GERRODEITE ET AL.: CONFIDENCE LIMITS FOR POPULATION PROJECTIONS 



same initial population vector, may be replicated a 

 given number of times. From these replicated projec- 

 tions, the mean, variance, and covariances of the 

 population vector are computed, together with 

 statistics on a variety of other demographic para- 

 meters. The distributions of the final population size 

 and the realized factor of increase are tabulated. 



The computer programs to accomplish these 

 stochastic projections are called, respectively, SPP 

 (Stochastic Population Projection) and SLT (Sto- 

 chastic Life Table simulation). Program listings and 

 guides to the use of both programs are given in Ger- 



dynamics of the population are given in Table 2 

 (taken from Goodman 1981: table 1) and confer a 

 population growth rate of about 8% per year. The 

 initial age vector in this case was chosen to be the 

 stable age distribution with a total of 100,000 

 females. Values for the standard deviations in vital 

 rates in Table 2 were selected by choosing reason- 

 able values for their coefficients of variation. Corre- 

 lations in vital rates were assumed to be 0.9 between 

 fecundities at different ages, 0.9 between survival 

 rates at different ages, and 0.5 between all fecun- 

 dities and survival rates. 



Table 1.— initial population vector, mean vital rates, and covariance matrix of vital rates for a 

 three age-class population projection. In the covariance matrix, F refers to fecundity rate, P to 

 survival rate, and numbers to age classes. 



rodette et al. (1983). Although lengthy, these pro- 

 grams are suitable for use on many microcompu- 

 ters. 



Numerical Examples 



Two numerical examples are presented to verify 

 various analytic results and to illustrate the use of 

 programs SPP and SLT in a management context. 



The first example is a simple artificial life table 

 with three age classes. The mean vital rates and the 

 covariance matrix for the vital rates are given in 

 Table 1. This example was used to compare the 

 predicted mean and variance in projected population 

 size based on Sykes' (1969) formulae with the actual 

 mean and variance from the simulation. The example 

 was also used to test the assumption that ultimate 

 population sizes will be lognormally distributed, and 

 in particular whether accurate confidence limits for 

 the tails of the distribution can be made based on this 

 assumption. 



The second example is based on a real population. 

 A northern fur seal, Callorhinus ursimis, population 

 is projected using vital rates consistent with a phase 

 of rapid growth which occurred earlier in this cen- 

 tury. The mean vital rates which govern the 



Table 2.— initial population vector, means, and standard 

 deviations (S.D.) of vital rates for a fur seal population projec- 

 tion used as a numerical example in the text. Mean rates are 

 taken from Goodman (1981: table 1). Each age class repre- 

 sents 1 yr, and only the female portion of the population is 

 tabulated. The initial population vector is in the stable age 

 distribution with a total of 100,000 females. 



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