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 ≥0.46 km2 are power-law distributed with a tail exponent (τ = 2.14) and fractal dimension (d = 1.4), similar to theoretical expectations (τ = 2.05; d = 4/3). Lakes <0.46 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

Magnitude and Origin of CO2 Evasion From High-Latitude Lakes

Lakes evade significant amounts of carbon dioxide (CO2) to the atmosphere; yet the magnitude and origin of the evasion are still poorly constrained. We quantified annual CO2 evasion and its origin (in-lake net ecosystem production vs. lateral inputs from terrestrial ecosystems) in 14 high-latitude lakes through high-frequency estimates of open water CO2 flux and ecosystem metabolism and inorganic carbon mass-balance before and after ice breakup. Annual CO2 evasion ranged from 1 to 25 g C m(-2) yr(-1) of which an average of 57% was evaded over a short period at ice-breakup. Annual internal CO2 production ranged from -6 to 21 g C m(-2) yr(-1), of which at least half was produced over winter. The contribution of internal versus external source contribution to annual CO2 evasion varied between lakes, ranging from fully internal to fully external with most lakes having over 75% of the evasion sustained through a single source. Overall, the study stresses the large variability in magnitude and control of CO2 evasion and suggests that environmental change impacts on CO2 evasion from high-latitude lakes are not uniform

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 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

Effects of Habitat-Specific Primary Production on Fish Size, Biomass, and Production in Northern Oligotrophic Lakes

Ecological theory predicts that the relative distribution of primary production across habitats influence fish size structure and biomass production. In this study, we assessed individual, population, and community-level consequences for brown trout (Salmo trutta) and Arctic char (Salvelinus alpinus) of variation in estimated habitat specific (benthic and pelagic) and total whole lake (GPP(whole)) gross primary production in 27 northern oligotrophic lakes. We found that higher contribution of benthic primary production to GPP(whole) was associated with higher community biomass and larger maximum and mean sizes of fish. At the population level, species-specific responses differed. Increased benthic primary production (GPP(Benthic)) correlated to higher population biomass of brown trout regardless of being alone or in sympatry, while Arctic char responded positively to pelagic primary production (GPP(Pelagic)) in sympatric populations. In sympatric lakes, the maximum size of both species was positively related to both GPP(Benthic) and the benthic contribution to GPP(Whole). In allopatric lakes, brown trout mean and maximum size and Arctic char mean size were positively related to the benthic proportion of GPP(Whole). Our results highlight the importance of light-controlled benthic primary production for fish biomass production in oligotrophic northern lakes. Our results further suggest that consequences of ontogenetic asymmetry and niche shifts may cause the distribution of primary production across habitats to be more important than the total ecosystem primary production for fish size, population biomass, and production. Awareness of the relationships between light availability and asymmetric resource production favoring large fish and fish production may allow for cost-efficient and more informed management actions in northern oligotrophic lakes

Bias in the shoreline development index: Ecological implications illustrated with an analysis of littoral-pelagic habitat coupling

We reexamined the relationship between the shoreline development index and metrics of habitat coupling using a bias-corrected variant of the shoreline development index. Our findings suggest that previously reported correlations may be artifacts of scale-dependent bias in shoreline development index measurements. The results highlight the need for careful measurement when seeking to understand links between lake morphology and ecological processes

A theory for the relationship between lake surface area and maximum depth

Maximum depth is crucial for many lake processes and biota, but attempts to explain its variation have achieved little predictive power. In this paper, we describe the probability distribution of maximum depths based on recent developments in the theory of fractal Brownian motions. The theoretical distribution is right-tailed and adequately captures variations in maximum depth in a dataset of 8164 lakes (maximum depths 0.1–135 m) from the northeastern United States. Maximum depth increases with surface area, but with substantial random variation—the 95% prediction interval spans more than an order of magnitude for lakes with any specific surface area. Our results explain the observed variability in lake maximum depths, capture the link between topographic characteristics and lake bathymetry, and provide a means to upscale maximum depth-dependent processes, which we illustrate by upscaling the diffusive flux of methane from northern lakes to the atmosphere

Simple model of morphometric constraint on carbon burial in boreal lakes

A geometric theory was developed to explain the empirical relationship between carbon burial and lake shape in boreal lakes. The key feature of this model is an attenuation length scale, analogous to models of marine organic carbon fluxes. This length scale is the ratio of how fast carbon is displaced vertically versus how fast it is respired and engenders a simple model with a single easily constrained free parameter. Lake depths are modeled based on fractal area–volume relationships that reflect the approximate scale invariance of Earth’s topography on idealized lake geometries. Carbon burial is estimated by applying the attenuation length scale to these depths. Using this model, we demonstrate the relationship between the dynamic ratio—a metric of lake morphometry calculated by dividing the square root of surface area by the mean depth—and carbon burial. We use scaling relationships to predict how dynamic ratio, and by extension carbon burial, varies across the lake size spectrum. Our model also provides a basis for generalizing empirical studies to the biome scale. By applying our model to a boreal lake census, we estimate boreal lake carbon burial to be 1.8 ± 0.5 g C/m2/yr or 1.1 ± 0.3 Tg C/yr among all boreal lakes

How does lake primary production scale with lake size?

Kleiber’s 3/4-scaling law for metabolism with mass is one of the most striking regularities in biological sciences. Kleiber’s law has been shown to apply not only to individual organisms but also to communities and even the whole-ecosystem properties such as the productivity of estuaries. Might Kleiber’s law also then apply to lake ecosystems? Here, we show that for a collection of whole-lake primary production measurements, production scales to the 3/4 power of lake volume, consistent with Kleiber’s law. However, this relationship is not explicable by analogy to theories developed for individual organisms. Instead, we argue that dimensional analysis offers a simple explanation. After accounting for latitudinal gradients in temperature and insolation, whole-lake primary production scales isometrically with lake area. Because Earth’s topography is self-affine, meaning there are global-scale differences between vertical and horizontal scaling of topography, lake volume scales super-linearly with lake surface area. 3/4 scaling for primary production by volume then results from these other two scaling relationships. The identified relationship between the primary production and temperature- and insolation-adjusted area may be useful for constraining lakes’ global annual productivity and photosynthetic efficiency. More generally, this suggests that there are multiple paths to realizing the 3/4 scaling of metabolism rather than a single unifying law, at least when comparing across levels of biological organization

Simulating the Cascading Effects of an Extreme Agricultural Production Shock: Global Implications of a Contemporary US Dust Bowl Event

Higher temperatures expected by midcentury increase the risk of shocks to crop production, while the interconnected nature of the current global food system functions to spread the impact of localized production shocks throughout the world. In this study, we analyze the global potential impact of a present-day event of equivalent magnitude to the US Dust Bowl, modeling the ways in which a sudden decline in US wheat production could cascade through the global network of agricultural trade. We use observations of country-level production, reserves, and trade data in a Food Shock Cascade model to explore trade adjustments and country-level inventory changes in response to a major, multiyear production decline. We find that a 4-year decline in wheat production of the same proportional magnitude as occurred during the Dust Bowl greatly reduces both wheat supply and reserves in the United States and propagates through the global trade network. By year 4 of the event, US wheat exports fall from 90.5 trillion kcal before the drought to 48 trillion to 52 trillion kcal, and the United States exhausts 94% of its reserves. As a result of reduced US exports, other countries meet their needs by leveraging their own reserves, leading to a 31% decline in wheat reserves globally. These findings demonstrate that an extreme production decline would lead to substantial supply shortfalls in both the United States and in other countries, where impacts outside the United States strongly depend on a country's reserves and on its relative position in the global trade network

Patterns and variation of littoral habitat size among lakes

The littoral zone varies in size among lakes from ∼3% to 100% of lake surface area. In this paper, we derive a simple theoretical scaling relationship that explains this variation, and test this theory using bathymetric data across the size spectra of freshwater lakes (surface area = 0.01–82,103 km2, maximum depth = 2–1,741 m). Littoral area primarily reflects the ratio of the maximum depth of photosynthesis to maximum lake depth. However, lakes that are similar in these characteristics can have different relative littoral areas because of variation in basin shape. Hypsometric (area-elevation) models that describe these patterns for individual lakes can be generalized among lakes to accurately predict the relative size of littoral habitat when there is incomplete bathymetric information. Collectively, our results provide simple rules for understanding patterns of littoral habitat size at the regional and global scales