## Introduction

Management of North American waterfowl relies heavily on survival rates (*S*) estimated from band recovery models (Brownie et al. 1985). Waterfowl are banded annually, primarily during late summer on the breeding grounds, and bands are recovered from hunters that harvest birds during the ensuing hunting season. Models used for estimating survival rates assume that there is no individual heterogeneity of the conditional band reporting rates, *r*. Seber (1970) defined band reporting rates (*r*) conditional on the bird dying, 1−*S*, so that the probability a band is reported is (1−*S*)*r*, which is equivalent to the band recovery rate (*f*) of Brownie et al. (1985).

Individual heterogeneity in *r* might occur for a myriad of reasons, including differential survival between time of banding and onset of hunting (Nichols et al. 1982; Zimmerman et al. 2010), differential vulnerability to harvest (Pollock and Raveling 1982; Pace and Afton 1999), or differential probability that hunters will report a recovered band (Henny and Burnham 1976; Reinecke et al. 1992). However, detection of individual heterogeneity in conditional band reporting rates is difficult, if not nearly impossible. The estimate of *r* is a purely binomial process, with each bird that dies having only a Bernoulli trial as to whether its band is reported. That is, a bird only dies once, and so there cannot be repeated trials of whether a band is reported that would allow detection of individual heterogeneity. In contrast, repeated trials of birds surviving annual intervals in a band reporting analysis provide the necessary information to detect individual heterogeneity in survival rates, and hence, estimation of σ_{S} in the models described below, and repeated recapture or resighting of living birds in Cormack–Jolly–Seber models allows for the detection of individual heterogeneity in detection probability (*P*).

One approach that might be used to detect individual heterogeneity of conditional band reporting rates would be to separate birds into independent analyses and then compare the estimates of *r* across these lots, in the sense of Burnham et al. (1987), Part 4. However, this approach is generally inefficient and would be unlikely to detect low amounts of heterogeneity. A second approach is the use of covariates or groups (Dorazio 1997). However, only covariates measured at the time of banding are available, because potential covariates at the time of recovery are only available for reported bands. Further, these covariates have to correlate with the conditional band reporting rate (*r*) which seems unrealistic except for a few easy to measure covariates such as age or body mass at time of banding (Pace and Afton 1999). Thus, the covariate approach is again not likely to provide much explanatory power for detecting individual heterogeneity of *r*.

Even if individual heterogeneity in *r* can be shown, the real issues are whether this effect causes bias in the estimates of survival and whether individual heterogeneity in *r* will result in the detection of nonexistent individual heterogeneity in *S*. Therefore, our objective was to evaluate the potential for incorrect inference about individual heterogeneity of *S* and the potential for biased estimates of *S* when considerable individual heterogeneity exists in *r*.