FISHERY BULLETIN: VOL. 83, NO. 3 



Table 6. — Accuracy of the 95% confidence limits (C.L.) on popula- 

 tion size estimated by the logarithmic and root transformations of 

 the distribution of total population size. For each transformation, 

 the estimated lower and upper confidence limits are shown for pro- 

 jections of the population given in Table 1 for 2, 5, and 10 time steps. 

 The columns labeled "Proportion beyond C.L." give the actual pro- 

 portion of 10,000 stochastic projections using program SLT which 

 fall below the estimated lower limit and above the estimated upper 

 limit for each transformation. Each set of projections was replicated 

 3 times. The root transformation estimates the 95% confidence in- 

 terval on population size more accurately, especially for short pro- 

 jections. 



example projection are shown in the columns on the 

 right side of Table 3. The mean and the 95% con- 

 fidence interval for the total population size and for 

 the realized factor of increase are given for each time 

 step. As the population vector approaches the stable 

 age distribution, the ratio between successive mean 

 total population sizes approaches the asymptotic 

 value 1.0240. The mean realized factor of increase 

 shown in Table 3, which is computed relative to the 

 initial population, does not converge on this asymp- 

 totic value; nor can the mean realized factor of in- 

 crease be computed from the ratio of the mean final 

 population size to the initial population size. Instead, 

 the mean and variance of the realized factor of in- 

 crease are computed by methods described above. 



The probability that the total population size will 

 have increased over its initial value is also shown for 

 each time step in the last column of Table 3. In this 

 particular example, since we did not begin with the 

 stable age distribution, this probability decreases at 

 first and then increases. As a further check, program 

 SLT computes the proportion of cases in which the 

 final population was greater than the initial popula- 



tion, and this answer (0.7954, Table 5) is close to the 

 probability computed analytically by program SPP 

 assuming that the realized factor of increase is nor- 

 mally distributed (0.7990, Table 3). Given a popula- 

 tion whose age structure and dynamics conform to 

 the values given in Table 1, therefore, we can make 

 the statement that there is an 80% chance that the 

 population will be larger 6 time steps from now and a 

 20% chance that it will be smaller. 



Example 2. 



The results of the stochastic projection of the 

 northern fur seal population by program SPP are 

 given in Table 7 and Figure 2. Table 7 shows that 

 after 5 yr, the expected (mean) number of 9-yr-olds, 

 for example, is 6,188 with a standard deviation of 

 333. The expected total population size is 147,982 

 with a standard deviation of 8,832. The mean and 

 standard deviation of the realized factor of increase 

 are 1.0812 and 0.0129, respectively; from these 

 values we compute the 99% confidence interval on 

 population size to be from 126,410 to 171,930. Note 



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