Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems

The worldwide loss of species diversity brings urgency to understanding how diverse ecosystems maintain stability. Whereas early ecological ideas and classic observations suggested that stability increases with diversity, ecological theory makes the opposite prediction, leading to the long-standing "diversity-stability debate." Here, we show that this puzzle can be resolved if growth scales as a sublinear power law with biomass (exponent <1), exhibiting a form of population self-regulation analogous to models of individual ontogeny. We show that competitive interactions among populations with sublinear growth do not lead to exclusion, as occurs with logistic growth, but instead promote stability at higher diversity. Our model realigns theory with classic observations and predicts large-scale macroecological patterns. However, it makes an unsettling prediction: Biodiversity loss may accelerate the destabilization of ecosystems.

The human cell count and size distribution

Cell size and cell count are adaptively regulated and intimately linked to growth and function. Yet, despite their widespread relevance, the relation between cell size and count has never been formally examined over the whole human body. Here, we compile a comprehensive dataset of cell size and count over all major cell types, with data drawn from >1,500 published sources. We consider the body of a representative male (70 kg), which allows further estimates of a female (60 kg) and 10-y-old child (32 kg). We build a hierarchical interface for the cellular organization of the body, giving easy access to data, methods, and sources (https://humancelltreemap.mis.mpg.de/). In total, we estimate total body counts of ≈36 trillion cells in the male, ≈28 trillion in the female, and ≈17 trillion in the child. These data reveal a surprising inverse relation between cell size and count, implying a trade-off between these variables, such that all cells within a given logarithmic size class contribute an equal fraction to the body's total cellular biomass. We also find that the coefficient of variation is approximately independent of mean cell size, implying the existence of cell-size regulation across cell types. Our data serve to establish a holistic quantitative framework for the cells of the human body, and highlight large-scale patterns in cell biology.

Global city densities: Re-examining urban scaling theory

Understanding scaling relations of social and environmental attributes of urban systems is necessary for effectively managing cities. Urban scaling theory (UST) has assumed that population density scales positively with city size. We present a new global analysis using a publicly available database of 933 cities from 38 countries. Our results showed that (18/38) 47% of countries analyzed supported increasing density scaling (pop ~ area) with exponents ~⅚ as UST predicts. In contrast, 17 of 38 countries (~45%) exhibited density scalings statistically indistinguishable from constant population densities across cities of varying sizes. These results were generally consistent in years spanning four decades from 1975 to 2015. Importantly, density varies by an order of magnitude between regions and countries and decreases in more developed economies. Our results (i) point to how economic and regional differences may affect the scaling of density with city size and (ii) show how understanding country- and region-specific strategies could inform effective management of urban systems for biodiversity, public health, conservation and resiliency from local to global scales.

200 word statement of contribution: Urban Scaling Theory (UST) is a general scaling framework that makes quantitative predictions for how many urban attributes spanning physical, biological and social dimensions scale with city size; thus, UST has great implications in guiding future city developments. A major assumption of UST is that larger cities become denser. We evaluated this assumption using a publicly available global dataset of 933 cities in 38 countries. Our scaling analysis of population size and area of cities revealed that while many countries analyzed showed increasing densities with city size, about 45% of countries showed constant densities across cities. These results question a key assumption of UST. Our results suggest policies and management strategies for biodiversity conservation, public health and sustainability of urban systems may need to be tailored to national and regional scaling relations to be effective.

Consistent predator-prey biomass scaling in complex food webs

The ratio of predator-to-prey biomass is a key element of trophic structure that is typically investigated from a food chain perspective, ignoring channels of energy transfer (e.g. omnivory) that may govern community structure. Here, we address this shortcoming by characterising the biomass structure of 141 freshwater, marine and terrestrial food webs, spanning a broad gradient in community biomass. We test whether sub-linear scaling between predator and prey biomass (a potential signal of density-dependent processes) emerges within ecosystem types and across levels of biological organisation. We find a consistent, sub-linear scaling pattern whereby predator biomass scales with the total biomass of their prey with a near ¾-power exponent within food webs - i.e. more prey biomass supports proportionally less predator biomass. Across food webs, a similar sub-linear scaling pattern emerges between total predator biomass and the combined biomass of all prey within a food web. These general patterns in trophic structure are compatible with a systematic form of density dependence that holds among complex feeding interactions across levels of organization, irrespective of ecosystem type.

The ratio of predator-to-prey biomass is a key element in food webs. Here, the authors report a unified analysis of predator-prey biomass scaling in complex food webs, finding general patterns of sub-linear scaling across ecosystems and levels of organization.

The global ocean size spectrum from bacteria to whales

It has long been hypothesized that aquatic biomass is evenly distributed among logarithmic body mass size classes. Although this community structure has been observed regionally, mostly among plankton groups, its generality has never been formally tested across all marine life over the global ocean, nor have the impacts of humans on it been globally assessed. Here, we bring together data at the global scale to test the hypothesis from bacteria to whales. We find that biomass within most order of magnitude size classes is indeed remarkably constant, near 1 gigatonne (Gt) wet weight (10¹⁵ g), but bacteria and large marine mammals are markedly above and below this value, respectively. Furthermore, human impacts appear to have significantly truncated the upper one-third of the spectrum. This dramatic alteration to what is possibly life’s largest-scale regularity underscores the global extent of human activities.

The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes

Ecosystems exhibit surprising regularities in structure and function across terrestrial and aquatic biomes worldwide. We assembled a global data set for 2260 communities of large mammals, invertebrates, plants, and plankton. We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾. This pervasive pattern implies that the structure of the biomass pyramid becomes increasingly bottom-heavy at higher biomass. Similar exponents are obtained for community production-biomass relations, suggesting conserved links between ecosystem structure and function. These exponents are similar to many body mass allometries, and yet ecosystem scaling emerges independently from individual-level scaling, which is not fully understood. These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory.

A dynamical approach to evaluate risk in resource management

With the depletion of many natural resources, we are growing aware of the need to understand the risks that stem from different management decisions. Here, we outline an approach to test the ability of different dynamical signatures to characterize time-series data: how likely is it that a natural population is declining, sustainable, or increasing, and at what rates are these temporal changes likely occurring? These dynamical signatures can serve as a robust foundation on which to formulate alternative scenarios in a decision analysis. They take account of much of the uncertainty in model parameters and have precise mathematical underpinnings with associated risks. We present methods to evaluate the likelihood of these scenarios, and ways that the analysis can be graphically represented. We discuss different ecological factors such as climate variability, life history, ecosystem interactions, and a changing population age structure, all of which impact the dynamics of natural populations. Considering the types of dynamical signatures that emerge from these factors can change our understanding of risk and the decisions that we make.