Building clone-consistent ecosystem models

Many ecological studies employ general models that can feature an arbitrary number of populations. A critical requirement imposed on such models is clone consistency: If the individuals from two populations are indistinguishable, joining these populations into one shall not affect the outcome of the model. Otherwise a model produces different outcomes for the same scenario. Using functional analysis, we comprehensively characterize all clone-consistent models: We prove that they are necessarily composed from basic building blocks, namely linear combinations of parameters and abundances. These strong constraints enable a straightforward validation of model consistency. Although clone consistency can always be achieved with sufficient assumptions, we argue that it is important to explicitly name and consider the assumptions made: They may not be justified or limit the applicability of models and the generality of the results obtained with them. Moreover, our insights facilitate building new clone-consistent models, which we illustrate for a data-driven model of microbial communities. Finally, our insights point to new relevant forms of general models for theoretical ecology. Our framework thus provides a systematic way of comprehending ecological models, which can guide a wide range of studies.Author summary: Mathematical models of population dynamics are an important tool to advance our understanding of ecosystems, which can be relevant for environmental, clinical, and industrial applications. One sanity check for such models is to virtually split a population into two with identical properties – allegorically, we paint half the individuals of the population in a different color. As we do not change the ecological situation, the outcome of the model should not change either; we call this feature clone consistency. We investigated the mathematical properties of clone-consistent models and deduced simple rules for their form. These rules allow to easily check clone consistency in existing models and ensure it when building new ones. The resulting framework can guide researchers in building models for specific ecosystems and in investigating general properties of ecosystems. We showcase our approach by applying it to models for bacterial communities causing urinary-tract infections. We further discuss that clone inconsistency, which occurs in several prominent models, reflects strong, often implicit, assumptions and it is important to check whether these are justified. Such assumptions may diminish the applicability of these models and the generality of results obtained with them.