Mortality produced by wind farms

There are at least two conceivable ways to incorporate additional mortality produced by wind farms. The first one considers a constant extraction each year, which means that the change in survival rate varies every year. This is because the ratio extraction-to-population changes as the population fluctuates. Alternatively, we may consider a fixed change in (expected) survival rate induced by the interaction with wind farms. Under this premise there is a density dependent mortality, by which the number of harriers dying at wind farms is proportional to the harrier population. While a density dependent mortality might be more realistic, we consider a constant extraction scenario to be more illustrative for management purposes and therefore we adopt this approach. In addition, very little is known about density dependence in harrier species' population parameters )  \cite{e2000}but it does play a role among other raptor species  \cite{SIMMONS_1993}\citep{2002} \cite{Elliott_2011}and it can  influence both productivity and age at first breeding and it may influence rare or recovering populations \citep{Morandini_2019} . Finally, due to the diminishing extent of favourable Black Harrier habitat \cite{Curtis2004}, we anticipate that vacant territories produced by wind farm mortality would be readily occupied by floating individuals, at least while population numbers allow it. This would produce a relatively constant exposure to wind farms more consistent with the constant extraction scenario. At present there is little evidence that Black Harriers breeding in or near South African wind farms abandon their territories (RE Simmons and M Martins unpubl data) and thus little evidence that this avoidance/displacement would  reduce mortality.pulation simulations
To investigate the behaviour of Black Harrier populations trajectories under different scenarios we run 500 Monte Carlo simulations of population trajectories 100 years long. The simulation process is as follows:
  1. For each trajectory we sampled population parameters from the prior distributions.
  2. To start each population trajectory we sample an initial population value.
  3. Within each trajectory, and using a step size of one year, we update the number of harriers in the different age categories according to the parameters sampled in step 1 and accounting for inter-annual variability.
  4. We compute population quantiles (90%, 75%, 50%, 25%, 10%) at each time step across population trajectories.
We repeat the simulation process using different levels of mortality produced by wind farms and compare the results.
We used R to run all the analysis \cite{R20} with the added functionality of the tidyverse packages \cite{wickham19}. The R package survival was used to fit a survival curve to the duration of the tracking period of birds in \citet{Garcia_Heras_2019}, using the Kaplan-Meier method, and 3 dead vs. 10 right censored birds \citep{survival-book}.