GROWTH 547 



The period of decline will depend on the nature of the environment and 

 the rate of growth. It may show a phase of increasing death rate, a ^ 

 logarithmic death rate, or a decreasing death rate, or these phases may 

 follow one another. 



Had the inoculum been taken from an old culture which had reached 

 the equilibrium or the period of decline, then there might have been 

 a stationary period (F), followed by a period of increasing rate of 

 growth (G), which would be followed by a constant relative rate (H), 

 shown by the curve becoming parallel with the A curve. It is advan- 

 tageous to know and to take into account these phases, in experiments with 

 populations of unicellular organisms. The duration of the stationary 

 and the lag phases will vary with the age of the inoculum and the effect 

 of the previous unfavorable environment of them. Populations from 

 old cells often provide considerable variation. Whenever possible, experi- 

 ments should be made during the logarithmic period, to insure uni- 

 formity of material. 



The detailed shape of the growth curve is often not known, because 

 of infrequent measurements. If the Protozoa divided synchronously at 

 the end of the generation time the curve would be like curve I. 



The difference between the number of organisms in a population, 

 shown by curves B or C, and the number theoretically possible, shown 

 by the extension of curve A, is a measure of the inadequacy of the 

 culture medium. The difference between the expected maximal number, 

 curve D, and the number at a given time measures the potential growth 

 yet to be achieved. The environmental resistance may be expressed as one 

 minus (the potential growth divided by the expected number). This 

 type of analysis, in terms of the logistic equation, has been made by - 

 Gause (1934) for the population growth of P. caudatum, and his in- 

 structive graph should be examined by all students of population growth. 

 For information on the mathematics of growth. Pearl (1925), Jahn 

 (1930), Richards and Kavanagh (1937) may be consulted. Protozoolo- 

 gists have not used mathematical methods to any extent. Park (1939) 

 also reviews Gause's analysis. Similar growth studies of other protozoan 

 populations, besides presenting local data, should contribute to the general 

 understanding of growth. 



Buchanan and Fulmer (1928) have reviewed the literature of the 

 growth of bacterial populations; Richards (1934) yeast populations; 



