A Process-Independent Explanation for the General Form of Taylor's Law

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.

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.

Temporal variability in quantitative human gut microbiome profiles and implications for clinical research

While clinical gut microbiota research is ever-expanding, extending reference knowledge of healthy between- and within-subject gut microbiota variation and its drivers remains essential; in particular, temporal variability is under-explored, and a comparison with cross-sectional variation is missing. Here, we perform daily quantitative microbiome profiling on 713 fecal samples from 20 Belgian women over six weeks, combined with extensive anthropometric measurements, blood panels, dietary data, and stool characteristics. We show substantial temporal variation for most major gut genera; we find that for 78% of microbial genera, day-to-day absolute abundance variation is substantially larger within than between individuals, with up to 100-fold shifts over the study period. Diversity, and especially evenness indicators also fluctuate substantially. Relative abundance profiles show similar but less pronounced temporal variation. Stool moisture, and to a lesser extent diet, are the only significant host covariates of temporal microbiota variation, while menstrual cycle parameters did not show significant effects. We find that the dysbiotic Bact2 enterotype shows increased between- and within-subject compositional variability. Our results suggest that to increase diagnostic as well as target discovery power, studies could adopt a repeated measurement design and/or focus analysis on community-wide microbiome descriptors and indices.

A unified framework for species spatial patterns: Linking the occupancy area curve, Taylor's Law, the neighborhood density function and two-plot species turnover

The description of spatial patterns in species distributions is central to research throughout ecology. In this manuscript, we demonstrate that five of the most widely used species‐level spatial patterns are not only related, but can in fact be quantitatively derived from each other under minimal assumptions: the occupancy area curve, Taylor's Law, the neighborhood density function, a two‐plot variant of Taylor's Law and two‐plot single‐species turnover. We present an overarching mathematical framework and derivations for several theoretical example cases, along with a simulation study and empirical analysis that applies the framework to data from the Barro Colorado Island tropical forest plot. We discuss how knowledge of this mathematical relationship can support the testing of ecological theory, suggest efficient field sampling schemes, highlight the relative importance of plot area and abundance in driving turnover patterns and lay the groundwork for future unified theories of community‐level spatial metrics and multi‐patch spatial patterns.

Spatial and temporal autocorrelations affect Taylor's law for US county populations: Descriptive and predictive models

Understanding the spatial and temporal distributions and fluctuations of living populations is a central goal in ecology and demography. A scaling pattern called Taylor's law has been used to quantify the distributions of populations. Taylor's law asserts a linear relationship between the logarithm of the mean and the logarithm of the variance of population size. Here, extending previous work, we use generalized least-squares models to describe three types of Taylor's law. These models incorporate the temporal and spatial autocorrelations in the mean-variance data. Moreover, we analyze three purely statistical models to predict the form and slope of Taylor's law. We apply these descriptive and predictive models of Taylor's law to the county population counts of the United States decennial censuses (1790-2010). We find that the temporal and spatial autocorrelations strongly affect estimates of the slope of Taylor's law, and generalized least-squares models that take account of these autocorrelations are often superior to ordinary least-squares models. Temporal and spatial autocorrelations combine with demographic factors (e.g., population growth and historical events) to influence Taylor's law for human population data. Our results show that the assumptions of a descriptive model must be carefully evaluated when it is used to estimate and interpret the slope of Taylor's law.

A Residence Time Theory for Biodiversity

From microorganisms to the largest macroorganisms, much of Earth's biodiversity is subject to forces of physical turnover. Residence time is the ratio of an ecosystem's size to its rate of flow and provides a means for understanding the influence of physical turnover on biological systems. Despite its use across scientific disciplines, residence time has not been integrated into the broader understanding of biodiversity, life history, and the assembly of ecological communities. Here we propose a residence time theory for the growth, activity, abundance, and diversity of traits and taxa in complex ecological systems. Using thousands of stochastic individual-based models to simulate energetically constrained life-history processes, we show that our predictions are conceptually sound and mutually compatible and that they support ecological relationships that underpin much of biodiversity theory. We discuss the importance of residence time across the ecological hierarchy and propose how residence time can be integrated into theories ranging from population genetics to macroecology.

Isometric scaling of faunal patchiness: Seagrass macrobenthic abundance across small spatial scales

Following earlier studies across 2115 → 33 m² scales (Barnes and Laurie, 2018), patchiness of macrobenthic abundance in intertidal Queensland seagrass was assessed by dispersion indices, spatial autocorrelation and hotspot analysis across a hierarchically-nested series of smaller scales (5.75 → 0.09 m²). Overall patterns of distribution and abundance over larger extents and with greater lag were mirrored across these smaller ones. Assemblage abundance per station varied by a factor of >10, but all three approaches showed effective constancy of total assemblage patchiness across all sub-2115 m² scales (across-scales-mean Lloyd's I_P of 1.06 and global Moran's I of 0.13). Equivalent constancy was also shown by most numerically-dominant species (scaling exponent β = 0.93-1.15). Decreasing patchiness of some species with decreasing scale, however, resulted in two no longer being patchily dispersed across small scales. Significant hotspots of abundance occurred at a constant proportion of stations across scales, against a background of randomly scattered peak-abundance points.

Proximate determinants of Taylor's law slopes

Taylor's law (TL), a commonly observed and applied pattern in ecology, describes variances of population densities as related to mean densities via log(variance) = log(a) + b*log(mean). Variations among datasets in the slope, b, have been associated with multiple factors of central importance in ecology, including strength of competitive interactions and demographic rates. But these associations are not transparent, and the relative importance of these and other factors for TL slope variation is poorly studied. TL is thus a ubiquitously used indicator in ecology, the understanding of which is still opaque. The goal of this study was to provide tools to help fill this gap in understanding by providing proximate determinants of TL slopes, statistical quantities that are correlated to TL slopes but are simpler than the slope itself and are more readily linked to ecological factors. Using numeric simulations and 82 multi-decadal population datasets, we here propose, test and apply two proximate statistical determinants of TL slopes which we argue can become key tools for understanding the nature and ecological causes of TL slope variation. We find that measures based on population skewness, coefficient of variation and synchrony are effective proximate determinants. We demonstrate their potential for application by using them to help explain covariation in slopes of spatial and temporal TL (two common types of TL). This study provides tools for understanding TL, and demonstrates their usefulness.

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.

Taylor’s Power Law for Leaf Bilateral Symmetry

Leaf shape and symmetry is of interest because of the importance of leaves in photosynthesis. Recently, a novel method was proposed to measure the extent of bilateral symmetry in leaves in which a leaf was divided into left and right sides by a straight line through the leaf apex and base, and a number of equidistant strips were drawn perpendicular to the straight line to generate an equivalent number of differences in area between the left and right parts. These areal differences are the basis for a measure of leaf bilateral symmetry, which was then examined to see how well it follows Taylor’s power law (TPL) using three classes of plants, namely, 10 geographical populations of Parrotia subaequalis (H.T. Chang) R.M. Hao et H.T. Wei, 10 species of Bambusoideae, and 10 species of Rosaceae. The measure of bilateral symmetry followed TPL for a single species or for a class of closely related species. The estimate of the exponent of TPL for bamboo plants was significantly larger than for the dicotyledonous trees, but its goodness of fit was the best among the three classes of plants. The heterogeneity of light falling on branches and leaves due to above-ground architectural patterns is an important contributor to leaf asymmetry.

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.

Individual size variation reduces spatial variation in abundance of tree community assemblage, not of tree populations

Research on individual trait variation has gained much attention because of its implication for ecosystem functions and community ecology. The effect of individual variation on population and community abundance (number of individuals) variation remains scarcely tested. Using two established ecological scaling laws (Taylor's law and abundance-size relationship), we derived a new scaling relationship between the individual size variation and spatial variation of abundance. Tested against multi-plot tree data from Diaoluo Mountain tropical forest in Hainan, China, the new scaling relationship showed that individual size variation reduced the spatial variation of community assemblage abundance, but not of taxon-specific population abundance. The different responses of community and population to individual variation were reflected by the validity of the abundance-size relationship. We tested and confirmed this scaling framework using two measures of individual tree size: aboveground biomass and diameter at breast height. Using delta method and height-diameter allometry, we derived the analytic relation of scaling exponents estimated under different individual size measures. In addition, we used multiple regression models to analyze the effect of taxon richness on the relationship between individual size variation and spatial variation of population or community abundance, for taxon-specific and taxon-mixed data, respectively. This work offers empirical evidence and a scaling framework for the negative effect of individual trait variation on spatial variation of plant community. It has implications for forest ecosystem and management where the role of individual variation in regulating population or community spatial variation is important but understudied.

Internode morphometrics and allometry of Tonkin Cane Pseudosasa amabilis

Pseudosasa amabilis (McClure) (Poales: Gramineae) is a typical bamboo species naturally distributed in large area of south China and famous for its culm strength. Although bamboos were found to share the same development rule, the detailed internode morphology of bamboo culm was actually not fully expressed. We explored internode morphology of P. amabilis using 11 different physical parameters in different dimensions (1–4). As Taylor's power law (TPL) is generally applicable to describe relationship between mean and variance of population density, here we used TPL to evaluate the differences between internodes, and further, the relationship between dimension and TPL. Results showed that length (L), hollow radius (HR), hollow area (HA), hollow cylinder volume (HCV), total cylinder volume (TCV), density (De), and weight (W) all presented positive skewed distribution in varying degrees. For the basic one‐dimensional parameters, the 9th internode was the longest, the 7th the heaviest, while thickness (T) decreased with internodes. Diameter (D) decreased in general but with an inconspicuous local mode at the 5–6th internodes, potentially due to the rapid height growth. The longest (9th) internode was the “turning point” for T‐D and HR‐D relationships. Scatter plot changing trends of W to the one‐dimensional parameters after the heaviest (7th) internode were reversed, indicating a deceleration of growth speed. TPL was not holding well in one‐dimensional parameters (R²: 0.5413–0.8125), but keep increasing as the parameter's dimension increasing (R² > 0.92 for two‐dimensional, R² > 0.97 for three‐dimensional, and R² > 0.99 for four‐dimensional parameters.), suggesting an emergence mechanism of TPL related to both the physical dimensions of morphological measures and the allometric growth of bamboo. From the physical fundamental level, all existences are the expression of energy distribution in different dimensions, implying a more general rule that energy distribution holds better TPL in higher dimension level.

When can we infer mechanism from parasite aggregation? A constraint-based approach to disease ecology

Few hosts have many parasites while many hosts have few parasites. This axiom of macroparasite aggregation is so pervasive it is considered a general law in disease ecology, with important implications for the dynamics of host-parasite systems. Because of these dynamical implications, a significant amount of work has explored both the various mechanisms leading to parasite aggregation patterns and how to infer mechanism from these patterns. However, as many disease mechanisms can produce similar aggregation patterns, it is not clear whether aggregation itself provides any additional information about mechanism. Here we apply a "constraint-based" approach developed in macroecology that allows us to explore whether parasite aggregation contains any additional information beyond what is provided by mean parasite load. We tested two constraint-based null models, both of which were constrained on the total number of parasites P and hosts H found in a sample, using data from 842 observed amphibian host-trematode parasite distributions. We found that constraint-based models captured ~85% of the observed variation in host-parasite distributions, suggesting that the constraints P and H contain much of the information about the shape of the host-parasite distribution. However, we also found that extending the constraint-based null models can identify the potential role of known aggregating mechanisms (such as host heterogeneity) and disaggregating mechanisms (such as parasite-induced host mortality) in constraining host-parasite distributions. Thus, by providing robust null models, constraint-based approaches can help guide investigations aimed at detecting biological processes that directly affect parasite aggregation above and beyond those that indirectly affect aggregation through P and H.

Heterogeneous 'proportionality constants' - A challenge to Taylor's Power Law for temporal fluctuations in abundance

Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes.

Scaling laws predict global microbial diversity

Scaling laws underpin unifying theories of biodiversity and are among the most predictively powerful relationships in biology. However, scaling laws developed for plants and animals often go untested or fail to hold for microorganisms. As a result, it is unclear whether scaling laws of biodiversity will span evolutionarily distant domains of life that encompass all modes of metabolism and scales of abundance. Using a global-scale compilation of ∼35,000 sites and ∼5.6⋅10(6) species, including the largest ever inventory of high-throughput molecular data and one of the largest compilations of plant and animal community data, we show similar rates of scaling in commonness and rarity across microorganisms and macroscopic plants and animals. We document a universal dominance scaling law that holds across 30 orders of magnitude, an unprecedented expanse that predicts the abundance of dominant ocean bacteria. In combining this scaling law with the lognormal model of biodiversity, we predict that Earth is home to upward of 1 trillion (10(12)) microbial species. Microbial biodiversity seems greater than ever anticipated yet predictable from the smallest to the largest microbiome.