For greater certainty, or if survey conditions were poor, we 

 could extend the upper limit expected to 1,464 (1,000/0.683). 

 For most winter and spring surveys, the true total population 

 probably fell within a narrower range of deviation from the 

 Lincoln estimate than would be indicated by standard 

 confidence intervals (Overton and Davis 1969) about the 

 estimate. 



In the example given above, with a Lincoln estimate of 

 1,250 deer, a 95% confidence interval estimated a possible 

 range in total numbers from 948 to 1,648. Both extremes were 

 unlikely. During all early winter surveys and half of those 

 in spring, the lower confidence estimate was below the number 

 of deer actually counted. Similarly, during most census 

 intervals, it was biologically and mathematically impossible 

 for deer numbers to increase from the lower limit calculated 

 for one period to the upper limit for the next (or vice versa) 

 when concurrent information on natality and mortality within 

 the population were considered. Those data reduced the 

 practical confidence interval to well within the standard 95% 

 limits. Because population estimates were made 3-4 times each 

 year with data on natality, mortality, and population 

 composition available, we are confident that "true" population 

 levels deviated within a very narrow range from the Lincoln 

 estimate. Arithmetic modeling indicated the likely direction 

 and degree of that deviation as provided by our ultimate, 

 modeled population estimate (Appendix A) . 



During years in which marked deer were available for 

 calculation of Lincoln indices, population trend and relative 

 annual changes in numbers were similar whether the Lincoln 

 estimates, the modeled estimates, or the actual counts were 

 used (Fig. 2.1). Thus, conclusions about population dynamics 

 would not be altered even if the precision of individual 

 estimates is questioned. 



Findings and methods developed during 1976-1987 enabled 

 us to refine previous early winter population estimates 

 (Mackie 1970, 1973, 1976) and construct models that estimated 

 autumn and spring populations on the study area each year from 

 1960 through 1975. Initial estimates for 1960-1963 were 

 developed by plotting numbers of mule deer observed by 

 location on gridded aerial photographs and from aerial surveys 

 during winter (Mackie 1970). Those for 1964-1975 were 

 developed by applying general observability indices ranging 

 from 60 to 70% (ave. 65%) (Mackie 1976) to numbers of deer 

 counted in helicopter surveys in early winter to calculate 

 relative densities within areas surveyed each year. Total 

 populations were calculated by extrapolating densities on 

 areas surveyed to the entire area. Arithmetic modeling 

 accounted for natality and known or estimated mortality and 

 reconciled sex and age composition between successive 



39 



