We represent the population of harriers at time \(t\) as a column vector \(\mathbf{N}_t = [n_{0,t}, n_{1,t}, n_{2,t}]^\intercal\), where \(n_{0,t}\) represents the number of fledglings , \(n_{1,t}\) the number of sub-adults and \(n_{2,t}\) the number of adults in the population. The change in the number of harriers from year \(t\) to year \(t+1\) is characterized by the transition matrix \(\mathbf{A}_t\) such that