Farnsworth and Simons (2005) questioned our use of their previously published fecundity model (Farnsworth and Simons 2001) in our assessment of the relationship between Mayfield nest-survival estimates and seasonal fecundity in the Black-throated Blue Warbler (Dendroica caerulescens) (Jones et al. 2005). Briefly, they disputed our finding that their model substantially underestimates seasonal fecundity and offered what they believe are the correct estimates based on the data we provided in our paper. After a detailed and amicable exchange with the model’s senior author (Farnsworth), we discovered an error in how we had translated the model’s description (“Model 1“ in Farnsworth and Simons 2001) onto an EXCEL spreadsheet. This error, which was solely the responsibility of the senior author (J. Jones), undervalued the contribution of late-season successful nests to seasonal fecundity. Here, we examine the consequences of this mistake.
As part of this examination, we believed it would be useful to redo our original analyses on the basis of the corrected estimates of fecundity provided by the model’s authors (Table 1). The corrected estimates exhibit a positive relationship with our observed fecundity values (major-axis model II: F = 7.93, df = 1 and 14, P = 0.01, r2 = 0.36, observed = −0.26 + [0.63 × estimated]). However, the slope of this relationship is still significantly different from 1.0 (t = 2.85, P < 0.02). The model estimates average 75.6 ± 8.9% (mean ± SE) higher (range: 22.1% to 150.2%) than observed fecundity values and are less representative at lower levels of observed fecundity (percentage of overestimate vs. observed fecundity; Pearson’s r = −0.55, P = 0.03). Finally, the model estimates generate a value of λ = 1.53 (95% confidence interval [CI]: 1.43 to 1.64; see Jones et al. 2005 for population model details). For comparison, our observed fecundity values generated a value of λ = 0.88 (95% CI: 0.79 to 0.97). Whereas the direction of the differences between the model estimates and our observed seasonal fecundity differs greatly from our initial analyses, the overall conclusions of our original manuscript remain unchanged. Farnsworth and Simons’s (2001) original model does not do a good job of predicting seasonal fecundity of a multibrooded species, and great care is needed in using nest-survival estimates (and models based on them) to assess population status or health.
In their letter, Farnsworth and Simons (2005) state that they did not intend for their original model to be used to estimate seasonal fecundity or to assess population status and offer three alterations to their original model to increase its use in a nontheoretical context: (1) relax the assumption that all females that can renest will do so if time permits, (2) restrict the number of successful broods to match empirical observations, and (3) use the number of fledglings per successful nest rather than clutch size to include the effects of partial predation. To test these recommendations, we reran our analyses using their updated model, now available online and easy to use. Although we assumed that all females that can renest would do so if there was enough time, we restricted the maximum number of broods (females never successfully raise more than two broods in a single season) and used the number of fledglings per successful nest rather than clutch size (Table 1). Grzybowski and Pease (2005:280) cautioned that “all estimates of seasonal fecundity in the literature derived by assuming a limited maximum number of nesting attempts or of successful broods are biased.“ However, we are confident that our modeling restrictions reflect realistic aspects of Black-throated Blue Warbler life history at Hubbard Brook.
The updated fecundity estimates (Table 1) exhibit a strong positive relationship with our observed values (major-axis model II: F = 14.34, df = 1 and 14, P = 0.002, r2 = 0.51, observed = −0.14 + [0.83 × estimated]), and the slope of that relationship is not significantly different from 1 (t = 0.74, P > 0.05). The model estimates average 27.8 ± 5.0% higher (range: 5.7% to 66.0%) than observed fecundity values and still show a tendency to be less representative at lower levels of observed fecundity (percentage of overestimate vs. observed; Pearson’s r = −0.47, P = 0.06). The updated model estimates generate a value of λ = 1.23 (95% CI: 1.14 to 1.32), which is significantly greater (no overlap in 95% CI) than the estimates based on our observations.
Consequently, even though the recommendations of Farnsworth and Simons (2005) greatly improve the predictive ability of their fecundity model (presumably, lowering the renesting probability would further improve the estimates), the results still might lead to incorrect assessments of population health (i.e. a growing rather than barely stable population). One way in which the updated Farnsworth and Simons model might be improved further is to incorporate variation (by age or calendar day) in nest-survival rates (Shaffer 2004). In conclusion, we believe that an important result of this exchange and Farnsworth and Simons’s updated model is their contribution to the growing recognition (see also Gzrybowski and Pease 2005) that researchers can no longer rely on simple measures (e.g. percentage of nest success or nest survival) or simple assumptions in the absence of detailed field data (e.g. all females attempt a fixed number of nests) when attempting to evaluate population status.
Estimates of seasonal fecundity (number of fledglings per female per year) for 16 years of data from a study population of Black-throated Blue Warblers at Hubbard Brook, New Hampshire. Sample sizes for empirical estimates and fledglings per successful nest are not necessarily the same within a given year