Extant timetrees are consistent with a myriad of diversification histories.

Time-calibrated phylogenies of extant species (referred to here as 'extant timetrees') are widely used for estimating diversification dynamics1. However, there has been considerable debate surrounding the reliability of these inferences2-5 and, to date, this critical question remains unresolved. Here we clarify the precise information that can be extracted from extant timetrees under the generalized birth-death model, which underlies most existing methods of estimation. We prove that, for any diversification scenario, there exists an infinite number of alternative diversification scenarios that are equally likely to have generated any given extant timetree. These 'congruent' scenarios cannot possibly be distinguished using extant timetrees alone, even in the presence of infinite data. Importantly, congruent diversification scenarios can exhibit markedly different and yet similarly plausible dynamics, which suggests that many previous studies may have over-interpreted phylogenetic evidence. We introduce identifiable and easily interpretable variables that contain all available information about past diversification dynamics, and demonstrate that these can be estimated from extant timetrees. We suggest that measuring and modelling these identifiable variables offers a more robust way to study historical diversification dynamics. Our findings also make it clear that palaeontological data will continue to be crucial for answering some macroevolutionary questions.

Microbiology of Big Soda Lake, a multi-extreme meromictic volcanic crater lake in the Nevada desert.

Big Soda Lake, Nevada, is a multi-extreme meromictic lake, whose hypersaline hyperalkaline bottom waters feature permanent anoxia and high concentrations of arsenic, sulphide and ammonia. These properties make Big Soda Lake-and the adjacent Little Soda Lake-a fascinating system for exploring life's boundaries, discovering novel microbial taxa and identifying biotechnologically useful strains. To date, the taxonomic diversity and metabolic capabilities of microorganisms in this system remain largely unknown. Here, we fill this gap using microbiome surveys across the Big and Little Soda Lake water columns, including 16S rRNA sequencing, fungal ITS2 sequencing and gene- and genome-resolved metagenomics. We accompany these surveys with measurements of salinity, pH, temperature, oxygen, ammonium and ammonia concentrations. Our analyses reveal rich bacterial communities, taxonomically and functionally differentiated along Big Soda Lake's oxycline and, to lesser extent, between lakes. Fungal communities were dominated by a small number of families, while nearly no archaea were detected. Pathways related to perchlorate reduction, anoxygenic phototrophy, fermentation, dissimilatory metabolism of arsenite/arsenate, sulphur compounds, nitrogen compounds and hydrogen, were particularly prevalent. A total of 129 high-quality bacterial and archaeal metagenome-assembled genomes (completeness ≥ 80%, contamination ≤ 5%) were recovered, yielding insight into the taxonomic distribution of microbial metabolic pathways.

Response to "Vast (but avoidable) underestimation of global biodiversity".

This Formal Comment provides clarifications on the authors' recent estimates of global bacterial diversity and the current status of the field, and responds to a Formal Comment from John Wiens regarding their prior work.

Transport-limited reactions in microbial systems.

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 (Pearson r ≥ 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.

Fundamental Identifiability Limits in Molecular Epidemiology.

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.

Phylogeographic Estimation and Simulation of Global Diffusive Dispersal.

The analysis of time-resolved phylogenies (timetrees) and geographic location data allows estimation of dispersal rates, for example, for invasive species and infectious diseases. Many estimation methods are based on the Brownian Motion model for diffusive dispersal on a 2D plane; however, the accuracy of these methods deteriorates substantially when dispersal occurs at global scales because spherical Brownian motion (SBM) differs from planar Brownian motion. No statistical method exists for estimating SBM diffusion coefficients from a given timetree and tip coordinates, and no method exists for simulating SBM along a given timetree. Here, I present new methods for simulating SBM along a given timetree, and for estimating SBM diffusivity from a given timetree and tip coordinates using a modification of Felsenstein's independent contrasts and maximum likelihood. My simulation and fitting methods can accommodate arbitrary time-dependent diffusivities and scale efficiently to trees with millions of tips, thus enabling new analyses even in cases where planar BM would be a sufficient approximation. I demonstrate these methods using a timetree of marine and terrestrial Cyanobacterial genomes, as well as timetrees of two globally circulating Influenza B clades. My methods are implemented in the R package "castor." [Independent contrasts; phylogenetic; random walk; simulation; spherical Brownian motion.].

Unifying Phylogenetic Birth-Death Models in Epidemiology and Macroevolution.

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.].

A census-based estimate of Earth's bacterial and archaeal diversity.

The global diversity of Bacteria and Archaea, the most ancient and most widespread forms of life on Earth, is a subject of intense controversy. This controversy stems largely from the fact that existing estimates are entirely based on theoretical models or extrapolations from small and biased data sets. Here, in an attempt to census the bulk of Earth's bacterial and archaeal ("prokaryotic") clades and to estimate their overall global richness, we analyzed over 1.7 billion 16S ribosomal RNA amplicon sequences in the V4 hypervariable region obtained from 492 studies worldwide, covering a multitude of environments and using multiple alternative primers. From this data set, we recovered 739,880 prokaryotic operational taxonomic units (OTUs, 16S-V4 gene clusters at 97% similarity), a commonly used measure of microbial richness. Using several statistical approaches, we estimate that there exist globally about 0.8-1.6 million prokaryotic OTUs, of which we recovered somewhere between 47%-96%, representing >99.98% of prokaryotic cells. Consistent with this conclusion, our data set independently "recaptured" 91%-93% of 16S sequences from multiple previous global surveys, including PCR-independent metagenomic surveys. The distribution of relative OTU abundances is consistent with a log-normal model commonly observed in larger organisms; the total number of OTUs predicted by this model is also consistent with our global richness estimates. By combining our estimates with the ratio of full-length versus partial-length (V4) sequence diversity in the SILVA sequence database, we further estimate that there exist about 2.2-4.3 million full-length OTUs worldwide. When restricting our analysis to the Americas, while controlling for the number of studies, we obtain similar richness estimates as for the global data set, suggesting that most OTUs are globally distributed. Qualitatively similar results are also obtained for other 16S similarity thresholds (90%, 95%, and 99%). Our estimates constrain the extent of a poorly quantified rare microbial biosphere and refute recent predictions that there exist trillions of prokaryotic OTUs.

Circumventing kinetics in biogeochemical modeling.

Microbial metabolism drives biogeochemical fluxes in virtually every ecosystem. Modeling these fluxes is challenged by the incredible diversity of microorganisms, whose kinetic parameters are largely unknown. In poorly mixed systems, such as stagnant water columns or sediments, however, long-term bulk microbial metabolism may become limited by physical transport rates of substrates across space. Here we mathematically show that under these conditions, biogeochemical fluxes are largely predictable based on the system's transport properties, chemical boundary conditions, and the stoichiometry of metabolic pathways, regardless of the precise kinetics of the resident microorganisms. We formalize these considerations into a predictive modeling framework and demonstrate its use for the Cariaco Basin subeuphotic zone, one of the largest anoxic marine basins worldwide. Using chemical concentration data solely from the upper boundary (depth 180 m) and lower boundary (depth 900 m), but without a priori knowledge of metabolite fluxes, chemical depth profiles, kinetic parameters, or microbial species composition, we predict the concentrations and vertical fluxes of biologically important substances, including oxygen, nitrate, hydrogen sulfide, and ammonium, across the entire considered depth range (180-900 m). Our predictions largely agree with concentration measurements over a period of 14 years ([Formula: see text] = 0.78-0.92) and become particularly accurate during a period where the system was near biogeochemical steady state (years 2007-2009, [Formula: see text] = 0.86-0.95). Our work enables geobiological predictions for a large class of ecosystems without knowledge of kinetic parameters or geochemical depth profiles. Conceptually, our work provides a possible explanation for the decoupling between microbial species composition and bulk metabolic function, observed in various ecosystems.

Simulating trees with millions of species.

MOTIVATION: The birth-death (BD) model constitutes the theoretical backbone of most phylogenetic tools for reconstructing speciation/extinction dynamics over time. Performing simulations of reconstructed trees (linking extant taxa) under the BD model in backward time, conditioned on the number of species sampled at present day and, in some cases, a specific time interval since the most recent common ancestor (MRCA), is needed for assessing the performance of reconstruction tools, for parametric bootstrapping and for detecting data outliers. The few simulation tools that exist scale poorly to large modern phylogenies, which can comprise thousands or even millions of tips (and rising). RESULTS: Here I present efficient software for simulating reconstructed phylogenies under time-dependent BD models in backward time, conditioned on the number of sampled species and (optionally) on the time since the MRCA. On large trees, my software is 1000-10 000 times faster than existing tools. AVAILABILITY AND IMPLEMENTATION: The presented software is incorporated into the R package 'castor', which is available on The Comprehensive R Archive Network (CRAN). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A General and Efficient Algorithm for the Likelihood of Diversification and Discrete-Trait Evolutionary Models.

As the size of phylogenetic trees and comparative data continue to grow and more complex models are developed to investigate the processes that gave rise to them, macroevolutionary analyses are becoming increasingly limited by computational requirements. Here, we introduce a novel algorithm, based on the "flow" of the differential equations that describe likelihoods along tree edges in backward time, to reduce redundancy in calculations and efficiently compute the likelihood of various macroevolutionary models. Our algorithm applies to several diversification models, including birth-death models and models that account for state- or time-dependent rates, as well as many commonly used models of discrete-trait evolution, and provides an alternative way to describe macroevolutionary model likelihoods. As a demonstration of our algorithm's utility, we implemented it for a popular class of state-dependent diversification models-BiSSE, MuSSE, and their extensions to hidden-states. Our implementation is available through the R package $\texttt{castor}$. We show that, for these models, our algorithm is one or more orders of magnitude faster than existing implementations when applied to large phylogenies. Our algorithm thus enables the fitting of state-dependent diversification models to modern massive phylogenies with millions of tips and may lead to potentially similar computational improvements for many other macroevolutionary models.

Efficient comparative phylogenetics on large trees.

Motivation: Biodiversity databases now comprise hundreds of thousands of sequences and trait records. For example, the Open Tree of Life includes over 1 491 000 metazoan and over 300 000 bacterial taxa. These data provide unique opportunities for analysis of phylogenetic trait distribution and reconstruction of ancestral biodiversity. However, existing tools for comparative phylogenetics scale poorly to such large trees, to the point of being almost unusable. Results: Here we present a new R package, named 'castor', for comparative phylogenetics on large trees comprising millions of tips. On large trees castor is often 100-1000 times faster than existing tools. Availability and implementation: The castor source code, compiled binaries, documentation and usage examples are freely available at the Comprehensive R Archive Network (CRAN). Contact: louca.research@gmail.com. Supplementary information: Supplementary data are available at Bioinformatics online.

Integrating biogeochemistry with multiomic sequence information in a model oxygen minimum zone.

Microorganisms are the most abundant lifeform on Earth, mediating global fluxes of matter and energy. Over the past decade, high-throughput molecular techniques generating multiomic sequence information (DNA, mRNA, and protein) have transformed our perception of this microcosmos, conceptually linking microorganisms at the individual, population, and community levels to a wide range of ecosystem functions and services. Here, we develop a biogeochemical model that describes metabolic coupling along the redox gradient in Saanich Inlet-a seasonally anoxic fjord with biogeochemistry analogous to oxygen minimum zones (OMZs). The model reproduces measured biogeochemical process rates as well as DNA, mRNA, and protein concentration profiles across the redox gradient. Simulations make predictions about the role of ubiquitous OMZ microorganisms in mediating carbon, nitrogen, and sulfur cycling. For example, nitrite "leakage" during incomplete sulfide-driven denitrification by SUP05 Gammaproteobacteria is predicted to support inorganic carbon fixation and intense nitrogen loss via anaerobic ammonium oxidation. This coupling creates a metabolic niche for nitrous oxide reduction that completes denitrification by currently unidentified community members. These results quantitatively improve previous conceptual models describing microbial metabolic networks in OMZs. Beyond OMZ-specific predictions, model results indicate that geochemical fluxes are robust indicators of microbial community structure and reciprocally, that gene abundances and geochemical conditions largely determine gene expression patterns. The integration of real observational data, including geochemical profiles and process rate measurements as well as metagenomic, metatranscriptomic and metaproteomic sequence data, into a biogeochemical model, as shown here, enables holistic insight into the microbial metabolic network driving nutrient and energy flow at ecosystem scales.

Moving forward in circles: challenges and opportunities in modelling population cycles.

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer-resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.

Taxonomic variability and functional stability in microbial communities infected by phages.

Microbial communities can display large variation in taxonomic composition, yet this variation can coincide with stable metabolic functional structure and performance. The mechanisms driving the taxonomic variation within functional groups remain largely unknown. Biotic interactions, such as predation by phages, have been suggested as potential cause of taxonomic turnover, but the conditions for this scenario have not been rigorously examined. Further, it is unknown how predation by phages affects community function, and how these effects are modulated by functional redundancy in the communities. Here, we address these questions using a model for a methanogenic microbial community that includes several interacting metabolic functional groups. Each functional group comprises multiple competing clades, and each clade is attacked by a specialist lytic phage. Our model predicts that phages induce intense taxonomic turnover, resembling the variability observed in previous experiments. The functional structure and performance of the community are also disturbed by phage predation, but they become more stable as the functional redundancy in the community increases. The extent of this stabilization depends on the particular functions considered. Our model suggests mechanisms by which functional redundancy stabilizes community function and supports the interpretation that biotic interactions promote taxonomic turnover within microbial functional groups.

Functional structure of the bromeliad tank microbiome is strongly shaped by local geochemical conditions.

Phytotelmata in tank-forming Bromeliaceae plants are regarded as potential miniature models for aquatic ecology, but detailed investigations of their microbial communities are rare. Hence, the biogeochemistry in bromeliad tanks remains poorly understood. Here we investigate the structure of bacterial and archaeal communities inhabiting the detritus within the tanks of two bromeliad species, Aechmea nudicaulis and Neoregelia cruenta, from a Brazilian sand dune forest. We used metagenomic sequencing for functional community profiling and 16S sequencing for taxonomic profiling. We estimated the correlation between functional groups and various environmental variables, and compared communities between bromeliad species. In all bromeliads, microbial communities spanned a metabolic network adapted to oxygen-limited conditions, including all denitrification steps, ammonification, sulfate respiration, methanogenesis, reductive acetogenesis and anoxygenic phototrophy. Overall, CO2 reducers dominated in abundance over sulfate reducers, and anoxygenic phototrophs largely outnumbered oxygenic photoautotrophs. Functional community structure correlated strongly with environmental variables, between and within a single bromeliad species. Methanogens and reductive acetogens correlated with detrital volume and canopy coverage, and exhibited higher relative abundances in N. cruenta. A comparison of bromeliads to freshwater lake sediments and soil from around the world, revealed stark differences in terms of taxonomic as well as functional microbial community structure.

Transient dynamics of competitive exclusion in microbial communities.

Microbial metabolism drives our planet's biogeochemistry and plays a central role in industrial processes. Molecular profiling in bioreactors has revealed that microbial community composition can be highly variable while maintaining constant functional performance. Furthermore, following perturbation bioreactor performance typically recovers rapidly, while community composition slowly returns to its original state. Despite its practical relevance, we still lack an understanding of the mechanisms causing the discrepancy between functional and compositional stability of microbial communities. Using a mathematical model for microbial competition, as well as simulations of a model for a nitrifying bioreactor, we explain these observations on grounds of slow non-equilibrium dynamics eventually leading to competitive exclusion. In the presence of several competing strains, metabolic niches are rapidly occupied by opportunistic populations, while subsequent species turnover and the eventual dominance of top competitors proceeds at a much slower rate. Hence, functional redundancy causes a separation of the time scales characterizing the functional and compositional stabilization of microbial communities. This effect becomes stronger with increasing richness because greater similarities between top competitors lead to longer transient population dynamics.

Assessing host extinction risk following exposure to Batrachochytrium dendrobatidis.

Wildlife diseases are increasingly recognized as a major threat to biodiversity. Chytridiomycosis is an emerging infectious disease of amphibians caused by the fungus Batrachochytrium dendrobatidis (Bd). Using a mathematical model and simulations, we study its effects on a generic riparian host population with a tadpole and adult life stage. An analytical expression for the basic reproduction quotient, Qo, of the pathogen is derived. By sampling the entire relevant parameter space, we perform a statistical assessment of the importance of all considered parameters in determining the risk of host extinction, upon exposure to Bd. We find that Qo not only gives a condition for the initial invasion of the fungus, but is in fact the best predictor for host extinction. We also show that the role of tadpoles, which in some species tolerate infections, is ambivalent. While tolerant tadpoles may provide a reservoir for the fungus, thus facilitating its persistence or even amplifying its outbreaks, they can also act as a rescue buffer for a stressed host population. Our results have important implications for amphibian conservation efforts.

Vocal convergence and social proximity shape the calls of the most basal Passeriformes, New Zealand Wrens.

Despite extensive research on avian vocal learning, we still lack a general understanding of how and when this ability evolved in birds. As the closest living relatives of the earliest Passeriformes, the New Zealand wrens (Acanthisitti) hold a key phylogenetic position for furthering our understanding of the evolution of vocal learning because they share a common ancestor with two vocal learners: oscines and parrots. However, the vocal learning abilities of New Zealand wrens remain unexplored. Here, we test for the presence of prerequisite behaviors for vocal learning in one of the two extant species of New Zealand wrens, the rifleman (Acanthisitta chloris). We detect the presence of unique individual vocal signatures and show how these signatures are shaped by social proximity, as demonstrated by group vocal signatures and strong acoustic similarities among distantly related individuals in close social proximity. Further, we reveal that rifleman calls share similar phenotypic variance ratios to those previously reported in the learned vocalizations of the zebra finch, Taeniopygia guttata. Together these findings provide strong evidence that riflemen vocally converge, and though the mechanism still remains to be determined, they may also suggest that this vocal convergence is the result of rudimentary vocal learning abilities.

Trait biases in microbial reference genomes.

Common culturing techniques and priorities bias our discovery towards specific traits that may not be representative of microbial diversity in nature. So far, these biases have not been systematically examined. To address this gap, here we use 116,884 publicly available metagenome-assembled genomes (MAGs, completeness ≥80%) from 203 surveys worldwide as a culture-independent sample of bacterial and archaeal diversity, and compare these MAGs to the popular RefSeq genome database, which heavily relies on cultures. We compare the distribution of 12,454 KEGG gene orthologs (used as trait proxies) in the MAGs and RefSeq genomes, while controlling for environment type (ocean, soil, lake, bioreactor, human, and other animals). Using statistical modeling, we then determine the conditional probabilities that a species is represented in RefSeq depending on its genetic repertoire. We find that the majority of examined genes are significantly biased for or against in RefSeq. Our systematic estimates of gene prevalences across bacteria and archaea in nature and gene-specific biases in reference genomes constitutes a resource for addressing these issues in the future.