Epidemics in Networks of Spatially Correlated Three-dimensional Root Branching Structures

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common 'SIR' epidemiological model onto the bond percolation problem, we show how the spatially-correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants, render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.Comment: 21 pages, 8 figure

Complexity and anisotropy in host morphology make populations safer against epidemic outbreaks

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to analyse separately the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.Comment: 21 pages, 8 figure

Spatial patterns of tree yield explained by endogenous forces through a correspondence between the Ising model and ecology.

Spatial patterning of periodic dynamics is a dramatic and ubiquitous ecological phenomenon arising in systems ranging from diseases to plants to mammals. The degree to which spatial correlations in cyclic dynamics are the result of endogenous factors related to local dynamics vs. exogenous forcing has been one of the central questions in ecology for nearly a century. With the goal of obtaining a robust explanation for correlations over space and time in dynamics that would apply to many systems, we base our analysis on the Ising model of statistical physics, which provides a fundamental mechanism of spatial patterning. We show, using 5 y of data on over 6,500 trees in a pistachio orchard, that annual nut production, in different years, exhibits both large-scale synchrony and self-similar, power-law decaying correlations consistent with the Ising model near criticality. Our approach demonstrates the possibility that short-range interactions can lead to long-range correlations over space and time of cyclic dynamics even in the presence of large environmental variability. We propose that root grafting could be the common mechanism leading to positive short-range interactions that explains the ubiquity of masting, correlated seed production over space through time, by trees

Two Phase Transitions for the Contact Process on Small Worlds

In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random from the grid. This modification is natural if one thinks of a town where an individual's interactions at school, at work, or in social situations introduces long-range connections. However, this change dramatically alters the behavior of the contact process, producing two phase transitions. We establish this by relating the small world to an infinite "big world" graph where the contact process behavior is similar to the contact process on a tree.Comment: 24 pages, 6 figures. We have rewritten the phase transition in terms of two parameters and have made improvements to our original result

Evaluating the connectivity, continuity and distance norm in mathematical models for community ecology, epidemiology and multicellular pathway prediction

The main global threats of the biosphere on our planet, such as a global biodiversity impairment, global health issues in the developing countries, associated with an environmental decay, unnoticed in previous eras, the rise of greenhouse gasses and global warming, urge for a new evaluation of the applicability of mathematical modelling in the physical sciences and its benefits for society. In this paper, we embark on a historical review of the mathematical models developed in the previous century, that were devoted to the study of the geographical spread of biological infections. The basic notions of connectivity, continuity and distance norm as applied by successive bio-mathematicians, starting with the names of Volterra, Turing and Kendall, are highlighted in order to demonstrate their usefulness in several new areas of bio-mathematical research. These new areas include the well-known fields of community ecology and epidemiology, but also the less well-known field of multicellular pathway prediction. The biological interpretation of these abstract mathematical notions, as well as the methodological criteria for these interpretative schemes and their corroboration with empirical evidence are discussed. In particular, we will focus on the boundedness norm in polynomial Lyapunov functions and its application in Markovian models for community assembly and in models f

A rigorous statistical framework for spatio-temporal pollution prediction and estimation of its long-term impact on health

In the United Kingdom, air pollution is linked to around 40000 premature deaths each year, but estimating its health effects is challenging in a spatio-temporal study. The challenges include spatial misalignment between the pollution and disease data; uncertainty in the estimated pollution surface; and complex residual spatio-temporal autocorrelation in the disease data. This article develops a two-stage model that addresses these issues. The first stage is a spatio-temporal fusion model linking modeled and measured pollution data, while the second stage links these predictions to the disease data. The methodology is motivated by a new five-year study investigating the effects of multiple pollutants on respiratory hospitalizations in England between 2007 and 2011, using pollution and disease data relating to local and unitary authorities on a monthly time scale

Plant Microbial Interactions in Wheat: Fusarium Head Blight and Arbuscular Mycorrhizal Fungi

Plant microbial interactions consist of the many relationships between plants and microbes which involve studies that observe the biology and molecular genetics of pathological, symbiotic, and associative interactions. Worldwide studies involving these interactions are scarcely available in wheat (Triticum aestivum L.). In South Dakota (SD), wheat research is a major platform used to understand the nature and consequences of these interactions. Specifically, our research efforts here at South Dakota State University (SDSU) concentrate on two different, but valuable, interactions in wheat: the fungal pathogen that causes fusarium head blight (FHB) and the symbiotic interaction of arbuscular mycorrhizae fungi (AMF) with wheat. These interactions were selected to help provide a better understanding of plant microbial interactions in wheat. In our first project, we studied FHB, which is one of the most devastating plant diseases in the world. It is responsible for significant economic loss due to lower crop yield and quality, as well as human health concern due to mycotoxin accumulation in infected grains. To date, no sources of resistance conferring complete resistance to FHB have been identified in wheat. Using double haploid (DH) populations derived from selected four-way crosses combining several sources of resistance, we developed wheat lines that display resistance to FHB. Screening evaluations followed by selections were conducted using both DH spring and winter wheat populations to further evaluate the potential usage of this material to enhance adapted wheat germplasms. Selection for resistance quantitative trait loci (QTL’s) and the use of fungicide (Prosaro) are two different approaches, which when combined, may present a better way of minimizing disease damage. We conducted a field experiment to evaluate the effect of combining resistance QTL’s and fungicide application on FHB severity. In our second project we studied AMF, which forms a mutualistic symbiotic interaction with the majority of land plants. Like many plant microbial interactions, not much information is available on AMF and wheat. Consequently, we conducted a field study to examine the contribution of AMF to nutrient uptake and biomass yields of spring wheat genotypes. Our results demonstrate that there are differences in mycorrhizal responsiveness and nutrient efficiency with the presence of AMF on wheat. This could suggest that there is a genetic control of these genotypic differences. Overall, our findings assist ongoing efforts aimed to describe the causes and benefits of these plant microbial interactions. Our studies are potential baselines that can assist both development and production of wheat and other major crops