(C) Modelling individual life-histories
The model describing life-history variation presented in table 1 in a
mixed-effect model form is:
\(y_{\text{gjki}}=u_{g}+\ \beta_{1g}S_{i}+\beta_{2g}H_{i}+C_{\text{gj}}+P_{\text{gk}}+e_{\text{gjki}}\), (eq. S5)
where \(y_{\text{gjk}i}\) represents life-history trait \(g\)(generation time, first age at reproduction, reproduction rate,
lifespan, lifetime reproductive success or individual growth rate) of
individual \(i\) in cohort j and population k . Here,\(u_{g}\) represents the statistical intercept for the model, which is
the estimated mean life-history trait for the reference category.\(\beta_{1g}\) is the coefficient reflecting average sex differences in
the life-history trait \(g\), where \(S_{i}\) represents the sex of
individual i (0 for females; 1for males). \(\beta_{2g}\) is
the coefficient describing the average life-history differences between
the type of island where an individual was breeding (0 for inner farm
islands; 1 for outer non-farm islands). \(C_{\text{gj}}\) represents the
cohort effects (n=16) on the life-history traits, and \(P_{\text{gk}}\)represents the population differences (n=8) in the average life-history
trait. In this case, \(e_{\text{gjki}}\) reflects individual differences
(n=1232) in the life-history traits, because there are no repeated
measures for each individual as the life-history traits are estimated
for the whole life. Cohort specific values \((C_{\text{gj}})\),
population specific values (\(P_{\text{gk}}\)) and individual specific
values \(e_{\text{gjki}}\), were all assumed to come from separate
normal distributions for each life-history trait with variance\(V_{C_{g}}\), \(V_{P_{g}}\) and \(V_{e_{g}}\).