Given a system of species equations that specifies two species, is there an algorithm to test if they are isomorphic?
Testing for isomorphism can be done by testing the equality of the coefficients of each species's molecular expansion. Thus, if there is an algorithm that computed some representation of these coefficients (e.g. a sequence), the problem reduces to comparing sequences for equality, which is a potentially simpler problem.
The Devmol Maple package described in "Computing the molecular expansion of species with the Maple package Devmol" by Auger, Labelle, and Leroux computes truncated molecular expansions, but does not compute explicit representations of entire molecular expansions.
A special case of this problem is testing if a species is the zero species. My guess is that this is not in general possible, but perhaps large sets of useful special cases are possible.