Globally, there are millions of small lakes, but a small number of large lakes. Most key ecosystem patterns and processes scale with lake size, thus this asymmetry between area and abundance is a fundamental constraint on broad-scale patterns in lake ecology. Nonetheless, descriptions of lake size-distributions are scarce and empirical distributions are rarely evaluated relative to theoretical predictions. Here we develop expectations for Earth’s lake area-distribution based on percolation theory and evaluate these expectations with data from a global lake census. Lake surface areas ≥8.5 km2 are power-law distributed with a tail exponent (τ = 1.97) and fractal dimension (d = 1.38), similar to theoretical expectations (τ = 2.05; d = 4/3). Lakes <8.5 km2 are not power-law distributed. An independently developed regional lake census exhibits a similar transition and consistency with theoretical predictions. Small lakes deviate from the power-law distribution because smaller lakes are more susceptible to dynamical change and topographic behavior at sub-kilometer scales is not self-similar. Our results provide a robust characterization and theoretical explanation for the lake size-abundance relationship, and form a fundamental basis for understanding and predicting patterns in lake ecology at broad scales.

Global lake volume estimates are scarce, highly variable, and poorly documented. We developed a rigorous method for estimating global lake depth and volume based on the Hurst coefficient of Earth's surface, which provides a mechanistic connection between lake area and volume. Volume‐area scaling based on the Hurst coefficient is accurate and consistent when applied to lake data sets spanning diverse regions. We applied these relationships to a global lake area census to estimate global lake volume and depth. The volume of Earth's lakes is 199,000 km3 (95% confidence interval 196,000–202,000 km3). This volume is in the range of historical estimates (166,000–280,000 km3), but the overall mean depth of 41.8 m (95% CI 41.2–42.4 m) is significantly lower than previous estimates (62–151 m). These results highlight and constrain the relative scarcity of lake waters in the hydrosphere and have implications for the role of lakes in global biogeochemical cycles.

We show that neither the Piggyback-the-Winner model nor coral reef virome data presented in Knowles et al. [1] support a mechanistic link between increases in lysogeny, suppression of lysis, and the decline of the virus-to-microbial cell ratio (VMR) at high microbial cell densities across environmental and humanassociated systems..

The future response of marine ecosystem diversity to continued anthropogenic forcing is poorly constrained. Phytoplankton are a diverse set of organisms that form the base of the marine ecosystem. Currently, ocean biogeochemistry and ecosystem models used for climate change projections typically include only 2−3 phytoplankton types and are, therefore, too simple to adequately assess the potential for changes in plankton community structure. Here, we analyse a complex ecosystem model with 35 phytoplankton types to evaluate the changes in phytoplankton community composition, turnover and size structure over the 21st century. We find that the rate of turnover in the phytoplankton community becomes faster during this century, that is, the community structure becomes increasingly unstable in response to climate change. Combined with alterations to phytoplankton diversity, our results imply a loss of ecological resilience with likely knock-on effects on the productivity and functioning of the marine environment.

Fossil-fuel emissions may impact phytoplankton primary productivity and carbon cycling by supplying bioavailable Fe to remote areas of the ocean via atmospheric aerosols. However, this pathway has not been confirmed by field observations of anthropogenic Fe in seawater. Here we present high-resolution trace-metal concentrations across the North Pacific Ocean (158°W from 25°to 42°N). A dissolved Fe maximum was observed around 35°N, coincident with high dissolved Pb and Pb isotope ratios matching Asian industrial sources and confirming recent aerosol deposition. Iron-stable isotopes reveal in situ evidence of anthropogenic Fe in seawater, with low δ56Fe (−0.23‰ > δ56Fe > −0.65‰) observed in the region that is most influenced by aerosol deposition. An isotope mass balance suggests that anthropogenic Fe contributes 21–59% of dissolved Fe measured between 35° and 40°N. Thus, anthropogenic aerosol Fe is likely to be an important Fe source to the North Pacific Ocean.

Climate change, amplified in the far north, has led to rapid sea ice decline in recent years. In the summer, melt ponds form on the surface of Arctic sea ice, significantly lowering the ice reflectivity (albedo) and thereby accelerating ice melt. Pond geometry controls the details of this crucial feedback; however, a reliable model of pond geometry does not currently exist. Here we show that a simple model of voids surrounding randomly sized and placed overlapping circles reproduces the essential features of pond patterns. The only two model parameters, characteristic circle radius and coverage fraction, are chosen by comparing, between the model and the aerial photographs of the ponds, two correlation functions which determine the typical pond size and their connectedness. Using these parameters, the void model robustly reproduces the ponds' area-perimeter and area-abundance relationships over more than 6 orders of magnitude. By analyzing the correlation functions of ponds on several dates, we also find that the pond scale and the connectedness are surprisingly constant across different years and ice types. Moreover, we find that ponds resemble percolation clusters near the percolation threshold. These results demonstrate that the geometry and abundance of Arctic melt ponds can be simply described, which can be exploited in future models of Arctic melt ponds that would improve predictions of the response of sea ice to Arctic warming.

Quantifying the fraction of primary production exported from the euphotic layer (termed the export efficiency ef) is a complicated matter. Studies have suggested empirical relationships with temperature which offer attractive potential for parameterization. Here we develop what is arguably the simplest mechanistic model relating the two, using established thermodynamic dependencies for primary production and respiration. It results in a single‐parameter curve that constrains the envelope of possible efficiencies, capturing the upper bounds of several ef‐T data sets. The approach provides a useful theoretical constraint on this relationship and extracts the variability in ef due to temperature but does not idealize out the remaining variability which evinces the substantial complexity of the system in question.

We describe the basis of a theory for interpreting measurements of two key biogeochemical fluxes—primary production by phytoplankton (p, μg C · L−1 · day−1) and biological carbon export from the surface ocean by sinking particles (f, mg C · m−2 · day−1)—in terms of their probability distributions. Given that p and f are mechanistically linked but variable and effectively measured on different scales, we hypothesize that a quantitative relationship emerges between collections of the two measurements. Motivated by the many subprocesses driving production and export, we take as a null model that large‐scale distributions of p and f are lognormal. We then show that compilations of p and f measurements are consistent with this hypothesis. The compilation of p measurements is extensive enough to subregion by biome, basin, depth, or season; these subsets are also well described by lognormals, whose log‐moments sort predictably. Informed by the lognormality of both p and f we infer a statistical scaling relationship between the two quantities and derive a linear relationship between the log‐moments of their distributions. We find agreement between two independent estimates of the slope and intercept of this line and show that the distribution of f measurements is consistent with predictions made from the moments of the p distribution. These results illustrate the utility of a distributional approach to biogeochemical fluxes. We close by describing potential uses and challenges for the further development of such an approach.