ECOLOGICAL REACTION OF CROP YIELDS 333 



Formula 4.3 may depict the growth factor water with parameters as 

 clay and humus content, depth of water table and rainfall, each with its own 

 characterising units and functions to express the part of the moisture factor 

 which they each represent if their activity is expressed in the same scale of 

 the growth factor. 



Formula 4.4 represents the general case with empirical growth indicators 

 where none of the parameters represent a theoretically pure growth factor. 

 An instance is the optimum curve, which may be given by a formula : 



q = A{i- e-Oi<Pi^) (i - e-P+02(Pi)) 



Here a stimulating factor •^^=^l(Pl) is correlated positively with the para- 

 meter pi, and an antagonistic growth factor dy= — p +^2(^1) ^^ correlated 

 negatively with pi. Other growth parameters may be added or subtracted 

 to the functions of p. Instead of a formula of the type of 1.4, formulae of the 

 type of 2.4 or 3.4 might just as well have been used here. The point to be 

 stressed is, that if for one growth parameter an optimum curve is found, 

 this means that two growth factors x and y are behind such a type of 

 reaction, and that each of the formulae given can easily depict such an 

 optimum reaction. 



If two plant physiologically independent growth factors are influencing 

 the yield, they may, however, comprise the same parameter. Humus, for 

 instance, may bind nutritive cations as well as water. Now a yield, 

 influenced by water and cations, may assume the following shape : 



q = A(i — e-9i(Pi)-g2(P2)-'"\ U — e-g3iPi)-gi(P3)-"-\ 



Here we see the expressions according to case 4.3 and 4.4 combined, as 

 humus represented by pi appears in two factors. In each of them humus is 

 combined with another parameter, with p^ representing rainfall in the 

 moisture factor and p^ representing artificial manure in a nutritive factor. 



The type of growth function depends on four considerations being, 

 (i) what assumption is made with respect to the growth formula, (2) what 

 expectations exist as to the component parts, which build up the separate 

 growth factor, (3) what knowledge is available as to the functions, which 

 reduce the parameters to the same scale and (4) what is the value of the 

 constants? These considerations should be mathematically, physically and 

 physiologically sound. The number of parameters in ecological investiga- 

 tions may be very large. The number of growth factors, however, is much 

 more restricted. It will be important to study how the parameters should 

 add up to the relevant growth factor and how the growth factors co-operate 

 in the yield. 



