Parameter Identifiability of the Generalized Lotka-Volterra Model for Microbiome Studies

Abstract Background Population dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research; predicting how populations change over time, determining how manipulations of microbiomes affect dynamics, and designing synthetic microbiomes to perform tasks are just a few examples. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka-Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka-Volterra model. Results We used structural identifiability analyses to determine the extent to which time series of relative abundances can be used to parameterize the generalized Lotka-Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Our results also indicate that the relative interaction rates that can be estimated using relative abundance data provide ample information to estimate relative changes of absolute abundance over time. Using synthetic data for which we know the underlying structure, we found our results to be robust to modest amounts of both process and measurement error. Conclusions Fitting the generalized Lotka-Volterra model to time-series sequencing data typically requires either assuming a constant population size or performing additional measurements to obtain absolute abundances. We have found that these assumptions are not strictly necessary because relative abundance data alone contain sufficient information to estimate relative rates of interaction, and thus to infer key drivers of microbial population dynamics.