## Examples of Allometric Principles

Numerous allometric principles have been published in the literature. A few allometric principles are presented below to illustrate that how these principles are working and how they can be applied in ecology to give firsthand estimations.

There is for instance a strong positive correlation between size and generation time, Tg, ranging from bacteria to the biggest mammals and trees, as shown in Figure 1. The per capita rate of increase, r, defined by the exponential or logistic growth equations, respectively, dN/dt = rN 

can be shown to be inversely proportional to the generation time. This implies that r is also related to the size of the organism, but falls actually into three groups: unicellular, heterotherms, and homeotherms (see Figure 2).

The respiration, food consumption, and ammonia excretion for fish can be found, when the weight, W, is known:

respiration = constant * W0'80 

feed consumption = constant * W0'65 

ammonia excretion = constant * W0'72 

The specific metabolic rate, the metabolic rate relative to the weight, m, is also following an allometric principle:

where k is roughly the same constant for all species, equal to about 5.6 kJ g— per day. It has been found that the exponent is —1/4, corresponding to the whole body metabolic rate I, which scales as I = Io W°'75.

The surface determines the contact with the environment quantitatively, and by that the possibility of taking up food and excreting waste substances. It is illustrated in Figures 3 and 4. The excretion rate and uptake rate (for aquatic organisms) follow the same trends as the metabolic rate, as shown in Figures 3 and 4. This is of course not surprising, as excretion is strongly dependent on metabolism and the direct uptake dependent on the surface. 