Estimating the Effects of Varying Temperature on the Rate of Development of Plants

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Abstract
Experiments on the effects of temperature on plant development usually yield measurements of the times at which recognizable stages of development are reached, and a record of the varying temperature patterns during development. Two complementary methods for analyzing such data to reveal the underlying relationships between rate of development and temperature are discussed. In both methods it is assumed that there exists a unique relationship between current rate of plant development and current temperature. In the ‘discrete-rate’ method, the rate of development function, r(T), is approximated by a set of discrete values r1, r2…ri…rn, each applicable over a given temperature range. The fractional state of development of a plant, S, is written as the sum of the products of these rates, ri, times the fraction of total time during development that temperature was within each range, fi, i.e. S = Σri. Systems of such equations can be solved for the ri, values, and this enables an assessment of the rate-temperature relationship without preconceived notions on the form of the plant response. This assessment can then be used as a basis for selecting a suitable interpolation function to be fitted to the data using the ‘rate-function’ method. Here a mathematical form for the function r(T) is selected at the outset. The temperature scale is divided into discrete intervals and a set of equations, similar to the above, is developed. These equations are solved for best values of the parameters of the r(T) function. These methods are illustrated by application to controlled-environment data on times from sowing to flowering in soybeans and pigeonpeas, and on rates of leaf appearance in maize. Advantages claimed for the two methods are that they provide a systematic approach for relating development to plant temperature and that they are based upon an explicit physiological hypothesis.

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