THE CONCEPTUAL FORMULATION AND MATHEMATICAL 



SOLUTION OF PRACTICAL PROBLEMS IN POPULATION 



INPUT-OUTPUT DYNAMICS 



K. E. F. Watt 



Statistical Research and Services, Canada, Dept. Agriculture, Ottawa 



INTRODUCTION 



A recent spate of books has focused attention on a spectre that has haunted 

 many thinking men since antiquity. Writers from Plato on have noted the 

 sickeningly destructive effect that civilization can have on the productivity 

 of the environment through shortsighted management practices. Brown 

 (1954), Castro (1952), Cook (i95^)» Darwin (1952), Ordway (i953)» Osborn 

 (1948, 1953), Sax (1955), Sears (i947)» Vogt (1948) and many others have 

 tried to alert the public to impending danger through their reahstic appraisals 

 of the staggering needs of man's increasing numbers in contrast to the 

 potential productivity of the earth. The effects of mushrooming human 

 populations against an increasingly more exhausted array of natural resources 

 can reduce all mankind to a bestial level of existence more surely than a row 

 of super-bombs stretching from here to Betelgeuse. 



It is eminently apparent that two problems are now of crucial importance. 

 First, the maximum amount of renewable natural resources that the world 

 can produce each year must be estimated with a high degree of precision 

 and accuracy. Second, it must be determined how maximum levels of 

 production can be attained and maintained. 



Soil science, hvestock and crop genetics, silviculture and many other 

 disciplines can aid in the solution of the above two problems. However, two 

 components of the conservation research programme occupy the domain of 

 the population ecologist. For a given^ population and conditions extrinsic to 

 the population, what age distribution and rate of exploitation will yield a 

 maximum harvest and still leave behind enough reproductive individuals so 

 that a maximum rate of biomass yield can be sustained ? Also, what is the 

 maximum thus obtained ? 



Through a combination of experimentation, field observation and 

 theoretical analysis, population ecologists can determine the form of the 

 interaction of various factors on population productivity, and evaluate the 



