Functions of time for growth characters, their evaluation and approximation to examine differences between genotypes

Summary

As a follow up to a previous paper on growth curves (Keuls & Garretsen, 1982) a procedure is described to derive functions of time for growth characters from elementary growth curves which are suited for statistical analysis.

For each plot from the parameters α, β, γ of the second degree growth curves of type α + β(t−t) + γ(t−t)², corresponding functions of time (of harvest) are obtained for the derived growth characters: relative growth rate (of dry weight per plant), net assimilation rate, leaf area ratio, specific leaf area, leaf weight ratio. The elementary growth curves concern ln W, ln LA and ln LW, where W = dry weight per plant, LA = leaf area per plant, LW = leaf dry weight per plant.

Only relative growth rate is a simple linear expression in t, i.e., α + 2γ(t−t), where t represents average harvest time.

The functions for the four other growth characters are approximated by quadratic functions in t, such that for each plot a curve is characterized by a triple of parameters f(t), f′(t), % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaKabGfaammaalaaaba% Gaaiymaaqaaiaackdaaaaaaa!3946!\[\frac{1}{2}\]f″(t), representing respectively mean, slope and curvature for that plot at time t The approximation of the function of time is given by f(t) + (t−t)f′(t) + % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaKabGfaammaalaaaba% Gaaiymaaqaaiaackdaaaaaaa!3946!\[\frac{1}{2}\](t−t)²f″(t).

These sets of parameters per plot: (α, β, γ) for ln W(t) etc.; (β, 2γ, 0) for RGR(t) or (f(t), f′(t), % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaKabGfaammaalaaaba% Gaaiymaaqaaiaackdaaaaaaa!3946!\[\frac{1}{2}\]f″(t)) for the four other growth characters can be analysed by the MANOVA-procedure for 3 parameters as exemplified by Keuls & Garretsen (1982).