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Mathematics of the Relationship between Plant Population and Individual Production of Maize (Zea mays L.)

Predominantly, field experiments aim to determine the optimal plant density for a unit area. High spatial variation results in lower attained yield than the genetic potential. To find the highest value of the product of mean individual production and crop density, their mathematical relationship is needed to be known. In this study, the relationship between the population and the weight of the individual fresh, dehusked ear of grain maize (Zea mays L.) was investigated, and a relevant mathematical simulation model was developed. Linear regression was disproved to describe this relationship properly based on the analysis of different mosaic sizes within a plot. The distribution of plant-to-plant distance was found to be binomial. The distribution of the ear weight was found to be lognormal. For the description of the population homogeneity, neither the standard deviation nor the variation coefficient was found to be applicable apart from the scale-independent relative variance. The simulation model, based on the above statistical functions, was validated with a real dataset, and it is recommended for the optimization of the plant population at farm scale.