Kurva pertumbuhan tanaman


1. Growth Response Curves Liebig (c. 1860, German) (linear)

Y = mX + b,   where:  Y = yield; m = slope – i.e. rate of yield increase, a function of the environment and nutrient; X = amount of nutrient added; b = minimum yield, one would get this yield with no nutrient additions.

2. Mitscherlich (c. 1910, German) (Law of Diminishing Returns)

(1) dy/dx = (A-Y)C.  if integrate equation (1), then get (2) log (A-Y) = log(A) – cX, where:

A = maximum possible yield (theoretical); Y = actual yield.

dy/dx = slope – i.e. rate of yield increase, a function of the environment, the nutrient, and amount of nutrient already present. This value gets smaller as nutrient amount increases.

x = amount of nutrient added; c = constant.

3. Bray (c. 1920, U. Illinois) (soil interactions)

Started with Mitscherlich’s basic equation, developed: log (A-Y) = log(A) – c1B – cX, where:  A = maximum possible yield (theoretical); Y = actual yield.

dy/dx = slope – i.e. rate of yield increase. It is a function of the environment, the nutrient, and amount of nutrient already present. This value gets smaller as nutrient amount increases.

X = amount of nutrient added; c1 = constant that is for B; c = constant.

B = value explaining behavior of ‘immobile’ nutrients (e.g. K, P, Ca, Mg). The c1B term takes into account the reality that nutrients interact with soil and not all nutrients behave identically.

4. Baule (c. 1920, German mathematician, worked with Mitscherlich) (nutrient interactions)

Baule developed idea of “half-way points.” Using the identical relationship as Mitscherlich,

Baule concluded that: Y = A – A(1/2) # Baule Units, where:

A = maximum possible yield (theoretical); Y = actual yield.

Baule Unit= the amount of nutrient that when added results in moving Y (yield) one-half  way closer to A (maximum possible yield).

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