. Each year harriers go through three phases: i) survive, ii) age and iii) reproduce, by this order. This means that a chick that survives the first year, becomes a juvenile; a juvenile that survives becomes an immature, etc. It also means that an immature individual that survives, becomes and adult and is immediately capable of breeding. This is important to ensure that immature individuals in a given year will be able to reproduce in the following year \cite{Kendall_2019}.
Deterministic population model
In the simplest version of the model, survival and fecundity are the same every year. The population of harriers at time \(t\) is represented by a column vector \(\mathbf{N}_t = [n_{0,t}, n_{1,t}, n_{2,t}, n_{3,t}]^\intercal\), where \(n_{0,t}\) represents the number of chicks in the population, \(n_{1,t}\)represents the number of juveniles, \(n_{2,t}\) the number of immature individuals and \(n_{3,t}\) the number of adults. We use the following conventions: i) population census are conducted post-breeding, ii) years span the period from one breeding event to the next, ii) birds breed on their birthday once they reach the maturity. The change in number of harriers from year \(t\) to year \(t+1\) is characterized by the dynamics matrix \(\mathbf{A}_{t}\) such that