If there are laws governing the fine-grained description of ecological mechanism, then these laws must be complicated, heterogeneous and dynamic. For essentially any ecological system, describing these mechanisms in full mathematical detail would require an enormous number of temporally- and spatially-varying parameters, and inferring these parameters from empirical data can seem overwhelmingly intractable. And yet as ecologists we often think in terms of simplified, coarse-grained concepts---whether there are well-defined species, or whether these species belong to distinct niches, and how many, or whether there are certain kinds of interactions between species, and what long-term outcomes these might lead to. These kinds of questions bridge studies of disease dynamics, community ecology, and beyond. Here we introduce two case studies to explore how we can coarse-grain both empirical data and theoretical models to infer broad classes of process, rather than specific, detailed parameters. The first focuses on inference of species interactions from Operational Taxonomic Units sampled at multiple time points from the human microbiome. The second is a phylodynamics framework that focuses on longer, evolutionary timescales, and we describe results from bacterial communities sampled from multiple habitat types.
Results/Conclusions
We tested the theoretical frameworks in both of our studies (short and long timescales) on simulated communities, before applying them to empirical data. In the case of the short-timescale data, we introduce a new approximation to stochastic Lotka-Volterra dynamics, and show how this can be used to infer species interaction rates from changes in taxon abundances sampled at multiple choices of time-interval. In the case of the long-timescale data, we combine both fast and slow time-scale diversification processes, and infer the respective rates for these processes by sampling simulated phylogenetic data, again on multiple timescales. We find in both cases that broad equivalence classes of parameters are sufficient to describe the dynamics when the data is sampled on more coarse-grained timescales. We briefly describe the application of both methods to (different) empirical data sets, drawn from publicly-available microbiome data. Using these data we infer specific sets of coarse-grained parameters, and estimate both numbers of distinct occupied niches and rate of filling up of the space of niches. One key conclusion is that by asking lower-dimensional question of our data, we can infer broad ecological conclusions with greater certainty.