Who Is and Is Not "Average'"? Random Effects Selection with Spike-and-Slab Priors

Mixed effects models are often employed to study individual differences in psychological science. Such analyses commonly entail testing whether between-subject variability exists, but this is typically the extent of such analyses. We argue that researchers have much to gain by explicitly focusing on the individual in individual differences research. To this end, we propose the spike-and-slab prior distribution for random effect selection in (generalized) mixed-effects models as a means to gain a more nuanced perspective of individual differences. The prior for each random effect, or deviation away from the fixed effect, is a two-component mixture consisting of a point-mass 'spike' centered at zero and a diffuse 'slab' capturing non-zero values. Effectively, such an approach allows researchers to answer questions about each particular individual; specifically, "who is average?'" in the sense of deviating from an average effect, such as the population-averaged or common slope. We begin with an illustrative example, where the spike-and-slab formulation is used to select random intercepts in logistic regression. This demonstrates the utility of the proposed methodology in a simple setting while also highlighting its flexibility in fitting different kinds of models. We then extend the approach to random slopes that capture experimental effects. In two cognitive tasks, we show that despite there being little variability in the slopes, there were many individual differences in performance. Most notably, over 25% of the sample differed from the common slope in their experimental effect. We conclude with future directions for the presented methodology.

Fine silt and clay content is the main factor defining maximal C and N accumulations in soils: a meta-analysis

When studying carbon (C) sequestration in soil, it is necessary to recognize the maximal storage potential and the main influencing factors, including the climate, land use, and soil properties. Here, we hypothesized that the silt and clay contents in soils as well as the clay mineralogy are the main factors affecting the maximal C and N storage levels of soils. This hypothesis was evaluated using a database containing the organic C contents of topsoils separated by ultrasonic dispersion to determine the particle size fractions. The slopes of the linear regressions between the C contents in silt and clay to the soil organic C (SOC) and between the N contents in silt and clay to the total N content were independent of the clay mineralogy (2:1, 1:1, calcareous soil, amorphous clays), climate type (tropical, temperate, and Mediterranean), and land use type (cropland, grassland, and forest). This clearly shows that the silt and clay content is the main factor defining an upper SOC level, which allowed us to propose a generalized linear regression (R2 > 0.95) model with a common slope, independent of the land use and climate type, to estimate the soil C sequestration potential. The implications of these findings are as follows: (1) a common slope regression was accurately calculated (0.83 ± 0.02 for C-silt + clay < 63 μm and 0.81 ± 0.02 for C-silt + clay < 20 μm) and (2) there was no asymptotic pattern found to support the existence of an SOC saturation pool.

Convergent nitrogen–phosphorus scaling relationships in different plant organs along an elevational gradient

A general relationship between the nitrogen (N) and phosphorus (P) content of all plant organs (e.g. leaf, stem, and root) is hypothesized to exist according to whole-plant economics spectrum (PES) theory, but the evidence supporting these expected patterns remains scarce. We measured the N and P content of the leaves, twigs and fine roots of 64 species in three different forest communities along an elevational gradient (evergreen broad-leaved forest, 1319 m a.s.l., coniferous and broad-leaved mixed forest, 1697 m a.s.l., and deciduous forest, 1818 m a.s.l.) in the Wuyishan National Nature Reserve, southeastern China. The scaling relationship between the N and P content and the linear regression relationship between the N:P ratio and N and P content were analysed. The leaf N and P content was significantly higher at the high-elevation site than at the low- or middle-elevation sites (P &lt; 0.001). The N and P content followed a power-law relationship with similar scaling slopes between organs. The N (common slope, 1.13) and P (common slope, 1.03) content isometrically covaried among leaves, twigs and roots. The scaling exponents of the N–P relationship were not significantly different from 1.0 in all organs, with a common slope of 1.08. The scaling constants of N–P decreased significantly (P &lt; 0.05) from the highest value in fine roots (β = 1.25), followed by leaves (β = 1.17), to the lowest value in twigs (β = 0.88). Standardized major axis (SMA) analyses and comparisons of 95 % confidence intervals also showed that the numerical values of the scaling slopes and the scaling constants did not differ regardless of elevation. The N content, but not the P content, accounted for a large proportion of the variation in the N:P ratio in leaves (N:P and N: r2 = 0.31, F = 33.36, P &lt; 0.001) and fine roots (N:P and N: r2 = 0.15, F = 10.65, P &lt; 0.05). In contrast, the N:P ratio was significantly related to both the N and P content in the twigs (N:P and N: r2 = 0.20, F = 17.86, P &lt; 0.001; N:P and P: r2 = 0.34, F = 35.03, P &lt; 0.001, respectively). Our results indicate that different organs of subtropical woody plants share a similar isometric scaling relationship between their N and P content, providing partial support for the PES hypothesis. Moreover, the effects of the N and P content on the N:P ratio differ between metabolic organs (leaves and fine roots) and structural organs (twigs), elucidating the stoichiometric regulatory mechanism of different organs.

Effect of Wetness Duration and Temperature on the Development of Anthracnose on Selected Almond Tissues and Comparison of Cultivar Susceptibility

Blossoms, leaves, fruit, and woody tissues of almond can be affected by anthracnose caused by Colletotrichum acutatum. Because the disease occurs throughout rainy spring seasons, the effect of temperature and wetness duration on disease development was evaluated in controlled studies. The lowest inoculum concentration where disease developed on leaves was 104 conidia/ml. Longer wetness durations were needed for leaves than for blossoms and disease increased linearly with increasing wetness durations. Inoculation temperature mainly affected final disease levels. Temperature during incubation affected the rate of disease development, while final disease levels were very similar at 10, 15, or 20°C. An analysis of covariance was performed to compare regressions of the effects of wetness and temperature on disease development for several almond cultivars. For blossom inoculations at 15°C in growth-chamber studies, a common slope model was statistically sufficient to describe all four cultivars. Cultivar Nonpareil (NP) had a significantly (P < 0.05) lower adjusted means at the midpoint than cultivars Carmel (CA), NePlus Ultra (NU), and Wood Colony (WC). For blossom inoculations at 20°C and for leaf inoculations at all temperatures evaluated, an unequal slope model was statistically justified for comparing regression lines. For blossoms, the slopes were significantly different (P < 0.05) for pair-wise comparisons of CA-NU, NU-WC, and NP-WC. For leaves, most of the cultivars responded differently to infection at different temperatures. Two of the pair-wise comparisons demonstrated unequal slopes at all three temperatures evaluated (i.e., NU-NP and NU-WC). Overall, for blossoms and leaves, NP was the least susceptible, NU was the most susceptible, and WC and CA showed an intermediate susceptibility. In field blossom and fruit studies, a common slope model was statistically sufficient to describe all four cultivars. NP had a significantly lower midpoint (i.e., was less susceptible) than CA or WC, whereas no significant difference (P > 0.1) occurred in comparisons between CA and WC.

Seasonal impacts on leaf attributes of several tree species growing in three diverse ecosystems of south-eastern Australia

Patterns of leaf attributes were examined for six woody species growing in a eucalypt woodland, a mangrove, or a heathland in coastal New South Wales, Australia, during winter and summer. It was found that the rate of assimilation per unit leaf dry mass (Amass) of the mangrove species was largest, woodland species exhibiting an intermediate rate and heathland species the smallest values of Amass. Mean habitat Amass did not change from winter to summer in the woodland or mangrove species but increased significantly in the heathland species. Average specific leaf area (SLA) was largest for the mangrove species and smallest for the heathland species, with woodland species showing intermediate values. SLA of all species within a habitat did not change from winter to summer. Mean foliar nitrogen (Nmass) of the mangrove species was highest, intermediate for woodland species and lowest for heathland species. Nmass was significantly related to Amass in both summer and winter and the individual slopes for this relationship in the summer and winter differed. In contrast, a common slope was fitted to the relationship between SLA and Amass for the two seasons. A common slope between seasons was also shown for the relationship between SLA and Nmass. There was no significant difference in slope elevation between summer and winter for the SLA v. Nmass relationship. Trends within relationships among leaf attributes were the same as those found for a wide range of plant species worldwide, but the absolute values were lower than those found elsewhere. Therefore, the 'global relationships' in terms of trends (positive or negative) that have been determined overseas apply in Australia but the elevation of the slope and the magnitude of the slope are reduced (Amass v. Nmass) or increased (Amass v. SLA and Nmass v. SLA) compared with global trends.

Conglomérats polygéniques ophiolitiques: anciens éboulis de talus de fond océanique?

Field observations on the polygenetic conglomerates associated with the ophiolitic complexes in the Eastern Townships are comparable to those on the common slope facies in the present-day ocean bottom. Sedimentary processes (submarine erosion, deposition) are probably responsible for the internal structures of the conglomerates. This working hypothesis replaces the explosion-origin interpretation previously proposed. [Journal Translation]