Quantifying how much host, pathogen, and other factors affect human protective adaptive immune responses.

Recognizing the "essential" factors that contribute to a clinical outcome is critical for designing appropriate therapies and prioritizing limited medical resources. Demonstrating a high correlation between a factor and an outcome does not necessarily imply an essential role of the factor to the outcome. Human protective adaptive immune responses to pathogens vary among (and perhaps within) pathogenic strains, human individual hosts, and in response to other factors. Which of these has an "essential" role? We offer three statistical approaches that predict the presence of newly contributing factor(s) and then quantify the influence of host, pathogen, and the new factors on immune responses. We illustrate these approaches using previous data from the protective adaptive immune response (cellular and humoral) by human hosts to various strains of the same pathogenic bacterial species. Taylor's law predicts the existence of other factors potentially contributing to the human protective adaptive immune response in addition to inter-individual host and intra-bacterial species inter-strain variability. A mixed linear model measures the relative contribution of the known variables, individual human hosts and bacterial strains, and estimates the summed contributions of the newly predicted but unknown factors to the combined adaptive immune response. A principal component analysis predicts the presence of sub-variables (currently not defined) within bacterial strains and individuals that may contribute to the combined immune response. These observations have statistical, biological, clinical, and therapeutic implications.

Taylor's law for exponentially growing local populations linked by migration.

We consider the dynamics of a collection of n>1 populations in which each population has its own rate of growth or decay, fixed in continuous time, and migrants may flow from one population to another over a fixed network, at a rate, fixed over time, times the size of the sending population. This model is represented by an ordinary linear differential equation of dimension n with constant coefficients arrayed in an essentially nonnegative matrix. This paper identifies conditions on the parameters of the model (specifically, conditions on the eigenvalues and eigenvectors) under which the variance of the n population sizes at a given time is asymptotically (as time increases) proportional to a power of the mean of the population sizes at that given time. A power-law variance function is known in ecology as Taylor's Law and in physics as fluctuation scaling. Among other results, we show that Taylor's Law holds asymptotically, with variance asymptotically proportional to the mean squared, on an open dense subset of the class of models considered here.

Nanomechanics of wild-type and mutant dimers of the tip-link protein protocadherin 15.

Mechanical force controls the opening and closing of mechanosensitive ion channels atop the hair bundles of the inner ear. The filamentous tip link connecting transduction channels to the tallest neighboring stereocilium modulates the force transmitted to the channels and thus changes their probability of opening. Each tip link comprises four molecules: a dimer of protocadherin 15 and a dimer of cadherin 23, all of which are stabilized by Ca2+ binding. Using a high-speed optical trap to examine dimeric PCDH15, we find that the protein's configuration is sensitive to Ca2+ and that the molecule exhibits limited unfolding at a physiological Ca2+ concentration. PCDH15 can therefore modulate its stiffness without undergoing large unfolding events in physiological Ca2+ conditions. The experimentally determined stiffness of PCDH15 accords with published values for the stiffness of the gating spring, the mechanical element that controls the opening of mechanotransduction channels. When PCDH15 has a point mutation, V507D, associated with non-syndromic hearing loss, unfolding events occur more frequently under tension and refolding events occur less often than in the wild-type protein. Our results suggest that the maintenance of appropriate tension in the gating spring is critical to the appropriate transmission of force to transduction channels, and hence to hearing.

COVID-19 cases and deaths in the United States follow Taylor's law for heavy-tailed distributions with infinite variance.

The spatial and temporal patterns of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases and COVID-19 deaths in the United States are poorly understood. We show that variations in the cumulative reported cases and deaths by county, state, and date exemplify Taylor's law of fluctuation scaling. Specifically, on day 1 of each month from April 2020 through June 2021, each state's variance (across its counties) of cases is nearly proportional to its squared mean of cases. COVID-19 deaths behave similarly. The lower 99% of counts of cases and deaths across all counties are approximately lognormally distributed. Unexpectedly, the largest 1% of counts are approximately Pareto distributed, with a tail index that implies a finite mean and an infinite variance. We explain why the counts across the entire distribution conform to Taylor's law with exponent two using models and mathematics. The finding of infinite variance has practical consequences. Local jurisdictions (counties, states, and countries) that are planning for prevention and care of largely unvaccinated populations should anticipate the rare but extremely high counts of cases and deaths that occur in distributions with infinite variance. Jurisdictions should prepare collaborative responses across boundaries, because extremely high local counts of cases and deaths may vary beyond the resources of any local jurisdiction.

Bilateral international migration flow estimates updated and refined by sex.

Females and males often migrate at different rates. Official data on sex-specific international migration flows are missing for most countries, prohibiting comparative measures to identify and address inequalities. Here we use six methods to estimate male and female five-year bilateral migration flows between 200 countries from 1990 to 2020. We validate the estimates from each method through correlations of several migration measures with equivalent reported statistics in countries that collect flow data. We find that the Pseudo-Bayesian demographic accounting method performs consistently better than the other estimation methods for both female and male estimated flows. The estimates from all methods indicate a decline in the share of female migration flows from 1990-1995 to 2005-2010 followed by a recovery over the decade since 2010.

Taylor's law of fluctuation scaling for semivariances and higher moments of heavy-tailed data.

We generalize Taylor's law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power [Formula: see text] The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power [Formula: see text] These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli-Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor's law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.

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.

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.

Heavy-tailed distributions, correlations, kurtosis and Taylor's Law of fluctuation scaling.

Pillai & Meng (Pillai & Meng 2016 Ann. Stat. 44, 2089-2097; p. 2091) speculated that 'the dependence among [random variables, rvs] can be overwhelmed by the heaviness of their marginal tails ·· ·'. We give examples of statistical models that support this speculation. While under natural conditions the sample correlation of regularly varying (RV) rvs converges to a generally random limit, this limit is zero when the rvs are the reciprocals of powers greater than one of arbitrarily (but imperfectly) positively or negatively correlated normals. Surprisingly, the sample correlation of these RV rvs multiplied by the sample size has a limiting distribution on the negative half-line. We show that the asymptotic scaling of Taylor's Law (a power-law variance function) for RV rvs is, up to a constant, the same for independent and identically distributed observations as for reciprocals of powers greater than one of arbitrarily (but imperfectly) positively correlated normals, whether those powers are the same or different. The correlations and heterogeneity do not affect the asymptotic scaling. We analyse the sample kurtosis of heavy-tailed data similarly. We show that the least-squares estimator of the slope in a linear model with heavy-tailed predictor and noise unexpectedly converges much faster than when they have finite variances.

Analyzing and interpreting spatial and temporal variability of the United States county population distributions using Taylor's law.

We study the spatial and temporal variation of the human population in the United States (US) counties from 1790 to 2010, using an ecological scaling pattern called Taylor's law (TL). TL states that the variance of population abundance is a power function of the mean population abundance. Despite extensive studies of TL for non-human populations, testing and interpreting TL using data on human populations are rare. Here we examine three types of TL that quantify the spatial and temporal variation of US county population abundance. Our results show that TL and its quadratic extension describe the mean-variance relationship of county population distribution well. The slope and statistics of TL reveal economic and demographic trends of the county populations. We propose TL as a useful statistical tool for analyzing human population variability. We suggest new ways of using TL to select and make population projections.

Bilateral international migration flow estimates for 200 countries.

Data on stocks and flows of international migration are necessary to understand migrant patterns and trends and to monitor and evaluate migration-relevant international development agendas. Many countries do not publish data on bilateral migration flows. At least six methods have been proposed recently to estimate bilateral migration flows between all origin-destination country pairs based on migrant stock data published by the World Bank and United Nations. We apply each of these methods to the latest available stock data to provide six estimates of five-year bilateral migration flows between 1990 and 2015. To assess the resulting estimates, we correlate estimates of six migration measures from each method with equivalent reported data where possible. Such systematic efforts at validation have largely been neglected thus far. We show that the correlation between the reported data and the estimates varies widely among different migration measures, over space, and over time. We find that the two methods using a closed demographic accounting approach perform consistently better than the four other estimation approaches.

How to Measure Population Aging? The Answer Is Less than Obvious: A Review.

Usually, population aging is measured to inform fiscal and social planning because it is considered to indicate the burden that an elderly population presents to the economic, social security, and health systems of a society. Measures of population aging are expected to indicate shifts in the distribution of individuals' attributes (e.g., chronological age, health) within a population that are relevant to assessing the burden. We claim that chronological age - even though it is the attribute most broadly used - may frequently not be the best measure to satisfy this purpose. A distribution of chronological age per se does not present a burden. Rather, burdens arise from the characteristics that supposedly or actually accompany chronological ages. We posit that in addition to chronological age, meaningful measures of population aging should reflect, for instance, the distribution of economic productivity, health, functional capacities, or biological age, as these attributes may more directly assess the burden on the socioeconomic and health systems. Here, we illustrate some limitations of measures of population aging based on each kind of measure, including chronological age, and review alternative measures that may better inform fiscal, social, and health planning.

Temporal scale of environmental correlations affects ecological synchrony.

Population densities of a species measured in different locations are often correlated over time, a phenomenon referred to as synchrony. Synchrony results from dispersal of individuals among locations and spatially correlated environmental variation, among other causes. Synchrony is often measured by a correlation coefficient. However, synchrony can vary with timescale. We demonstrate theoretically and experimentally that the timescale-specificity of environmental correlation affects the overall magnitude and timescale-specificity of synchrony, and that these effects are modified by population dispersal. Our laboratory experiments linked populations of flour beetles by changes in habitat size and dispersal. Linear filter theory, applied to a metapopulation model for the experimental system, predicted the observed timescale-specific effects. The timescales at which environmental covariation occurs can affect the population dynamics of species in fragmented habitats.

Chagas disease vector control and Taylor's law.

BACKGROUND: Large spatial and temporal fluctuations in the population density of living organisms have profound consequences for biodiversity conservation, food production, pest control and disease control, especially vector-borne disease control. Chagas disease vector control based on insecticide spraying could benefit from improved concepts and methods to deal with spatial variations in vector population density. METHODOLOGY/PRINCIPAL FINDINGS: We show that Taylor's law (TL) of fluctuation scaling describes accurately the mean and variance over space of relative abundance, by habitat, of four insect vectors of Chagas disease (Triatoma infestans, Triatoma guasayana, Triatoma garciabesi and Triatoma sordida) in 33,908 searches of people's dwellings and associated habitats in 79 field surveys in four districts in the Argentine Chaco region, before and after insecticide spraying. As TL predicts, the logarithm of the sample variance of bug relative abundance closely approximates a linear function of the logarithm of the sample mean of abundance in different habitats. Slopes of TL indicate spatial aggregation or variation in habitat suitability. Predictions of new mathematical models of the effect of vector control measures on TL agree overall with field data before and after community-wide spraying of insecticide. CONCLUSIONS/SIGNIFICANCE: A spatial Taylor's law identifies key habitats with high average infestation and spatially highly variable infestation, providing a new instrument for the control and elimination of the vectors of a major human disease.

Body size and hosts of Triatoma infestans populations affect the size of bloodmeal contents and female fecundity in rural northwestern Argentina.

Human sleeping quarters (domiciles) and chicken coops are key source habitats of Triatoma infestans-the principal vector of the infection that causes Chagas disease-in rural communities in northern Argentina. Here we investigated the links among individual bug bloodmeal contents (BMC, mg), female fecundity, body length (L, mm), host blood sources and habitats. We tested whether L, habitat and host blood conferred relative fitness advantages using generalized linear mixed-effects models and a multimodel inference approach with model averaging. The data analyzed include 769 late-stage triatomines collected in 120 sites from six habitats in 87 houses in Figueroa, Santiago del Estero, during austral spring. L correlated positively with other body-size surrogates and was modified by habitat type, bug stage and recent feeding. Bugs from chicken coops were significantly larger than pig-corral and kitchen bugs. The best-fitting model of log BMC included habitat, a recent feeding, bug stage, log Lc (mean-centered log L) and all two-way interactions including log Lc. Human- and chicken-fed bugs had significantly larger BMC than bugs fed on other hosts whereas goat-fed bugs ranked last, in consistency with average blood-feeding rates. Fecundity was maximal in chicken-fed bugs from chicken coops, submaximal in human- and pig-fed bugs, and minimal in goat-fed bugs. This study is the first to reveal the allometric effects of body-size surrogates on BMC and female fecundity in a large set of triatomine populations occupying multiple habitats, and discloses the links between body size, microsite temperatures and various fitness components that affect the risks of transmission of Trypanosoma cruzi.

Synchrony affects Taylor's law in theory and data.

Taylor's law (TL) is a widely observed empirical pattern that relates the variances to the means of groups of nonnegative measurements via an approximate power law: variance g ≈ a [Formula: see text] mean gb , where g indexes the group of measurements. When each group of measurements is distributed in space, the exponent b of this power law is conjectured to reflect aggregation in the spatial distribution. TL has had practical application in many areas since its initial demonstrations for the population density of spatially distributed species in population ecology. Another widely observed aspect of populations is spatial synchrony, which is the tendency for time series of population densities measured in different locations to be correlated through time. Recent studies showed that patterns of population synchrony are changing, possibly as a consequence of climate change. We use mathematical, numerical, and empirical approaches to show that synchrony affects the validity and parameters of TL. Greater synchrony typically decreases the exponent b of TL. Synchrony influenced TL in essentially all of our analytic, numerical, randomization-based, and empirical examples. Given the near ubiquity of synchrony in nature, it seems likely that synchrony influences the exponent of TL widely in ecologically and economically important systems.

Linking parasite populations in hosts to parasite populations in space through Taylor's law and the negative binomial distribution.

The spatial distribution of individuals of any species is a basic concern of ecology. The spatial distribution of parasites matters to control and conservation of parasites that affect human and nonhuman populations. This paper develops a quantitative theory to predict the spatial distribution of parasites based on the distribution of parasites in hosts and the spatial distribution of hosts. Four models are tested against observations of metazoan hosts and their parasites in littoral zones of four lakes in Otago, New Zealand. These models differ in two dichotomous assumptions, constituting a 2 × 2 theoretical design. One assumption specifies whether the variance function of the number of parasites per host individual is described by Taylor's law (TL) or the negative binomial distribution (NBD). The other assumption specifies whether the numbers of parasite individuals within each host in a square meter of habitat are independent or perfectly correlated among host individuals. We find empirically that the variance-mean relationship of the numbers of parasites per square meter is very well described by TL but is not well described by NBD. Two models that posit perfect correlation of the parasite loads of hosts in a square meter of habitat approximate observations much better than two models that posit independence of parasite loads of hosts in a square meter, regardless of whether the variance-mean relationship of parasites per host individual obeys TL or NBD. We infer that high local interhost correlations in parasite load strongly influence the spatial distribution of parasites. Local hotspots could influence control and conservation of parasites.

Population dynamics, synchrony, and environmental quality of Hokkaido voles lead to temporal and spatial Taylor's laws.

Taylor's law (TL) asserts that the variance in a species' population density is a power-law function of its mean population density: log(variance) = a + b × log(mean). TL is widely verified. We show here that empirical time series of density of the Hokkaido gray-sided vole, Myodes rufocanus, sampled 1962-1992 at 85 locations, satisfied temporal and spatial forms of TL. The slopes (b ± standard error) of the temporal and spatial TL were estimated to be 1.613 ± 0.141 and 1.430 ± 0.132, respectively. A previously verified autoregressive Gompertz model of the dynamics of these populations generated time series of density which reproduced the form of temporal and spatial TLs, but with slopes that were significantly steeper than the slopes estimated from data. The density-dependent components of the Gompertz model were essential for the temporal TL. Adding to the Gompertz model assumptions that populations with higher mean density have reduced variance of density-independent perturbations and that density-independent perturbations are spatially correlated among populations yielded simulated time series that satisfactorily reproduced the slopes from data. The slopes (b ± standard error) of the enhanced simulations were 1.619 ± 0.199 for temporal TL and 1.575 ± 0.204 for spatial TL.

More tornadoes in the most extreme U.S. tornado outbreaks.

Tornadoes and severe thunderstorms kill people and damage property every year. Estimated U.S. insured losses due to severe thunderstorms in the first half of 2016 were $8.5 billion (US). The largest U.S. effects of tornadoes result from tornado outbreaks, which are sequences of tornadoes that occur in close succession. Here, using extreme value analysis, we find that the frequency of U.S. outbreaks with many tornadoes is increasing and that it is increasing faster for more extreme outbreaks. We model this behavior by extreme value distributions with parameters that are linear functions of time or of some indicators of multidecadal climatic variability. Extreme meteorological environments associated with severe thunderstorms show consistent upward trends, but the trends do not resemble those currently expected to result from global warming.

Longer Food Chains in Pelagic Ecosystems: Trophic Energetics of Animal Body Size and Metabolic Efficiency.

Factors constraining the structure of food webs can be investigated by comparing classes of ecosystems. We find that pelagic ecosystems, those based on one-celled primary producers, have longer food chains than terrestrial ecosystems. Yet pelagic ecosystems have lower primary productivity, contrary to the hypothesis that greater energy flows permit higher trophic levels. We hypothesize that longer food chain length in pelagic ecosystems, compared with terrestrial ecosystems, is associated with smaller pelagic animal body size permitting more rapid trophic energy transfer. Assuming negative allometric dependence of biomass production rate on body mass at each trophic level, the lowest three pelagic animal trophic levels are estimated to add biomass more rapidly than their terrestrial counterparts by factors of 12, 4.8, and 2.6. Pelagic animals consequently transport primary production to a fifth trophic level 50-190 times more rapidly than animals in terrestrial webs. This difference overcomes the approximately fivefold slower pelagic basal productivity, energetically explaining longer pelagic food chains. In addition, ectotherms, dominant at lower pelagic animal trophic levels, have high metabolic efficiency, also favoring higher rates of trophic energy transfer in pelagic ecosystems. These two animal trophic flow mechanisms imply longer pelagic food chains, reestablishing an important role for energetics in food web structure.