Computational protocol: Genetic Susceptibility, Colony Size, and Water Temperature Drive White-Pox Disease on the Coral Acropora palmata

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Protocol publication

[…] We took a Bayesian space-time modeling approach adapted from Cameletti and colleagues to analyze the presence or absence of white-pox disease on the monitored 69 colonies of A. palmata (). We let y(si,t) represent the realization of the spatio-temporal binomial process Y(·,·), which denotes the presence or absence of white-pox disease at colony i  =  1,…,d, located at si and day t = 1,…,T. We assumed that y(si,t)  =  z(si,t) β + ξ(si,t) + ε(si,t)where z(si,t) is [z1(si,t),…zp(si,t)] that represents the vector of p covariates for colony location si at time t. β is (β1,…,βp), the coefficient vector. ξ(si,t) is the realization of the state process, which is the unobserved level of disease occurrence that is assumed to be a spatio-temporal Gaussian field that changes over time with first order autoregressive dynamics. ε(si,t) is the measurement error defined by a Gaussian white-noise process (∼ N (0, σ2ε). We used the specified model with a binomial response variable . The output of the model provides the mean, the standard deviation, the 2.5% and 97.5% quantiles, and the mode for the correlation coefficients of each covariate. Significant values are those with 2.5% and 97.5% quantile ranges that do not span zero. Positive and negative values depict the direction of the association.Our approach used a Gaussian Markov Random Field (GMRF) function, which is a spatial process that models the spatial dependence of data observed on geographic regions . The GMRF computational properties were enhanced by using Integrated Nested Laplace Approximations (INLA) for Bayesian inference. INLA is a computationally effective algorithm that produces fast and accurate approximations of posterior distributions . All analyses were conducted using R version 3.0.1 and the INLA package (www.r-inla.org; see ).For the last decade, Markov Chain Monte Carlo (MCMC) techniques have been used in Bayesian analysis to predict the posterior marginal distribution. We note that INLA is a recent alternative to MCMC techniques in spatial-temporal modelling to predict the posterior marginal distribution. INLA techniques combine Gaussian Field with Matérn covariance functions to produce GMRFs by using stochastic partial differential equations (SPDE). This process speeds up the estimates and accuracy, and INLA does not have the same convergence problems as MCMC techniques. The SPDE approach also uses a finite element representation to define the Matérn field by triangulation of the domain. This approach is appropriate for our data, which were taken at irregular discrete locations on a coral reef ().Eight covariates were tested to determine whether they had a significant association with the presence or absence of white-pox disease on individual colonies through time (). These covariates included: the spatial location of each colony measured as (i) the easting, and (ii) the northing locations (as georeferenced Universal Transverse Mercator (UTM) units), (iii) colony size (in cm3), (iv) the number of previous incidences of white-pox disease for each colony (we note that, although some colonies may have had a long history of disease before our study commenced, we started every colony at zero at the commencement of our study), (v) the distance to the nearest neighboring colony, (vi) the distance from a previously infected colony, (vii) water temperature, and (viii) solar insolation. Because water temperature and solar insolation vary on scales larger than the size of Haulover Bay , these covariate values were the same for all colonies within each time step, but varied for each time step. To illustrate spatial patterns in coral colony density and intensity of disease activity, a kernel smoothed intensity function was applied and plotted to the point pattern spatial data using the spatstat package in R . […]

Pipeline specifications

Software tools Spdep, spatstat
Applications Miscellaneous, Conventional fluorescence microscopy
Diseases Leukoencephalopathies