Recovery Plan for the Northern Spotted Owl - DRAFT

Now, if f, and sy are uncorrelated (which will be true if they vary independentlyof each other), then1 Jsfl=f sj (3)in which caseave. -N_ a (4)so if we measured sa, f, and sJ for several years (and if the correlation between ftand s,, was sufficiently close to zero) then the average change among years (x)could be calculated as in equation (4).Several practical problems arise in estimating x for owls from demographicrates. Most of these problems are related to the fact that nonterritorial birds,and a few territorial ones, usually are missed during the surveys at the start ofeach year. Survival rates can be estimated from telemetry data but obtaining alarge enough sample is difficult. As a result, capture-recapture methods mustbe used to estimate the survival rates.Three common problems encountered in estimating population trends fromdemographic rates are described here. We discuss them with reference to thesimple equation for X described earlier, but note that in reality more complexequations generally must be used. Eq. 4, however, will suffice for illustratingthe problems and providing a general indication of how much error theseproblems may cause in estimating X. Before discussing the three problems, itmay be helpful to define the terms above in more detail. We define these termsusing all birds (i.e., males and females) whereas demographic analyses areusually based solely on females.Oft =no. fledglings produced in year tN.Satno. of the N. still alive at the start of year t+ 1N.no. of the ft still alive at the start of year t+ 1sitft1. Overestimation off.Nt includes all birds alive at the start of year t, but the number of fledglings per pairusually is estimated solely from territorial birds. Thus, N. is underestimated andIt is usually overestimated unless there are no floaters. One way to investigate thisproblem is by replacing f with fgpg where pg is the proportion of birds alive atthe start of the year that are territorial and fg is the average number offledglings per territorial bird. Omitting jig is equivalent to assuming that itequals 1.0. If it is less than 1.0, but is omitted, then population change isoverestimated by the quantity f-s(1 - Pg). For example, with f = sJ = 0.3 and Pg= 0.7, the error would be 0.027, so if population change was actually 0.975,265