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A Mathematical Model Relating Plant Yield with Arrangement for Regularly Spaced Crops

1967; Oxford University Press; Volume: 23; Issue: 3 Linguagem: Inglês

10.2307/2528011

1541-0420

Geoffrey Berry,

Forest ecology and management

where w is the yield per plant or biologically definable part of plant (e.g. leaves, roots), p is the number of plants per unit area, and a and c are constants. As density increases, the total yield per unit area (wp) given by (1) approaches an asymptotic maximum yield (1/c). An equivalent relationship was proposed independently by De Wit and Ennik [1959] and by Holliday [1960]. Holliday considered it typical where yield was the result of vegetative growth but inadequate to describe cases where yield was the result of reproductive growth, since he then found that a maximum yield per unit area occurred for some finite density, with higher densities resulting in lower yields. For convenience such relationships will be referred to as parabolic, although this term is not to be understood as applying in the strict mathematical sense. Bleasdale and Nelder [1960] queried the generalization that yields influenced mainly by vegeta-tive and reproductive growth give asymptotic and parabolic relationships respectively, but also found that equation (1) was inadequate. They proposed a modification to allow for both asymptotic and parabolic relationships, a simplified