Eco-evolutionary feedbacks can rescue cooperation in microbial populations

Bacterial populations whose growth depends on the cooperative production of public goods are usually threatened by the rise of cheaters that do not contribute but just consume the common resource. Minimizing cheater invasions appears then as a necessary mechanism to maintain these populations. However, that invasions result instead in the persistence of cooperation is a prospect that has yet remained largely unexplored. Here, we show that the demographic collapse induced by cheaters in the population can actually contribute to the rescue of cooperation, in a clear illustration of how ecology and evolution can influence each other. The effect is made possible by the interplay between spatial constraints and the essentiality of the shared resource. We validate this result by carefully combining theory and experiments, with the engineering of a synthetic bacterial community in which the public compound allows survival to a lethal stress. The characterization of the experimental system identifies additional factors that can matter, like the impact of the lag phase on the tolerance to stress, or the appearance of spontaneous mutants. Our work explains the unanticipated dynamics that eco-evolutionary feedbacks can generate in microbial communities, feedbacks that reveal fundamental for the adaptive change of ecosystems at all scales

Inference for stochastic chemical kinetics using moment equations and system size expansion

Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity

Parameterizing state–space models for infectious disease dynamics by generalized profiling: measles in Ontario

Parameter estimation for infectious disease models is important for basic understanding (e.g. to identify major transmission pathways), for forecasting emerging epidemics, and for designing control measures. Differential equation models are often used, but statistical inference for differential equations suffers from numerical challenges and poor agreement between observational data and deterministic models. Accounting for these departures via stochastic model terms requires full specification of the probabilistic dynamics, and computationally demanding estimation methods. Here, we demonstrate the utility of an alternative approach, generalized profiling, which provides robustness to violations of a deterministic model without needing to specify a complete probabilistic model. We introduce novel means for estimating the robustness parameters and for statistical inference in this framework. The methods are applied to a model for pre-vaccination measles incidence in Ontario, and we demonstrate the statistical validity of our inference through extensive simulation. The results confirm that school term versus summer drives seasonality of transmission, but we find no effects of short school breaks and the estimated basic reproductive ratio ℛ0 greatly exceeds previous estimates. The approach applies naturally to any system for which candidate differential equations are available, and avoids many challenges that have limited Monte Carlo inference for state–space models