A New Model Relating Crop Yield and Plant Arrangement

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Abstract
A new model is proposed which relates the weight of plants to their spatial arrangement. The weight of each plant is calculated as the integral of the function f(r) = L(cr2 + 1)−2 over an area allocated to it, r being distance from the plant, with L and c parameters to be specified. The model is thus concise, general, in that it can be used to describe the effects of any spatial arrangement on plant weight, and the parameters L and c have a biological interpretation. It is also consistent with the commonly-used relationship between plant weight (w) and density (p), w−1 = a+bp. We show for carrots (Daucus carota L.) and red beet (Beta vulgaris L.), that the mean weights fitted by the model agree as well with the experimentally observed mean plot weight as those fitted by more complex models with more parameters, some of which are not as general. We show also that the parameter c can be predicted from the time from sowing to harvest, with good results when tested on sets of data independent of those to which the model had been fitted. The assumptions on which the model is based, its application, and extensions to it are discussed.