Effect of soil structure on temporal and spatial dynamics of bacteria

Soil is a complex heterogeneous system comprising of highly variable and dynamic micro-habitats that have significant impacts on the growth and activity of resident microbiota. A question addressed in this research is how soil structure affects the temporal dynamics and spatial distribution of bacteria. Using repacked microcosms, the effect of bulk-density, aggregate sizes and water content on growth and distribution of introduced Pseudomonas fluorescens and Bacillus subtilis bacteria was determined. Soil bulk-density and aggregate sizes were altered to manipulate the characteristics of the pore volume where bacteria reside and through which distribution of solutes and nutrients is controlled. X-ray CT was used to characterise the pore geometry of repacked soil microcosms. Soil porosity, connectivity and soil-pore interface area declined with increasing bulk-density. In samples that differ in pore geometry, its effect on growth and extent of spread of introduced bacteria was investigated. The growth rate of bacteria reduced with increasing bulk-density, consistent with a significant difference in pore geometry. To measure the ability of bacteria to spread thorough soil, placement experiments were developed. Bacteria were capable of spreading several cm’s through soil. The extent of spread of bacteria was faster and further in soil with larger and better connected pore volumes. To study the spatial distribution in detail, a methodology was developed where a combination of X-ray microtopography, to characterize the soil structure, and fluorescence microscopy, to visualize and quantify bacteria in soil sections was used. The influence of pore characteristics on distribution of bacteria was analysed at macro- and microscales. Soil porosity, connectivity and soil-pore interface influenced bacterial distribution only at the macroscale. The method developed was applied to investigate the effect of soil pore characteristics on the extent of spread of bacteria introduced locally towards a C source in soil. Soil-pore interface influenced spread of bacteria and colonization, therefore higher bacterial densities were found in soil with higher pore volumes. Therefore the results in this showed that pore geometry affects the growth and spread of bacteria in soil. The method developed showed showed how thin sectioning technique can be combined with 3D X-ray CT to visualize bacterial colonization of a 3D pore volume. This novel combination of methods is a significant step towards a full mechanistic understanding of microbial dynamics in structured soils.

Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| < ∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts.