By Allen R. Overman

Insightful reference/text describes the appliance of potential mathematical types in info research to extend crop progress and yields, highlighting potent, analytical capabilities which were chanced on worthwhile for the comparability of other administration innovations to maximise water and nutrient assets.

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**Extra info for Mathematical Models of Crop Growth and Yield**

**Example text**

Construct the plot shown in Fig. 5. h. 0/Y À 1Þ to the table. i. 0/Y À 1Þ vs. N to obtain parameters b and c in Eq. 7]. j. Use these parameters to construct the regression curve for Fig. 5. k. Discuss the results. 3 Solar radiation data adapted from Russell (1950). t ¼ calendar time since Jan. 1, wk; R ¼ average monthly solar radiation, kcal cmÀ2 moÀ1 . 22 Variation of average monthly solar radiation with calendar time for Rothamsted, England. Data from Russell (1950). 23 Probability plot of average monthly solar radiation for Rothamsted, England for data of Russell (1950).

1990a, 1990b) and Overman and Wilson (1999). Additional details will be covered in Chapter 4. 2 EXTENDED LOGISTIC MODEL The logistic model can be extended to cover plant nutrient uptake as well as dry matter production. A starting point for this model is three postulates: (1) annual dry matter yield follows logistic response to applied N, (2) annual plant N uptake follows logistic response to applied N, and (3) the N response coeﬃcients are the same for both. Postulate 1 can be written mathematically as A ½2:1 Y¼ 1 þ exp ðb À cNÞ where Y ¼ seasonal dry matter yield, Mg haÀ1 ; N ¼ applied nitrogen, kg haÀ1 ; A ¼ maximum seasonal dry matter yield, Mg haÀ1 ; b ¼ intercept 35 36 Chapter 2 parameter for dry matter; and c ¼ N response coeﬃcient for dry matter, ha kgÀ1 .

23, with the line drawn from Eq. 35]. Incorporation of an environmental function into the growth models will be discussed in Chapter 3. 18 Dependence of plant Ca accumulation on dry matter accumulation by wheat for experiment of Knowles and Watkins (1931). Line drawn from Eq. 33] and curve drawn from Eq. 34]. 5 SUMMARY In this chapter we have used data from the literature to illustrate the application of several mathematical models. Some of these data came from studies as early as the mid-1800s.