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Does an animal being small or large determine its abundance?

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I'm sympathetic to @Dirigible that this seems like the kind of thing that should be easy to research, but I was surprised to see that there's not an answer to this already on SE.Biology. So very quickly:

Yes, there is what is known as an "allometry" relationship between body size and abundance in which the two tend to be inversely related.

Here is one meta-analysis that attempts to describe the relationship across food webs. Here is a review article that may be easier to read describing the law in somewhat more general terms. Here is a figure from the review with plots showing the relationships in different kinds of organisms from different studies:

enter image description here

In some cases people talk about the population density in some area rather than overall abundance, as density is easier to estimate and can be thought of as a local measure of abundance. From the review you can see that there are some equations that people have derived to describe the relationship:

For large compilations of population densities, the relationship between the average mass of a species (Msp) and its average density (Ncomp) is generally well fit by a power function ($r^2 > 80\%$), with an exponent near 0.75 so that $N_{comp} = cM^{\frac{-3}{4}}$, where c is a constant (also known as Damuth’s Rule)...

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