ECOLOGICAL REACTION OF CROP YIELDS 



337 



A second instance deals with the influence of sprinkling irrigation and 

 nitrogen supply on the number of grazing days of cattle on perennial 

 grassland. The original data were not very accurate and a rehable fitting of 

 the yield curves was only possible if the functional relation between the 

 yield, the nitrogen and the appHed amount of water was given in advance 

 (Fig. ii). 



pQ^Production grazing days 



800 



700- 



600 



500 



400 



lOO 



200 300 400 500 



mm overhead irrigation 



900 



800 



700- 



600 



500 



400 



ICO 200 300 400 500 

 kg/ ha nitrogen 



Fig. II. The influence of sprinkling irrigation and nitrogen on grazing days can best 

 be described with formula 3.4 for the law of the limiting factors. The result for a dry 

 year was found as depicted above. 



It is well known that the yield function for the growth factors water and 

 nitrogen may often be approximated by a straight line if quantities of 

 water, nitrogen and yield are plotted against each other. This suggests that 

 the law of limiting factors applies and formula 3 . 4 in the shape 



(x+A-rt^) (y+B-^ {Q-q) = D 



may be used. The constants A and B mean that part of the moisture and 

 nitrogen, used by the plant, originate from rainfall, combined with soil 

 moisture and from nitrification respectively. For the dry year, the value 

 of .4 was found to be 350 mm whereas a appeared to be 500 1 water per kg 

 dry material. B was found to be 400 kg and h equal to 20 kg dry material 

 per kg N. The values for A and B correspond well with what might be 

 expected. The rainfall may accoimt for 220 mm of the value o£A, and 

 130 mm extracted water from the profile is not in contradiction with the 6 

 to 14 sprinklings given with an average of 28ommappHedwater(Fig. 11). 

 It would have been difficult to fmd the relation between the yield and 

 the two growth factors without an assumption as to what kind of relation 

 might be expected. Reasoning about the model of the yield function to be 



