Computational protocol: Linking Ecology and Epidemiology to Understand Predictors of Multi-Host Responses to an Emerging Pathogen, the Amphibian Chytrid Fungus

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Protocol publication

[…] Phylogenetic signal can be defined as a pattern of trait variation whereby more closely related species have more similar traits (i.e., trait disparity among species is correlated with the phylogenetic distance that separates them). We tested for phylogenetic signal in host responses to Bd and our explanatory variables (i.e., species habitat affiliations, ecological associations and life history traits) using a standard measure of phylogenetic signal: Blomberg’s K []. Blomberg’s K varies between zero and ∞, with values of zero indicating phylogenetic independence, values <1 indicating partial phylogenetic dependence (i.e., weaker signal) than expected under a Brownian motion model of character evolution, and values >1 indicating greater phylogenetic dependence than expected under Brownian motion. Blomberg’s K was calculated for all three measures of susceptibility to chytrid fungus (our response variables) as well as all predictor variables used to build models of susceptibility. Evolutionary trends among response variables were visualized using maximum likelihood ancestral character reconstruction [] with the software package Picante v1.6–2 [], implemented in R v3.0.1. Two phylogenetic trees were used to quantify phylogenetic distance among species (). One tree was based on previous studies of anuran phylogeny and assumed a speciational model of trait evolution (i.e., all branch lengths were set to one), and the other tree was estimated via maximum likelihood from 2500 bp of mitochondrial sequence data obtained from GenBank. Further details of the methods used to create these two trees are detailed in . The statistical significance of observed signal was assessed using a randomization procedure [] and 1000 permutations per trait. Evolutionary trends among response variables were visualized using maximum likelihood ancestral character reconstruction []), implemented in the R package ape v 3.1–4 []. We used phylogenetic least squares (PGLS) implemented using the R package Caper v. 0.5 [] to construct models of response variables [], and additionally tested for non-linear relationships among variables with generalized additive models (GAM) implemented in mgcv v 1.7–28 [].Preliminary analyses showed that some of the response variables and many of the predictor variables showed weak but statistically significant phylogenetic signal. We therefore initially used a phylogenetically informed method, phylogenetic generalized least squares (PGLS, []), to construct models of response variables. This method was implemented using the R package Caper v. 0.5 []. A priori we had identified a number of variables that might explain variation in the response variables, but lacked evidence as to which would be most important or even if all of the explanatory variables would be correlated with all of the response variables. Therefore, for each response variable, we compared the AICc scores (using AICc rather than AIC scores to correct for the small sample sizes from which our models were constructed), of models that included every possible combination of response variables. When fitting our PGLS models we used a maximum likelihood estimate of lambda [], a measure of phylogenetic signal similar to Blomberg’s K, to determine the amount of phylogenetic correction to be applied to variables in the model. Somewhat surprisingly, the maximum likelihood value of lambda estimated by Caper invariably proved to be zero, indicating that no phylogenetic correction was applied to variables included in a given model (). This generally indicates a lack of phylogenetic signal in the residual error of a PGLS model []. Further exploratory analyses confirmed that forcing the inclusion of phylogenetic correction by manually setting lambda values other than zero hurt overall model fits and result in inflated AICc scores.One limitation of the PGLS method is that it assumes that linear relationships between predictor and response variables. To determine the direction of relationships between predictor and response variables and to test for possible nonlinear relationships between predictor and response variables we reconstructed all of our best fitting models, defined as the set of models with AICc scores that differed by less than two from that of the model with the lowest AICc score for a given response variable using generalized additive models (GAM) implemented in mgcv v 1.7–28 []. In basic terms, a GAM is a type of generalized linear model that can detect non-parametric relationships by incorporating smoothing functions [–]. Each smoothing function allows for some departure from strict linearity, and in mgcv model fits are evaluated using penalized likelihood so that the simplest model that is a reasonable fit to the data is preferred []. With the exception of geographic range area and lifespan, these analyses confirmed that the relationship between predictor and response variables were linear, and thus that the assumptions of the PGLS analysis had been met, with two notable exceptions (). […]

Pipeline specifications

Software tools PHYSIG, Picante, APE
Application Phylogenetics
Organisms Fungi, Batrachochytrium dendrobatidis