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I was reading Hydroperiods of created and natural vernal pools in central Ohio: A comparison of depth and duration of inundation by Debra L. Gamble and William J. Mitsch (2008), and I came across this statement:

The dominant tree species in the vernal pool area were Acer saccharinum and Quercus palustris, while Ulmus americana, though smaller in diameter than the other trees listed, was the must abundant species...As at the New Albany, the most dominant tree species in the vernal pool area was Acer saccharinum, followed by Fraxinus pennsylvanica, while Fagus grandifolia was the most abundant species.

There seems to be a distinction between the terms dominance and abundance in the context of ecology. I've read some of the wikipedia articles on them, but I can't seem to find the difference in their meanings. They seem to both deal with the frequency that a species is in a population.

Any help is greatly appreciated.

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There is a difference between dominance and abundance in vegetation science, and your citation is about vegetation.

Abundance is the relative representation of a species in a particular ecosystem. It is usually measured as the number of individuals found per sample.

Ecological dominance is the degree to which a taxon is more numerous than its competitors in an ecological community, or makes up more of the biomass.

In vegetation science, abundance is usually measured as the number of individuals or the percentage of coverage of that species in a plot. An abundant species would typically have a lot of individuals in the plot. A dominant species dominates the other species, so typically covers more than 50% (up to 100%) of the plot. Doing this, it also takes away space (and light!) for other plants.
Usually abundant species also cover a lot, but small species (for example grasses) can be abundant without becoming dominant while large species (like trees) can be dominant with relatively few individuals.

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The terms are roughly the same, either is fine and you can choose depending on the audience or the nature of the topic and based on your preference.

A scientific journal examiner won't judge you for use of one or the other. Words outline ideas the same as color terms outline the rainbow, it's not very precise and two words can have similar and different meanings.

If you check the journal articles referring to species dominance and abundance, they are to similar to call a difference:

https://scholar.google.fr/scholar?as_ylo=2017&q=species+dominance&hl=en&as_sdt=0,5

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