B. B. Cael

The size-distribution of Earth's lakes

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.

On the temperature dependence of oceanic export efficiency

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.

The volume and mean depth of Earth's lakes

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 Earths ...

The Good, the Bad, and the Tiny: A Simple, Mechanistic-Probabilistic Model of Virus-Nutrient Colimitation in Microbes.

For phytoplankton and other microbes, nutrient receptors are often the passages through which viruses invade. This presents a bottom-up vs. top-down, co-limitation scenario; how do these would-be-hosts balance minimizing viral susceptibility with maximizing uptake of limiting nutrient(s)? This question has been addressed in the biological literature on evolutionary timescales for populations, but a shorter timescale, mechanistic perspective is lacking, and marine viral literature suggests the strong influence of additional factors, e.g. host size; while the literature on both nutrient uptake and host-virus interactions is expansive, their intersection, of ubiquitous relevance to marine environments, is understudied. I present a simple, mechanistic model from first principles to analyze the effect of this co-limitation scenario on individual growth, which suggests that in environments with high risk of viral invasion or spatial/temporal heterogeneity, an individual host’s growth rate may be optimized with respect to receptor coverage, producing top-down selective pressure on short timescales. The model has general applicability, is suggestive of hypotheses for empirical exploration, and can be extended to theoretical studies of more complex behaviors and systems.

Can Rates of Ocean Primary Production and Biological Carbon Export Be Related Through Their Probability Distributions

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.

Particle flux parameterizations: quantitative and mechanistic similarities and differences

The depth-attenuation of sinking particulate organic carbon (POC) is of particular importance for the oceans role in the global carbon cycle. Numerous idealized flux-versus-depth relationships are available to parameterize this process in Earth System Models. Here we show that these relationships are statistically indistinguishable from available POC flux profile data. Despite their quantitative similarity, we also show these relationships have very different implications for the flux leaving the upper ocean, as well as for the mechanisms governing POC flux. We discuss how this tension might be addressed both observationally and in modeling studies.

The ocean's saltiness and its overturning: THE OCEAN'S SALTINESS AND ITS OVERTURNING

Here we explore the relationship between the mean salinity S̄ of the ocean and the strength of its Atlantic and Pacific Meridional Overturning Circulations (AMOC and PMOC). We compare simulations performed with a realistically configured coarse-grained ocean model, spanning a range of mean salinities. We find that the AMOC strength increases approximately linearly with S̄. In contrast, the PMOC strength declines approximately linearly with S̄ until it reaches a small background value similar to the present-day ocean. Well-established scaling laws for the overturning circulation explain both of these dependencies on S̄.