THE GROWTH OF EPIDERMAL STRUCTURES 



139 



Such a community of interest functioning in terms of an economy of 

 supply and demand might well maintain a constant ratio of cell-types while 

 permitting an unlimited growth of the total population. However, the fact 

 is ((c) above), that in all organisms the adult size is a rather well-defined 

 limit and the growth curve follows a characteristic sigmoid course (Fig. 56). 



Fig. 56. The sigmoid growth curve. N is the number of individuals 



(cells). The population N early passes through a phase of approximately 



exponential growth, later a logistic law is a better fit. 



It is evidently necessary to suppose that a further control mechanism 

 exists which maintains this size and is responsible for the shape of the 

 growth curve. 



That many natural populations follow what is referred to as the logistic 

 law: 



oW 



= eN-hN* 



(Where N = number of individuals, e and h are constants) has long been 

 known. A population obeying such a law tends towards a limit W = 

 e/h. When h is negligible, dN/dt = e N and the population increases 

 exponentially, N = N e a . This type of increase may be observed in 

 cellular populations during a limited period (the " log phase ") when 

 conditions are favourable, but sooner or later limiting factors appear, the 

 growth rate declines and a logistic law is more applicable. The problem is 

 usually to identify the limiting factors. 



The sigmoid shape of the growth curve can be simulated in a formal 

 sense by a number of physicochemical models, e.g. by the autocatalytic 

 monomolecular reaction, by systems which make demands in proportion 

 to their mass (L 3 ) and are able to accumulate (or lose) in proportion to 

 their surface areas (L 2 ). Such physicochemical models have a broad 



