Ectomycorrhizal symbiosis can enhance plant nutrition through improved access to discrete organic nutrient patches of high resource quality

It is known that roots can respond to patches of fertility; however, root proliferation is often too slow to exploit resources fully, and organic nutrient patches may be broken down and leached, immobilized or chemically fixed before they are invaded by the root system. The ability of fungal hyphae to exploit resource patches is far greater than that of roots due to their innate physiological and morphological plasticity, which allows comprehensive exploration and rapid colonization of resource patches in soils. The fungal symbionts of ectomycorrhizal plants excrete significant quantities of enzymes such as chitinases, phosphatases and proteases. These might allow the organic residue to be tapped directly for nutrients such as N and P. Pot experiments conducted with nutrient-stressed ectomycorrhizal and control willow plants showed that when high quality organic nutrient patches were added, they were colonized rapidly by the ectomycorrhizal mycelium. These established willows (0.5 m tall) were colonized by Hebeloma syrjense P. Karst. for 1 year prior to nutrient patch addition. Within days after patch addition, colour changes in the leaves of the mycorrhizal plants (reflecting improved nutrition) were apparent, and after I month the concentration of N and P in the foliage of mycorrhizal plants was significantly greater than that in non-mycorrhizal plants subject to the same nutrient addition. It seems likely that the mycorrhizal plants were able to compete effectively with the wider soil microbiota and tap directly into the high quality organic resource patch via their extra-radical mycelium. We hypothesize that ectomycorrhizal plants may reclaim some of the N and P invested in seed production by direct recycling from failed seeds in the soil. The rapid exploitation of similar discrete, transient, high-quality nutrient patches may have led to underestimations when determining the nutritional benefits of ectomycorrhizal colonization.

Intraindividual relations between achievement goals and discrete achievement emotions: an experience sampling approach

Theories on the link between achievement goals and achievement emotions focus on their within-person functional relationship (i.e., intraindividual relations). However, empirical studies have failed to analyze these intraindividual relations and have instead examined between-person covariation of the two constructs (i.e., interindividual relations). Aiming to better connect theory and empirical research, the present study (N = 120 10th grade students) analyzed intraindividual relations by assessing students’ state goals and emotions using experience sampling (N = 1,409 assessments within persons). In order to replicate previous findings on interindividual relations, students’ trait goals and emotions were assessed using self-report questionnaires. Despite being statistically independent, both types of relations were consistent with theoretical expectations, as shown by multi-level modeling: Mastery goals were positive predictors of enjoyment and negative predictors of boredom and anger; performance-approach goals were positive predictors of pride; and performance-avoidance goals were positive predictors of anxiety and shame. Reasons for the convergence of intra- and interindividual findings, directions for future research, and implications for educational practice are discussed.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.