months prior to the time of birth.-* Thus, the 

 exponential average density is a proxy vari- 

 able which summarizes all relevant causal 

 influences of the real system. The casual in- 

 fluences are indicated in Figure 2, but are not 

 explicitly programmed into the computer. 



In the model, losses are defined as either 

 natural or due to hunting. Natural losses are 

 the residual of losses after accounting for the 

 recorded hunter kill. The natural losses will 

 include those due to age, the plane of nutrition, 

 the action of predators, disease, and accidents 

 on the highways. Both natural and hunting 

 losses are computed each time period. Natural 

 losses are computed for each category of deer 

 by reference to functions relating the density 

 of deer at the beginning of the period to the 

 rate of mortality. Here, density is the proxy 

 variable for an array of causal relationships, 

 as indicated by Figure 2. These natural mor- 

 tality functions were based upon biological 

 theory and the available empirical evidence. 

 The paucity of data, however, precluded sta- 

 tistical estimation; hence, use was made of 

 interpolation techniques between data points 

 to derive the mortality rates for particular 

 densities. Natural losses are therefore endog- 

 enous to the model. 



Hunting losses are treated differently. The 

 hunting loss rates are defined by age category 

 and the time period in which hunting is allow- 

 ed, as specified prior to the execution of a com- 

 puter iTin. The hunting losses could be made 

 endogenous, but in the first generation model, 

 where accent is on formulating a reasonable 

 biological model, it is advantageous to man- 

 ipulate these losses to test the model. In the 

 real world, hunting strategies are fomulated 

 cognizant of political considerations, regula- 

 tions, management capability, and the demand 

 for hunting. They are the consequences of 



^ The exponential average density each month is 

 computed as follows; 



EAD, = EAD,_i + in (D, - EAD, ,) 



interactions which are not fully indicated by 

 Figure 2. 



Thus far, the model has been presented as 

 deterministic. The real world is characterized 

 by random variability. The response of the 

 deer biosystem to a particular set of conditions 

 is variable, due to random, uncontrollable 

 elements such as the weather conditions. Ran- 

 domness must be accounted for in any simu- 

 lation which purports to model reality. 



In the deer model, a random number gener- 

 ator is used to generate variability.'^ Vari- 

 ability is due to weather conditions which are 

 assumed to result in particular forage quality- 

 quantity relationships or forage conditions. 

 The notion of a forage factor is used as an 

 index of forage conditions. Each year, a random 

 number is computed which, in turn, implies 

 a particular forage factor. Only five forage 

 conditions are identified. A forage factor of 

 five corresponds to average conditions; and 

 a forage factor of one corresponds to poor con- 

 ditions. Forage factors of two and four cor- 

 respond to below and average conditions, res- 

 pectively. 



The probability distribution of forage factors 

 can be easily modified, consistent with the 

 investigation of the impact of changes in the 

 pattern of forage conditions over time. Once 

 the forage factor is selected for the year, it is 

 used to modify the components of the system 

 which are considered to be subject to vari- 

 ability due to changes in the forage conditions 

 — namely, natural mortality rates and birth 

 rates. The notion of the forage factor has 

 proved most useful in the development of the 

 computer model, in addition to its primary role 

 in carrying out experiments with the model 

 after development. 



Thus, the biomanagement system is present- 

 ed as a network of flows, rates, and levels. The 

 system being modeled is complex, but by suit- 

 able abstraction, a workable dynamic model 

 which permits examination of the system in 

 a manner not permitted by the usual compara- 

 tive statics formulation, can be developed. 



where: t = Time period (month) 



EAD = Exponential average density (deer/ 



square mile) 

 D = Density (deer/square mile) 



T = Exponential smoothing time con- 



stant (number of months) 



" The computer program generates a sequence of 

 pseudo-random numbers which provides the facilities 

 for comparing results of different i-uns under identical 

 simulated conditions. 



125 



