GROWTH CURVES 



567 



cordance with prevailing environmental conditions, but simply that the relative 

 rate of growth at any time during the growth period normally bears a definite 

 relation to the relative growth increment which has already occurred and 

 which may be expected to occur subsequently. A maize plant, for example, 

 which has developed under adverse environmental conditions may attain only 

 half the stature of a similar plant which has completed its growth under more 

 favorable circumstances, yet if curves representing the growth rate of the two 

 plants be plotted both will assume the characteristic shape exhibited by Fig. 

 122, //, although the actual magnitude of the values on the two curves will 

 be very different. 



If the total increment of growth instead of the rate of growth be plotted 

 against time the resulting curve will assume a typical sigmoid shape (Fig. 122, 

 B). Any growth phenomenon which is represented by a curve of the type 

 shown in Fig. 122, A, when plotted in terms of growth rates, will yield a 

 sigmoid curve when depicted graphically in terms of growth increments. 

 Hence such sigmoid curves of growth are 

 characteristic of a wide variety of growth 

 phenomena. | 



Equations can be derived which indicate °- 

 in mathematical terms growth relations such o 

 as those depicted graphicallv in Fig. 122, B. ^ 



o 



A number of attempts have been made to 1- 

 attach some special significance to such math- u 

 ematical formulations of the rate of growth, > 

 It has been considered, for example, that the 

 mathematical expression representing a sig- 

 moid growth curve is identical with the equa- 

 tion of a monomolecular autocatalytic reac- 

 tion (Robertson, 1923; Reed, 1920) and by 



others as representing the same type of equation as that expressing the increase 

 in a sum of money at compound interest (Blaclcman, 19 19). All such con- 

 cepts are, however, of doubtful or limited validity, at least as applied to the 

 higher plants, and will receive no further attention in this discussion. 



A growth curve plotted in terms of the increment in dry weight for the 

 entire life history of an annual plant will assume the generalized form in- 

 dicated in Fig. 123. Such a curve can most readily be pictured as represent- 

 ing the growth increment in terms of dry weight of a crop plant such as maize. 

 During the germination stage there is usually a slight loss of dry weight due 

 to respiration at a time when photosynthesis has not yet attained any appre- 

 ciable rate. Following this the curve swings into the characteristic sigmoid 



Fig. 123. Generalized growth 

 curve for the life cycle of an 

 annual plant. 



