Chapter 1 Allometry of Body Size and Abundance in 166 Food Webs

Protection promotes energetically efficient structures in marine communities

The sustainability of marine communities is critical for supporting many biophysical processes that provide ecosystem services that promote human well-being. It is expected that anthropogenic disturbances such as climate change and human activities will tend to create less energetically-efficient ecosystems that support less biomass per unit energy flow. It is debated, however, whether this expected development should translate into bottom-heavy (with small basal species being the most abundant) or top-heavy communities (where more biomass is supported at higher trophic levels with species having larger body sizes). Here, we combine ecological theory and empirical data to demonstrate that full marine protection promotes shifts towards top-heavy energetically-efficient structures in marine communities. First, we use metabolic scaling theory to show that protected communities are expected to display stronger top-heavy structures than disturbed communities. Similarly, we show theoretically that communities with high energy transfer efficiency display stronger top-heavy structures than communities with low transfer efficiency. Next, we use empirical structures observed within fully protected marine areas compared to disturbed areas that vary in stress from thermal events and adjacent human activity. Using a nonparametric causal-inference analysis, we find a strong, positive, causal effect between full marine protection and stronger top-heavy structures. Our work corroborates ecological theory on community development and provides a quantitative framework to study the potential restorative effects of different candidate strategies on protected areas.

Community size structure varies with predator-prey size relationships and temperature across Australian reefs

Climate change and fisheries exploitation are dramatically changing the abundances, species composition, and size spectra of fish communities. We explore whether variation in 'abundance size spectra', a widely studied ecosystem feature, is influenced by a parameter theorized to govern the shape of size-structured ecosystems-the relationship between the sizes of predators and their prey (predator-prey mass ratios, or PPMRs). PPMR estimates are lacking for avast number of fish species, including at the scale of trophic guilds. Using measurements of 8128 prey items in gut contents of 97 reef fish species, we established predator-prey mass ratios (PPMRs) for four major trophic guilds (piscivores, invertivores, planktivores, and herbivores) using linear mixed effects models. To assess the theoretical predictions that higher community-level PPMRs leads to shallower size spectrum slopes, we compared observations of both ecosystem metrics for ~15,000 coastal reef sites distributed around Australia. PPMRs of individual fishes were remarkably high (median ~71,000), with significant variation between different trophic guilds (~890 for piscivores; ~83,000 for planktivores), and ~8700 for whole communities. Community-level PPMRs were positively related to size spectrum slopes, broadly consistent with theory, however, this pattern was also influenced by the latitudinal temperature gradient. Tropical reefs showed a stronger relationship between community-level PPMRs and community size spectrum slopes than temperate reefs. The extent that these patterns apply outside Australia and consequences for community structure and dynamics are key areas for future investigation.

Size compartmentalization of energy channeling in terrestrial belowground food webs

Size-structured food webs form integrated trophic systems where energy is channeled from small to large consumers. Empirical evidence suggests that size structure prevails in aquatic ecosystems, whereas in terrestrial food webs trophic position is largely independent of body size. Compartmentalization of energy channeling according to size classes of consumers was suggested as a mechanism that underpins functioning and stability of terrestrial food webs including those belowground, but their structure has not been empirically assessed across the whole size spectrum. Here we used stable isotope analysis and metabolic regressions to describe size structure and energy use in eight belowground communities with consumers spanning 12 orders of magnitude in living body mass, from protists to earthworms. We showed a negative correlation between trophic position and body mass in invertebrate communities and a remarkable nonlinearity in community metabolism and trophic positions across all size classes. Specifically, we found that the correlation between body mass and trophic level is positive in the small-sized (protists, nematodes, arthropods below 1 μg in body mass), neutral in the medium-sized (arthropods of 1 μg to 1 mg), and negative in the large-sized consumers (large arthropods, earthworms), suggesting that these groups form compartments with different trophic organization. Based on this pattern, we propose a concept of belowground food webs being composed of (1) size-structured micro-food web driving fast energy channeling and nutrient release, for example in microbial loop; (2) arthropod macro-food web with no clear correlation between body size and trophic level, hosting soil arthropod diversity and subsidizing aboveground predators; and (3) "trophic whales," sequestering energy in their large bodies and restricting its propagation to higher trophic levels in belowground food webs. The three size compartments are based on a similar set of basal resources, but contribute to different ecosystem-level functions and respond differently to variations in climate, soil characteristics and land use. We suggest that the widely used vision of resource-based energy channeling in belowground food webs can be complemented with size-based energy channeling, where ecosystem multifunctionality, biodiversity, and stability are supported by a balance across individual size compartments.

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.

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.

Bending the rules: exploitation of allochthonous resources by a top-predator modifies size-abundance scaling in stream food webs

Body mass-abundance (M-N) allometries provide a key measure of community structure, and deviations from scaling predictions could reveal how cross-ecosystem subsidies alter food webs. For 31 streams across the UK, we tested the hypothesis that linear log-log M-N scaling is shallower than that predicted by allometric scaling theory when top predators have access to allochthonous prey. These streams all contained a common and widespread top predator (brown trout) that regularly feeds on terrestrial prey and, as hypothesised, deviations from predicted scaling increased with its dominance of the fish assemblage. Our study identifies a key beneficiary of cross-ecosystem subsidies at the top of stream food webs and elucidates how these inputs can reshape the size-structure of these 'open' systems.

Energetic and ecological constraints on population density of reef fishes

Population ecology has classically focused on pairwise species interactions, hindering the description of general patterns and processes of population abundance at large spatial scales. Here we use the metabolic theory of ecology as a framework to formulate and test a model that yields predictions linking population density to the physiological constraints of body size and temperature on individual metabolism, and the ecological constraints of trophic structure and species richness on energy partitioning among species. Our model was tested by applying Bayesian quantile regression to a comprehensive reef-fish community database, from which we extracted density data for 5609 populations spread across 49 sites around the world. Our results indicate that population density declines markedly with increases in community species richness and that, after accounting for richness, energetic constraints are manifested most strongly for the most abundant species, which generally are of small body size and occupy lower trophic groups. Overall, our findings suggest that, at the global scale, factors associated with community species richness are the major drivers of variation in population density. Given that populations of species-rich tropical systems exhibit markedly lower maximum densities, they may be particularly susceptible to stochastic extinction.

The paradox of inverted biomass pyramids in kelp forest fish communities

Theory predicts that bottom-heavy biomass pyramids or 'stacks' should predominate in real-world communities if trophic-level increases with body size (mean predator-to-prey mass ratio (PPMR) more than 1). However, recent research suggests that inverted biomass pyramids (IBPs) characterize relatively pristine reef fish communities. Here, we estimated the slope of a kelp forest fish community biomass spectrum from underwater visual surveys. The observed biomass spectrum slope is strongly positive, reflecting an IBP. This is incongruous with theory because this steep positive slope would only be expected if trophic position decreased with increasing body size (consumer-to-resource mass ratio, less than 1). We then used δ(15)N signatures of fish muscle tissue to quantify the relationship between trophic position and body size and instead detected strong evidence for the opposite, with PPMR ≈ 1650 (50% credible interval 280-12 000). The natural history of kelp forest reef fishes suggests that this paradox could arise from energetic subsidies in the form of movement of mobile consumers across habitats, and from seasonally pulsed production inputs at small body sizes. There were four to five times more biomass at large body sizes (1-2 kg) than would be expected in a closed steady-state community providing a measure of the magnitude of subsidies.

The marine diversity spectrum

Distributions of species body sizes within a taxonomic group, for example, mammals, are widely studied and important because they help illuminate the evolutionary processes that produced these distributions. Distributions of the sizes of species within an assemblage delineated by geography instead of taxonomy (all the species in a region regardless of clade) are much less studied but are equally important and will illuminate a different set of ecological and evolutionary processes. We develop and test a mechanistic model of how diversity varies with body mass in marine ecosystems. The model predicts the form of the 'diversity spectrum', which quantifies the distribution of species' asymptotic body masses, is a species analogue of the classic size spectrum of individuals, and which we have found to be a new and widely applicable description of diversity patterns. The marine diversity spectrum is predicted to be approximately linear across an asymptotic mass range spanning seven orders of magnitude. Slope -0.5 is predicted for the global marine diversity spectrum for all combined pelagic zones of continental shelf seas, and slopes for large regions are predicted to lie between -0.5 and -0.1. Slopes of -0.5 and -0.1 represent markedly different communities: a slope of -0.5 depicts a 10-fold reduction in diversity for every 100-fold increase in asymptotic mass; a slope of -0.1 depicts a 1.6-fold reduction. Steeper slopes are predicted for larger or colder regions, meaning fewer large species per small species for such regions. Predictions were largely validated by a global empirical analysis. Results explain for the first time a new and widespread phenomenon of biodiversity. Results have implications for estimating numbers of species of small asymptotic mass, where taxonomic inventories are far from complete. Results show that the relationship between diversity and body mass can be explained from the dependence of predation behaviour, dispersal, and life history on body mass, and a neutral assumption about speciation and extinction.

A cure for the plague of parameters: constraining models of complex population dynamics with allometries

A major goal of ecology is to discover how dynamics and structure of multi-trophic ecological communities are related. This is difficult, because whole-community data are limited and typically comprise only a snapshot of a community instead of a time series of dynamics, and mathematical models of complex system dynamics have a large number of unmeasured parameters and therefore have been only tenuously related to real systems. These are related problems, because long time-series, if they were commonly available, would enable inference of parameters. The resulting 'plague of parameters' means most studies of multi-species population dynamics have been very theoretical. Dynamical models parametrized using physiological allometries may offer a partial cure for the plague of parameters, and these models are increasingly used in theoretical studies. However, physiological allometries cannot determine all parameters, and the models have also rarely been directly tested against data. We confronted a model of community dynamics with data from a lake community. Many important empirical patterns were reproducible as outcomes of dynamics, and were not reproducible when parameters did not follow physiological allometries. Results validate the usefulness, when parameters follow physiological allometries, of classic differential-equation models for understanding whole-community dynamics and the structure-dynamics relationship.

Size-energy relationships in ecological communities

Hypotheses that relate body size to energy use are of particular interest in community ecology and macroecology because of their potential to facilitate quantitative predictions about species interactions and to clarify complex ecological patterns. One prominent size-energy hypothesis, the energetic equivalence hypothesis, proposes that energy use from shared, limiting resources by populations or size classes of foragers will be independent of body size. Alternative hypotheses propose that energy use will increase with body size, decrease with body size, or peak at an intermediate body size. Despite extensive study, however, size-energy hypotheses remain controversial, due to a lack of directly-measured data on energy use, a tendency to confound distinct scaling relationships, and insufficient attention to the ecological contexts in which predicted relationships are likely to occur. Our goal, therefore, was to directly evaluate size-energy hypotheses while clarifying how results would differ with alternate methods and assumptions. We comprehensively tested size-energy hypotheses in a vertebrate frugivore guild in a tropical forest in Madagascar. Our test of size-energy hypotheses, which is the first to examine energy intake directly, was consistent with the energetic equivalence hypothesis. This finding corresponds with predictions of metabolic theory and models of energy distribution in ecological communities, which imply that body size does not confer an advantage in competition for energy among populations or size classes of foragers. This result was robust to different assumptions about energy regulation. Our results from direct energy measurement, however, contrasted with those obtained with conventional methods of indirect inference from size-density relationships, suggesting that size-density relationships do not provide an appropriate proxy for size-energy relationships as has commonly been assumed. Our research also provides insights into mechanisms underlying local size-energy relationships and has important implications for predicting species interactions and for understanding the structure and dynamics of ecological communities.

The relationship between body mass and field metabolic rate among individual birds and mammals

Summary

The authors provide the first comprehensive empirical analysis of the scaling relationship between field metabolic rate and body mass in individual birds and mammals. The analysis reveals the importance of heterogeneity in the scaling exponent, with consequences for biomass and nutrient flow through communities, and the structure and functioning of whole ecosystems.

Ecosystem ecology: size-based constraints on the pyramids of life

Biomass distribution and energy flow in ecosystems are traditionally described with trophic pyramids, and increasingly with size spectra, particularly in aquatic ecosystems. Here, we show that these methods are equivalent and interchangeable representations of the same information. Although pyramids are visually intuitive, explicitly linking them to size spectra connects pyramids to metabolic and size-based theory, and illuminates size-based constraints on pyramid shape. We show that bottom-heavy pyramids should predominate in the real world, whereas top-heavy pyramids indicate overestimation of predator abundance or energy subsidies. Making the link to ecological pyramids establishes size spectra as a central concept in ecosystem ecology, and provides a powerful framework both for understanding baseline expectations of community structure and for evaluating future scenarios under climate change and exploitation.

Climate change impacts in multispecies systems: drought alters food web size structure in a field experiment

Experimental data from intergenerational field manipulations of entire food webs are scarce, yet such approaches are essential for gauging impacts of environmental change in natural systems. We imposed 2 years of intermittent drought on stream channels in a replicated field trial, to measure food web responses to simulated climate change. Drought triggered widespread losses of species and links, with larger taxa and those that were rare for their size, many of which were predatory, being especially vulnerable. Many network properties, including size-scaling relationships within food chains, changed in response to drought. Other properties, such as connectance, were unaffected. These findings highlight the need for detailed experimental data from different organizational levels, from pairwise links to the entire food web. The loss of not only large species, but also those that were rare for their size, provides a newly refined way to gauge likely impacts that may be applied more generally to other systems and/or impacts.

Taylor's law and body size in exploited marine ecosystems

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

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

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

Dimensionality of consumer search space drives trophic interaction strengths

Trophic interactions govern biomass fluxes in ecosystems, and stability in food webs. Knowledge of how trophic interaction strengths are affected by differences among habitats is crucial for understanding variation in ecological systems. Here we show how substantial variation in consumption-rate data, and hence trophic interaction strengths, arises because consumers tend to encounter resources more frequently in three dimensions (3D) (for example, arboreal and pelagic zones) than two dimensions (2D) (for example, terrestrial and benthic zones). By combining new theory with extensive data (376 species, with body masses ranging from 5.24 × 10(-14) kg to 800 kg), we find that consumption rates scale sublinearly with consumer body mass (exponent of approximately 0.85) for 2D interactions, but superlinearly (exponent of approximately 1.06) for 3D interactions. These results contradict the currently widespread assumption of a single exponent (of approximately 0.75) in consumer-resource and food-web research. Further analysis of 2,929 consumer-resource interactions shows that dimensionality of consumer search space is probably a major driver of species coexistence, and the stability and abundance of populations.

A common scaling rule for abundance, energetics, and production of parasitic and free-living species

The metabolic theory of ecology uses the scaling of metabolism with body size and temperature to explain the causes and consequences of species abundance. However, the theory and its empirical tests have never simultaneously examined parasites alongside free-living species. This is unfortunate because parasites represent at least half of species diversity. We show that metabolic scaling theory could not account for the abundance of parasitic or free-living species in three estuarine food webs until accounting for trophic dynamics. Analyses then revealed that the abundance of all species uniformly scaled with body mass to the -&frac34; power. This result indicates "production equivalence," where biomass production within trophic levels is invariant of body size across all species and functional groups: invertebrate or vertebrate, ectothermic or endothermic, and free-living or parasitic.

Food web complexity and allometric scaling relationships in stream mesocosms: implications for experimentation

1. Mesocosms are used extensively by ecologists to gain a mechanistic understanding of ecosystems based on the often untested assumption that these systems can replicate the key attributes of natural assemblages. 2. Previous investigations of stream mesocosm utility have explored community composition, but here for the first time, we extend the approach to consider the replicability and realism of food webs in four outdoor channels (4 m(2)). 3. The four food webs were similarly complex, consisting of diverse assemblages (61-71 taxa) with dense feeding interactions (directed connectance 0.09-0.11). Mesocosm food web structural attributes were within the range reported for 82 well-characterized food webs from natural streams and rivers. When compared with 112 additional food webs from standing freshwater, marine, estuarine and terrestrial environments, stream food webs (including mesocosms) had similar characteristic path lengths, but typically lower mean food chain length and exponents for the species-link relationship. 4. Body size (M) abundance (N) allometric scaling coefficients for trivariate taxonomic mesocosm food webs (-0.53 to -0.49) and individual size distributions (-0.60 to -0.58) were consistent and similar to those from natural systems, suggesting that patterns of energy flux between mesocosm consumers and resources were realistic approximations. 5. These results suggest that stream mesocosms of this scale can support replicate food webs with a degree of biocomplexity that is comparable to 'natural' streams. The findings highlight the potential value of mesocosms as model systems for performing experimental manipulations to test ecological theories, at spatiotemporal scales of relevance to natural ecosystems.

Food webs are more than the sum of their tritrophic parts

Many studies have aimed to understand food webs by investigating components such as trophic links (one consumer taxon eats one resource taxon), tritrophic interactions (one consumer eats an intermediate taxon, which eats a resource), or longer chains of links. We show here that none of these components (links, tritrophic interactions, and longer chains), individually or as an ensemble, accounts fully for the properties of the next higher level of organization. As a cell is more than its molecules, as an organ is more than its cells, and as an organism is more than its organs, in a food web, new structure emerges at every organizational level up to and including the whole web. We demonstrate the emergence of properties at progressively higher levels of structure by using all of the directly observed, appropriately organized, publicly available food web datasets with relatively complete trophic link data and with average body mass and population density data for each taxon. There are only three such webs, those of Tuesday Lake, Michigan, in 1984 and 1986, and Ythan Estuary, Scotland. We make the data freely available online with this report. Differences in web patterns between Tuesday Lake and Ythan Estuary, and similarities of Tuesday Lake in 1984 and 1986 despite 50% turnover of species, suggest that the patterns we describe respond to major differences between ecosystem types.