ECOLOGICAL REACTION OF CROP YIELDS 

 2nd solution 



= aL 



329 



(3.5) 



i {x+B^){y+B^){z+B,)... 

 The eqs. 2.4 and 2.5 are depicted in the Figs. 3 and 4 



Discussion 



In formula 2.1 the yield increase is supposed to increase in relation to the 

 yield deficit and inversely with the level of fertility. The growth equation 

 is a projective function and the inverse value of the yield deficit bears a 

 linear relation with the growth factor as given in 2.3. In the multifactorial 

 formula the logarithm of the yield or the yield deficit is, as in the Mitscher- 

 hch equation, the sum of the logarithms of the influences of every growth 

 factor separately as appears from the first and the second solution. This 

 property is important for a graphical analysis of the effect of a number of 

 growth factors on the yield. 



The curves in Figs. 3 and 4 offer a picture of the relations given by the 



Growth factor X 



Growth factor X 



Fig. 3. Shape of growth curves for projective law of plant growth. The curves are 

 somewhat steeper for low yields and give a somewhat more gradual increase in 

 yield at high fertility levels than the exponential curves of Fig. i. The part valid for 

 practical yield levels may approach the exponential curves very closely. The yields in 

 per cent of the maximum give the same curves for different values of the y-factor. 

 Fig. 4. Second solution of the differential equation to be compared with the curves 

 in Fig. 3. The curves may be derived from one single curve by expanding it in a 

 vertical and horizontal way by means of two multiphcation factors. Shape of growth 

 relation often found in field experiments. 



formulae 2.4 and 2.5. The curves in Fig. 3 may be derived from each other 

 by changing the vertical scale, the curves in Fig. 4 by changing the hori- 

 zontal scale. If instead of the horizontal scale of .v, the curves are plotted 



