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.     

Theoretical study of electron transfer process between fullerenes and neurotransmitters; acetylcholine,dopamine, serotonin and epinephrine in nanostructures [neurotransmitters].C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> complexes

Neurotransmitters are the compounds which allow the transmission of signals from one neuron to the next across synapses. They are the brain chemicals that communicate information throughout brain and body. Fullerenes are a family of carbonallotropes, molecules composed entirely of carbon, that take the forms of spheres, ellipsoids, and cylinders. Various empty carbon fullerenes (C_n) with different carbon atoms have been obtained and investigated. Topological indices have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, the number of carbon atoms in the fullerenes was used as an index to establish a relationship between the structures of neurotransmitters (NTs) acetylcholine (AC) 1, dopamine (DP) 2, serotonin (SE) 3, and epinephrine (EP) 4 as the well-known redox systems and fullerenes C_n (n = 60, 70, 76, 82, and 86) which create [NT].C_n; A-1 to A-5 up to D-1 to D-5. The relationship between the number of carbon atoms and the free energy of electron transfer (ΔG_et(n); n = 1–4) is assessed using the Rehm-Weller equation for A-1 to A-5 up to D-1 to D-5 supramolecular [NT].C_n complexes. The calculations are presented for the four reduction potentials (^Red.E₁ to ^Red.E₄) of fullerenes C_n. The results were used to calculate the four free energy values of electron transfer (ΔG_et(1) to ΔG_et(4)) of the supramolecular complexes A-1 to A-8 up to D-1 to D-8 for fullerenes C₆₀ to C₁₂₀. The first to fourth free activation energy values of electron transfer and the maximum wavelength of the electron transfers, ΔG^#_et(n) and λ_et (n = 1–4), respectively, were also calculated in this study for A-1 to A-8 up to D-1 to D-8 in accordance with the Marcus theory.     

Direct and inverse relationships between Riccati systems coupled with multiplicative terms

An analytical and computational framework for the derivation of solitary solutions to biological systems describing the cooperation and competition of species and expressed by the system of Riccati equations coupled with multiplicative terms is presented in this paper. It is demonstrated that relationships between these solitary solutions can be either direct or inverse. Thus, an infinitesimal perturbation of one population would lead to an infinitesimal change in the other population – if only both solitary solutions are coupled with the direct relationship. But, in general, that is not true if solitary solutions are coupled with the inverse relationship – an infinitesimal perturbation of one population may result into a non-infinitesimal change in the other population. Necessary and sufficient conditions for the existence of solitary solutions are derived in the space of the system's parameters and initial conditions.     

From robustness to resilience: A network Price identity approach

We model a closed-loop network of agents distributed among subnetworks and study the sustainability of network structures in presence of random perturbations. The model outcomes show that the stability of compartmentalized networks built on uniform operators depends on perturbations on between-subnetwork coupling, while the stability of networks built on mutation operators depends on their assimilation capacity. Through the study of eigenvalues of the Laplacian, we succeed in measuring the degree of network robustness and resilience. Our results also permit to situate the Price theorem, both in its standard and expanded forms, in the context of network evolutionary variational identity.     

Enantiomerization of Allylic Trifluoromethyl Sulfoxides Studied by HPLC Analysis and DFT Calculations

Enantiomerization of allylic trifluoromethyl sulfoxides occurs spontaneously at room temperature through the corresponding allylic trifluoromethanesulfenates via a [2,3]‐sigmatropic rearrangement. Dynamic enantioselective high‐performance liquid chromatography (HPLC) analysis revealed the stereodynamics of these sulfoxides ranging from chromatographic resolution to peak coalescence at temperatures between 5 and 53 °C. The rate constant of enantiomerization and activation parameters were determined and compared with Density Functional Theory (DFT) calculations. Chirality 28:136–142, 2016. © 2015 Wiley Periodicals, Inc.     

ENSO and NAO affect long‐term leaf litter dynamics and stoichiometry of Scots pine and European beech mixedwoods

Litterfall dynamics (production, seasonality and nutrient composition) are key factors influencing nutrient cycling. Leaf litter characteristics are modified by species composition, site conditions and water availability. However, significant evidence on how large‐scale, global circulation patterns affect ecophysiological processes at tree and ecosystem level remains scarce due to the difficulty in separating the combined influence of different factors on local climate and tree phenology. To fill this gap, we studied links between leaf litter dynamics with climate and other forest processes, such as tree‐ring width (TRW) and intrinsic water‐use efficiency (iWUE) in two mixtures of Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) in the south‐western Pyrenees. Temporal series (18 years) of litterfall production and elemental chemical composition were decomposed following the ensemble empirical mode decomposition method and relationships with local climate, large‐scale climatic indices, TRW and Scots pine's iWUE were assessed. Temporal trends in N:P ratios indicated increasing P limitation of soil microbes, thus affecting nutrient availability, as the ecological succession from a pine‐dominated to a beech‐dominated forest took place. A significant influence of large‐scale patterns on tree‐level ecophysiology was explained through the impact of the North Atlantic Oscillation (NAO) and El Niño–Southern Oscillation (ENSO) on water availability. Positive NAO and negative ENSO were related to dry conditions and, consequently, to early needle shedding and increased N:P ratio of both species. Autumn storm activity appears to be related to premature leaf abscission of European beech. Significant cascading effects from large‐scale patterns on local weather influenced pine TRW and iWUE. These variables also responded to leaf stoichiometry fallen 3 years prior to tree‐ring formation. Our results provide evidence of the cascading effect that variability in global climate circulation patterns can have on ecophysiological processes and stand dynamics in mixed forests.     

Evolutionary stasis of a heritable morphological trait in a wild fish population despite apparent directional selection

Comparing observed versus theoretically expected evolutionary responses is important for our understanding of the evolutionary process, and for assessing how species may cope with anthropogenic change. Here, we document directional selection for larger female size in Atlantic salmon, using pedigree‐derived estimates of lifetime reproductive success as a fitness measure. We show the trait is heritable and, thus, capable of responding to selection. The Breeder's Equation, which predicts microevolution as the product of phenotypic selection and heritability, predicted evolution of larger size. This was at odds, however, with the observed lack of either phenotypic or genetic temporal trends in body size, a so‐called “paradox of stasis.” To investigate this paradox, we estimated the additive genetic covariance between trait and fitness, which provides a prediction of evolutionary change according to Robertson's secondary theorem of selection (STS) that is unbiased by missing variables. The STS prediction was consistent with the observed stasis. Decomposition of phenotypic selection gradients into genetic and environmental components revealed a potential upward bias, implying unmeasured factors that covary with trait and fitness. These results showcase the power of pedigreed, wild population studies—which have largely been limited to birds and mammals—to study evolutionary processes on contemporary timescales.