In New England Wildlife, a compendium of the life history of New England’s vertebrates species, there’s a passage that reads: “The redback [sic] salamander is the most abundant terrestrial vertebrate in New England and accounts for the greatest amount of vertebrate biomass in the Hubbard Brook Experimental Forest in New Hampshire (Burton and Likens 1975).” I believe it’s this passage that has given rise to the extrapolation that salamanders must also account for the greatest amount of vertebrate biomass in all of New England.
The cited study is a fascinating read. The researchers used a few different methods to estimate population sizes, with pretty different results. Using mark-recapture (and the assumption that only 2-32% of a population of salamanders are found in the top 2.5cm of soil), they determined that the population of red-backed salamanders at Hubbard Brook was somewhere between 1,650 and 27,200 per hectare, which scales up to 427,350 and 7,044,800 individuals per square mile!! Burlington is 10.5 square miles, so prior to European colonization when the area was forested, at the high end, the population would be ~72 million salamanders (roughly the population of the UK or Thailand).
The number was less impressive when they used transects to count red-backs. These estimates were closer to 2,000 individuals per hectare. Averaging their various counts/methods, they list the population of a 36 hectare plot in Hubbard Brook as 90,000 individuals, about 648,000 red-backed salamanders per square mile).