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 (in contrast to genetic drift), 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 they are widespread in biological populations, significantly affecting evolutionary and ecological dynamics.

Spatial and temporal Taylor's law in 1D chaotic maps

By using low-dimensional chaotic maps, the power-law relationship established between the sample mean and variance called Taylor's Law (TL) is studied. In particular, we aim to clarify the relationship between TL from the spatial ensemble (STL) and the temporal ensemble (TTL). Since the spatial ensemble corresponds to independent sampling from a stationary distribution, we confirm that STL is explained by the skewness of the distribution. The difference between TTL and STL is shown to be originated in the temporal correlation of a dynamics. In case of logistic and tent maps, the quadratic relationship in the sample mean and variance, called Bartlett's law, is found analytically. On the other hand, TTL in the Hassell model can be well explained by the chunk structure of the trajectory, whereas the TTL of the Ricker model has a different mechanism originated from the specific form of the map.

Low complexity model to study scale dependence of phytoplankton dynamics in the tropical Pacific

We demonstrate that a simple model based on reaction-diffusion-advection (RDA) equation forced by realistic surface velocities and nutrients is skilled in reproducing the distributions of the surface phytoplankton chlorophyll in the tropical Pacific. We use the low-complexity RDA model to investigate the scale relationships in the impact of different drivers (turbulent diffusion, mean and eddy advection, primary productivity) on the phytoplankton chlorophyll concentrations. We find that in the 1/4^{∘} (∼25 km) model, advection has a substantial impact on the rate of primary productivity, while the turbulent diffusion term has a fairly negligible impact. Turbulent diffusion has an impact on the phytoplankton variability, with the impact being scale propagated and amplified by the larger scale surface currents. We investigate the impact of a surface nutrient decline and some changes to mesoscale eddy kinetic energy (climate change projections) on the surface phytoplankton concentrations. The RDA model suggests that unless mesoscale eddies radically change, phytoplankton chlorophyll scales sublinearly with the nutrients, and it is relatively stable with respect to the nutrient concentrations. Furthermore, we explore how a white multiplicative Gaussian noise introduced into the RDA model on its resolution scale propagates across spatial scales through the nonlinear model dynamics under different sets of phytoplankton drivers. The unifying message of this work is that the low-complexity (e.g., RDA) models can be successfully used to realistically model some specific aspects of marine ecosystem dynamics and by using those models one can explore many questions that would be beyond computational affordability of the higher-complexity ecosystem models.

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.

Assessing and Interpreting the Metagenome Heterogeneity With Power Law

There are two major sequencing technologies for investigating the microbiome: the amplicon sequencing that generates the OTU (operational taxonomic unit) tables of marker genes (e.g., bacterial 16S-rRNA), and the metagenomic shotgun sequencing that generates metagenomic gene abundance (MGA) tables. The OTU table is the counterpart of species abundance tables in macrobial ecology of plants and animals, and has been the target of numerous ecological and network analyses in recent gold rush for microbiome research and in great efforts for establishing an inclusive theoretical ecology. Nevertheless, MGA analyses have been largely limited to bioinformatics pipelines and ad hoc statistical methods, and systematic approaches to MGAs guided by classic ecological theories are still few. Here, we argue that, the difference between “gene kinds” and “gene species” are nominal, and the metagenome that a microbiota carries is essentially a ‘community’ of metagenomic genes (MGs). Each row of a MGA table represents a metagenome of a microbiota, and the whole MGA table represents a ‘meta-metagenome’ (or an assemblage of metagenomes) of N microbiotas (microbiome samples). Consequently, the same ecological/network analyses used in OTU analyses should be equally applicable to MGA tables. Here we choose to analyze the heterogeneity of metagenome by introducing classic Taylor’s power law (TPL) and its recent extensions in community ecology. Heterogeneity is a fundamental property of metagenome, particularly in the context of human microbiomes. Recent studies have shown that the heterogeneity of human metagenomes is far more significant than that of human genomes. Therefore, without deep understanding of the human metagenome heterogeneity, personalized medicine of the human microbiome-associated diseases is hardly feasible. The TPL extensions have been successfully applied to measure the heterogeneity of human microbiome based on amplicon-sequencing reads of marker genes (e.g., 16s-rRNA). In this article, we demonstrate the analysis of the metagenomic heterogeneity of human gut microbiome at whole metagenome scale (with type-I power law extension) and metagenomic gene scale (type-III), as well as the heterogeneity of gene clusters, respectively. We further examine the influences of obesity, IBD and diabetes on the heterogeneity, which is of important ramifications for the diagnosis and treatment of human microbiome-associated diseases.

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.

Comparative power law analysis for the spatial heterogeneity scaling of the hot-spring microbiomes

Spatial heterogeneity is a fundamental property of any natural ecosystems, including hot spring and human microbiomes. Two important scales that spatial heterogeneity exhibits are population and community scales, and Taylor's power law (PL) and its extensions (PLEs) offer ideal quantitative models to assess population- and community-level heterogeneities. Here we analyse 165 hot spring microbiome samples at the global scale that cover a wide range of temperatures (7.5-99°C) and pH levels (3.3-9). We explore a question of fundamental importance for measuring the spatial heterogeneity of the hot-spring microbiome and further discuss their ecological implications: How do critical environmental factors such as temperature and pH influence the scaling of community spatial heterogeneity? We are particularly interested in the existence of a universal scaling model that is independent of environmental gradients. By applying PL and PLEs, we were able to obtain such scaling parameters of the hot spring at both community and population levels, which are temperature- and pH-invariant. These findings suggest that while the hot-spring microbiomes located at different regions may have different environmental conditions, they share a fundamental heterogeneity scaling parameter, analogically similar to the gravitational acceleration on Earth, which may vary slightly depending on altitude and latitude, but is invariant overall. In contrast, similar to the physics of the Moon and Earth, which have different gravitational accelerations, the hot spring and human microbiomes can have different scaling parameters as demonstrated in this study.

Inter-specific competition influences apex predator–prey populations

Abstract ContextTiger (Panthera tigris), leopard (Panthera pardus) and dhole (Cuon alpinus) represent a typical multi-predator system of species of conservation concern. Several studies have addressed this system, with heterogeneous results, and there’s a lack of information on population dynamics of multi-species assemblages. We studied a time series (1998–2009) of abundance indices for three predators and five prey species in Bor Wildlife Sanctuary (BWS), Maharashtra, India, before it was declared as Bor Tiger Reserve (BTR) in 2009. AimsTo analyse the complex relationships within a predator–prey system in a dynamic fashion, to analyse data collected in a stable and undisturbed area and to form a comparison basis for future studies within the sanctuary after its declaration as a Tiger Reserve. MethodsA 24-h effort was made annually to census the BWS. Predators were counted at waterholes from arboreal hideouts. The prey populations were censused along 353-km line-transects. For each species, we analysed the yearly growth rate, testing the effect of inter-species abundance. Key resultsTiger growth rate did not depend on any particular prey, whereas mesopredators seemed to depend on medium-sized prey. A die-out of dholes in 2001 was followed by an increase in tiger populations (from 4 to 11), which, in turn, negatively affected leopard numbers (from 6 to 2).We found no direct evidence of top-down effect, but the density dependence for three of five prey species could be linked to predation pressure. We found some evidence of interspecific competition among prey species, especially among ungulates, potentially being mediated by predation pressure. ConclusionsThe relationships among species in a predator–prey system are very complex and often could be explained only by more-than-two-species interactions. The disappearance of one predator, not necessarily the top predator, could bring multiple effects, for which it could be difficult to detect causal relationships. ImplicationsAll subsequent changes in human activities in the sanctuary, as a consequence of its designation as the BTR in 2009, should be evaluated with respect to the results of the present study. The conservation of large predators should rely on the maintenance of a rich and abundant prey base, in which different-sized prey could lessen interactive-competition among the predators.

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.

Twenty-Five Years of the Binary Power Law for Characterizing Heterogeneity of Disease Incidence

Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor's power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.

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.

Colonial, more widely distributed and less abundant bird species undergo wider population fluctuations independent of their population trend

Understanding temporal variability in population size is important for conservation biology because wide population fluctuations increase the risk of extinction. Previous studies suggested that certain ecological, demographic, life-history and genetic characteristics of species might be related to the degree of their population fluctuations. We checked whether that was the case in a large sample of 231 European breeding bird species while taking a number of potentially confounding factors such as population trends or similarities among species due to common descent into account. When species-specific characteristics were analysed one by one, the magnitude of population fluctuations was positively related to coloniality, habitat, total breeding range, heterogeneity of breeding distribution and natal dispersal, and negatively related to urbanisation, abundance, relative number of subspecies, parasitism and proportion of polymorphic loci. However, when abundance (population size) was included in the analyses of the other parameters, only coloniality, habitat, total breeding range and abundance remained significantly related to population fluctuations. The analysis including all these predictors simultaneously showed that population size fluctuated more in colonial, less abundant species with larger breeding ranges. Other parameters seemed to be related to population fluctuations only because of their association with abundance or coloniality. The unexpected positive relationship between population fluctuations and total breeding range did not seem to be mediated by abundance. The link between population fluctuations and coloniality suggests a previously unrecognized cost of coloniality. The negative relationship between population size and population fluctuations might be explained by at least three types of non-mutually exclusive stochastic processes: demographic, environmental and genetic stochasticity. Measurement error in population indices, which was unknown, may have contributed to the negative relationship between population size and fluctuations, but apparently only to a minor extent. The association between population size and fluctuations suggests that populations might be stabilized by increasing population size.

Nematode spatial distribution and the frequency of zeros in samples

In the first longitudinal study of nematode spatial distribution with sufficiently large samples to estimate Taylor’s power law (TPL), we concluded that TPL is sensitive to life history strategy. We also observed that the value of TPL slope b was generally higher for more widespread and abundant taxa. We deduce that removal of empty samples increases b and discuss the results in relation to known causes of bias in estimating TPL. Only one cause might explain an increase in b with removal of empty quadrats: the underestimation of variance. Although bias cannot be ruled out in rare taxa, the consistency of the pattern with very abundant genera suggests a different explanation. TPL appears sensitive to the number of samples in a survey that do not contain the taxon of interest. We conclude that TPL measures the space between individuals as well as the density-dependence of the numerical distribution of abundance.

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.

Onwards and upwards - aphid flight trends follow climate change

The world faces an uncertain future; climate change and the concerns about the security of food production feature prominently on political and scientific agendas world-wide. In this issue, Bell et al. (), drawing on the unique 50-year data set amassed by the suction trap network run by the Rothamsted Insect Survey (RIS), elucidate the mechanisms advancing aphid phenology under climate change and show how by using biological traits we can make predictions about emerging crop pests. Here, I discuss their findings in the context of phenological coincidence and host plant availability.

Direct evidence that density-dependent regulation underpins the temporal stability of abundant species in a diverse animal community

To understand how ecosystems are structured and stabilized, and to identify when communities are at risk of damage or collapse, we need to know how the abundances of the taxa in the entire assemblage vary over ecologically meaningful timescales. Here, we present an analysis of species temporal variability within a single large vertebrate community. Using an exceptionally complete 33-year monthly time series following the dynamics of 81 species of fishes, we show that the most abundant species are least variable in terms of temporal biomass, because they are under density-dependent (negative feedback) regulation. At the other extreme, a relatively large number of low abundance transient species exhibit the greatest population variability. The high stability of the consistently common high abundance species—a result of density-dependence—is reflected in the observation that they consistently represent over 98% of total fish biomass. This leads to steady ecosystem nutrient and energy flux irrespective of the changes in species number and abundance among the large number of low abundance transient species. While the density-dependence of the core species ensures stability under the existing environmental regime, the pool of transient species may support long-term stability by replacing core species should environmental conditions change.

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

Taylor's law (TL) describes the scaling relationship between the mean and variance of populations as a power law. TL is widely observed in ecological systems across space and time, with exponents varying largely between 1 and 2. Many ecological explanations have been proposed for TL, but it is also commonly observed outside ecology. We propose that TL arises from the constraining influence of two primary variables: the number of individuals and the number of censuses or sites. We show that most possible configurations of individuals among censuses or sites produce the power-law form of TL, with exponents between 1 and 2. This "feasible set" approach suggests that TL is a statistical pattern driven by two constraints, providing an a priori explanation for this ubiquitous pattern. However, the exact form of any specific mean-variance relationship cannot be predicted in this way, that is, this approach does a poor job of predicting variation in the exponent, suggesting that TL may still contain ecological information.

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.

Long-term phenological trends, species accumulation rates, aphid traits and climate: five decades of change in migrating aphids

Aphids represent a significant challenge to food production. The Rothamsted Insect Survey (RIS) runs a network of 12·2-m suction-traps throughout the year to collect migrating aphids. In 2014, the RIS celebrated its 50th anniversary. This paper marks that achievement with an extensive spatiotemporal analysis and the provision of the first British annotated checklist of aphids since 1964. Our main aim was to elucidate mechanisms that advance aphid phenology under climate change and explain these using life-history traits. We then highlight emerging pests using accumulation patterns. Linear and nonlinear mixed-effect models estimated the average rate of change per annum and effects of climate on annual counts, first and last flights and length of flight season since 1965. Two climate drivers were used: the accumulated day degrees above 16 °C (ADD16) indicated the potential for migration during the aphid season; the North Atlantic Oscillation (NAO) signalled the severity of the winter before migration took place. All 55 species studied had earlier first flight trends at rate of β = -0·611 ± SE 0·015 days year(-1). Of these species, 49% had earlier last flights, but the average species effect appeared relatively stationary (β = -0·010 ± SE 0·022 days year(-1)). Most species (85%) showed increasing duration of their flight season (β = 0·336 ± SE 0·026 days year(-1)), even though only 54% increased their log annual count (β = 0·002 ± SE <0·001 year(-1)). The ADD16 and NAO were shown to drive patterns in aphid phenology in a spatiotemporal context. Early in the year when the first aphids were migrating, the effect of the winter NAO was highly significant. Further into the year, ADD16 was a strong predictor. Latitude had a near linear effect on first flights, whereas longitude produced a generally less-clear effect on all responses. Aphids that are anholocyclic (permanently parthenogenetic) or are monoecious (non-host-alternating) were advancing their phenology faster than those that were not. Climate drives phenology and traits help explain how this takes place biologically. Phenology and trait ecology are critical to understanding the threat posed by emerging pests such as Myzus persicae nicotianae and Aphis fabae cirsiiacanthoidis, as revealed by the species accumulation analysis.

Estimation of density-dependent mortality of juvenile bivalves in the Wadden Sea

We investigated density-dependent mortality within the early months of life of the bivalves Macoma balthica (Baltic tellin) and Cerastoderma edule (common cockle) in the Wadden Sea. Mortality is thought to be density-dependent in juvenile bivalves, because there is no proportional relationship between the size of the reproductive adult stocks and the numbers of recruits for both species. It is not known however, when exactly density dependence in the pre-recruitment phase occurs and how prevalent it is. The magnitude of recruitment determines year class strength in bivalves. Thus, understanding pre-recruit mortality will improve the understanding of population dynamics. We analyzed count data from three years of temporal sampling during the first months after bivalve settlement at ten transects in the Sylt-Rømø-Bay in the northern German Wadden Sea. Analyses of density dependence are sensitive to bias through measurement error. Measurement error was estimated by bootstrapping, and residual deviances were adjusted by adding process error. With simulations the effect of these two types of error on the estimate of the density-dependent mortality coefficient was investigated. In three out of eight time intervals density dependence was detected for M. balthica, and in zero out of six time intervals for C. edule. Biological or environmental stochastic processes dominated over density dependence at the investigated scale.

Predicting ecosystem stability from community composition and biodiversity

As biodiversity is declining at an unprecedented rate, an important current scientific challenge is to understand and predict the consequences of biodiversity loss. Here, we develop a theory that predicts the temporal variability of community biomass from the properties of individual component species in monoculture. Our theory shows that biodiversity stabilises ecosystems through three main mechanisms: (1) asynchrony in species' responses to environmental fluctuations, (2) reduced demographic stochasticity due to overyielding in species mixtures and (3) reduced observation error (including spatial and sampling variability). Parameterised with empirical data from four long-term grassland biodiversity experiments, our prediction explained 22-75% of the observed variability, and captured much of the effect of species richness. Richness stabilised communities mainly by increasing community biomass and reducing the strength of demographic stochasticity. Our approach calls for a re-evaluation of the mechanisms explaining the effects of biodiversity on ecosystem stability.

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.

Seabird aggregative patterns: a new tool for offshore wind energy risk assessment

The emerging development of offshore wind energy has raised public concern over its impact on seabird communities. There is a need for an adequate methodology to determine its potential impacts on seabirds. Environmental Impact Assessments (EIAs) are mostly relying on a succession of plain density maps without integrated interpretation of seabird spatio-temporal variability. Using Taylor's power law coupled with mixed effect models, the spatio-temporal variability of species' distributions can be synthesized in a measure of the aggregation levels of individuals over time and space. Applying the method to a seabird aerial survey in the Ebro Delta, NW Mediterranean Sea, we were able to make an explicit distinction between transitional and feeding areas to define and map the potential impacts of an offshore wind farm project. We use the Ebro Delta study case to discuss the advantages of potential impacts maps over density maps, as well as to illustrate how these potential impact maps can be applied to inform on concern levels, optimal EIA design and monitoring in the assessment of local offshore wind energy projects.

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.

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

Populations vary in time and in space, and temporal variation may differ from spatial variation. Yet, in the past half century, field data have confirmed both the temporal and spatial forms of Taylor's power Law, a linear relationship between log(variance) and log(mean) of population size. Recent theory predicted that competitive species interactions should reduce the slope of the temporal version of Taylor's Law. We tested whether this prediction applied to the spatial version of Taylor's Law using simple, well-controlled laboratory populations of two species of bacteria that were cultured either separately or together for 24 h in media of widely varying nutrient richness. Experimentally, the spatial form of Taylor's Law with a slope of 2 held for these simple bacterial communities, but competitive interactions between the two species did not reduce the spatial Taylor's Law slope. These results contribute to the widespread usefulness of Taylor's Law in population ecology, epidemiology and pest control.

Disturbance-driven changes in the variability of ecological patterns and processes

Understanding how disturbance shapes the dynamics of ecological systems is of fundamental importance in ecology. One emerging approach to revealing and appreciating disturbance effects involves examining disturbance-driven changes in the variability of ecological responses. Variability is rarely employed as a response variable to assess the influence of disturbance, but recent studies indicate that it can be an extremely sensitive metric, capturing differences obscured by averaging and conveying important ecological information about underlying causal processes. In this paper, we present a conceptual model to understand and predict the effects of disturbance on variability. The model estimates qualitative changes in variability by considering disturbance extent, frequency and intensity, as well as ecosystem recovery, and thereby captures not only the immediate effects of disturbance but also those that arise over time due to the biotic response to an event. We evaluate how well the model performs by comparing predictions with empirical results from studies examining a wide variety of disturbances and ecosystems, and discuss factors that may modify or even confound predictions. We include a concise guide to characterizing and detecting changes in variability, highlighting the most common and easily applied methods and conclude by describing several future directions for research. By considering variability as a response to disturbance, we gain another metric of fundamental system behaviour, an improved ability to identify organizing features of ecosystems and a better understanding of the predictability of disturbance-driven change - all critical aspects of assessing ecosystem response to disturbance.