GERRODETTE ET AL.: CONFIDENCE LIMITS FOR POPULATION PROJECTIONS 



Table 7.— Results of the 5-yr stochastic pro- 

 jection of the northern fur seal population, bas- 

 ed on the age structure and vital rates given in 

 Table 2. Probability that the final population 

 > initial population = 0.999 -t-. 



that, as will generally be the case, the confidence in- 

 terval for total population size is not symmetric 

 about the mean value. 



In the last line of Table 7, the probability of an in- 

 creased population is shown to be very close to 1.0. 

 In other words, it is virtually certain that the popula- 

 tion will have increased in size after 5 yr. Figure 2 

 presents the results for total population size graph- 

 ically. The 95% and 99% confidence limits computed 

 by program SPP are shown for each time step. The 

 confidence limits grow nearly geometrically. 



DISCUSSION 



Fishery and wildlife management often involves 

 predictions of population size, and, owing to im- 

 perfect knowledge of the world, these predictions are 

 uncertain. Accordingly, a practical analysis attaches 

 estimates of confidence intervals for any given 

 prediction. The programs described in this paper 

 carry out the computation of confidence intervals for 

 projections of age- structured populations, if we can 



specify the statistics of the variation in the age- 

 specific vital rates. Realistically, we do not expect 

 there to be be many examples where the statistics of 

 the variation in vital rates are genuinely known with 

 substantial precision, for these rates are difficult to 

 measure in natural populations. Nevertheless, in an 

 imperfect world, management decisions must be 

 made with imperfect data. A considerable compo- 

 nent of the uncertainty in a population prediction will 

 be owing to the phenomena treated in this paper. 

 Thus, even the use of very rough guesses at the sta- 

 tistics of the variation in the age-specific vital rates, 

 in order to estimate confidence intervals in a popula- 

 tion projection, is preferable to neglecting this 

 source of variation entirely. At the very least, incor- 

 poration of speculative estimates in this applied con- 

 text will allow the exploration of "what if " questions 

 in a fashion that can indicate priorities for future 

 data gathering. 



In many fish and aquatic invertebrate species, 

 there is an enormous variation in the success of year 

 classes. In such cases the population dynamics may 

 be dominated by the overwhelming abundance of one 



180 |- 95% Confidence limits 



99% Confidence limits 



■g 160 



12 3 4 5 

 YEARS IN FUTURE 



Figure 2. -Confidence limits for future total female population size 

 for the northern fur seal, based on the schedule of vital rates in 

 Table 2. The solid line plots the mean population trajectory. 



213 



