where \(\zeta_t\) corresponds to the rate of change of the mean number of individuals per site in year \(t\). We further incorporate all we know about the life history of the Black Harrier to model \(\zeta_t\).
To structure the life history of the Black Harrier, we defined three age classes:  fledglings  - individuals that have left the nest up to 1 year old , sub-adults for individuals that are  one year old, and adults - for individuals two years and older. Adult individuals are the only birds capable of breeding. In addition to an age structure, we defined survival rate as the probability of survival in a given year, and fecundity as the number of offspring per adult bird per year (note that fecundity usually refers to offspring per female, but we have redefined this to simplify notation later).