Table 1.
Summary of the 36 candidate models tested. (The model formula presents the full model for each trend fitted. All intermediate models were tested, see appendix (table S1 and S4 in the electronic supplementary material). Bs, breeding success; Bp, breeding probability; bsann, inter-annual variations in breeding success; bpann, inter-annual variations in breeding probability; SOI, southern oscillation index; SIEautumn, sea ice extent values for autumn; asterisk stands for an interaction.)
| model formula | biological meaning | number |
|---|---|---|
| Bs (or Bp)∼1 | no effect of age on reproduction | 1 |
| Bs (or Bp)∼age | linear effect of age on reproduction | 2 |
| Bs (or Bp)∼age+age2+bsann (or bpann)+SOI+SIEautumn | quadratic effect of age on reproduction | 3–10 |
| Bs (or Bp)∼log(age)+bsann (or bpann)+SOI+SIEautumn | logarithmic effect of age on reproduction | 11–18 |
| Bs (or Bp)∼bsann (or bpann) | mean annual breeding output only explains variations of reproduction | 19 |
| Bs (or Bp)∼T1+T2+ bsann (or bpann)+SOI+SIEautumn | existence of one threshold age (6<τ1<34) | 20 to 27 |
| Bs (or Bp)∼T1+T2+T3+ bsann (or bpann)+SOI+SIEautumn | existence of two threshold ages (6<τ1<20, 21<τ2<34) | 28–35 |
| Bs (or Bp)∼T1+T2+T3+ bsann (or bpann)+bsann (or bpann)*T3 | existence of two threshold ages and an interaction between year quality and age | 36 |