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)