# Damuth law

There is a relationship between body mass and population density, namely:

$$d = aW^{-\frac{3}{4}}$$

Where \$d\$ is the density, and \$W\$ is the average body mass[@zotero-705Laws of Population Ecology].

This law is used, for example, to calculate the population density of T. Rex at any one point in time[@marshall2021Absolute abundance and preservation rate of Tyrannosaurus rex].

It must be noted that the law is a 0-order approximation. Flesh-eating mammals have a 150-fold variation in population density for species of the same body mass[@marshall2021Absolute abundance and preservation rate of Tyrannosaurus rex].

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