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Abstract Birth–death stochastic processes are the foundations of many phylogenetic models and are widely used to make inferences about epidemiological and macroevolutionary dynamics. There are a large number of birth–death model variants that have been developed; these impose different assumptions about the temporal dynamics of the parameters and about the sampling process. As each of these variants was individually derived, it has been difficult to understand the relationships between them as well as their precise biological and mathematical assumptions. Without a common mathematical foundation, deriving new models is nontrivial. Here, we unify these models into a single framework, prove that many previously developed epidemiological and macroevolutionary models are all special cases of a more general model, and illustrate the connections between these variants. This unification includes both models where the process is the same for all lineages and those in which it varies across types. We also outline a straightforward procedure for deriving likelihood functions for arbitrarily complex birth–death(-sampling) models that will hopefully allow researchers to explore a wider array of scenarios than was previously possible. By rederiving existing single-type birth–death sampling models, we clarify and synthesize the range of explicit and implicit assumptions made by these models. [Birth–death processes; epidemiology; macroevolution; phylogenetics; statistical inference.] 

Abstract Viral phylogenies provide crucial information on the spread of infectious diseases, and many studies fit mathematical models to phylogenetic data to estimate epidemiological parameters such as the effective reproduction ratio (Re) over time. Such phylodynamic inferences often complement or even substitute for conventional surveillance data, particularly when sampling is poor or delayed. It remains generally unknown, however, how robust phylodynamic epidemiological inferences are, especially when there is uncertainty regarding pathogen prevalence and sampling intensity. Here, we use recently developed mathematical techniques to fully characterize the information that can possibly be extracted from serially collected viral phylogenetic data, in the context of the commonly used birth-death-sampling model. We show that for any candidate epidemiological scenario, there exists a myriad of alternative, markedly different, and yet plausible “congruent” scenarios that cannot be distinguished using phylogenetic data alone, no matter how large the data set. In the absence of strong constraints or rate priors across the entire study period, neither maximum-likelihood fitting nor Bayesian inference can reliably reconstruct the true epidemiological dynamics from phylogenetic data alone; rather, estimators can only converge to the “congruence class” of the true dynamics. We propose concrete and feasible strategies for making more robust epidemiological inferences from viral phylogenetic data. 

Predicting microbial metabolic rates and emergent biogeochemical fluxes remains challenging due to the many unknown population dynamical, physiological and reaction‐kinetic parameters and uncertainties in species composition. Here, we show that the need for these parameters can be eliminated when population dynamics and reaction kinetics operate at much shorter time scales than physical mixing processes. Such scenarios are widespread in poorly mixed water columns and sediments. In this ‘fast‐reaction‐transport’ (FRT) limit, all that is required for predictions are chemical boundary conditions, the physical mixing processes and reaction stoichiometries, while no knowledge of species composition, physiology or population/reaction kinetic parameters is needed. Using time‐series data spanning years 2001–2014 and depths 180–900 m across the permanently anoxic Cariaco Basin, we demonstrate that the FRT approach can accurately predict the dynamics of major electron donors and acceptors (Pearsonr ≥ 0.9 in all cases). Hence, many microbial processes in this system are largely transport limited and thus predictable regardless of species composition, population dynamics and kinetics. Our approach enables predictions for many systems in which microbial community dynamics and kinetics are unknown. Our findings also reveal a mechanism for the frequently observed decoupling between function and taxonomy in microbial systems.

 

Permanently anoxic regions in the ocean are widespread and exhibit unique microbial metabolic activity exerting substantial influence on global elemental cycles and climate. Reconstructing microbial metabolic activity rates in these regions has been challenging, due to the technical difficulty of direct rate measurements. In Cariaco Basin, which is the largest permanently anoxic marine basin and an important model system for geobiology, long‐term monitoring has yielded time series for the concentrations of biologically important compounds; however, the underlying metabolite fluxes remain poorly quantified. Here, we present a computational approach for reconstructing vertical fluxes and in situ net production/consumption rates from chemical concentration data, based on a 1‐dimensional time‐dependent diffusive transport model that includes adaptive penalization of overfitting. We use this approach to estimate spatiotemporally resolved fluxes of oxygen, nitrate, hydrogen sulfide, ammonium, methane, and phosphate within the sub‐euphotic Cariaco Basin water column (depths 150–900 m, years 2001–2014) and to identify hotspots of microbial chemolithotrophic activity. Predictions of the fitted models are in excellent agreement with the data and substantially expand our knowledge of the geobiology in Cariaco Basin. In particular, we find that the diffusivity, and consequently fluxes of major reductants such as hydrogen sulfide, and methane, is about two orders of magnitude greater than previously estimated, thus resolving a long‐standing apparent conundrum between electron donor fluxes and measured dark carbon assimilation rates.