Many metagenomic and environmental DNA studies require the taxonomic assignment of individual reads or sequences by aligning reads to a reference database, known as taxonomic binning. When a read aligns to more than one reference sequence, it is often classified based on sequence similarity. This step can assign reads to incorrect taxa, at a rate which depends both on the assignment algorithm and on underlying population genetic and database parameters. In particular, as we move towards using environmental DNA to study eukaryotic taxa subject to regular recombination, we must take into account issues concerning gene tree discordance. Though accuracy is often compared across algorithms using a fixed data set, the relative impact of these population genetic and database parameters on accuracy has not yet been quantified. Here, we develop both a theoretical and simulation framework in the simplified case of two reference species, and compute binning accuracy over a wide range of parameters, including sequence length, species-query divergence time, divergence times of the reference species, reference database completeness, sample age and effective population size. We consider two assignment methods and contextualize our results using parameters from a recent ancient environmental DNA study, comparing them to the commonly used discriminative k-mer-based method Clark (Current Biology, 31, 2021, 2728; BMC Genomics, 16, 2015, 1). Our results quantify the degradation in assignment accuracy as the samples diverge from their closest reference sequence, and with incompleteness of reference sequences. We also provide a framework in which others can compute expected accuracy for their particular method or parameter set. Code is available at https://github.com/bdesanctis/binning-accuracy.