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

Methods For Detecting Early Warnings Of Critical Transitions In Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.Organismic and Evolutionary Biolog

Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data

Reserves and trade jointly determine exposure to food supply shocks

While a growing proportion of global food consumption is obtained through international trade, there is an ongoing debate on whether this increased reliance on trade benefits or hinders food security, and specifically, the ability of global food systems to absorb shocks due to local or regional losses of production. This paper introduces a model that simulates the short-term response to a food supply shock originating in a single country, which is partly absorbed through decreases in domestic reserves and consumption, and partly transmitted through the adjustment of trade flows. By applying the model to publicly-available data for the cereals commodity group over a 17 year period, we find that differential outcomes of supply shocks simulated through this time period are driven not only by the intensification of trade, but as importantly by changes in the distribution of reserves. Our analysis also identifies countries where trade dependency may accentuate the risk of food shortages from foreign production shocks; such risk could be reduced by increasing domestic reserves or importing food from a diversity of suppliers that possess their own reserves. This simulation-based model provides a framework to study the short-term, nonlinear and out-of-equilibrium response of trade networks to supply shocks, and could be applied to specific scenarios of environmental or economic perturbations

Stream diatom assemblages in an arctic catchment : Diversity and relationship to ecosystem-scale primary production

We quantified benthic diatom diversity in streams in the Miellajokka catchment, about 200 km north of the Arctic circle in Sweden. Beta diversity among sites was related to local-scale environmental heterogeneity (occurring on the order of 1 km or less), and its magnitude was equal (Sørensen Index = 0.62) to levels previously reported for rivers on regional environmental gradients across hundreds of kilometres of Arctic Fennoscandia. Species turnover was the dominant (77%) component of beta diversity in the Miellajokka catchment. Small, stress-tolerant taxa dominated the assemblages, and there were no clear patterns of functional class among sites. Site ordinates from non-metric dimensional scaling were most strongly correlated with flood frequency (r = 0.83) and water temperature (r = 0.89), which was higher in harsh tundra sites than below treeline. Additionally, site ordinates were correlated (r = 0.83) with ecosystem-scale gross primary production — indicative of a link between diatom diversity and ecosystem function. Our results advance understanding of patterns diatom diversity in Arctic streams by quantifying local-scale variation that is understudied in this region, and by identifying the consequences of this local-scale diversity for an ecosystem-scale process

The Scaling Relationship for the Length of Tributaries to Lakes

Globally, the length of tributaries to lakes varies from 0 to more than 15,000 km, but scaling relationships describing this aspect of lake-river connectivity are lacking. In this study, we describe a simple theoretical scaling relationship for tributary length based on the principle of line intercepts of topographic features, and test this theory using data from Scandinavia. Tributary length increases by 73% for each doubling of lake area. This pattern reflects the relationship between catchment and lake area, and is modified by inlet frequency, junction angle, and lake shape—factors related to specific geologic and hydrologic processes. The theory is precise (r2 = 0.74), with low bias (mean error is 14% of mean tributary length) when the characteristic junction angle (∼76°) is estimated statistically. Our study bridges the gap between geomorphic and large-scale statistical relationships to provide simple rules for understanding complex patterns of lake-river connectivity

Inequality or injustice in water use for food?

The global distributions of water availability and population density are uneven and therefore inequality exists in human access to freshwater resources. Is this inequality unjust or only regrettable? To examine this question we formulated and evaluated elementary principles of water ethics relative to human rights for water, and the need for global trade to improve societal access to water by transferring 'virtual water' embedded in plant and animal commodities. We defined human welfare benchmarks and evaluated patterns of water use with and without trade over a 25-year period to identify the influence of trade and inequality on equitability of water use. We found that trade improves mean water use and wellbeing, relative to human welfare benchmarks, suggesting that inequality is regrettable but not necessarily unjust. However, trade has not significantly contributed to redressing inequality. Hence, directed trade decisions can improve future conditions of water and food scarcity through reduced inequality