Determination of the structure of $γ$-alumina from interatomic potential and first-principles calculations: The requirement of significant numbers of nonspinel positions to achieve an accurate structural model

Determination of the structure of $γ$-alumina from interatomic potential and first-principles calculations: The requirement of significant numbers of nonspinel positions to achieve an accurate structural model. Paglia, G., Rohl, A. L, Buckley, C. E, & Gale, J. D Physical Review B - Condensed Matter and Materials Physics, 71(22):224115, June, 2005. ISBN: 1098-0121
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1. The distribution of relative abundances between the species of a plant community has been remarkably little analysed. We examine differences in relative abundance distribution (RAD) between different soil fertility levels, and trends through time in the development of a community, using data from three grassland experiments: Monks Wood grassland restoration, Park Grass long-term fertilizer trial and Compton grassland restoration. 2. Comparing plots with different fertilizer treatments, the evenness of plant species abundance was higher where phosphorus had been applied; other effects of soil fertility on evenness were inconsistent. There were no consistent effects of soil fertility on the relative fit of the Geometric, General Log-normal and Zipf-Mandelbrot models of RAD, contrary to previous theories. However, the Broken Stick model fitted relatively better, though still poorly in absolute terms, in plots with high species richness and where phosphorus had been applied. Parameter gamma of the General Log-normal distribution was higher in the high-nitrogen and species-poor plots, disproving the theory that gamma should be constant. Parameter beta of the Zipf-Mandelbrot model was higher in more species-rich and in high-phosphorus plots, a result not predicted in the literature. The variation in gamma and beta seems to be largely a reflection of the variation in evenness and in species dominance. The consistency in species dominance across space (rank consistency) was higher in plots with phosphorus addition. It is concluded that resource availability had little effect on which model of community assembly fitted. However, under high phosphorus conditions the community was more spatially consistent, and there was less dominance. 3. Through time, the evenness of species abundances increased, consistently between two separate experiments. Examining the shape of the abundance distribution at a more detailed level, there were no time trends in which relative abundance model fitted best, except that the fit of the Broken Stick model became less poor. However, the shape of the General Log-normal and Zipf-Mandelbrot curves, as seen in indices gamma and beta, respectively, changed through time, consistently between two separate experiments, supporting the implication from increased evenness of increasing niche diversification. Rank consistency increased in the early years of succession, then decreased, supporting the Three-phase succession model of Gitay & Wilson (1995), in which a middle 'building' phase has higher rank consistency than the preceding 'pioneer' phase or the succeeding 'mature' phase

@article{Paglia2005a,
title = {Determination of the structure of \$γ\$-alumina from interatomic potential and first-principles calculations: {The} requirement of significant numbers of nonspinel positions to achieve an accurate structural model},
volume = {71},
issn = {10980121},
doi = {10.1103/PhysRevB.71.224115},
abstract = {1. The distribution of relative abundances between the species of a plant community has been remarkably little analysed. We examine differences in relative abundance distribution (RAD) between different soil fertility levels, and trends through time in the development of a community, using data from three grassland experiments: Monks Wood grassland restoration, Park Grass long-term fertilizer trial and Compton grassland restoration. 2. Comparing plots with different fertilizer treatments, the evenness of plant species abundance was higher where phosphorus had been applied; other effects of soil fertility on evenness were inconsistent. There were no consistent effects of soil fertility on the relative fit of the Geometric, General Log-normal and Zipf-Mandelbrot models of RAD, contrary to previous theories. However, the Broken Stick model fitted relatively better, though still poorly in absolute terms, in plots with high species richness and where phosphorus had been applied. Parameter gamma of the General Log-normal distribution was higher in the high-nitrogen and species-poor plots, disproving the theory that gamma should be constant. Parameter beta of the Zipf-Mandelbrot model was higher in more species-rich and in high-phosphorus plots, a result not predicted in the literature. The variation in gamma and beta seems to be largely a reflection of the variation in evenness and in species dominance. The consistency in species dominance across space (rank consistency) was higher in plots with phosphorus addition. It is concluded that resource availability had little effect on which model of community assembly fitted. However, under high phosphorus conditions the community was more spatially consistent, and there was less dominance. 3. Through time, the evenness of species abundances increased, consistently between two separate experiments. Examining the shape of the abundance distribution at a more detailed level, there were no time trends in which relative abundance model fitted best, except that the fit of the Broken Stick model became less poor. However, the shape of the General Log-normal and Zipf-Mandelbrot curves, as seen in indices gamma and beta, respectively, changed through time, consistently between two separate experiments, supporting the implication from increased evenness of increasing niche diversification. Rank consistency increased in the early years of succession, then decreased, supporting the Three-phase succession model of Gitay \& Wilson (1995), in which a middle 'building' phase has higher rank consistency than the preceding 'pioneer' phase or the succeeding 'mature' phase},
number = {22},
journal = {Physical Review B - Condensed Matter and Materials Physics},
author = {Paglia, Gianluca and Rohl, Andrew L and Buckley, Craig E and Gale, Julian D},
month = jun,
year = {2005},
note = {ISBN: 1098-0121},
keywords = {0705Tp, 6166Fn, numbers: 6112Ld},
pages = {224115},
}

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Parameter gamma of the General Log-normal distribution was higher in the high-nitrogen and species-poor plots, disproving the theory that gamma should be constant. Parameter beta of the Zipf-Mandelbrot model was higher in more species-rich and in high-phosphorus plots, a result not predicted in the literature. The variation in gamma and beta seems to be largely a reflection of the variation in evenness and in species dominance. The consistency in species dominance across space (rank consistency) was higher in plots with phosphorus addition. It is concluded that resource availability had little effect on which model of community assembly fitted. However, under high phosphorus conditions the community was more spatially consistent, and there was less dominance. 3. Through time, the evenness of species abundances increased, consistently between two separate experiments. 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Parameter gamma of the General Log-normal distribution was higher in the high-nitrogen and species-poor plots, disproving the theory that gamma should be constant. Parameter beta of the Zipf-Mandelbrot model was higher in more species-rich and in high-phosphorus plots, a result not predicted in the literature. The variation in gamma and beta seems to be largely a reflection of the variation in evenness and in species dominance. The consistency in species dominance across space (rank consistency) was higher in plots with phosphorus addition. It is concluded that resource availability had little effect on which model of community assembly fitted. However, under high phosphorus conditions the community was more spatially consistent, and there was less dominance. 3. Through time, the evenness of species abundances increased, consistently between two separate experiments. 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