Tripartite Partition Research Articles

Structural Organization of Human Full-Length PAR3 and the aPKC–PAR6 Complex

The tripartite partition defect (PAR) polarity complex, which includes the proteins PAR3, atypical protein kinase C (aPKC), and PAR6, is a major regulator of cellular polarity. It is highly conserved and expressed in various tissues. Its largest component, PAR3, controls protein–protein interactions of the PAR complex with a variety of interaction partners, and PAR3 self-association is critical for the formation of filament-like structures. However, little is known about the structure of the PAR complex. Here, we purified non-filamentous PAR3 and the aPKC–PAR6 complex and characterized them by single-particle electron microscopy (EM). We expressed and purified an oligomerization-deficient form of PAR3, PAR3V13D,D70K, and the active aPKC–PAR6 dimer. For PAR3, engineering at two positions is sufficient to form stable single particles with a maximum dimension of 20 nm. aPKC–PAR6 forms a complex with a maximum dimension of 13.5 nm that contains single copies of aPKC. Thus, the data present a basis for further high-resolution studies of PAR proteins and PAR complex formation.

Interpreting the effects of plant species diversity and genotypic diversity within a dominant species on above- and belowground overyielding

Biodiversity loss, either intraspecific or interspecific level, could alter community processes and ecosystem functioning. Exploring the mechanisms by which biodiversity at different levels influences ecosystem functioning is a major challenge in the field of ecology. In this study, by constructing plant communities with different diversity levels of both dominant species (Stipa grandis) genotype and common species in a mesocosm experiment, we analyzed the relative importance of dominant genotype diversity and common species diversity on biomass production through Fox's tripartite partition, and the relationships between community functional diversity and biomass production. For common species mixtures (G0S5), a significant positive net diversity effect on belowground biomass was found, and the net effect was contributed by a significant positive dominance effect and a significant negative trait-independent complementarity effect. For genotype mixtures of S. grandis (G5S0), a significant positive net diversity effect on aboveground biomass and a non-significant positive net diversity effect on belowground biomass were found, and both the effects were driven by positive trait-independent complementarity effects. The increases in both dominant genotype and common species diversity (G5S5) led to remarkable positive net diversity effects, with a significant positive trait-independent complementarity effect on belowground biomass and all the three biodiversity effect components on aboveground biomass being significantly positive. Only a small proportion (3/22) of relationships between community functional diversity and biomass were linear by a first order polynomial estimation. The significant positive trait-independent complementarity effect in G5S0 and trait-dependent complementarity effect in G5S5 could not be explained by the smaller intraspecific trait variation. These findings highlight the underestimated and overlooked roles of dominant genotypic diversity for ecosystem functioning, and are very important for grassland protection and management, especially in the semi-arid typical steppe.

Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples

Ancient books on East Asian mathematics introduced to the Korean Peninsula enrich our understanding of the arithmetic notions that mold the creative thought processes of the ancients. They believed that all objects in the universe could be composed of circles and squares and all items could be expressed in terms of geometrical profiles. Through the combination of circles and squares, the ancient East Asians expressed the order of the world and unraveled it mathematically. These principles are evident in the construction principles of early Korean stone pagodas. In particular, the square root of 2 (√2) is a very important number in the delineation represented in the consolidation of inscribed and circumscribed circles with squares. Further, the square root of 2 is applied as a design principle in the construction of the stone pagodas at the temples Chŏngnimsa and Kamŭnsa. This article demonstrates that the ancients on the continuous impact of the Jiuzhang Suanshu and the Zhoubi Suanshu constructed the pagodas complying with design principles based on the arithmetic and geometric proportional systems of √2 times, which are intended to adjust compositional proportions and the gradual decrease in length to shape the tripartite partition of the foundation, the pagoda body, and the finial in stone pagodas.

Green roof plant species diversity improves ecosystem multifunctionality

Summary Constructed ecosystems such as green roofs often contain monocultures or low‐diversity plant communities, but adding more plant species to these systems can increase ecosystem service provisioning. Mixture advantage, when species‐rich treatments outperform the best monocultures, is desirable in constructed ecosystems due to the cost of increasing diversity. However, there have not been any studies in constructed ecosystems that have quantitatively compared mixtures with the best monocultures for multifunctionality, and there have been few studies that have examined how provision of ecosystem services changes over time as plant communities develop. In a green roof system, I predicted (i) that the mixture advantage would be stronger for ecosystem multifunctionality than for single ecosystem functions and (ii) that ecosystem service provisioning and complementarity in above‐ground biomass would increase over time. Fifteen monocultures of plant species from five life‐form groups (succulents, tall forbs, dwarf shrubs, creeping forbs, grasses) were compared with three‐species mixtures of the same life‐form and mixtures of species from three and five different life‐forms in a modular green roof system. Indicators of ecosystem services including above‐ground production, thermal regulation, stormwater retention, nutrient uptake and carbon sequestration and two indices of ecosystem multifunctionality were compared. Canopy density increased over time while substrate temperature decreased, suggesting higher provisioning of valuable ecosystem services. For single services, the positive relationship between planted species richness and ecosystem service grew stronger over time, but was consistently strong over time for multifunctionality. Quantile regression indicated a weak mixture advantage for several services including both multifunctionality indices. While the effects were small, different species optimized different functions, thus multifunctioning is enhanced in more diverse mixtures by combining species that maximize different functions. Tripartite partitioning of canopy density showed that overyielding and trait‐independent complementarity fluctuated between years in response to shifts in species abundances, but dominance and trait‐dependent complementarity increased over time. Synthesis and applications. This study provides the first evidence in a constructed ecosystem that mixtures can outperform the best monocultures for multiple ecosystem services. Mixtures of plant life‐forms can improve green roof performance. The biodiversity–ecosystem function relationships observed in natural ecosystems can also occur in novel and highly simplified engineered ecosystems.

How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem

We analyze cosmology assuming unitary quantum mechanics, using a tripartite partition into system, observer and environment degrees of freedom. This generalizes the second law of thermodynamics to "The system's entropy can't decrease unless it interacts with the observer, and it can't increase unless it interacts with the environment." The former follows from the quantum Bayes Theorem we derive. We show that because of the long-range entanglement created by cosmological inflation, the cosmic entropy decreases exponentially rather than linearly with the number of bits of information observed, so that a given observer can reduce entropy by much more than the amount of information her brain can store. Indeed, we argue that as long as inflation has occurred in a non-negligible fraction of the volume, almost all sentient observers will find themselves in a post-inflationary low-entropy Hubble volume, and we humans have no reason to be surprised that we do so as well, which solves the so-called inflationary entropy problem. An arguably worse problem for unitary cosmology involves gamma-ray-burst constraints on the "Big Snap", a fourth cosmic doomsday scenario alongside the "Big Crunch", "Big Chill" and "Big Rip", where an increasingly granular nature of expanding space modifies our life-supporting laws of physics. Our tripartite framework also clarifies when it is valid to make the popular quantum gravity approximation that the Einstein tensor equals the quantum expectation value of the stress-energy tensor, and how problems with recent attempts to explain dark energy as gravitational backreaction from super-horizon scale fluctuations can be understood as a failure of this approximation.

Plant density affects measures of biodiversity effects

Aims: We tested for the effect of final sowing plant density (i.e. density of established seedlings) on the values of biodiversity effects [transgressive overyielding, net effect, complementarity effect (CE) and selection effect (SE), trait-dependent complementarity and dominance effect] in a glasshouse pot experiment. Methods: We conducted a single-season (4 months) glasshouse experiment. Species monocultures and mixtures containing up to four common meadow species from different functional groups were sown and subsequently thinned to five density levels (8–128 individuals per pot, i.e. 200–3200 individuals m � 2 ). Community functioning was characterized by yield (both living and dead biomass) of all constituent species. Important Findings: Our results show that plant density (final sowing density in our case, but this finding can be generalized) affects the yields of both monocultures and mixtures. As these and their relationships are the basis for calculation of biodiversity effects, these effects also varied along the density gradient. Net biodiversity effect, CE and SE all increased with density. The net biodiversity effect and the CE switched from negative to quite positive in the four-species mixture. Using Fox’s tripartite partitioning, trait-dependent complementarity was minor in comparison to the dominance effect. One of our experimental species did not follow the density–productivity relationship, called constant final yield (CFY), which was reflected in the biodiversity measures. The shape of the density–productivity relationship for experimental species affects also the values of biodiversity indices, particularly when species do not follow the CFY relationship. According to our data and recent simulation experiments, the values of commonly used biodiversity effects can be rather misleading if a species has, e.g. a unimodal dependence of yield for the density gradient and the density level used in the experiment is higher than the peak density.

Impacts of species interactions on grass community productivity under contrasting management regimes

Productivity-diversity relationships are routinely described mainly in terms of species richness. However, these relationships can be affected by the functional strategy and physiological plasticity characterizing each species as they respond to environment and management changes. This study, therefore, aimed to analyze species interactions in grass communities presenting the same number of species (n = 6) but different growth strategies, and the impact on community productivity across several forms of field management (two different fertilizer application rates, i.e. 120 and 360 kg N ha(-1) year(-1), and two cutting frequencies, i.e. 3 and 6 cuts per year). For this purpose, we applied the tripartite partitioning method introduced for the analysis of biodiversity effects (BE). Grass species were cultivated on small plots (4.2 m(2)) in both mixtures and monocultures. Different management regimes altered both net BE and its component effects: dominance and potential for complementarity. A higher cutting frequency significantly reduced net BE, via a reduction in dominance effect. We found that increased N supply could either increase or decrease complementary effect according to grass mixture composition, i.e. species strategy. Regardless of management intensity, net BE was in general significantly positive especially when including individual species-specific plasticity effects. We conclude that a combination of different grasses has a positive effect on community biomass. Furthermore, both the functional strategy and the functional plasticity of component species play an important role in the intensity of BE. Therefore, biological mechanisms leading to enhanced biomass in six-grass communities are as effective for productivity as management conditions.

Partitioning the mechanisms by which genetic diversity of parasite infections affects total parasite load

Genetically‐diverse parasite infections are common in nature, however what mechanisms influence parasite load are still under debate. Rauch et al. found consistently lower parasite loads in genetically‐mixed infections compared to uniform infections. Using the additive partition of Loreau and Hector they demonstrated that this lower parasite load was due to negative complementarity effects, but they only found weak selection effects. Complementarity effects arise from differentiation among genotypes that accrue equally to all genotypes, while selection effects arise from unexpectedly high performance of certain genotypes in mixed infections. However, selection effects might arise either because genotypes with certain traits perform unexpectedly well in mixed infections at the expense of other genotypes (‘dominance effects’, DEs), or because genotypes with certain traits perform unexpectedly well, but not at the expense of others genotypes (‘trait dependent complementarity effects’, TDCEs). Here, we reanalyze the data of Rauch et al. using the tripartite partition of Fox to separate DEs, TDCEs and trait‐independent complementarity effects (TICEs, corresponding to the complementarity effect of Loreau and Hector). We found significantly negative TDCEs that contribute strongly to the low parasite loads in mixed infections. We suggest novel, testable hypotheses to explain negative TDCEs. Ours is the first study to demonstrate consistently‐strong TDCEs, which are rare in studies of the productivity of plant mixtures. Our results highlight the importance of testing for TDCEs, rather than assuming them to be small. We discuss the interpretation and value of the tripartite partition as an analytical tool complementary to more mechanistic approaches.

Detecting the role of individual species for overyielding in experimental grassland communities composed of potentially dominant species

Several studies have shown that the contribution of individual species to the positive relationship between species richness and community biomass production cannot be easily predicted from species monocultures. Here, we used a biodiversity experiment with a pool of nine potentially dominant grassland species to relate the species richness-productivity relationship to responses in density, size and aboveground allocation patterns of individual species. Aboveground community biomass increased strongly with the transition from monocultures to two-species mixtures but only slightly with the transition from two- to nine-species mixtures. Tripartite partitioning showed that the strong increase shown by the former was due to trait-independent complementarity effects, while the slight increase shown by the latter was due to dominance effects. Trait-dependent complementarity effects depended on species composition. Relative yield total (RYT) was greater than 1 (RYT>1) in mixtures but did not increase with species richness, which is consistent with the constant complementarity effect. The relative yield (RY) of only one species, Arrhenatherum elatius, continually increased with species richness, while those of the other species studied decreased with species richness or varied among different species compositions within richness levels. High observed/expected RYs (RYo/RYe>1) of individual species were mainly due to increased module densities, whereas low observed/expected RYs (RYo/RYe<1) were due to more pronounced decreases in module density (species with stoloniferous or creeping growth) or module size (species with clearly-defined plant individuals). The trade-off between module density and size, typical for plant populations under the law of constant final yield, was compensated among species. The positive trait-independent complementarity effect could be explained by an increase in community module density, which reached a maximum at low species richness. In contrast, the increasing dominance effect was attributable to the species-specific ability, in particular that of A. elatius, to increase module size, while intrinsic growth limitations led to a suppression of the remaining species in many mixtures.

Overyielding and stable species coexistence

The concept of overyielding originated in plant sciences in the 1950s and 1960s and was widely used in the following decades to assess whether mixtures of plants performed better than expected when compared with monocultures. Overyielding has re-emerged in the last few years as an important method in the analysis of biodiversity experiments (Hector, 1998; Loreau, 1998; Loreau et al., 2001, 2002; Hooper et al., 2005) and other new research areas (Bernasconi et al., 2003). Biodiversity experiments manipulate community diversity (while holding other factors constant) to investigate impacts on ecosystem functioning. Previously, use of the overyielding concept has been limited mainly to the analysis of community ecology experiments on species interactions and in agricultural research, particularly intercropping. However, there has been relatively little work that assesses the overyielding concept in the context of community ecology theory. Loreau (2004) used the classical Lotka–Volterra competition model to investigate overyielding and functional redundancy of species in the context of theory on the stable coexistence of species (Fig. 1). In this issue, Beckage & Gross (pp. 140–148) also use Lotka–Volterra competition models to assess the frequency and degree of overyielding of theoretical communities.

Interpreting the ‘selection effect’ of biodiversity on ecosystem function

AbstractExperimental ecosystems often function differently than expected under the null hypothesis that intra‐ and interspecific interactions are identical. Recent theory attributes this to the ‘selection effect’ (dominance by species with particular traits), and the ‘complementarity effect’ (niche differentiation and/or facilitative interactions). Using the Price Equation, I show that the ‘selection effect’ only partially reflects dominance by species with particular traits at the expense of other species, and therefore is only partially analogous to natural selection. I then derive a new, tripartite partition of the difference between observed and expected ecosystem function. The ‘dominance effect’ is analogous to natural selection. ‘Trait‐independent complementarity’ occurs when species function better than expected, independent of their traits and not at the expense of other species. ‘Trait‐dependent complementarity’ occurs when species with particular traits function better than expected, but not at the expense of other species. I illustrate the application of this new partition using experimental data.