Taylor's Law holds in experimental bacterial populations but competition does not influence the slope

Taylor's power law for freshwater fishes: Functional traits beyond statistical inevitability

Taylor's power law (TPL) describes the expected range of parameters of the mean-variance scaling relationship and has been extensively used in studies examining temporal variations in abundance. Few studies though have focused on biological and ecological covariates of TPL, while its statistical inherences have been extensively debated. In the present study, we focused on species-specific features (i.e. functional traits) that could be influential to temporal TPL. We combined field surveys of 180 fish species from 972 sites varying from small streams to large rivers with data on 31 ecological traits describing species-specific characteristics related to three main niche dimensions (trophic ecology, life history, and habitat use). For each species, the parameters of temporal TPL (intercept and slope) were estimated from the log-log mean-variance relationships while controlling for spatial dependencies and biological covariates (species richness and evenness). Then, we investigated whether functional traits explained variations in TPL parameters. Differences in TPL parameters among species were explained mostly by life history and environmental determinants, especially TPL slope. Life history was the main determinant of differences in TPL parameters and thereby aggregation patterns, with traits related to body size being the most influential, thus showing a high contrast between small-sized species with short lifespans and large-bodied migratory fishes, even after controlling for phylogenetic resemblances. We found that life history traits, especially those related to body size, mostly affect TPL and, as such, can be determinants of temporal variability of fish populations. We also found that statistical effects and phylogenetic resemblances are embedded in mean-variance relationships for fish, and that environmental drivers can interact with ecological characteristics of species in determining temporal fluctuations in abundance.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations

Large stochastic population abundance fluctuations are ubiquitous across the tree of life1-7, impacting the predictability of population dynamics and influencing eco-evolutionary outcomes. It has generally been thought that these large abundance fluctuations do not strongly impact evolution, as the relative frequencies of alleles in the population will be unaffected if the abundance of all alleles fluctuate in unison. However, we argue that large abundance fluctuations can lead to significant genotype frequency fluctuations if different genotypes within a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related E. coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from models of genetic drift. We develop a flexible, effective model that explains the abundance fluctuations as arising from correlated offspring numbers between individuals, and the large frequency fluctuations result from even slight decoupling in offspring numbers between genotypes. This model accurately describes the observed abundance and frequency fluctuation scaling behaviors. Our findings suggest chaotic dynamics underpin these giant fluctuations, causing initially similar trajectories to diverge exponentially; subtle environmental changes can be magnified, leading to batch correlations in identical growth conditions. Furthermore, we present evidence that such decoupling noise is also present in mixed-genotype S. cerevisiae populations. We demonstrate that such decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of asynchronous fluctuations, we anticipate that they are widespread in biological populations, significantly affecting evolutionary and ecological dynamics.

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 macroecological perspective on genetic diversity in the human gut microbiome

While the human gut microbiome has been intensely studied, we have yet to obtain a sufficient understanding of the genetic diversity that it harbors. Research efforts have demonstrated that a considerable fraction of within-host genetic variation in the human gut is driven by the ecological dynamics of co-occurring strains belonging to the same species, suggesting that an ecological lens may provide insight into empirical patterns of genetic diversity. Indeed, an ecological model of self-limiting growth and environmental noise known as the Stochastic Logistic Model (SLM) was recently shown to successfully predict the temporal dynamics of strains within a single human host. However, its ability to predict patterns of genetic diversity across human hosts has yet to be tested. In this manuscript I determine whether the predictions of the SLM explain patterns of genetic diversity across unrelated human hosts for 22 common microbial species. Specifically, the stationary distribution of the SLM explains the distribution of allele frequencies across hosts and predicts the fraction of hosts harboring a given allele (i.e., prevalence) for a considerable fraction of sites. The accuracy of the SLM was correlated with independent estimates of strain structure, suggesting that patterns of genetic diversity in the gut microbiome follow statistically similar forms across human hosts due to the existence of strain-level ecology.

Interactions between strains govern the eco-evolutionary dynamics of microbial communities

Genomic data has revealed that genotypic variants of the same species, that is, strains, coexist and are abundant in natural microbial communities. However, it is not clear if strains are ecologically equivalent, and at what characteristic genetic distance they might exhibit distinct interactions and dynamics. Here, we address this problem by tracking 10 taxonomically diverse microbial communities from the pitcher plant Sarracenia purpurea in the laboratory for more than 300 generations. Using metagenomic sequencing, we reconstruct their dynamics over time and across scales, from distant phyla to closely related genotypes. We find that most strains are not ecologically equivalent and exhibit distinct dynamical patterns, often being significantly more correlated with strains from another species than their own. Although even a single mutation can affect laboratory strains, on average, natural strains typically decouple in their dynamics beyond a genetic distance of 100 base pairs. Using mathematical consumer-resource models, we show that these taxonomic patterns emerge naturally from ecological interactions between community members, but only if the interactions are coarse-grained at the level of strains, not species. Finally, by analyzing genomic differences between strains, we identify major functional hubs such as transporters, regulators, and carbohydrate-catabolizing enzymes, which might be the basis for strain-specific interactions. Our work suggests that fine-scale genetic differences in natural communities could be created and stabilized via the rapid diversification of ecological interactions between strains.

Yeast facilitates the multiplication of Drosophila bacterial symbionts but has no effect on the form or parameters of Taylor's law

Interactions between microbial symbionts influence their demography and that of their hosts. Taylor’s power law (TL)–a well-established relationship between population size mean and variance across space and time–may help to unveil the factors and processes that determine symbiont multiplications. Recent studies suggest pervasive interactions between symbionts in Drosophila melanogaster. We used this system to investigate theoretical predictions regarding the effects of interspecific interactions on TL parameters. We assayed twenty natural strains of bacteria in the presence and absence of a strain of yeast using an ecologically realistic set-up with D. melanogaster larvae reared in natural fruit. Yeast presence led to a small increase in bacterial cell numbers; bacterial strain identity largely affected yeast multiplication. The spatial version of TL held among bacterial and yeast populations with slopes of 2. However, contrary to theoretical prediction, the facilitation of bacterial symbionts by yeast had no detectable effect on TL’s parameters. These results shed new light on the nature of D. melanogaster’s symbiosis with yeast and bacteria. They further reveal the complexity of investigating TL with microorganisms.

Macroecological laws describe variation and diversity in microbial communities

How the coexistence of many species is maintained is a fundamental and unresolved question in ecology. Coexistence is a puzzle because we lack a mechanistic understanding of the variation in species presence and abundance. Whether variation in ecological communities is driven by deterministic or random processes is one of the most controversial issues in ecology. Here, I study the variation of species presence and abundance in microbial communities from a macroecological standpoint. I identify three macroecological laws that quantitatively characterize the fluctuation of species abundance across communities and over time. Using these three laws, one can predict species' presence and absence, diversity, and commonly studied macroecological patterns. I show that a mathematical model based on environmental stochasticity, the stochastic logistic model, quantitatively predicts the three macroecological laws, as well as non-stationary properties of community dynamics.

Spatial variance-mass allometry of population density in felids from camera-trapping studies worldwide

Power laws are cornerstone relationships in ecology and evolutionary biology. The density-mass allometry (DMA), which predicts an allometric scaling of population abundance, and Taylor’s law (TL), which predicts a decrease in the population abundance variation along with a decrease in population density, have enhanced our knowledge of inter- and intra-specific variation in population abundance. When combined, these two power laws led to the variance-mass allometry (VMA), which states that larger species have lower spatial variation in population density than smaller species. The VMA has been predicted through theoretical models, however few studies have investigated if this law is also supported by empirical data. Here, to formally test the VMA, we have used the population density estimates obtained through worldwide camera trapping studies for an emblematic and ecologically important carnivorous taxa, the Felidae family. Our results showed that the VMA law hold in felids, as well as the TL and the DMA laws; bigger cat species showed less variation for the population density than smaller species. These results have important implications for the conservation of wildlife population and confirm the validity of important ecological concepts, like the allometric scaling of population growth rate and the slow-fast continuum of life history strategies.

Impacts of residual insecticide spraying on the abundance and habitat occupancy of Triatoma sordida and co-occurrence with Triatoma infestans: A three-year follow-up in northeastern Argentina

Triatoma infestans, the main vector in the Gran Chaco region, may competitively displace other sympatric species such as Triatoma sordida. We conducted a three-year longitudinal study of site- and house-level infestation and abundance of triatomine bugs before and after an area-wide insecticide spraying campaign followed by sustained vector surveillance in a well-defined rural section of the Argentine Chaco encompassing 368-411 houses. Here, we tested whether insecticide applications targeting and virtually suppressing T. infestans reduced the abundance of T. sordida and modified its habitat occupancies, and whether their joint spatial distribution was random, aggregated or uniform, and varied over time. Systematic timed-manual searches of 18,031 sites yielded 2,226 T. sordida over seven postintervention surveys. Triatoma sordida failed to colonize human sleeping quarters after interventions, and its prime and secondary habitats remained virtually unmodified. Residual insecticide spraying and seasonality best described variations in the house-level abundance of T. sordida as determined using a generalized estimating equation model. Two-species foci occurred in 3.2% of sites ever positive for any species. The habitat-adjusted relative odds of catching one species was 10.8 times greater when the other species was present, with no evidence of heterogeneity among ORs, suggesting no antagonistic interactions throughout the follow-up. The spatial occurrence of both species was significantly aggregated within 300-500 m before and after interventions, and was random at broader spatial scales. The habitat occupancies of T. sordida may be used as a proxy for potential infestation with T. infestans and to guide targeted vector control actions.

Robust Analysis of Time Series in Virome Metagenomics

Metagenomics is a powerful tool for assessing the functional and taxonomic contents in biological samples as it makes feasible to study, simultaneously, the whole living community related to a host organism or medium: all the microbes, including virus, bacteria, archaea, fungi, and protists. New DNA and RNA sequencing technologies are dramatically decreasing the cost per sequenced base, so metagenomic sequencing is becoming more and more widespread in biomedical and environmental research. This is opening the possibility of complete longitudinal metagenomic studies, which could unravel the dynamics of microbial communities including intra-microbiome and host-microbiome interactions through in-depth analysis of time series. For viruses, this is particularly interesting because it allows broad interaction studies of viruses and hosts in different time scales, as in bacteria-phages coevolution studies.This chapter presents computational methods for an automatic and robust analysis of metagenomic time series in virome metagenomics (RATSVM). The same theoretical frame and computational protocol is also suitable for longitudinal studies of spatial series to uncover the dynamics of a microbial community with viruses along a selected dimension in the space. In order to conveniently illustrate the procedure, real data from a published virome study is used. The computational protocol presented here requires only basic computational knowledge. Several scripts have been prepared to ease and automate the most complicate steps, they are available in the RATSVM public repository. For some of the methods a mid-range computing server is advisable, and for some others, it is required. A fat-node with large memory and fast I/O would be the best choice for optimum results.

Taylor's power law captures the effects of environmental variability on community structure: An example from fishes in the North Sea

Taylor's power law (TPL) describes the relationship between the mean and variance in abundance of populations, with the power law exponent considered a measure of aggregation. However, the usefulness of TPL exponents as an ecological metric has been questioned, largely due to its apparent ubiquity in various complex systems. The aim of this study was to test whether TPL exponents vary systematically with potential drivers of animal aggregation in time and space and therefore capture useful ecological information of the system of interest. We derived community TPL exponents from a long-term, standardised and spatially dense data series of abundance and body size data for a strongly size-structured fish community in the North Sea. We then compared TPL exponents between regions of contrasting environmental characteristics. We find that, in general, TPL exponents vary more than expected under random conditions in the North Sea for size-based populations compared to communities considered by species. Further, size-based temporal TPL exponents are systematically higher (implying more temporally aggregated distributions) along hydrographic boundaries. Time series of size-based spatial TPL exponents also differ between hydrographically distinct basins. These findings support the notion that TPL exponents contain ecological information, capturing community spatio-temporal dynamics as influenced by external drivers.

Biological and statistical processes jointly drive population aggregation: using host-parasite interactions to understand Taylor's power law

The macroecological pattern known as Taylor's power law (TPL) represents the pervasive tendency of the variance in population density to increase as a power function of the mean. Despite empirical illustrations in systems ranging from viruses to vertebrates, the biological significance of this relationship continues to be debated. Here we combined collection of a unique dataset involving 11 987 amphibian hosts and 332 684 trematode parasites with experimental measurements of core epidemiological outcomes to explicitly test the contributions of hypothesized biological processes in driving aggregation. After using feasible set theory to account for mechanisms acting indirectly on aggregation and statistical constraints inherent to the data, we detected strongly consistent influences of host and parasite species identity over 7 years of sampling. Incorporation of field-based measurements of host body size, its variance and spatial heterogeneity in host density accounted for host identity effects, while experimental quantification of infection competence (and especially virulence from the 20 most common host-parasite combinations) revealed the role of species-by-environment interactions. By uniting constraint-based theory, controlled experiments and community-based field surveys, we illustrate the joint influences of biological and statistical processes on parasite aggregation and emphasize their importance for understanding population regulation and ecological stability across a range of systems, both infectious and free-living.

Garay C. Health and Disease Imprinted in the Time Variability of the Human Microbiome

The animal microbiota (including the human microbiota) plays an important role in keeping the physiological status of the host healthy. Research seeks greater insight into whether changes in the composition and function of the microbiota are associated with disease. We analyzed published 16S rRNA and shotgun metagenomic sequencing (SMS) data pertaining to the gut microbiotas of 99 subjects monitored over time. Temporal fluctuations in the microbial composition revealed significant differences due to factors such as dietary changes, antibiotic intake, age, and disease. This article shows that a fluctuation scaling law can describe the temporal changes in the gut microbiota. This law estimates the temporal variability of the microbial population and quantitatively characterizes the path toward disease via a noise-induced phase transition. Estimation of the systemic parameters may be of clinical utility in follow-up studies and have more general applications in fields where it is important to know whether a given community is stable or not. IMPORTANCE The human microbiota correlates closely with the health status of its host. This article analyzes the microbial composition of several subjects under different conditions over time spans that ranged from days to months. Using the Langevin equation as the basis of our mathematical framework to evaluate microbial temporal stability, we proved that stable microbiotas can be distinguished from unstable microbiotas. This initial step will help us to determine how temporal microbiota stability is related to a subject's health status and to develop a more comprehensive framework that will provide greater insight into this complex system.

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.

Random sampling of skewed distributions implies Taylor's power law of fluctuation scaling

Taylor's law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species' population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)(b), a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared.

Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Taylor's law (TL) asserts that the variance of the density (individuals per area or volume) of a set of comparable populations is a power-law function of the mean density of those populations. Despite the empirical confirmation of TL in hundreds of species, there is little consensus about why TL is so widely observed and how its estimated parameters should be interpreted. Here, we report that the Lewontin-Cohen (henceforth LC) model of stochastic population dynamics, which has been widely discussed and applied, leads to a spatial TL in the limit of large time and provides an explicit, exact interpretation of its parameters. The exponent of TL exceeds 2 if and only if the LC model is supercritical (growing on average), equals 2 if and only if the LC model is deterministic, and is less than 2 if and only if the LC model is subcritical (declining on average). TL and the LC model describe the spatial variability and the temporal dynamics of populations of trees on long-term plots censused over 75 years at the Black Rock Forest, Cornwall, NY, USA.

Taylor's law and body size in exploited marine ecosystems

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density-mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance-mass allometry). Marine size spectra are known to exhibit density-mass allometry, but variance-mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size-at-entry fishing, in which only fish above a certain size may legally be caught.

Allometric scaling of population variance with mean body size is predicted from Taylor's law and density-mass allometry

Two widely tested empirical patterns in ecology are combined here to predict how the variation of population density relates to the average body size of organisms. Taylor's law (TL) asserts that the variance of the population density of a set of populations is a power-law function of the mean population density. Density-mass allometry (DMA) asserts that the mean population density of a set of populations is a power-law function of the mean individual body mass. Combined, DMA and TL predict that the variance of the population density is a power-law function of mean individual body mass. We call this relationship "variance-mass allometry" (VMA). We confirmed the theoretically predicted power-law form and the theoretically predicted parameters of VMA, using detailed data on individual oak trees (Quercus spp.) of Black Rock Forest, Cornwall, New York. These results connect the variability of population density to the mean body mass of individuals.

Contingency and statistical laws in replicate microbial closed ecosystems

Contingency, the persistent influence of past random events, pervades biology. To what extent, then, is each course of ecological or evolutionary dynamics unique, and to what extent are these dynamics subject to a common statistical structure? Addressing this question requires replicate measurements to search for emergent statistical laws. We establish a readily replicated microbial closed ecosystem (CES), sustaining its three species for years. We precisely measure the local population density of each species in many CES replicates, started from the same initial conditions and kept under constant light and temperature. The covariation among replicates of the three species densities acquires a stable structure, which could be decomposed into discrete eigenvectors, or "ecomodes." The largest ecomode dominates population density fluctuations around the replicate-average dynamics. These fluctuations follow simple power laws consistent with a geometric random walk. Thus, variability in ecological dynamics can be studied with CES replicates and described by simple statistical laws.