THE GROWTH FORM OF POPULATIONS 



305 



population at some future specified date 

 —a warning that we view sympathetically. 

 They say: "If by the statement that the 

 logistic ... is the law of population 

 growth, one means only that the formula 

 is well suited to fitting the census enumer- 

 ations for the period of a century or so 

 when such enumerations have actually been 

 made, we can take no exception to it. . . . 

 But if the statement is to be considered as 

 signifying that the formula aflFords a ra- 

 tional law to such an extent as to permit 

 the extrapolation of the curve for forecast- 

 ing purposes and the interpretation of the 

 constants as constants of nature, we are 

 forced to take serious exception to it" (p. 

 342). 



We return to the logistic curve in the 

 next chapter, on Growth Form, in which 



we show its breadth of application, and 

 again in Chapter 22. Our present interest 

 has been to show (1) that it does provide 

 in many cases a convenient description of 

 population growth; (2) that it is well estab- 

 lished in population literature; (3) that it 

 directs attention to certain compound, gen- 

 eral factors that play a causative role in 

 population trends and permits these factors 

 to be arithmetically evaluated; and (4) 

 that, while the logistic curve does not iden- 

 tify such factors biologically, it does stress 

 their existence and recommends their fur- 

 ther study. Despite the criticisms that can 

 be leveled against it, the logistic curve, 

 when not overinterpreted and when used 

 intelligently purely as an empirical record 

 of population growth, is a valuable demo- 

 graphic tool. 



21. THE GROWTH FORM OF POPULATIONS 



The major trend in size of a population 

 through time, or, as we prefer to call it, 

 its "growth form," is basic to the develop- 

 ment of the population problem. The coor- 

 dinates of growth form are some expression 

 or index of numbers (ordinate) against time 

 (abscissa). Growth form is roughly analo- 

 gous to knowledge of, say, the anthropo- 

 metry of a man, which provides a sort of 

 general statement about his total structural 

 development, or to such physiological in- 

 dices as basal metabolic rate, respiration 

 rate, heart rate, body temperature, and so 

 forth, which evaluate in a way his total 

 metabohc relationships. 



This chapter is devoted to a description 

 of the various population growth forms. The 

 major trends as they might exist in a hypo- 

 thetical population are discussed first. This 

 defines the possibilities. Then, actual illus- 

 trations drawn rather extensively from 

 the literature dealing with laboratory, 

 natural, and human populations are pre- 

 sented. Data covering the course of a par- 

 ticular population over an extended period 

 are unfortunately rare. Thus, we are forced 

 to use one example to make one point and 

 another example to make another. Chapter 

 22 deals with the relations of growth form 

 to natality, mortality, and dispersion and, 

 further, its relation to population integra- 

 tion. 



DEFINITIONS: THE PATTERNS OF 

 GRO\An"H FORM 



It is convenient to define the following 

 stages of population growth form: 



I. The period of positive, sigmoid 

 growth (the population increasing) : 



A. The establishment of the popula- 

 tion i.e., its initiation or "taking 

 hold" in its environment 



B. The period of rapid growth rate 



(sometimes called the "logarith- 

 mic phase," especially by micro- 

 biologists) 



C. The period of decreased growth 

 rate as the asymptote is ap- 

 proached 



II. The equilibrium position. Equilib- 

 rium is defined as mean numerical 

 stability 



III. Oscillations and fluctuations. These 

 are departures (in both phase and 

 amplitude) from equilibrium: 



A. Oscillations: relatively symmetri- 

 cal departures 



B. Fluctuations: relatively asymmet- 

 rical departures 



IV. The period of negative growth 



(population decline or contraction). 

 Consistent and progressive reduction 

 of the population below equilibrium 

 or below the lower range of usual 

 fluctuations and/or oscillations. 



