I have 3 sites, that have been measured annually for abundance of species A and abundance of species B. Do I use a paired t-test to see if species A is having an impact on species B abundance?
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No - a paired t-test would test for a difference in the abundance of species A and species B.
You could use a regression to test for an effect of species A abundance on species B abundance. Species B abundance would be your response, and Species A abundance would be your predictor.
As your response is count data, you might want to use a generalized linear model, with a poisson distribution.
You might also want to think about using a mixed effects model, and including site, and maybe year, as random effects.
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