338 W. C. VISSER 



considered, valid leads to the formula for the law of hmiting factors. Curve 

 fitting without such a formula would not easily lead to results acceptable 

 from a plant physiological standpoint. It should be mentioned here, that 

 the exact mathematical treatment of the equation for the hmiting factors 

 does lead to considerable difficulties, if the aim should be to determine the 

 unknown constants a, h. A, B and C. 



Summary and Conclusion 



Growth functions should be constructed with regard to plant physiological 

 reasoning. Differential equations, giving the increase in yield per unit of 

 the growth factor, supply the basic relations. Simple assumptions for the 

 relation between the yield increase, the yield and the growth factors already 

 give useful formulae for the yield patterns, but increased refinement of the 

 assumptions are needed to obtain the flexibihty to depict the different 

 relations which may be encountered. 



The growth equations are able to handle any number of ecological 

 variables and allow the description of complex productivity situations. 

 It is, however, necessary to know how these empirical productivity 

 magnitudes should be inserted into the formulae. There are only a restricted 

 number of growth factors, but only seldom will it be possible to obtain 

 quantitative observations of a theoretically correct, uncontaminated growth 

 factor, for which alone the simple solutions of the differential equations are 

 vahd. The value of the theoretically correct growth factor has to be built 

 up from the values for the relevant ecological parameters. 



This reconstruction of the value of the real growth factor may be attained 

 by using a function of the ecological factor instead of the value itself. Also 

 it may be necessary to construct the growth factor using a number of 

 different yield parameters or the same parameter may be necessary to 

 describe different growth factors. This makes the equations very flexible, 

 but it may be rather difficult to give empirical yield parameters their correct 

 place in the equation. 



It seems that the assumption 3.1 provides the most acceptable basis for a 

 yield equation, because the law of limiting factors is more easily justified 

 than the law of diminishing returns, described by formula i.i. Also 

 equation 3 gives a better account of what might be physiologically expected 

 with regard to the interaction between growth factors. 



The main problem in ecological research is, however, to translate the 

 description of the ecological situation with many values into a description 

 of the restricted number of well-defined but complex growth factors. 

 Every growth factor should be constructed using the relevant ecological 



