With the logit transformation above we ensure that mean fecundity per harrier stays within zero and two birds (i.e. four birds per pair). Because we standardized annual rainfall values, the coefficient
\(\beta_0\) informs the (logit) fecundity under conditions of average rainfall for the study period; whereas
\(\beta_1\)modifies fecundity depending on rainfall levels. We used accumulated rainfall in the south west of South Africa as this is where the core
of the Black Harrier breeding population occurs \citep{m-s2020}. More precisely, we identified all weather stations in a 400 km radius of Laingsburg (Latitude: -33.2, Longitude: 20.9) and summed up the accumulated rainfall they registered in each year. We used the data provided by the Global Historical Climatology Network (
www.ncdc.noaa.gov), retrieved using the R package
rnoaa \citep{rnoaa20}.
Fitting the dynamic occupancy model in a Bayesian framework allows us to incorporate what we know about the life history parameters of the Black Harrier as priors into the model (see \citealt{Ellison2004} and table \ref{tbl:post_param}). We also estimate the exponential survival curve, annual fecundity and probability of detection simultaneously, making more effective use of the information \citep{Schaub_2010}. We can then estimate the joint posterior distribution of all parameters, and from it, simulate population trajectories to investigate possible future scenarios for the species.