reciprocal equation
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AIP Advances ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 095001
Author(s):  
Lianyun Liu ◽  
Xu Zheng ◽  
Zhiyong Hao ◽  
Yi Qiu

1982 ◽  
Vol 33 (2) ◽  
pp. 171 ◽  
Author(s):  
o Soeton ◽  
DW Puckridge

The spatial relationships and growth of individual plants were studied in barley and wheat crops to determine the influence of size and distance of neighbouring plants on the development of individuals within the population. Plants were harvested individually, and their positions recorded by X and Y coordinates. The dry weights within quadrats were categorized in 10 weight classes and plotted for visual analysis. A reciprocal equation was used to relate the weight of individual plants to 'competitive pressure' of near neighbours. The estimate of competitive pressure was based on the weight and distance of neighbours. Both visual analysis and numerical analysis failed to find a direct effect of space available or the location of near neighbours on the growth of individual plants. It is suggested that in dense cereal crops differences in time of emergence and quality of soil environment may over-ride the advantage of an increased spatial environment for individual plants.


1974 ◽  
Vol 83 (2) ◽  
pp. 189-195 ◽  
Author(s):  
H. D. Voldeng ◽  
G. E. Blackman

SUMMARYThe interacting effects of genotype and density on the yield of dry matter by mature shoots were examined at Oxford, England. There were six hybrids, either pure dent or flint × dent crosses, together with two open-pollinated flint varieties of very early maturity. Over a range of 15 densities (5·0–30·8 plants/m2) for all the genotypes the relationship between the yield of the shoot and density can be adequately described by the reciprocal equation 1/w = A + Bp, where w = weight per plant, p = number of plants per unit area and A and B are constants for any particular set of conditions. Values of both 1/B (asymptotic yields) and 1/A (weight per plant at very low densities) were dependent upon the genotype. In a regression analysis between 1/w and p, the variance of 1/w was over 40 times as great at high as at low densities and a weighted analysis was necessary. Some hybrids approached maximal yields at 5 plants/m2, whereas others required a density of 10–15 plants/m2. The possible reasons for these interactions are discussed and improvements in experimental design suggested.


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