Some Large-Sample Tests for Nonnormality in the Linear Regression Model

Nutrient-dependent cross-kingdom interactions in the hyphosphere of an arbuscular mycorrhizal fungus

Introduction

The hyphosphere of arbuscular mycorrhizal (AM) fungi is teeming with microbial life. Yet, the influence of nutrient availability or nutrient forms on the hyphosphere microbiomes is still poorly understood.

Methods

Here, we examined how the microbial community (prokaryotic, fungal, protistan) was affected by the presence of the AM fungus Rhizophagus irregularis in the rhizosphere and the root-free zone, and how different nitrogen (N) and phosphorus (P) supplements into the root-free compartment influenced the communities.

Results

The presence of AM fungus greatly affected microbial communities both in the rhizosphere and the root-free zone, with prokaryotic communities being affected the most. Protists were the only group of microbes whose richness and diversity were significantly reduced by the presence of the AM fungus. Our results showed that the type of nutrients AM fungi encounter in localized patches modulate the structure of hyphosphere microbial communities. In contrast we did not observe any effects of the AM fungus on (non-mycorrhizal) fungal community composition. Compared to the non-mycorrhizal control, the root-free zone with the AM fungus (i.e., the AM fungal hyphosphere) was enriched with Alphaproteobacteria, some micropredatory and copiotroph bacterial taxa (e.g., Xanthomonadaceae and Bacteroidota), and the poorly characterized and not yet cultured Acidobacteriota subgroup GP17, especially when phytate was added. Ammonia-oxidizing Nitrosomonas and nitrite-oxidizing Nitrospira were significantly suppressed in the presence of the AM fungus in the root-free compartment, especially upon addition of inorganic N. Co-occurrence network analyses revealed that microbial communities in the root-free compartment were complex and interconnected with more keystone species when AM fungus was present, especially when the root-free compartment was amended with phytate.

Conclusion

Our study showed that the form of nutrients is an important driver of prokaryotic and eukaryotic community assembly in the AM fungal hyphosphere, despite the assumed presence of a stable and specific AM fungal hyphoplane microbiome. Predictable responses of specific microbial taxa will open the possibility of using them as co-inoculants with AM fungi, e.g., to improve crop performance.

Examining the Role of Student Responsiveness in Treatment Effects of a Tier 2 Program Targeting Reductions in Problem Behavior

Student responsiveness's role in promoting intervention outcomes for students who exhibit problem behavior is understudied. Due to the relational nature of many interventions delivered by teachers that target social, emotional, or behavioral outcomes of students in classrooms, it is essential to assess how responsive students are to teachers' attempts to engage them in the intervention, particularly for students with problem behaviors that may impede teachers' attempts to engage these students in intervention effectively. In the current study, we combine samples from four randomized controlled trials to examine the relationship between student outcomes and teacher attempts to deliver BEST in CLASS, a Tier 2 intervention, via student responsiveness. Delivery of BEST in CLASS and student responsiveness were assessed through direct observations and teachers' reported measures. Results suggest that teacher adherence and competence in delivering BEST in CLASS practices was associated with reductions in problem behavior from pretest to post-test via student responsiveness. Limitations of the current study and implications for future research are discussed.

Mycorrhiza governs plant-plant interactions through preferential allocation of shared nutritional resources: A triple (13C, 15N and 33P) labeling study

Plant-plant interactions and coexistence can be directly mediated by symbiotic arbuscular mycorrhizal (AM) fungi through asymmetric resource exchange between the plant and fungal partners. However, little is known about the effects of AM fungal presence on resource allocation in mixed plant stands. Here, we examined how phosphorus (P), nitrogen (N) and carbon (C) resources were distributed between coexisting con- and heterospecific plant individuals in the presence or absence of AM fungus, using radio- and stable isotopes. Congeneric plant species, Panicum bisulcatum and P. maximum, inoculated or not with Rhizophagus irregularis, were grown in two different culture systems, mono- and mixed-species stands. Pots were subjected to different shading regimes to manipulate C sink-source strengths. In monocultures, P. maximum gained more mycorrhizal phosphorus uptake benefits than P.bisulcatum. However, in the mixed culture, the AM fungus appeared to preferentially transfer nutrients (33P and 15N) to P.bisulcatum compared to P. maximum. Further, we observed higher 13C allocation to mycorrhiza by P.bisulcatum in mixed- compared to the mono-systems, which likely contributed to improved competitiveness in the mixed cultures of P.bisulcatum vs. P. maximum regardless of the shading regime. Our results suggest that the presence of mycorrhiza influenced competitiveness of the two Panicum species in mixed stands in favor of those with high quality partner, P. bisulcatum, which provided more C to the mycorrhizal networks. However, in mono-species systems where the AM fungus had no partner choice, even the lower quality partner (i.e., P.maximum) could also have benefitted from the symbiosis. Future research should separate the various contributors (roots vs. common mycorrhizal network) and mechanisms of resource exchange in such a multifaceted interaction.

The Influence of Land Use Evolution on the Visitor Economy in Wuhan from the Perspective of Ecological Service Value

This research used transfer matrix, dynamic attitude, and a linear regression model to investigate the characteristics of land-use change and evolution of ecological service values and their impacts on Wuhan’s visitor economy. The results showed that: (1) the land-use scale in the Wuhan metropolitan area changed significantly from 1990 to 2018. The area of arable land, forest land, and grassland decreased at a faster rate, whereas that of water and construction land continued to increase; (2) there were differences in the dynamic attitudes of land-use at different stages. The dynamic attitude of construction land-use changed the most with cultivated land, water area, forest land, unused land, and grassland. From 1990 to 2005, land-use change exhibited a relatively gentle trend, whereas from 2005 to 2020, it accelerated; (3) although land-use regulation service, support service, and cultural service values positively responded to tourism economic growth, their influences were dissimilar. This study clarifies the effects of urban land-use on tourism economic development and provides a reference for its effective control.

Confounder detection in linear mediation models: Performance of kernel-based tests of independence

It is well-known that the identification of direct and indirect effects in mediation analysis requires strong unconfoundedness assumptions. Even when the predictor is under experimental control, unconfoundedness assumptions must be imposed on the mediator-outcome relation in order to guarantee valid indirect-effect identification. Researchers are therefore advised to test for unconfoundedness when estimating mediation effects. Significance tests to evaluate unconfoundedness usually rely on an instrumental variable (IV)-that is, a variable that is nonindependent of the explanatory variable and, at the same time, independent of all exogenous factors that affect the outcome when the explanatory variable is held constant. Because IVs may be hard to come by, the present study shows that confounders of the mediator-outcome relation can be detected without making use of IVs when variables are nonnormal. We show that kernel-based tests of independence are able to detect confounding under nonnormality. Results from a simulation study are presented that suggest that these tests perform well in terms of Type I error protection and statistical power, independent of the distribution or measurement level of the confounder. A real-world data example from the Job Search Intervention Study (JOBS II) illustrates how the presented approach can be used to minimize the risk of obtaining biased indirect-effect estimates. The data requirements and role of unconfoundedness tests as diagnostic tools are discussed. A Monte Carlo-based power analysis tool for sample size planning is also provided.

Direction dependence analysis: A framework to test the direction of effects in linear models with an implementation in SPSS

In nonexperimental data, at least three possible explanations exist for the association of two variables x and y: (1) x is the cause of y, (2) y is the cause of x, or (3) an unmeasured confounder is present. Statistical tests that identify which of the three explanatory models fits best would be a useful adjunct to the use of theory alone. The present article introduces one such statistical method, direction dependence analysis (DDA), which assesses the relative plausibility of the three explanatory models on the basis of higher-moment information about the variables (i.e., skewness and kurtosis). DDA involves the evaluation of three properties of the data: (1) the observed distributions of the variables, (2) the residual distributions of the competing models, and (3) the independence properties of the predictors and residuals of the competing models. When the observed variables are nonnormally distributed, we show that DDA components can be used to uniquely identify each explanatory model. Statistical inference methods for model selection are presented, and macros to implement DDA in SPSS are provided. An empirical example is given to illustrate the approach. Conceptual and empirical considerations are discussed for best-practice applications in psychological data, and sample size recommendations based on previous simulation studies are provided.

Significance tests to determine the direction of effects in linear regression models

Previous studies have discussed asymmetric interpretations of the Pearson correlation coefficient and have shown that higher moments can be used to decide on the direction of dependence in the bivariate linear regression setting. The current study extends this approach by illustrating that the third moment of regression residuals may also be used to derive conclusions concerning the direction of effects. Assuming non-normally distributed variables, it is shown that the distribution of residuals of the correctly specified regression model (e.g., Y is regressed on X) is more symmetric than the distribution of residuals of the competing model (i.e., X is regressed on Y). Based on this result, 4 one-sample tests are discussed which can be used to decide which variable is more likely to be the response and which one is more likely to be the explanatory variable. A fifth significance test is proposed based on the differences of skewness estimates, which leads to a more direct test of a hypothesis that is compatible with direction of dependence. A Monte Carlo simulation study was performed to examine the behaviour of the procedures under various degrees of associations, sample sizes, and distributional properties of the underlying population. An empirical example is given which illustrates the application of the tests in practice.

Direction of Effects in Multiple Linear Regression Models

Previous studies analyzed asymmetric properties of the Pearson correlation coefficient using higher than second order moments. These asymmetric properties can be used to determine the direction of dependence in a linear regression setting (i.e., establish which of two variables is more likely to be on the outcome side) within the framework of cross-sectional observational data. Extant approaches are restricted to the bivariate regression case. The present contribution extends the direction of dependence methodology to a multiple linear regression setting by analyzing distributional properties of residuals of competing multiple regression models. It is shown that, under certain conditions, the third central moments of estimated regression residuals can be used to decide upon direction of effects. In addition, three different approaches for statistical inference are discussed: a combined D'Agostino normality test, a skewness difference test, and a bootstrap difference test. Type I error and power of the procedures are assessed using Monte Carlo simulations, and an empirical example is provided for illustrative purposes. In the discussion, issues concerning the quality of psychological data, possible extensions of the proposed methods to the fourth central moment of regression residuals, and potential applications are addressed.