Scaling body size fluctuations

Size-related variability of oxygen consumption rates in individual human hepatic cells

Accurate descriptions of the variability in single-cell oxygen consumption and its size-dependency are key to establishing more robust tissue models. By combining microfabricated devices with multiparameter identification algorithms, we demonstrate that single human hepatocytes exhibit an oxygen level-dependent consumption rate and that their maximal oxygen consumption rate is significantly lower than that of typical hepatic cell cultures. Moreover, we found that clusters of two or more cells competing for a limited oxygen supply reduced their maximal consumption rate, highlighting their ability to adapt to local resource availability and the presence of nearby cells. We used our approach to characterize the covariance of size and oxygen consumption rate within a cell population, showing that size matters, since oxygen metabolism covaries lognormally with cell size. Our study paves the way for linking the metabolic activity of single human hepatocytes to their tissue- or organ-level metabolism and describing its size-related variability through scaling laws.

The human cell count and size distribution

Cell size and cell count are adaptively regulated and intimately linked to growth and function. Yet, despite their widespread relevance, the relation between cell size and count has never been formally examined over the whole human body. Here, we compile a comprehensive dataset of cell size and count over all major cell types, with data drawn from >1,500 published sources. We consider the body of a representative male (70 kg), which allows further estimates of a female (60 kg) and 10-y-old child (32 kg). We build a hierarchical interface for the cellular organization of the body, giving easy access to data, methods, and sources (https://humancelltreemap.mis.mpg.de/). In total, we estimate total body counts of ≈36 trillion cells in the male, ≈28 trillion in the female, and ≈17 trillion in the child. These data reveal a surprising inverse relation between cell size and count, implying a trade-off between these variables, such that all cells within a given logarithmic size class contribute an equal fraction to the body's total cellular biomass. We also find that the coefficient of variation is approximately independent of mean cell size, implying the existence of cell-size regulation across cell types. Our data serve to establish a holistic quantitative framework for the cells of the human body, and highlight large-scale patterns in cell biology.

A general theory for temperature dependence in biology

At present, there is no simple, first principles-based, and general model for quantitatively describing the full range of observed biological temperature responses. Here we derive a general theory for temperature dependence in biology based on Eyring-Evans-Polanyi's theory for chemical reaction rates. Assuming only that the conformational entropy of molecules changes with temperature, we derive a theory for the temperature dependence of enzyme reaction rates which takes the form of an exponential function modified by a power law and that describes the characteristic asymmetric curved temperature response. Based on a few additional principles, our model can be used to predict the temperature response above the enzyme level, thus spanning quantum to classical scales. Our theory provides an analytical description for the shape of temperature response curves and demonstrates its generality by showing the convergence of all temperature dependence responses onto universal relationships-a universal data collapse-under appropriate normalization and by identifying a general optimal temperature, around 25 ^∘C, characterizing all temperature response curves. The model provides a good fit to empirical data for a wide variety of biological rates, times, and steady-state quantities, from molecular to ecological scales and across multiple taxonomic groups (from viruses to mammals). This theory provides a simple framework to understand and predict the impact of temperature on biological quantities based on the first principles of thermodynamics, bridging quantum to classical scales.

Evolving perspective on the origin and diversification of cellular life and the virosphere

The tree of life (TOL) is a powerful framework to depict the evolutionary history of cellular organisms through time, from our microbial origins to the diversification of multicellular eukaryotes that shape the visible biosphere today. During the past decades, our perception of the TOL has fundamentally changed, in part, due to profound methodological advances, which allowed a more objective approach to studying organismal and viral diversity and led to the discovery of major new branches in the TOL as well as viral lineages. Phylogenetic and comparative genomics analyses of these data have, among others, revolutionized our understanding of the deep roots and diversity of microbial life, the origin of the eukaryotic cell, eukaryotic diversity, as well as the origin, and diversification of viruses. In this review, we provide an overview of some of the recent discoveries on the evolutionary history of cellular organisms and their viruses and discuss a variety of complementary techniques that we consider crucial for making further progress in our understanding of the TOL and its interconnection with the virosphere.

Linking species traits and demography to explain complex temperature responses across levels of organization

Microbial communities regulate ecosystem responses to climate change. However, predicting these responses is challenging because of complex interactions among processes at multiple levels of organization. Organismal traits that determine individual performance and ecological interactions are essential for scaling up environmental responses from individuals to ecosystems. We combine protist microcosm experiments and mathematical models to show that key traits-cell size, shape, and contents-each explain different aspects of species' demographic responses to changes in temperature. These differences in species' temperature responses have complex cascading effects across levels of organization-causing nonlinear shifts in total community respiration rates across temperatures via coordinated changes in community composition, equilibrium densities, and community-mean species mass in experimental protist communities that tightly match theoretical predictions. Our results suggest that traits explain variation in population growth, and together, these two factors scale up to influence community- and ecosystem-level processes across temperatures. Connecting the multilevel microbial processes that ultimately influence climate in this way will help refine predictions about complex ecosystem-climate feedbacks and the pace of climate change itself.

Scaling of joint mass and metabolism fluctuations in in silico cell-laden spheroids

Allometric scaling has many applications, from the prediction of pharmacokinetics in animals and humans to the probing of ecosystem dynamics. Most studies have neglected to account for variations and fluctuations, although they are intrinsic features of all biological systems. To understand how metabolic scaling emerges in the presence of variations, we developed computer-generated models of cell-laden spheroids to define the experimental size range of cell cultures with quantifiable similitudes in terms of fluctuations and metabolic scaling with living organisms. We show that the estimates of scaling exponents may change with increasing variability in both mass and metabolic rate. The computational pipeline described underpins the sound design of statistically meaningful cell-based models, with impacts in both biomedical science and ecology.

Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here, we describe a computational pipeline for identifying the range of three-dimensional (3D) cell-aggregate sizes in which nonisometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. The 3D cell-laden spheroids with size and single-cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modeling oxygen diffusion and reaction. Then, a method for estimating scaling exponents of correlated variables through statistically significant data collapse of joint probability distributions was developed. The method was used to identify a physiologically relevant range of spheroid sizes, where both nonisometric scaling and a minimum oxygen concentration (0.04 mol⋅m⁻³) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. Using the pipeline, we also show that scaling exponents may be significantly different in the presence of joint mass and metabolic-rate variations typically found in cells. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo and brings insights for the design of more predictive and physiologically relevant in vitro models.

Second-order phase transition in phytoplankton trait dynamics

Key traits of unicellular species, such as cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of realistic individual-based model classes is difficult. Here, we reveal new empirical scaling evidence associated with a transition in the population and the chlorophyll dynamics of phytoplankton. We offer a possible explanation for these observations by deriving scaling laws in the vicinity of the critical point of a new universality class of non-local cell growth and division models. This "criticality hypothesis" can be tested through new scaling predictions derived for our model class, for the response of chlorophyll distributions to perturbations. The derived scaling laws may also be generalized to other cellular traits and environmental drivers relevant to phytoplankton ecology.

Dynamic metabolic adaptation can promote species coexistence in competitive microbial communities

Microbes are capable of physiologically adapting to diverse environmental conditions by differentially varying the rates at which they uptake different nutrients. In particular, microbes can switch hierarchically between different energy sources, consuming first those that ensure the highest growth rate. Experimentally, this can result in biphasic growth curves called "diauxic shifts" that typically arise when microbes are grown in media containing several nutrients. Despite these observations are well known in microbiology and molecular biology, the mathematical models generally used to describe the population dynamics of microbial communities do not account for dynamic metabolic adaptation, thus implicitly assuming that microbes cannot switch dynamically from one resource to another. Here, we introduce dynamic metabolic adaptation in the framework of consumer-resource models, which are commonly used to describe competitive microbial communities, allowing each species to temporally change its preferred energy source to maximize its own relative fitness. We show that dynamic metabolic adaptation enables the community to self-organize, allowing several species to coexist even in the presence of few resources, and to respond optimally to a time-dependent environment, thus showing that dynamic metabolic adaptation could be an important mechanism for maintaining high levels of diversity even in environments with few energy sources. We show that introducing dynamic metabolic strategies in consumer-resource models is necessary for reproducing experimental growth curves of the baker's yeast Saccharomyces cerevisiae growing in the presence of two carbon sources. Even though diauxic shifts emerge naturally from the model when two resources are qualitatively very different, the model predicts that the existence of such shifts is not a prerequisite for species coexistence in competitive communities.

How pulse disturbances shape size-abundance pyramids

Ecological pyramids represent the distribution of abundance and biomass of living organisms across body-sizes. Our understanding of their expected shape relies on the assumption of invariant steady-state conditions. However, most of the world's ecosystems experience disturbances that keep them far from such a steady state. Here, using the allometric scaling between population growth rate and body-size, we predict the response of size-abundance pyramids within a trophic guild to any combination of disturbance frequency and intensity affecting all species in a similar way. We show that disturbances narrow the base of size-abundance pyramids, lower their height and decrease total community biomass in a nonlinear way. An experimental test using microbial communities demonstrates that the model captures well the effect of disturbances on empirical pyramids. Overall, we demonstrate both theoretically and experimentally how disturbances that are not size-selective can nonetheless have disproportionate impacts on large species.

Island woodiness underpins accelerated disparification in plant radiations

The evolution of secondary (insular) woodiness and the rapid disparification of plant growth forms associated with island radiations show intriguing parallels between oceanic islands and tropical alpine sky islands. However, the evolutionary significance of these phenomena remains poorly understood and the focus of debate. We explore the evolutionary dynamics of species diversification and trait disparification across evolutionary radiations in contrasting island systems compared with their nonisland relatives. We estimate rates of species diversification, growth form evolution and phenotypic space saturation for the classical oceanic island plant radiations - the Hawaiian silverswords and Macaronesian Echium - and the well-studied sky island radiations of Lupinus and Hypericum in the Andes. We show that secondary woodiness is associated with dispersal to islands and with accelerated rates of species diversification, accelerated disparification of plant growth forms and occupancy of greater phenotypic trait space for island clades than their nonisland relatives, on both oceanic and sky islands. We conclude that secondary woodiness is a prerequisite that could act as a key innovation, manifest as the potential to occupy greater trait space, for plant radiations on island systems in general, further emphasizing the importance of combinations of clade-specific traits and ecological opportunities in driving adaptive radiations.

Generalized size scaling of metabolic rates based on single-cell measurements with freshwater phytoplankton

Kleiber's law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber's law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber's law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber's law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.

On the probabilistic nature of the species-area relation

The Species-Area Relation (SAR), which describes the increase in the number of species S with increasing area A, is under intense scrutiny in contemporary ecology, in particular to probe its reliability in predicting the number of species going extinct as a direct result of habitat loss. Here, we focus on the island SAR, which is measured across a set of disjoint habitat patches, and we argue that the SAR portrays an average trend around which fluctuations are to be expected due to the stochasticity of community dynamics within the patches, external perturbations, and habitat heterogeneity across different patches. This probabilistic interpretation of the SAR, though already implicit in the theory of island biogeography and manifest in the scatter of data points in plots of empirical SAR curves, has not been investigated systematically from the theoretical point of view. Here, we show that the two main contributions to SAR fluctuations, which are due to community dynamics within the patches and to habitat heterogeneity between different patches, can be decoupled and analyzed independently. To investigate the community dynamics contribution to SAR fluctuations, we explore a suite of theoretical models of community dynamics where the number of species S inhabiting a patch emerges from diverse ecological and evolutionary processes, and we compare stationary predictions for the coefficient of variation of S, i.e. the fluctuations of S with respect to the mean. We find that different community dynamics models diverge radically in their predictions. In island biogeography and in neutral frameworks, where fluctuations are only driven by the stochasticity of diversification and extinction events, relative fluctuations decay when the mean increases. Computational evidence suggests that this result is robust in the presence of competition for space or resources. When species compete for finite resources, and mass is introduced as a trait determining species' birth, death and resource consumption rates based on empirical allometric scalings, relative fluctuations do not decay with increasing mean S due to the occasional introduction of new species with large resource demands causing mass extinctions in the community. Given this observation, we also investigate the contribution of external disturbance events to fluctuations of S in neutral community dynamics models and compare this scenario with the community dynamics in undisturbed non-neutral models. Habitat heterogeneity within a single patch, in the context of metapopulation models, causes variability in the number of coexisting species which proves negligible with respect to that caused by the stochasticity of the community dynamics. The second contribution to SAR fluctuations, which is due to habitat heterogeneity among different patches, introduces corrections to the coefficient of variation of S. Most importantly, inter-patches heterogeneity introduces a constant, lower bound on the relative fluctuations of S equal to the coefficient of variation of a habitat variable describing the heterogeneity among patches. Because heterogeneity across patches is inevitably present in natural ecosystems, we expect that the relative fluctuations of S always tend to a constant in the limit of large mean S or large patch area A, with contributions from community dynamics, inter-patches heterogeneity or both. We provide a theoretical framework for modelling these two contributions and we show that both can affect significantly the fluctuations of the SAR.

The Empirical Fluctuation Pattern of E. coli Division Control

In physics, it is customary to represent the fluctuations of a stochastic system at steady state in terms of linear response to small random perturbations. Previous work has shown that the same framework describes effectively the trade-off between cell-to-cell variability and correction in the control of cell division of single E. coli cells. However, previous analyses were motivated by specific models and limited to a subset of the measured variables. For example, most analyses neglected the role of growth rate variability. Here, we take a comprehensive approach and consider several sets of available data from both microcolonies and microfluidic devices in different growth conditions. We evaluate all the coupling coefficients between the three main measured variables (interdivision times, cell sizes and individual-cell growth rates). The linear-response framework correctly predicts consistency relations between a priori independent experimental measurements, which confirms its validity. Additionally, the couplings between the cell-specific growth rate and the other variables are typically non zero. Finally, we use the framework to detect signatures of mechanisms in experimental data involving growth rate fluctuations, finding that (1) noise-generating coupling between size and growth rate is a consequence of inter-generation growth rate correlations and (2) the correlation patterns agree with a near-adder model where the added size has a dependence on the single-cell growth rate. Our findings define relevant constraints that any theoretical description should reproduce, and will help future studies aiming to falsify some of the competing models of the cell cycle existing today in the literature.

Modeling Cell Size Regulation: From Single-Cell-Level Statistics to Molecular Mechanisms and Population-Level Effects

Most microorganisms regulate their cell size. In this article, we review some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics that they generate. We review the biologically relevant insights obtained from these models. We then describe cell cycle regulation and its molecular implementations, protein number regulation, and population growth, all in relation to size regulation. Finally, we discuss several future directions for developing understanding beyond phenomenological models of cell size regulation.

Fundamental principles in bacterial physiology-history, recent progress, and the future with focus on cell size control: a review

Bacterial physiology is a branch of biology that aims to understand overarching principles of cellular reproduction. Many important issues in bacterial physiology are inherently quantitative, and major contributors to the field have often brought together tools and ways of thinking from multiple disciplines. This article presents a comprehensive overview of major ideas and approaches developed since the early 20th century for anyone who is interested in the fundamental problems in bacterial physiology. This article is divided into two parts. In the first part (sections 1-3), we review the first 'golden era' of bacterial physiology from the 1940s to early 1970s and provide a complete list of major references from that period. In the second part (sections 4-7), we explain how the pioneering work from the first golden era has influenced various rediscoveries of general quantitative principles and significant further development in modern bacterial physiology. Specifically, section 4 presents the history and current progress of the 'adder' principle of cell size homeostasis. Section 5 discusses the implications of coarse-graining the cellular protein composition, and how the coarse-grained proteome 'sectors' re-balance under different growth conditions. Section 6 focuses on physiological invariants, and explains how they are the key to understanding the coordination between growth and the cell cycle underlying cell size control in steady-state growth. Section 7 overviews how the temporal organization of all the internal processes enables balanced growth. In the final section 8, we conclude by discussing the remaining challenges for the future in the field.

Field migration rates of tidal meanders recapitulate fluvial morphodynamics

Meandering tidal channel networks play a central role in the ecomorphodynamic evolution of the landscapes they cut through. Despite their ubiquitous presence and relevance to sedimentary and landscape features, few observations of tidal-meander evolution exist, and we lack a full understanding of the governing processes. Field analyses show that tidal meanders, traditionally viewed as stable landscape features, display modes of migration and migration rates per unit width quite similar to those characterizing their fluvial counterparts, with important implications for the characterization of the related sedimentary products. The results presented here contribute to our understanding of the morphological evolution of tidal landscapes.

The majority of tidal channels display marked meandering features. Despite their importance in oil-reservoir formation and tidal landscape morphology, questions remain on whether tidal-meander dynamics could be understood in terms of fluvial processes and theory. Key differences suggest otherwise, like the periodic reversal of landscape-forming tidal flows and the widely accepted empirical notion that tidal meanders are stable landscape features, in stark contrast with their migrating fluvial counterparts. On the contrary, here we show that, once properly normalized, observed migration rates of tidal and fluvial meanders are remarkably similar. Key to normalization is the role of tidal channel width that responds to the strong spatial gradients of landscape-forming flow rates and tidal prisms. We find that migration dynamics of tidal meanders agree with nonlinear theories for river meander evolution. Our results challenge the conventional view of tidal channels as stable landscape features and suggest that meandering tidal channels recapitulate many fluvial counterparts owing to large gradients of tidal prisms across meander wavelengths.

Evolution of density-dependent movement during experimental range expansions

Range expansions and biological invasions are prime examples of transient processes that are likely impacted by rapid evolutionary changes. As a spatial process, range expansions are driven by dispersal and movement behaviour. Although it is widely accepted that dispersal and movement may be context-dependent, for instance density-dependent, and best represented by reaction norms, the evolution of density-dependent movement during range expansions has received little experimental attention. We therefore tested current theory predicting the evolution of increased movement at low densities at range margins using highly replicated and controlled range expansion experiments across multiple genotypes of the protist model system Tetrahymena thermophila. Although rare, we found evolutionary changes during range expansions even in the absence of initial standing genetic variation. Range expansions led to the evolution of negatively density-dependent movement at range margins. In addition, we report the evolution of increased intrastrain competitive ability and concurrently decreased population growth rates in range cores. Our findings highlight the importance of understanding movement and dispersal as evolving reaction norms and plastic life-history traits of central relevance for range expansions, biological invasions and the dynamics of spatially structured systems in general.

Cell-to-cell variability and robustness in S-phase duration from genome replication kinetics

Genome replication, a key process for a cell, relies on stochastic initiation by replication origins, causing a variability of replication timing from cell to cell. While stochastic models of eukaryotic replication are widely available, the link between the key parameters and overall replication timing has not been addressed systematically. We use a combined analytical and computational approach to calculate how positions and strength of many origins lead to a given cell-to-cell variability of total duration of the replication of a large region, a chromosome or the entire genome. Specifically, the total replication timing can be framed as an extreme-value problem, since it is due to the last region that replicates in each cell. Our calculations identify two regimes based on the spread between characteristic completion times of all inter-origin regions of a genome. For widely different completion times, timing is set by the single specific region that is typically the last to replicate in all cells. Conversely, when the completion time of all regions are comparable, an extreme-value estimate shows that the cell-to-cell variability of genome replication timing has universal properties. Comparison with available data shows that the replication program of three yeast species falls in this extreme-value regime.

The scaling structure of the global road network

Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide. To model the effects of this increase, it is crucial to understand whether possible self-organized patterns are inherent in the global road network structure. Here, we use the largest updated database comprising all major roads on the Earth, together with global urban and cropland inventories, to suggest that road length distributions within croplands are indistinguishable from urban ones, once rescaled to account for the difference in mean road length. Such similarity extends to road length distributions within urban or agricultural domains of a given area. We find two distinct regimes for the scaling of the mean road length with the associated area, holding in general at small and at large values of the latter. In suitably large urban and cropland domains, we find that mean and total road lengths increase linearly with their domain area, differently from earlier suggestions. Scaling regimes suggest that simple and universal mechanisms regulate urban and cropland road expansion at the global scale. As such, our findings bear implications for global road infrastructure growth based on land-use change and for planning policies sustaining urban expansions.

Covariations in ecological scaling laws fostered by community dynamics

Scaling laws in ecology, intended both as functional relationships among ecologically relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances, and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked has been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply, and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such a framework is consistent with the stationary-state statistics of a broad class of resource-limited community dynamics models, regardless of parameterization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations.

Relevant parameters in models of cell division control

A recent burst of dynamic single-cell data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different models were used to propose specific mechanisms, but the links between them are poorly explored. The lack of comparative studies makes it difficult to appreciate how well any particular mechanism is supported by the data. Here, we describe a simple and generic framework in which two common formalisms can be used interchangeably: (i) a continuous-time division process described by a hazard function and (ii) a discrete-time equation describing cell size across generations (where the unit of time is a cell cycle). In our framework, this second process is a discrete-time Langevin equation with simple physical analogues. By perturbative expansion around the mean initial size (or interdivision time), we show how this framework describes a wide range of division control mechanisms, including combinations of time and size control, as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria. As we show by analytical estimates and numerical simulations, the available data are described precisely by the first-order approximation of this expansion, i.e., by a "linear response" regime for the correction of size fluctuations. Hence, a single dimensionless parameter defines the strength and action of the division control against cell-to-cell variability (quantified by a single "noise" parameter). However, the same strength of linear response may emerge from several mechanisms, which are distinguished only by higher-order terms in the perturbative expansion. Our analytical estimate of the sample size needed to distinguish between second-order effects shows that this value is close to but larger than the values of the current datasets. These results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division.

A mechanistic stochastic framework for regulating bacterial cell division

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells add a fixed size (volume) from birth to division, irrespective of their size at birth. To mechanistically explain the adder principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distribution of the added volume when scaled by its mean becomes invariant of the growth rate. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for controlling size.

Law of corresponding states for open collaborations

We study the relation between number of contributors and product size in Wikipedia and GitHub. In contrast to traditional production, this is strongly probabilistic, but is characterized by two quantitative nonlinear laws: a power-law bound to product size for increasing number of contributors, and the universal collapse of rescaled distributions. A variant of the random-energy model shows that both laws are due to the heterogeneity of contributors, and displays an intriguing finite-size scaling property with no equivalent in standard systems. The analysis uncovers the right intensive densities, enabling the comparison of projects with different numbers of contributors on equal grounds. We use this property to expose the detrimental effects of conflicting interactions in Wikipedia.

Individuality and universality in the growth-division laws of single E. coli cells

The mean size of exponentially dividing Escherichia coli cells in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time, and individual growth rate are only starting to be characterized. Recent studies in bacteria reported a universal trend where the spread in both size and doubling times is a linear function of the population means of these variables. Here we combine experiments and theory and use scaling concepts to elucidate the constraints posed by the second observation on the division control mechanism and on the joint fluctuations of sizes and doubling times. We found that scaling relations based on the means collapse both size and doubling-time distributions across different conditions and explain how the shape of their joint fluctuations deviates from the means. Our data on these joint fluctuations highlight the importance of cell individuality: Single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time. Our calculations show that these results emerge from a broad class of division control mechanisms requiring a certain scaling form of the "division hazard rate function," which defines the probability rate of dividing as a function of measurable parameters. This "model free" approach gives a rationale for the universal body-size distributions observed in microbial ecosystems across many microbial species, presumably dividing with multiple mechanisms. Additionally, our experiments show a crossover between fast and slow growth in the relation between individual-cell growth rate and division time, which can be understood in terms of different regimes of genome replication control.

BEMOVI, software for extracting behavior and morphology from videos, illustrated with analyses of microbes

Microbes are critical components of ecosystems and provide vital services (e.g., photosynthesis, decomposition, nutrient recycling). From the diverse roles microbes play in natural ecosystems, high levels of functional diversity result. Quantifying this diversity is challenging, because it is weakly associated with morphological differentiation. In addition, the small size of microbes hinders morphological and behavioral measurements at the individual level, as well as interactions between individuals. Advances in microbial community genetics and genomics, flow cytometry and digital analysis of still images are promising approaches. They miss out, however, on a very important aspect of populations and communities: the behavior of individuals. Video analysis complements these methods by providing in addition to abundance and trait measurements, detailed behavioral information, capturing dynamic processes such as movement, and hence has the potential to describe the interactions between individuals. We introduce BEMOVI, a package using the R and ImageJ software, to extract abundance, morphology, and movement data for tens to thousands of individuals in a video. Through a set of functions BEMOVI identifies individuals present in a video, reconstructs their movement trajectories through space and time, and merges this information into a single database. BEMOVI is a modular set of functions, which can be customized to allow for peculiarities of the videos to be analyzed, in terms of organisms features (e.g., morphology or movement) and how they can be distinguished from the background. We illustrate the validity and accuracy of the method with an example on experimental multispecies communities of aquatic protists. We show high correspondence between manual and automatic counts and illustrate how simultaneous time series of abundance, morphology, and behavior are obtained from BEMOVI. We further demonstrate how the trait data can be used with machine learning to automatically classify individuals into species and that information on movement behavior improves the predictive ability.

Characterizing the size and shape of sea ice floes

Monitoring drift ice in the Arctic and Antarctic regions directly and by remote sensing is important for the study of climate, but a unified modeling framework is lacking. Hence, interpretation of the data, as well as the decision of what to measure, represent a challenge for different fields of science. To address this point, we analyzed, using statistical physics tools, satellite images of sea ice from four different locations in both the northern and southern hemispheres, and measured the size and the elongation of ice floes (floating pieces of ice). We find that (i) floe size follows a distribution that can be characterized with good approximation by a single length scale , which we discuss in the framework of stochastic fragmentation models, and (ii) the deviation of their shape from circularity is reproduced with remarkable precision by a geometric model of coalescence by freezing, based on random Voronoi tessellations, with a single free parameter expressing the shape disorder. Although the physical interpretations remain open, this advocates the parameters and as two independent indicators of the environment in the polar regions, which are easily accessible by remote sensing.

Generalized receptor law governs phototaxis in the phytoplankton Euglena gracilis

Phototaxis, the process through which motile organisms direct their swimming toward or away from light, is implicated in key ecological phenomena (including algal blooms and diel vertical migration) that shape the distribution, diversity, and productivity of phytoplankton and thus energy transfer to higher trophic levels in aquatic ecosystems. Phototaxis also finds important applications in biofuel reactors and microbiopropellers and is argued to serve as a benchmark for the study of biological invasions in heterogeneous environments owing to the ease of generating stochastic light fields. Despite its ecological and technological relevance, an experimentally tested, general theoretical model of phototaxis seems unavailable to date. Here, we present accurate measurements of the behavior of the alga Euglena gracilis when exposed to controlled light fields. Analysis of E. gracilis' phototactic accumulation dynamics over a broad range of light intensities proves that the classic Keller-Segel mathematical framework for taxis provides an accurate description of both positive and negative phototaxis only when phototactic sensitivity is modeled by a generalized "receptor law," a specific nonlinear response function to light intensity that drives algae toward beneficial light conditions and away from harmful ones. The proposed phototactic model captures the temporal dynamics of both cells' accumulation toward light sources and their dispersion upon light cessation. The model could thus be of use in integrating models of vertical phytoplankton migrations in marine and freshwater ecosystems, and in the design of bioreactors.

Sample and population exponents of generalized Taylor's law

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b = 2. Some theoretical models of population growth, however, predict a broad range of values for the population exponent b pertaining to the mean and variance of population density, depending on details of the growth process. Is the widely reported sample exponent b ≃ 2 the result of ecological processes or could it be a statistical artifact? Here, we apply large deviations theory and finite-sample arguments to show exactly that in a broad class of growth models the sample exponent is b ≃ 2 regardless of the underlying population exponent. We derive a generalized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth cumulants. The sample exponent b(jk) depends predictably on the number of samples and for finite samples we obtain b(jk) ≃ k = j asymptotically in time, a prediction that we verify in two empirical examples. Thus, the sample exponent b ≃ 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly. Given the broad class of models investigated, our results apply to many fields where TL is used although inadequately understood.

Eco-evolutionary feedbacks during experimental range expansions

Understanding biological range expansions and invasions is of great ecological and economical interest. Importantly, spatial dynamics can be deeply affected by rapid evolution depending on the ecological context. Using experimental evolution in replicated microcosm landscapes and numerical analyses we show experimentally that the ecological process of range expansions leads to the evolution of increased dispersal. This evolutionary change counter-intuitively feeds back on (macro-)ecological patterns affecting the spatial distribution of population densities. While existing theory suggests that densities decrease from range cores to range margins due to K-selection, we show the reverse to be true when competition is considered explicitly including resource dynamics. We suggest that a dispersal-foraging trade-off, leading to more ‘prudent' foraging at range margins, is the driving mechanism behind the macroecological pattern reported. In conclusion, rapid multi-trait evolution and eco-evolutionary feedbacks are highly relevant for understanding macroecological patterns and designing appropriate conservation strategies.

Biological range expansions and invasions can be affected by rapid evolution. Here the authors show an evolutionary increase of dispersal during range expansions and an increase of population densities from range cores to range margins in microcosm experiments with a freshwater ciliate.

Cell-size control and homeostasis in bacteria

How cells control their size and maintain size homeostasis is a fundamental open question. Cell-size homeostasis has been discussed in the context of two major paradigms: "sizer," in which the cell actively monitors its size and triggers the cell cycle once it reaches a critical size, and "timer," in which the cell attempts to grow for a specific amount of time before division. These paradigms, in conjunction with the "growth law" [1] and the quantitative bacterial cell-cycle model [2], inspired numerous theoretical models [3-9] and experimental investigations, from growth [10, 11] to cell cycle and size control [12-15]. However, experimental evidence involved difficult-to-verify assumptions or population-averaged data, which allowed different interpretations [1-5, 16-20] or limited conclusions [4-9]. In particular, population-averaged data and correlations are inconclusive as the averaging process masks causal effects at the cellular level. In this work, we extended a microfluidic "mother machine" [21] and monitored hundreds of thousands of Gram-negative Escherichia coli and Gram-positive Bacillus subtilis cells under a wide range of steady-state growth conditions. Our combined experimental results and quantitative analysis demonstrate that cells add a constant volume each generation, irrespective of their newborn sizes, conclusively supporting the so-called constant Δ model. This model was introduced for E. coli [6, 7] and recently revisited [9], but experimental evidence was limited to correlations. This "adder" principle quantitatively explains experimental data at both the population and single-cell levels, including the origin and the hierarchy of variability in the size-control mechanisms and how cells maintain size homeostasis.

Active colonization dynamics and diversity patterns are influenced by dendritic network connectivity and species interactions

Habitat network connectivity influences colonization dynamics, species invasions, and biodiversity patterns. Recent theoretical work suggests dendritic networks, such as those found in rivers, alter expectations regarding colonization and dispersal dynamics compared with other network types. As many native and non-native species are spreading along river networks, this may have important ecological implications. However, experimental studies testing the effects of network structure on colonization and diversity patterns are scarce. Up to now, experimental studies have only considered networks where sites are connected with small corridors, or dispersal was experimentally controlled, which eliminates possible effects of species interactions on colonization dynamics. Here, we tested the effect of network connectivity and species interactions on colonization dynamics using continuous linear and dendritic (i.e., river-like) networks, which allow for active dispersal. We used a set of six protist species and one rotifer species in linear and dendritic microcosm networks. At the start of the experiment, we introduced species, either singularly or as a community within the networks. Species subsequently actively colonized the networks. We periodically measured densities of species throughout the networks over 2 weeks to track community dynamics, colonization, and diversity patterns. We found that colonization of dendritic networks was faster compared with colonization of linear networks, which resulted in higher local mean species richness in dendritic networks. Initially, community similarity was also greater in dendritic networks compared with linear networks, but this effect vanished over time. The presence of species interactions increased community evenness over time, compared with extrapolations from single-species setups. Our experimental findings confirm previous theoretical work and show that network connectivity, species-specific dispersal ability, and species interactions greatly influence the dispersal and colonization of dendritic networks. We argue that these factors need to be considered in empirical studies, where effects of network connectivity on colonization patterns have been largely underestimated.

Form, function, and evolution of living organisms

Despite the vast diversity of sizes and shapes of living organisms, life's organization across scales exhibits remarkable commonalities, most notably through the approximate validity of Kleiber's law, the power law scaling of metabolic rates with the mass of an organism. Here, we present a derivation of Kleiber's law that is independent of the specificity of the myriads of organism species. Specifically, we account for the distinct geometries of trees and mammals as well as deviations from the pure power law behavior of Kleiber's law, and predict the possibility of life forms with geometries intermediate between trees and mammals. We also make several predictions in excellent accord with empirical data. Our theory relates the separate evolutionary histories of plants and animals through the fundamental physics underlying their distinct overall forms and physiologies.

Concerted control of Escherichia coli cell division

The coordination of cell growth and division is a long-standing problem in biology. Focusing on Escherichia coli in steady growth, we quantify cell division control using a stochastic model, by inferring the division rate as a function of the observable parameters from large empirical datasets of dividing cells. We find that (i) cells have mechanisms to control their size, (ii) size control is effected by changes in the doubling time, rather than in the single-cell elongation rate, (iii) the division rate increases steeply with cell size for small cells, and saturates for larger cells. Importantly, (iv) the current size is not the only variable controlling cell division, but the time spent in the cell cycle appears to play a role, and (v) common tests of cell size control may fail when such concerted control is in place. Our analysis illustrates the mechanisms of cell division control in E. coli. The phenomenological framework presented is sufficiently general to be widely applicable and opens the way for rigorous tests of molecular cell-cycle models.

Emerging predictable features of replicated biological invasion fronts

Biological dispersal shapes species' distribution and affects their coexistence. The spread of organisms governs the dynamics of invasive species, the spread of pathogens, and the shifts in species ranges due to climate or environmental change. Despite its relevance for fundamental ecological processes, however, replicated experimentation on biological dispersal is lacking, and current assessments point at inherent limitations to predictability, even in the simplest ecological settings. In contrast, we show, by replicated experimentation on the spread of the ciliate Tetrahymena sp. in linear landscapes, that information on local unconstrained movement and reproduction allows us to predict reliably the existence and speed of traveling waves of invasion at the macroscopic scale. Furthermore, a theoretical approach introducing demographic stochasticity in the Fisher-Kolmogorov framework of reaction-diffusion processes captures the observed fluctuations in range expansions. Therefore, predictability of the key features of biological dispersal overcomes the inherent biological stochasticity. Our results establish a causal link from the short-term individual level to the long-term, broad-scale population patterns and may be generalized, possibly providing a general predictive framework for biological invasions in natural environments.

Evidence for soft bounds in Ubuntu package sizes and mammalian body masses

The development of a complex system depends on the self-coordinated action of a large number of agents, often determining unexpected global behavior. The case of software evolution has great practical importance: knowledge of what is to be considered atypical can guide developers in recognizing and reacting to abnormal behavior. Although the initial framework of a theory of software exists, the current theoretical achievements do not fully capture existing quantitative data or predict future trends. Here we show that two elementary laws describe the evolution of package sizes in a Linux-based operating system: first, relative changes in size follow a random walk with non-Gaussian jumps; second, each size change is bounded by a limit that is dependent on the starting size, an intriguing behavior that we call "soft bound." Our approach is based on data analysis and on a simple theoretical model, which is able to reproduce empirical details without relying on any adjustable parameter and generates definite predictions. The same analysis allows us to formulate and support the hypothesis that a similar mechanism is shaping the distribution of mammalian body sizes, via size-dependent constraints during cladogenesis. Whereas generally accepted approaches struggle to reproduce the large-mass shoulder displayed by the distribution of extant mammalian species, this is a natural consequence of the softly bounded nature of the process. Additionally, the hypothesis that this model is valid has the relevant implication that, contrary to a common assumption, mammalian masses are still evolving, albeit very slowly.