Irakli Loladze

Rising atmospheric CO2 and human nutrition: toward globally imbalanced plant stoichiometry?

Abstract Terrestrial vascular plants obtain their major constituent – carbon (C) – from atmospheric carbon dioxide (CO 2 ), but draw all other chemical elements largely from the soil. Concentrations of these elements, however, do not change in unison with steadily increasing concentrations of CO 2 [CO 2 ]. Thus, relative to pre-industrial times, modern plants are experiencing a global elemental imbalance. Could this imbalance affect the elemental composition of plants, the most important food source on Earth? Apart from an overall decline in nitrogen concentration, very little is known about the effects of high [CO 2 ] on other chemical elements, such as iron, iodine and zinc, which are already deficient in the diets of the half of human population. Here, I apply stoichiometric theory to argue that high [CO 2 ], as a rule, should alter the elemental composition of plants, thus affecting the quality of human nutrition. The first compilation, to my knowledge, of published data supports the claim and shows an overall decline of the (essential elements):C ratio. Therefore, high [CO 2 ] could intensify the already acute problem of micronutrient malnutrition.

The origins of the Redfield nitrogen‐to‐phosphorus ratio are in a homoeostatic protein‐to‐rRNA ratio

One of the most intriguing patterns in the biosphere is the similarity of the atomic nitrogen-to-phosphorus ratio (N:P) = 16 found in waters throughout the deep ocean and in the plankton in the upper ocean. Although A.C. Redfield proposed in 1934 that the intracellular properties of plankton were central to this pattern, no theoretical significance for N:P = 16 in cells had been found. Here, we use theoretical modelling and a compilation of literature data for prokaryotic and eukaryotic microbes to show that the balance between two fundamental processes, protein and rRNA synthesis, results in a stable biochemical attractor that homoeostatically produces a given protein:rRNA ratio. Furthermore, when biochemical constants and reasonable kinetic parameters for protein synthesis and ribosome production under nutrient-replete conditions are applied in the model, it predicts a stable protein:rRNA ratio of 3 ± 0.7, which corresponds to N:P = 16 ± 3. The model also predicts that N-limitation, by constraining protein synthesis rates, will result in N:P ratios below the Redfield value while P-limitation, by constraining RNA production rates, will produce ratios above the Redfield value. Hence, one of most biogeochemically significant patterns on Earth is inherently rooted in the fundamental structure of life.

Competition and stoichiometry: coexistence of two predators on one prey.

The competitive exclusion principle (CEP) states that no equilibrium is possible if n species exploit fewer than n resources. This principle does not appear to hold in nature, where high biodiversity is commonly observed, even in seemingly homogenous habitats. Although various mechanisms, such as spatial heterogeneity or chaotic fluctuations, have been proposed to explain this coexistence, none of them invalidates this principle. Here we evaluate whether principles of ecological stoichiometry can contribute to the stable maintenance of biodiverse communities. Stoichiometric analysis recognizes that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P) that are present in various proportions in organisms. We incorporate these principles into a standard predator-prey model to analyze competition between two predators on one autotrophic prey. The model tracks two essential elements, C and P, in each species. We show that a stable equilibrium is possible with two predators on this single prey. At this equilibrium both predators can be limited by the P content of the prey. The analysis suggests that chemical heterogeneity within and among species provides new mechanisms that can support species coexistence and that may be important in maintaining biodiversity.

Hidden shift of the ionome of plants exposed to elevated CO2 depletes minerals at the base of human nutrition

Mineral malnutrition stemming from undiversified plant-based diets is a top global challenge. In C3 plants (e.g., rice, wheat), elevated concentrations of atmospheric carbon dioxide (eCO2) reduce protein and nitrogen concentrations, and can increase the total non-structural carbohydrates (TNC; mainly starch, sugars). However, contradictory findings have obscured the effect of eCO2 on the ionome—the mineral and trace-element composition—of plants. Consequently, CO2-induced shifts in plant quality have been ignored in the estimation of the impact of global change on humans. This study shows that eCO2 reduces the overall mineral concentrations (−8%, 95% confidence interval: −9.1 to −6.9, p<0.00001) and increases TNC:minerals > carbon:minerals in C3 plants. The meta-analysis of 7761 observations, including 2264 observations at state of the art FACE centers, covers 130 species/cultivars. The attained statistical power reveals that the shift is systemic and global. Its potential to exacerbate the prevalence of ‘hidden hunger’ and obesity is discussed. DOI: http://dx.doi.org/10.7554/eLife.02245.001

Biodiversity, habitat area, resource growth rate and interference competition

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.

Dynamics of a mechanistically derived stoichiometric producer-grazer model

One of the simplest predator-prey models that tracks the quantity and the quality of prey is the one proposed by [I. Loladze, Y. Kuang, and J.J. Elser, Stoichiometry in producer-grazer systems: Linking energy flow with element cycling, Bull. Math. Biol. 62 (2000) pp. 1137–1162.] (LKE model). In it, the ratio of two essential chemical elements, carbon to phosphorus, C:P, represents prey quality. However, that model does not explicitly track P neither in the prey nor in the media that supports the prey. Here, we extend the LKE model by mechanistically deriving and accounting for P in both the prey and the media. Bifurcation diagrams and simulations show that our model behaves similarly to the LKE model. However, in the intermediate range of the carrying capacity, especially near the homoclinic bifurcation point for the carrying capacity, quantitative behaviour of our model is different. We analyze positive invariant region and stability of boundary steady states. We show that as the uptake rate of P by producer becomes infinite, LKE models become the limiting case of our model. Furthermore, our model can be readily extended to multiple producers and consumers.

Rising atmospheric CO2 is reducing the protein concentration of a floral pollen source essential for North American bees

At present, there is substantive evidence that the nutritional content of agriculturally important food crops will decrease in response to rising levels of atmospheric carbon dioxide, Ca. However, whether Ca-induced declines in nutritional quality are also occurring for pollinator food sources is unknown. Flowering late in the season, goldenrod (Solidago spp.) pollen is a widely available autumnal food source commonly acknowledged by apiarists to be essential to native bee (e.g. Bombus spp.) and honeybee (Apis mellifera) health and winter survival. Using floral collections obtained from the Smithsonian Natural History Museum, we quantified Ca-induced temporal changes in pollen protein concentration of Canada goldenrod (Solidago canadensis), the most widespread Solidago taxon, from hundreds of samples collected throughout the USA and southern Canada over the period 1842–2014 (i.e. a Ca from approx. 280 to 398 ppm). In addition, we conducted a 2 year in situ trial of S. canadensis populations grown along a continuous Ca gradient from approximately 280 to 500 ppm. The historical data indicated a strong significant correlation between recent increases in Ca and reductions in pollen protein concentration (r2 = 0.81). Experimental data confirmed this decrease in pollen protein concentration, and indicated that it would be ongoing as Ca continues to rise in the near term, i.e. to 500 ppm (r2 = 0.88). While additional data are needed to quantify the subsequent effects of reduced protein concentration for Canada goldenrod on bee health and population stability, these results are the first to indicate that increasing Ca can reduce protein content of a floral pollen source widely used by North American bees.

Competitive coexistence in stoichiometric chaos.

Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.

Dynamics of a stoichiometric discrete producer-grazer model

In the last decade, several theoretical models based on stoichiometric principles as well as field and laboratory experiments have shown that nutritional quality of the prey can have dramatic and counterintuitive impact. For example, the predator can become extinct while having plentiful prey in a completely deterministic system. The explanation lies in the bad nutritional quality of the prey that precludes the predator from efficiently converting the consumed food into its own biomass. Another effect is the halt of oscillations that are ubiquitous to predator-prey systems, which happens when bad prey quality drives the system through a saddle-node bifurcation. We note that all the existing models exhibiting these effects are continuous in time. However, in experiments, data are collected on discrete time intervals and many producers in nature have non-overlapping generations. Such scenarios call for discrete equation models. Hence we ask: (1) to what degree stoichiometric effects are just artifacts of continuous time models? (2) Can novel stoichiometric effects arise in discrete systems? Here, by comparing a continuous stoichiometric model to its discrete analog, we show that stoichiometric impacts of prey quality persist in discrete system. Moreover, not only bad prey quality can pull the system out of oscillations but also it can halt chaotic dynamics that surfaces in the discrete system. Stoichiometric mechanisms become increasingly important in our understanding of food web dynamics and our results suggest the robustness of these mechanisms to the discretization of time.

A stoichiometric producer-grazer model incorporating the effects of excess food-nutrient content on consumer dynamics

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. For example, modeling under this framework allows food quality to affect consumer dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon is known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, and needs to be incorporated into mathematical models. Here we present a Lotka-Volterra type model to investigate the growth response of Daphnia to algae of varying P:C ratios capturing the mechanism of the stoichiometric knife edge.