Raptors are exposed to a wide variety of human-related mortality agents, and yet population-level effects are rarely quantified. Doing so requires modeling vital rates in the context of species life-history, behavior, and population dynamics theory.
In this paper, we explore the details of such an analysis by focusing on the demography of a resident, tree-nesting population of golden eagles (Aquila chrysaetos) in the vicinity of an extensive (142 km2 ) windfarm in California. During 1994–2000, we tracked the fates of >250 radio-marked individuals of four life-stages and conducted five annual surveys of territory occupancy and reproduction. Collisions with wind turbines accounted for 41% of 88 uncensored fatalities, most of which were subadults and nonbreeding adults (floaters). A consistent overall male preponderance in the population meant that females were the limiting sex in this territorial, monogamous species.
Estimates of potential population growth rate and associated variance indicated a stable breeding population, but one for which any further decrease in vital rates would require immigrant floaters to fill territory vacancies. Occupancy surveys 5 and 13 years later (2005 and 2013) showed that the nesting population remained intact, and no upward trend was apparent in the proportion of subadult eagles as pair members, a condition that would have suggested a deficit of adult replacements. However, the number of golden eagle pairs required to support windfarm mortality was large. We estimated that the entire annual reproductive output of 216–255 breeding pairs would have been necessary to support published estimates of 55–65 turbine blade-strike fatalities per year. Although the vital rates forming the basis for these calculations may have changed since the data were collected, our approach should be useful for gaining a clearer understanding of how anthropogenic mortality affects the health of raptor populations, particularly those species with delayed maturity and naturally low reproductive rates.
Demographic cost of windfarm mortality
To assess the direct influence of blade-strike mortality, we estimated the number of golden eagle pairs required to sustain it. The reasoning behind our analysis began with an estimate of the number of pairs necessary to produce a single fatality (S4 Appendix). Consider that the observed average number of fledglings (of both sexes) per pair was 0.638 during our study, so the death of a recent fledgling would consume the issue of 1/0.638 = 1.567 pairs. We estimated, however, that the average age of blade-strike death during 1987–1997 was 40 months, that is, assuming all adult fatalities were first-year adults (see Methods). Our survival data (with turbine deaths censored) showed the probability of a fledgling surviving 40 months as 0.695, meaning that an eagle of that age was the sole survivor of 1.448 fledglings, the production of which demanded the existence of 2.256 territorial pairs. These pairs were, of course, not self-sustaining in that the 4.512 pair-members each incurred an annual mortality risk of 0.080, thus requiring 4.512 x 0.080 = 0.361 annual replacements (floaters) of at least 56 months of age. We calculated that a 56-month-old eagle is the sole survivor of 1.653 fledglings and therefore 2.590 pairings, meaning that an additional 2.590 x 0.361 = 0.935 pairs were necessary to supply those recruits, yielding a subtotal of 2.256 + 0.935 = 3.190 pairs. Continuing the process through five additional steps leads to 3.844, an approximation of the number of territories supplying each blade-strike death. Model 1 in S4 Appendix formalizes this incremental procedure and provides a simple computational formula with result 3.931 for the exact count towards which the previous counts asymptote.
Published estimates of blade-strike deaths occurring during 1998–2007 ranged from about 55 to 65 individuals per year . Thus, if the vital rates we estimated remained valid during that period, the least of those estimates—55 deaths—would have consumed the annual production of 55 x 3.931 = 216 pairs existing at the demographic break-even point, producing no buffer of recruits in excess of that required to sustain themselves. The estimate of 65 annual windfarm deaths reported by Bell and Smallwood  would have required the existence of 255 occupied territories. If one assumes that 90% of the population contributing to windfarm mortality was resident to the DR study area, as the radio-tracking data suggested, and that the likelihood of bladestrike death in the Altamont was a function of natal distance to the windfarm (our data are ambivalent here), then we can estimate a footprint of its influence upon the population in the DR study area. The minimum geographic extent of that influence (90% of 55–65 fatalities) would thus be defined by the distribution of the nearest 195–230 territories. Indeed, the estimated total number of territorial pairs in the DR study area in 2014–2015 was 280 pairs (95% CI = 256–305 pairs) , suggesting that the golden eagle population of that area was sufficient to withstand the mortality occurring within it.
Note that this approach to estimating population cost is not limited to windfarms and other spatially localized hazards, but can apply to a variety of mortality regimes so long as an expected annual number of fatalities can be estimated. Our method does, however, require knowledge of background population vital rates, and the latter are difficult to obtain with precision. With regard to the applicability of our analysis to the current effect of the Altamont windfarm on the golden eagle population, we acknowledge that much of the data we draw on is relatively old, and that conditions have changed with recent repowering efforts . Moreover, our 5-year sample of reproduction surveys was doubtless insufficient to accommodate weather effects, including the periodicity of drought cycles in this region  and predictions thereof . Another contingency was that reproductive performance in the core study area may not have accurately represented that of the entire DR study area with its greater array of habitat variation . These and other uncertainties suggest that the value of the analysis lies mainly in what it reveals about the proportional cost of human-related mortality to raptor populations, particularly those species with delayed maturity and naturally low reproductive rates. Even so, and despite the many challenges associated with this kind of approach, there will be cases in which the impact of a mortality agent must be evaluated in the absence of vital rates data specific to an area. Here, the application of general estimates might nevertheless yield useful approximations of the burden upon a population of a given number of fatalities within the context of its metapopulation.