Due to the advent and utility of high-throughput sequencing, modern biomedical research abounds with multivariate count data. Yet such sequence count data is often extremely sparse; that is, much of the data is zero values. Such zero values are well known to cause problems for statistical analyses. In this work we provide a systematic description of different processes that can give rise to zero values as well as the types of methods for addressing zeros in sequence count studies. Importantly, we systematically review how various models perform on each type of zero generating process. Our results demonstrate that zero-inflated models can have substantial biases in both simulated and real data settings. Additionally, we find that zeros due to biological absences can, for many applications, be approximated as originating from under sampling. Beyond these results, this work provides a paired categorization scheme for models and zero generating processes to facilitate discussions and future research into the analysis of sequence count data.