In the above matrices \(\rho_t\) and \(\phi\) represent fecundity and survival rate, respectively. As a reminder, we defined fecundity as the mean number of offspring per female and year and survival as the proportion of birds that survive a given year on average. The subscript 1 indicates the parameter is associated with fledglings and the subscript 2 that is associated with either sub-adults or adults. Fecundity in Black Harriers is known to be affected by rainfall (see below) and is therefore allowed to vary across years. The rate at which the population changes from time \(t\) to time \(t+1\) is given by the main eigenvalue of the matrix \(\mathbf{A}_t\), which we denote by \(\zeta_t\) (\citealp{Caswell2001,al} en prep), and we substitute in equation (\ref{eq:dyn_lambda}) to link observed population dynamics with the life history parameters of the Black Harrier. The main eigenvalue of matrix \(\mathbf{A}_t\), is calculated as