The relationship between crop yield (or mean plant weight) of lettuce and plant density, length of growing period, and initial plant weight

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Abstract
SUMMARY: Lettuce obeys the Shinozaki–Kira relationship in which the reciprocal of plant weight is linearly related to plant density. The intercept (a) represents the reciprocal of the weight of an isolated plant and the slope (b) represents the reciprocal of yield/unit area at high densities (the ‘ceiling yield’). This work examines the time course of (a) and (b) in an ‘ideal environment’ in which water and nutrients are non-limiting, and the light/temperature regime is constant.Two pot experiments are described: the first showed that the growth of isolated lettuces follows a logistic expression, which can therefore be substituted for a–1 in the Shinozaki-Kira equation. It was then hypothesized that b–1, the ‘ceiling yield’ would be constant over time. This was confirmed by the second experiment, giving the equationw–1t = w–10 e1–kt × w–1max × bd,in which wt is mean plant weight at time t, w0 and wmax are the initial and final weights of isolated plants, k is the early relative growth rate of such plants, b–1 is the constant ceiling yield, and d is the plant density.Two examples of the use of the equation are given: one shows how it predicts the interaction between seed size and plant density within a species (subterranean clover): the other illustrates how it can be used to explain why lettuce growth appears to be log-linear against time whereas cereal growth is more nearly just linear.
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