Appendix S3. Sensitivity analysis and additional results.
1.
Alternative definition of the breeding success (BS’)
All analyses were performed considering a more restricted definition of the breeding success
BS’ (i.e., excluding “NB” pairs that did not lay in a given year).
Table A9. Model-averaged partial regression coefficients (β) and unconditional 95% confidence
intervals (CIs) from generalized linear mixed-effects models of breeding success (BS’) in the
Monteiro’s Storm-petrel population monitored on Praia Islet (2000–2012, n=644) in relation to
climatic and oceanic conditions. NAO(qx), SST(qx) and Chl-a(qx) respectively denote the North Atlantic
Oscillation index, Sea Surface Temperature and Chlorophyll a concentration computed for the xth
quarter of the current year. NAO(t-1) denotes the North Atlantic Oscillation index computed for the 4th
quarter of the previous year. Akaike weight (w) for a covariate indicates relative importance of the
covariate based on summing weights across models where the covariate occurs. Random effects for
pair identity and nest identity are fitted for all models. Variance components for the global model are
0.67 and 0.0001 for pair identity and nest identity, respectively. Coefficients are in bold where CIs do
not include zero. Only covariates occurring in the subset of best models (ΔAICc<2) are presented.
Variable
w
β
Lower CI
Upper CI
Chl-a(q3)
0.50
16.03
2.13
29.94
SST(q2)
0.85
0.75
0.09
1.42
Chl-a(q2)
0.56
2.9
0.41
5.41
SST(q3)
0.07
-0.18
-0.49
0.13
Chl-a(q1)
0.12
-3.22
-10.16
3.71
NAO(q2)
0.16
0.21
-0.21
0.64
NAO(t-1)
0.12
0.10
-0.46
0.68
SST(q1)
0.19
0.28
-0.49
1.06
NAO(q1)
0.05
-0.11
-0.55
0.31
Table A10. Model-averaged partial regression coefficients (β) and unconditional 95% confidence
intervals (CIs) from generalized linear mixed-effects models of nest fidelity (FidNest, n=422) in the
Monteiro’s Storm-petrel population monitored on Praia Islet (2000–2012) in relation to (i) a reduced
set of oceanic variables: Sea Surface Temperature computed for the 2nd quarter of the year (SST(q2))
and Chlorophyll a concentration computed for the 2nd and 3rd quarters (Chl-a(q2) and Chl-a(q3)); (ii) the
breeding success at the pair level (BS’) and (iii) all first order interactions between BS’ and other
covariates. Akaike weight (w) for a covariate indicates relative importance of the covariate based on
summing weights across models where the covariate occurs. Random effects for pair identity and
nest identity are fitted for all models. Variance components of the global model are 0.07 and 0.1 for
nest identity and year, respectively. Coefficients are in bold where CIs do not include zero. Only
covariates occurring in the subset of best models (ΔAICc<2) are presented.
Variable
w
β
Lower CI
Upper CI
BS’
1.0
3.94
0.16
7.74
Chl-a(q2)
0.64
6.76
-1.47
15.00
Chl-a(q3)
0.98
-40.46
-90.25
9.31
BS’×Chl-a(q2)
0.44
-7.38
-14.63
-0.15
BS’×Chl-a(q3)
0.54
-34.92
-82.72
12.87
SST(q2)
0.47
-0.63
-1.72
0.44
2. Individual-based approach
In order to check that conclusions are robust to model and variable construction at the
pair level (and in particular, FidNest , which quantifies nest fidelity at the pair level,
whether or not mates remain together), we conducted alternative modeling of nest
fidelity considering an individual-based approach (instead of pair-based), with separate
datasets for males (n=323) and females (n=304). As in the main analysis, we examined
the interactions between best environmental predictors of breeding success (determined
using multi-model inference) and the individual breeding outcome (BS). In this analysis,
individual identity (instead of pair identity) was fitted as a random effects variable in all
models. Despite reduced sample sizes (due to individuals with unknown sex, which were
not considered here), results were in qualitative agreement with the main analysis (see
below).
Table A11. Model-averaged partial regression coefficients (β) and unconditional 95% confidence
intervals (CIs) from generalized linear mixed-effects models of nest fidelity (FidNest) in the Monteiro’s
Storm-petrel population monitored on Praia Islet (2000–2012) in relation to (i) a reduced set of
oceanic variables: Sea Surface Temperature computed for the 2nd quarter of the year (SST(q2)) and
Chlorophyll a concentration computed for the 2nd and 3rd quarters (Chl-a(q2) and Chl-a(q3)); (ii) the
breeding success at the individual level (BS) and (iii) all first order interactions between BS and other
covariates. Akaike weight (w) for a covariate indicates relative importance of the covariate based on
summing weights across models where the covariate occurs. Random effects for individual identity
and nest identity are fitted for all models. Coefficients are in bold where 95% CIs do not include zero.
Coefficients are in italics where 90% CIs do not include zero. Only covariates occurring in the subset of
best models (ΔAICc<2) are presented.
Males
Variable
w
β
Lower CI
Upper CI
BS
1
5.01
1.34
8.69
Chl-a(q3)
O.99
-17.5
-45.58
10.39
BS×Chl-a(q3)
0.76
-41.9
-75.99
-8.01
Chl-a(q2)
0.45
1.5
-3.34
6.36
NAO(q2)
0.41
-0.13
-0.65
0.37
Females
BS
1
1.60
-1.98
5.19
Chl-a(q2)
1
8.71
0.33
17.09
Chl-a(q3)
0.83
-85.6
-131.79
-39.58
BS×Chl-a(q2)
0.51
-7.6
-17.72
2.39
BS×Chl-a(q3)
0.36
37.6
-33.55
108.90
3. Use of composite environmental variables
A. Principal Component Analysis
We performed a Principal Component Analysis (PCA) on climatic and oceanic parameters,
including all North Atlantic Oscillation (NAO(t-1), NAO(q1), NAO(q2), NAO(q3)), sea surface
temperature (SST(q1), SST(q2), SST(q3)) and chlorophyll a (Chl-a(q1), Chl-a(q2), Chl-a(q3)) variables.
Subsequent analysis was based on the first four axes of the PCA, which jointly explained
more that 80% of the interannual variation in climatic and oceanic parameters (see Fig. A1
for a graphical representation of the first two axes.
Figure A1. Biplots of the two first principal components (PC1 and PC2) obtained from Principal
Component Analysis of climatic and oceanic parameters. The proportions of variance explained by
PC1, PC2, PC3 and PC4 are 0.303, 0.261, 0.150 and 0.113, respectively.
0
2
4
11
2
0.4
0.6
4
-2
13
chla_Q1 108
5
SST_Q2
SST_Q1
0
7
12
SST_Q3
6
0.0
PC2
0.2
9
4
NA0_q1
-2
NA0_q3
NA0_q2
-0.4
-0.2
1
2
-0.6
chla_Q3chla_Q2
3
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
PC1
B. Relationship between principal components (PCs) and the breeding success (BS)
We performed the same multi-model analysis as in the main results, considering the first
four principal components of the PCA presented above in the global model. Model averaging results
indicated that BS was strongly, negatively correlated to the second component of the PCA (PC2) (see
Table A12 below).
Table A12. Model-averaged partial regression coefficients (β) and unconditional 95% confidence
intervals (CIs) from generalized linear mixed-effects models of breeding success (BS) in the Monteiro’s
Storm-petrel population monitored on Praia Islet (2000–2012, n=701) in relation to the principal
components presented above (PC1 to PC4). Akaike weight (w) for a covariate indicates relative
importance of the covariate based on summing weights across models where the covariate occurs.
Random effects for pair identity and nest identity are fitted for all models. Coefficients are in bold
where CIs do not include zero. Only covariates occurring in the subset of best models (ΔAICc<2) are
presented.
Variable
w
β
Lower CI
Upper CI
PC2
0.99
-0.27
-0.42
-0.12
PC4
0.3
-0.05
-0.21
0.11
PC1
0.3
-0.03
-0.13
0.07
PC3
0.27
-0.007
-0.14
0.13
C. Analysis of the interaction between breeding outcome at the pair level BS and
composite environmental variables on nest fidelity FidNest
We then examined the interaction between the first four principal components (PCs) of the
above analysis and BS on Nest fidelity (FidNest). All first order interactions between BS and
PCs were included in the global model as fixed effects variables. As in the main analysis,
results uncovered significant negative interaction of BS and environmental quality. The best
index of environmental quality (PC2, as uncovered from the above analysis) was strongly
related to FidNest, in interaction with BS. As PC2 is negatively correlated with breeding
success, the positive BS×PC2 interaction term means that FidNest is high for successful
breeding pairs when conditions are bad, as in the main analysis (see Table A13 below).
Table A13. Model-averaged partial regression coefficients (β) and unconditional 95% confidence
intervals (CIs) from generalized linear mixed-effects models of nest fidelity (FidNest, n=445) in the
Monteiro’s Storm-petrel population monitored on Praia Islet (2000–2012) as a function of the
interaction of the breeding success (BS) and the first four principal component of the principal
component analysis presented above (PC1 to PC4). Akaike weight (w) for a covariate indicates relative
importance of the covariate based on summing weights across models where the covariate occurs.
Random effects for pair identity and nest identity are fitted. Coefficients are in bold where CIs do not
include zero.
Variable
w
β
Lower CI
Upper CI
BS
1.0
0.59
0.04
1.15
PC2
1.0
0.01
-0.38
0.41
BS×PC2
0.98
0.84
0.29
1.39
PC3
0.55
0.13
-0.12
0.37
PC4
0.48
-0.13
-0.39
0.13
PC1
0.45
0.11
-0.11
0.33
BS×PC3
0.18
0.17
-0.25
0.59
BS×PC1
0.15
-0.18
-0.60
0.23
BS×PC4
0.14
-0.13
-0.60
0.34
D. Alternative analysis excluding pairs monitored only once with a history of
fidelity and non-fidelity to their nest
In order to check that our general result is related to within pair variation (i.e., variation of
the behavioral response of a given pair depending on environmental conditions) and not
variation between pairs, we conducted the same analysis as above (section C of the present
appendix) by keeping only breeding pairs monitored more than once with a history of fidelity
and non-fidelity to their nest.
Exclusion of the breeding pairs monitored only once for fidelity led to a significant reduction
of sample size (n=337 instead of n=445 for the main analysis) but did not change the
qualitative result. As in the main analysis, results uncovered significant negative interaction
of BS and environmental quality. The best index of environmental quality (PC2, as uncovered
from the above analysis) was strongly related to FidNest, in interaction with BS. (i.e., FidNest
was high for successful breeding pairs when conditions were bad, as in the main analysis, see
Table A14 below).
Table A14. Model-averaged partial regression coefficients (β) and unconditional 95% confidence
intervals (CIs) from generalized linear mixed-effects models of nest fidelity (FidNest, n=337) in the
Monteiro’s Storm-petrel population monitored on Praia Islet (2000–2012) as a function of the
interaction of the breeding success (BS) and the first four principal component of the principal
component analysis presented above (PC1 to PC4). Akaike weight (w) for a covariate indicates relative
importance of the covariate based on summing weights across models where the covariate occurs.
Random effects for pair identity and nest identity are fitted. Coefficients are in bold where CIs do not
include zero.
Variable
w
β
Lower CI
Upper CI
PC2
1.0
0.11
-0.34
0.56
BS
0.98
0.37
-0.30
1.03
BS×PC2
0.88
0.81
0.19
1.43
PC4
0.47
-0.14
-0.43
0.15
PC3
0.44
0.04
-0.29
0.38
PC1
0.35
-0.03
-0.27
0.20
BS×PC3
0.18
0.31
-0.20
0.82
BS×PC4
0.13
-0.14
-0.67
0.39
BS×PC1
0.10
0.09
-0.39
0.57
4. Predictability of individual reproductive outcome in good versus bad years
We investigated the predictability of reproductive outcome of pairs in good and in bad years
by (1) considering the breeding success of a given pair in a given year t (BSt) as a predictor of
the breeding success of the pair in year t+1 (BSt+1); (2) considering the three univariate
predictors of BS as indices of environmental quality in year t; (3) considering a dichotomy
between “good” and “bad” years (t) based on these indices (median cuts); (4) assessing the
statistical relationships between BSt+1 and BSt in good versus bad years. Results indicate that
BSt+1 is generally positively correlated with BSt when conditions in year t are unfavorable, and
that this statistical association disappears when year t offers favorable conditions (see Table
A15 below).
Table A15. Generalized linear mixed-effects model of pair breeding success in year t+1 (BSt+1). The
fixed effects independent variable is the breeding success in the year t (BSt). Models are fitted for
several datasets corresponding to “good” or “bad” years according to three different oceanic and
climatic parameters (see text). In each model, random effects for pair identity, nest identity and year
were fitted. n is the sample size.
Envir. index
Type of year
Variable
n
Estimate
St.Error
Z-value
Chl-a(q2)
Good
BSt
210
0.25
0.38
0.64
Bad
BSt
138
1.26
0.53
2.39
Good
BSt
200
-0.13
0.39
-0.34
Bad
BSt
148
1.37
0.49
2.75
Good
BSt
197
2.45
1.16
2.1
Bad
BSt
151
0.63
0.38
1.7
Chl-a(q3)
NAO(q2)