F(3,20) = 15.401, p < 0.00002. Corresponding text in the main article under
headings: Results; Gametogenesis, embryogenesis and larval development.
Variable
Intercept
cos θ
sin θ
cos 2θ
b
SE of b
t
p - value
19667.70 952.881 20.64025 0.000000
3968.28 1347.577 2.94475 0.008011
-6568.79 1347.577 -4.87452 0.000092
-5000.62 1347.577 -3.71082 0.001382
23
16. Proportion fertilized propagules over increasing temperature
Predicted vs. Residual Scores
Dependent variable: % fertilised propagule
Include cases: 1:6
4
2
Residuals
0
-2
-4
-6
-8
5
10
15
20
25
30
35
Predicted Values
40
45
0.95 Conf.Int.
Figure A16.1: Residual plot of proportion fertilized propagule (dependent variable) over increasing
temperature (July to December) over cycle 1 (time, θ). Corresponding text in the main article under
headings: Results; Gametogenesis, embryogenesis and larval development.
Table A16.2: Summary statistics of forward stepwise regression of proportion fertilized propagule
over increasing temperature (July to December) over cycle 1 (time, θ). Red texts represent
significant results. Corresponding text in the main article under headings: Results; Gametogenesis,
embryogenesis and larval development.
Variable
cos θ
cos 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.948540
0.899728
0.899728
0.003904
2
0.966856
0.934811
0.035083
0.293442
24
Table A16.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
fertilized propagule over increasing temperature (July to December) (dependent variable) over
cycle 1 (time, θ). No evidence of temporal autocorrelation was detected. Refer to reference table
above for interpretations.
Sample size (n)
6
Number regressors (k)
1
dL
0.39
dU
1.142
d
2.34842
4-d
1.65158
Table A16.4: Summary statistics of multiple regression of proportion fertilized propagule over
increasing temperature (July to December) (dependent variable) over cycle 1 (time, θ). Only the cos
θ variable was included in the model. Red texts represent significant results. b represents the model
coefficient of each variable. R2 = 0.90, F(1,4) = 35.892, p < 0.0039. Corresponding text in the main
article under headings: Results; Gametogenesis, embryogenesis and larval development.
Variable
b
SE of b
t
p - value
29.15146
2.300154
12.67370
0.000223
Intercept
19.48804 3.252909 5.99096 0.003904
cos θ
Predicted vs. Residual Scores
Dependent variable: % fertilised propagule
Include cases: 7:12
0.5
0.4
0.3
Residuals
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-5
0
5
10
15
20
25
Predicted Values
30
35
40
45
50
0.95 Conf.Int.
Figure A16.5: Residual plot of proportion fertilized propagule (dependent variable) over increasing
temperature (July to December) over cycle 2 (time, θ). Corresponding text in the main article under
headings: Results; Gametogenesis, embryogenesis and larval development.
25
Table A16.6: Summary statistics of forward stepwise regression of proportion fertilized propagule
over increasing temperature (July to December) over cycle 2 (time, θ). Red texts represent
significant results. Corresponding text in the main article under headings: Results; Gametogenesis,
embryogenesis and larval development.
Variable
cos θ
sin 2θ
cos 2θ
sin θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.993354
0.986752
0.986752
0.000066
2
0.997660
0.995326
0.008574
0.100695
3
0.999241
0.998483
0.003158
0.178073
4
0.999847
0.999694
0.001210
0.296651
Table A16.7: Summary statistics of Durbin-Watson test for temporal autocorrelation of proportion
fertilized propagule over increasing temperature (July to December) (dependent variable) over
cycle 2 (time, θ). No evidence of temporal autocorrelation was detected. Refer to reference table
above for interpretations.
Sample size (n)
6
Number regressors (k)
1
dL
0.39
dU
1.142
d
2.024022
4-d
1.975978
Table A16.4: Summary statistics of multiple regression of proportion fertilized propagule over
increasing temperature (July to December) (dependent variable) over cycle 2 (time, θ). Only the cos
θ variable was included in the model. Red texts represent significant results. b represents the model
coefficient of each variable. R2 = 0.99, F(1,4) = 297.93, p < 0.00007. Corresponding text in the main
article under headings: Results; Gametogenesis, embryogenesis and larval development.
Variable
b
SE of b
t
p - value
Intercept 24.57690 0.984713 24.95844 0.000015
cos θ 24.03696 1.392594 17.26056 0.000066
Table A16.5: Summary statistics of homogeneity of slope model (HSM) test of fertilized propagule
over increasing temperature (July to December) (dependent variable) between cycles (i.e. year 1
and year 2) over two reproductive cycles (time, θ). Only the cos θ variable were included as the
continuous variable (covariate) and cycle as the categorical variable (treatment factor) in the model.
Red texts represent significant results. Corresponding text in the main article under headings:
Results; Gametogenesis, embryogenesis and larval development.
Effect
Intercept
Cycle
cosθ
Cycle*cosθ
Error
SS
Deg. Freedom
8179.087
1
MS
F
p
8179.087 461.1130 0.000000
59.292
1
2683.771
1
59.292
29.315
1
29.315
141.902
8
17.738
3.3427
0.104908
2683.771 151.3031 0.000002
1.6527
0.234558
26
17. Male ROI across two cycle
Predicted vs. Residual Scores
Dependent variable: Mean ROI
Include cases: 1:12
1.0
0.8
0.6
Residuals
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Predicted Values
2.6
2.8
3.0
3.2
0.95 Conf.Int.
Figure A17.1: Residual plot of male reproductive output index (ROI) (dependent variable) over cycle
1 (time, θ). Corresponding text in the main article under headings: Results; Reproductive output
index.
Table A17.2: Summary statistics of forward stepwise regression of male reproductive output index
(ROI) over cycle 1 (time, θ). Red texts represent significant results. Corresponding text in the main
article under headings: Results; Gametogenesis, embryogenesis and larval development.
Variable
sin θ
cos 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.815005
0.664234
0.664234
0.001239
2
0.912349
0.832381
0.168147
0.014842
27
Table A17.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of male
reproductive output index (ROI) (dependent variable) over cycle 1 (time, θ). No evidence of
temporal autocorrelation was detected. Refer to reference table above for interpretations.
Sample size (n)
12
Number regressors (k)
2
dL
0.569
dU
1.274
d
1.505728
4-d
2.494272
Table A17.4: Summary statistics of multiple regression of male reproductive output index (ROI)
(dependent variable) over cycle 1 (time, θ). Only the sin θ and cos 2θ variables were included in the
model. Red texts represent significant results. b represents the model coefficient of each variable. R2
= 0.83, F(2,9) = 22.347, p < 0.00032. Corresponding text in the main article under headings: Results;
Gametogenesis, embryogenesis and larval development.
Variable
b
SE of b
t
p - value
Intercept 1.33467 0.132577 10.06712 0.000003
-1.11970 0.187492 -5.97200 0.000210
sin θ
cos 2θ -0.56336 0.187492 -3.00472 0.014842
Predicted vs. Residual Scores
Dependent variable: Mean ROI
Include cases: 13:24
1.2
1.0
0.8
Residuals
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0.0
0.5
1.0
1.5
2.0
2.5
Predicted Values
3.0
3.5
4.0
4.5
0.95 Conf.Int.
Figure A17.5: Residual plot of male reproductive output index (ROI) (dependent variable) over cycle
2 (time, θ). Corresponding text in the main article under headings: Results; Reproductive output
index.
28
Table A17.6: Summary statistics of forward stepwise regression of male reproductive output index
(ROI) over cycle 2 (time, θ). Red texts represent significant results. Corresponding text in the main
article under headings: Results; Gametogenesis, embryogenesis and larval development.
Variable
sin θ
cos 2θ
cos θ
sin 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.753290
0.567446
0.567446
0.004675
2
0.895447
0.801825
0.234379
0.009799
3
0.921259
0.848718
0.046893
0.153969
4
0.931839
0.868325
0.019607
0.341266
Table A17.7: Summary statistics of Durbin-Watson test for temporal autocorrelation of male
reproductive output index (ROI) (dependent variable) over cycle 2 (time, θ). No evidence of
temporal autocorrelation was detected. Refer to reference table above for interpretations.
Sample size (n)
12
Number regressors (k)
2
dL
0.569
dU
1.274
d
2.379774
4-d
1.620226
Table A17.8: Summary statistics of multiple regression of male reproductive output index (ROI)
(dependent variable) over cycle 2 (time, θ). Only the sin θ and cos 2θ variables were included in the
model. Red texts represent significant results. b represents the model coefficient of each variable. R2
= 0.80, F(2,9) = 18.207, p < 0.00069. Corresponding text in the main article under headings: Results;
Gametogenesis, embryogenesis and larval development.
Variable
b
SE of b
t
Intercept 1.70960 0.200067 8.54515
-1.43631 0.282937 -5.07644
sin θ
cos 2θ -0.92310 0.282937 -3.26255
p - value
0.000013
0.000666
0.009799
29
Table A17.5: Summary statistics of homogeneity of slope model (HSM) test of male reproductive
output index (ROI) (dependent variable) between cycles (i.e. year 1 and year 2) over two
reproductive cycles (time, θ). Only the sin θ and cos 2θ variables were included as the continuous
variables (covariate) and cycle as the categorical variable (treatment factor) in the model. Red texts
represent significant results. Corresponding text in the main article under headings: Results;
Gametogenesis, embryogenesis and larval development.
Effect
Intercept
Cycle
sinθ
cos2θ
Cycle*sinθ
Cycle*cos2θ
sinθ*cos2θ
Cycle*sinθ*cos2θ
Error
SS
Deg. Freedom
MS
F
p
55.60544
1
0.84345
1
0.84345
2.4121
0.139956
6.72785
1
6.72785
19.2402
0.000460
6.62866
1
6.62866
18.9566
0.000492
0.05250
1
0.05250
0.1501
0.703518
0.38823
1
0.38823
1.1103
0.307679
0.57600
1
0.57600
1.6472
0.217613
0.05034
1
0.05034
0.1440
0.709364
5.59482
16
0.34968
55.60544 159.0197 0.000000
30
18. Female ROI across cycle 1
Predicted vs. Residual Scores
Dependent variable: Mean ROI
Include cases: 1:12
1.2
1.0
0.8
Residuals
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
Predicted Values
3.0
3.2
0.95 Conf.Int.
Figure A18.1: Residual plot of female reproductive output index (ROI) (dependent variable) over
cycle 1 (time, θ). Corresponding text in the main article under headings: Results; Reproductive output
index.
Table A18.2: Summary statistics of forward stepwise regression of female reproductive output
index (ROI) over cycle 1 (time, θ). Red texts represent significant results. Corresponding text in the
main article under headings: Results; Gametogenesis, embryogenesis and larval development.
Variable
sin θ
cos 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.785505
0.617018
0.617018
0.002463
2
0.891453
0.794689
0.177670
0.021028
Table A18.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of female
reproductive output index (ROI) (dependent variable) over cycle 1 (time, θ). No evidence of
temporal autocorrelation was detected. Refer to reference table above for interpretations.
Sample size (n)
12
Number regressors (k)
2
dL
0.569
dU
1.274
d
3.256113
4-d
0.743887
31
Table A18.4: Summary statistics of multiple regression of female reproductive output index (ROI)
(dependent variable) over cycle 1 (time, θ). Only the sin θ and cos 2θ variables were included in the
model. Red texts represent significant results. b represents the model coefficient of each variable. R2
= 0.79, F(2,9) = 17.418, p < 0.00081. Corresponding text in the main article under headings: Results;
Gametogenesis, embryogenesis and larval development.
Variable
b
SE of b
t
Intercept 1.27636 0.149012 8.56550
-1.09597 0.210734 -5.20072
sin θ
cos 2θ -0.58811 0.210734 -2.79076
p - value
0.000013
0.000564
0.021028
32
19. PoSPi across two reproductive cycles
Predicted vs. Residual Scores
Dependent variable: Relative PoSPI
0.5
0.4
0.3
Residuals
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.95 Conf.Int.
Predicted Values
Figure A19.1: Residual plot of population sexual productivity index (PoSPi) (dependent variable)
over two reproductive cycles (time, θ). Corresponding text in the main article under headings:
Results; Population sexual productivity index (PoSPi).
Table A19.2: Summary statistics of forward stepwise regression of population sexual productivity
index (PoSPi) over two reproductive cycles (time, θ). Red texts represent significant results.
Corresponding text in the main article under headings: Results; Population sexual productivity index
(PoSPi).
Variable
sin θ
cos θ
sin 2θ
Step
Multiple R Multiple R-square R-square change p-value
1
0.527035
0.277766
0.277766
0.008140
2
0.647295
0.418990
0.141225
0.034622
3
0.726447
0.527725
0.108735
0.044338
33
Table A19.3: Summary statistics of Durbin-Watson test for temporal autocorrelation of population
sexual productivity index (PoSPi) (dependent variable) over two reproductive cycles (time, θ). No
evidence of temporal autocorrelation was detected. Refer to reference table above for
interpretations.
Sample size (n)
24
Number regressors (k)
3
dL
0.881
dU
1.407
d
2.505963
4-d
1.494037
Table A19.4: Summary statistics of multiple regression of population sexual productivity index
(PoSPi) (dependent variable) over two reproductive cycles (time, θ). Only the sin θ, cos θ and sin 2θ
variables were included in the model. Red texts represent significant results. b represents the model
coefficient of each variable. R2 = 0.53, F(3,20) = 7.4494, p < 0.00154. Corresponding text in the main
article under headings: Results; Population sexual productivity index (PoSPi).
Variable
Intercept
sin θ
cos θ
sin 2θ
b
SE of b
t
p - value
0.116560 0.026269 4.43715 0.000253
-0.127414 0.037150 -3.42971 0.002653
0.090852 0.037150 2.44553 0.023842
-0.079719 0.037150 -2.14586 0.044338
References
Savin NE, White KJ (1977) The Durbin-Watson test for serial correlation with extreme sample sizes or
many regressors. Econometrica 45:1989-1996
34