FORMULAE FOR THE ECOLOGICAL REACTION 



OF CROP YIELDS 



W.C.VlSSER 



Instituut voor Cultuurtechniek en Waterhuishouding, 

 Wageniiigen, Netherlands 



Many investigations dealing with the influence of growth factors on crop 

 yield will profit from the description of the result by a growth function. 



The flexibihty of freehand curves through scatter diagrams or of poly- 

 nomials, fitted through the data, may be narrowed down by taking into 

 account the mathematical properties of a growth formula. If the yield has 

 to be described as the result of a complex system of productivity parameters, 

 the description will never be very exact without the help of a formula. 

 The modern technique of processing observations with electronic calculat- 

 ing machines requires a functional expression. A growth function based on 

 biologically acceptable principles may be valuable, particularly if the 

 growth factor has to be described by a comphcated system of plant, soil 

 and moisture parameters as is the case with moisture. 



In the past, growth functions have attracted much attention, but interest 

 has decreased in later years. This may be due to insufficient integration of 

 mathematical reasoning and plant physiological insight. An extension of 

 already known formulae seems possible to make up for imperfections. 



Growth functions are often considered to be entirely empirical and of no 

 fundamental value. As will be shown, the best known formulae, of entirely 

 different origin, have so much in common that one will have to consider 

 whether the assumptions behind these formulae have not a value exceeding 

 the quahfication 'empirical'. 



Whatever the situation may be, it will be valuable to have a model 

 available describing in principle the activity of a growth factor with respect 

 to the maximum yield and the interaction between a number of growth 

 factors. 



THE GROWTH FUNCTION 



The oldest formula, but still the best known, is that of MitscherHch. The 

 most important of his ideas was, that the increase in yield per unit increase 

 in growth factor should bear an expHcable plant physiological relation with 



