Biota of Lakes and Reservoirs - Hydro-Environmental Analysis: Freshwater Environments - page 415

common approach assumes that the limiting factor is the one that is in least supply (relative to the
growth requirement). That is the basis for Liebig's “law of the minimum.” The principle is most
commonly illustrated using a wooden barrel, in which each stave represents some growth require-
ment (Figure 15.4). If water is added to the barrel, the amount of water that the barrel can hold is
determined by the shortest stave.
Liebig's law of the minimum in determining growth requirements is similar to the Redield
approach, but different. For example, using the Redield ratios, if the molar ratio of N:P is greater
than 16:1, this implies that phosphorus is limiting, regardless of the molar concentration. The rela-
tionship between nutrients and growth is also described using the Michaelis-Menton equation
(Chapra 1997), as illustrated by Figure 15.5. That is, if concentrations were very low in relation
to the growth requirement, then the relationship between the rates of growth (due to the impact
of this limiting nutrient) would be linear. At some point, if the concentrations were high enough,
then the growth rate would approach its maximum value (1.0 times the maximum growth rate).
The half-saturation concentration ( K s , see Table 15.1) would be that concentration at which the rate
of growth would be one-half of its maximum value. Using this model would imply that where N
and/or P (and/or silica for diatoms to form their frustules) were in very high concentrations, the

Minimum

FIGURE 15.4 The leaky barrel. (Courtesy of Wikimedia Commons.)

1.0

N

=

R

K s + N

0.5

Nutrient

K s

FIGURE 15.5 Michaelis-Menton relationship between nutrients and growth.