eaglesFWS:

# Conclusions

### Primary Takeaways

The use of prior distributions of exposure probability can strongly affect the predicted eagle take at wind energy facilities.  Among 26 wind farms, the average difference between 80^th^ percentiles of Bayesian versus site-specific estimates of eagle fatalities was `r round(mean(abs((Bay_16$U_F - Bay_16$U))), 2)` eagles per year (max = `r round(max((Bay_16$U_F - Bay_16$U)), 2)`, s.d. = `r round(sd((Bay_16$U_F - Bay_16$U)), 2)`).  Across our range of simulated values for eagle activity rates and survey effort, site-specific and Bayesian fatality estimates differed by as much as `r round(max(abs(sim$U_F - sim$U))*mean(Bay_16$SCALE), 2)` eagles per year.

The discrepancy between site-specific and Bayesian estimates of predicted fatality increases as the eagle activity observed at a site is more extreme.  Controlling for the effect of survey effort, the discrepancy between estimates increases by `r round(src_discrep$SRC[2,1]*sd(rgamma(5000, mean(Bay16$FLIGHT_MIN), mean(Bay16$EFFORT)))/sd(sim$eagle_rate)*sd(sim$U_F - sim$U)*mean(Bay16$SCALE)*-1, 2)` eagles for every standard deviation an observed level of eagle activity falls from the prior mean.

Survey effort can also change the magnitude of this effect.  At the minimum survey effort required by FWS, the difference between site-specific and Bayesian fatality estimates ranged from `r round(min((sim$U_F - sim$U)*mean(Bay_16$SCALE)), 2)` to `r round(max((sim$U_F - sim$U)*mean(Bay_16$SCALE)), 2)` eagles per year. For a site with minimum eagle exposure rates (0.01 min/hrxkm^3^), adding an additional survey hour per month, or survey plot, to the FWS minimum will decrease discrepancy by `r round(((sim$U_F[1] - sim$U[1])-(sim$U_F[2] - sim$U[2])) * mean(Bay16$SCALE), 2)` predicted annual fatalities, on average.

### Recommendations
The relationship between deviation of observed exposure rates from the mean of the prior and estimate discrepancy suggest thresholds for trigger points at which FWS may want to consider a different approach to permitting and mitigation, or require additional survey effort.  These thresholds should be based on the standardized distance initially observed eagle activity rates at a site are from the mean of the prior distribution.

Increasing minimum survey effort - either number of plots, or number of hours - will reduce the influence of general priors, increasing confidence in the posterior estimates.  This will benefit both wind developers, who can be less skeptical that mitigation requirements are being artificially inflated, and FWS, which can be more confident that Bayesian priors are not underpredicting fatality rates at sites with high eagle activity.

The addition of covariates to the prior distribution of exposure probabilities may also help alleviate the effect of priors on predictions at sites with extreme observed eagle activity.  Rather than integrating site specific values with prior information from all wind projects, they could be integrated with distributions from sites sharing similar characteristics.

### Discussion

An advantage of Bayesian modeling is to moderate the effect of random outlier observations.  However, this also means that where surveys accurately detect extreme observed eagle activity, this site-specific information can be effectively washed out.  Thus, an important question is when do extreme eagle activity levels observed during surveys accurately reflect site-specific eagle exposure, rather than representing random anomallies.  At two of four sites where Bayesian estimates were lower than site-specific estimates, the observed fataility estimate fell outside of the bayesian 80th percentile using priors, but was covered by the 80th percentile of the site-specific estimate.  These sites reported 2 of the top 3 eagle exposure rates, and illustrate instances where site-specific information should carry more weight.  In both cases, survey effort was in the lower 25% of all sites.
Permits are re-evaluated every 5 years.  Thus, the mean observed discrepancy of `r round(mean(abs((Bay_16$UQ_F - Bay_16$UQ))), 0)` fatalities per year could equate to the unexpected take of an additional `r round(mean(abs((Bay_16$UQ_F - Bay_16$UQ)))*5, 0)` eagles before models are updated.  FWS advises that if permitted eagle take exceeds 1% of the estimated population size of either species within the LAP area, additional take is a concern.  If take exceeds 5% of the estimated population size within the LAP area, additional take is considered inadvisable.  Cummulative authorized take must not exceed 5% of local populations.  Underestimating eagle take by a few individuals per year over a 5 year permit, could approach these thresholds.  The inverse is not ideal from the perspective of regulated entities, as wind developers could pay mitigation costs for an unwarranted 5 additional incidental takes.

It should be noted that our Bayesian fatality estimates were generated by integrating observed measures of eagle flight time and survey effort with prior defined by the mean of these values across survey sites.  Survey effort is used to adjust the rate parameter of the gamma distribution used to define the eagle exposure prior.  Thus, increased survey effort leads to a narrower posterior distribution, and smaller 80% CI.  In practice, this makes sense, as we have greater confidence that the results of more intensive surveys are reflective of consistent patterns, rather than conditions during a limited number of instances.