The quantitative mapping of food web flows based on empirical data is a crucial yet difficult task in ecology. The difficulty arises from the under-sampling of food webs, because most data sets are incomplete and uncertain. In this article, we review methods to quantify food web flows based on empirical data using linear inverse models (LIM). The food web in a LIM is described as a linear function of its flows, which are estimated from empirical data by inverse modeling. The under-sampling of food webs implies that infinitely many different solutions exist that are consistent with a given data set. The existing approaches to food web LIM select a single solution from this infinite set by invoking additional assumptions: either a specific selection criterion that has no solid ecological basis is used or the data set is artificially upgraded by assigning fixed values to, for example, physiological parameters. Here, we advance a likelihood approach (LA) that follows a different solution philosophy. Rather than singling out one particular solution, the LA generates a large set of possible solutions from which the marginal probability density function (mPDF) of each flow and correlations between flows can be derived. The LA is exemplified with an example model of a soil food web and is made available in the open-source R-software. Moreover, we show how stoichiometric data, stable isotope signatures, and fatty acid compositions can be included in the LIM to alleviate the under-sampling problem. Overall, LIM prove to be a powerful tool in food web research, which can bridge the gap between empirical data and the analysis of food web structures.

We tracked flows of carbon and nitrogen during an experimental phytoplankton bloom in a natural estuarine assemblage in Randers Fjord, Denmark. We used ¹³C‐labeled dissolved inorganic carbon to trace the transfer of carbon from phytoplankton to bacteria. Ecosystem development was followed over a period of 9 d through changes in the stocks of inorganic nutrients, pigments, particulate organic carbon and nitrogen, dissolved organic carbon (DOC), and algal and bacterial polar‐lipid‐derived fatty acids (PLFA). We quantified the incorporation of ¹³C in phytoplankton and bacterial biomass by carbon isotope analysis of specific PLFA. A dynamic model based on unbalanced algal growth and balanced growth of bacteria and zooplankton adequately reproduced the observations and provided an integral view of carbon and nitrogen dynamics. There were three phases with distinct carbon and nitrogen dynamics. During the first period, nutrients were replete, an algal bloom was observed, and carbon and nitrogen uptake occurred at a constant ratio. Because there was little algal exudation of DOC, transfer of ¹³C from phytoplankton to bacteria was delayed by 1 d, compared with the labeling of phytoplankton. In the second phase, the exhaustion of dissolved inorganic nitrogen resulted in decoupling of carbon and nitrogen flows caused by unbalanced algal growth and the exudation of carbon‐rich dissolved organic matter by phytoplankton. During the final, nutrient‐depleted phase, carbon and nitrogen cycling were dominated by the microbial loop and there was accumulation of DOC. The main source (60%) of DOC was exudation by phytoplankton growing under nitrogen limitation. Heterotrophic processes were the main source of dissolved organic nitrogen (94%). Most of the carbon exudated by algae was respired by the bacteria and did not pass to higher trophic levels. The dynamic model successfully reproduced the evolution of trophic pathways during the transition from nutrient‐replete to ‐depleted conditions, which indicates that simple models provide a powerful tool to study the response of pelagic ecosystems to external forcings.

Hypotheses on the existence of a universal “Root Economics Spectrum” (RES) has received arguably the least attention of all trait spectra, despite the key role root trait variation plays in resource acquisition potential. There is growing interest in quantifying intraspecific trait variation (ITV) in plants, but there are few studies evaluating i) the existence of an intraspecific RES within a plant species, or ii) how a RES may be coordinated with other trait spectra within species, such as a leaf economics spectrum (LES). Using Coffea arabica (Rubiaceae) as a model species, we measured seven morphological and chemical traits of intact lateral roots, which were paired with information on four key LES traits. Field collections were completed across four nested levels of biological organization. The intraspecific trait coefficient of variation (CV) ranged from 25 to 87% with root diameter and specific root tip density showing the lowest and highest CV, respectively. Between 27-68% of root ITV was explained by site identity alone for five of the seven traits measured. Multiple factor analysis revealed significant orthogonal relationships between root and leaf spectra. A single principal component explained 56.2 % of root trait covariation, with plants falling along a RES from resource acquiring to conserving traits. RES traits were strongly orthogonal with respect to LES traits, suggesting these traits vary independently from one another in response to environmental cues. This study provides among the first evidence that plants from the same species differentiate from one another along an intraspecific RES. We find that in one of the world’s most widely cultivated crops, an intraspecific RES is orthogonal to an intraspecific LES, indicating that above and belowground responses of plants to managed (or natural) environmental gradients are likely to occur independently from one another.