B) Estimates of individual life-history traits
Based on the pedigree, we used the number of recruits produced by each individual in each year to calculate all the elements of the individual projection matrices and derive some key life-history traits, such as individual expected growth rate and generation time (McGraw & Caswell 1996). To calculate an individual’s generation time, it must have produced a recruit. Thus, only individuals that produced at least one recruit during their lifetime were considered in these analyses of individual life-histories, resulting in a total of 1052 individuals (552 females and 500 males, see Table S1 for more details).
To estimate the projection matrix A(i) of individual i we need to know the number of successful recruits it produced (\(F_{h}^{(i)}\)) at each age h and the age when it diedd (McGraw & Caswell 1996). Where survival \(S_{h}^{(i)}\)will be equal to one for all h = (1, 2, …, d-1) and zero forh = d :
\(A^{(i)}=\par \begin{bmatrix}F_{1}^{(i)}&F_{2}^{(i)}&\cdots&F_{d}^{(i)}\\ S_{1}^{(i)}&0&\cdots&0\\ &\ddots&&\\ 0&&S_{d-1}^{(i)}&0\\ \end{bmatrix}\) . (eq. S1a)
Once an individual transition matrix \(A^{(i)}\) is formed, the dominant eigenvalue \(\lambda^{(i)}\) of this matrix measures the asymptotic population growth rate for a collection of individuals with the propensities to survive and reproduce equal to individual i(McGraw & Caswell 1996); that is, it is an estimate of the expected growth rate of a population consisting of individuals with the characteristics of individual i (i.e. expected individual growth rate):
\(1=\sum_{h=1}^{d^{\left(i\right)}}{F_{h}^{\left(i\right)}{(\lambda^{\left(i\right)})}^{-h}}\). (eq. S1b)
A similar life-history measure can be defined as an individual’s reproductive rate (\(r^{(i)}\)), which is the mean number of recruits an individual produced per year:
\(r^{(i)}=\frac{1}{d^{(i)}}\sum_{h=1}^{d^{\left(i\right)}}F_{h}^{(i)}\). (eq. S2)
The lifetime reproductive success \(R^{(i)}\) of individual \(i\) can be estimated as the sum of the fecundities at each age h :
\(R^{(i)}=\sum_{h=1}^{d^{\left(i\right)}}F_{h}^{(i)}\) . (eq. S3)
The first age at reproduction was calculated as the first age hat which individual i managed to successfully produce a recruit (\(F_{h}^{(i)}\)>0), and the lifespan was the age dwhen individual i was last observed. We estimated an individual measure of generation time \(T^{(i)}\ \)as the weighted mean age of an individual when it reproduced as:
\(T^{(i)}=\frac{\sum_{h=1}^{d^{\left(i\right)}}\text{hF}_{h}^{(i)}}{\sum_{h=1}^{d^{\left(i\right)}}F_{h}^{(i)}}\). (eq. S4)