Prior sensitivity analysis for denning survival

[ChloeRN]

For denning survival (S0), we are using a highly informative prior directly taken from the results of the arctic fox IPM (truncated Normal with mean = 0.74 and sd = 0.06). While this is probably not very far off, we do not actually know how appropriate this prior is. We also know from sensitivity analyses that denning survival is a potentially influential vital rate, and that why it is important to run a prior sensitivity analysis for it.

To do that, we should re-run models with slightly different priors, e.g. higher mean, lower mean, larger sd.

[ChloeRN]

Doro and Stijn have also found some opportunistic observations of numbers of pups on dens (from camera traps and/or den hunts) and we can also test models that use this data.

[ChloeRN]

We see that the majority of vital rate estimates are quite robust to the choice of S0 prior with the exception of harvest mortality. Using a completely flat prior (Uniform[0, 1]) we see that we get estimation issues for both S0 and mH, with some chains landing at unrealistically low S0 values (around 0.25) and - consequently - higher harvest mortality. Changes in means and SD of the S0 prior are mirrored almost directly in mH: higher S0 -> lower mH, more uncertain S0 -> more uncertain mH. What is interesting is that when we increase the prior standard deviation, i.e. give the model more "wiggle-room", the mean of S0 also shifts towards a lower value. This seems to indicate that the model would "prefer" a somewhat lower S0.

[ChloeRN]

At the population level, we see that the model with a higher mean S0 (0.84) produces larger estimates of population size on average but also has extremely high uncertainty. Decreasing mean S0 results in slightly lower population sizes during population peaks, while increasing SD of S0 results in slightly lower population sizes overall. In the grand scheme of things though, population size estimates do not appear very sensitive to small changes in the S0 prior (unless the mean is increased or prior information removed).

[ChloeRN]

The comparisons with models including opportunistic data on numbers of pups on dens lead to quite similar conclusions:

First off, adding data to a model using the original informative prior has almost no effect, highlighting jsut how powerful/dominating that prior is. Adding data to a model with a flat prior (Uniform[0,1]), on the other hand, gives us results rather similar to the ones above using higher uncertainty in the prior: the estimate of S0 is more uncertain and has a lower mean on average. The uncertainty propagates into the mH and population size estimates, while the lower mean gives us ever so slightly lower population sizes:

Note also how including the opportunistic data gets rid of the very high uncertainty in popualtion-level estimates for year 2018.

[ChloeRN]

[Different priors for S0 seem to only have minimal effects on the median estimates for environmental effects and random year variation in other vital rates. Uncertainty propagates, however]

[ChloeRN]

Included the new setup for more flexible prior / data likelihood specification for S0 via #43