Computational protocol: Experimental evidence that the Ornstein-Uhlenbeck model best describes the evolution of leaf litter decomposability

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[…] The litter decomposition constant k-values (hereafter, called k-values in short) were calculated for each species as follows (Olson ): the mass remaining was ln-transformed; the regression slope of the ln-transformed percent mass remaining against time is the species' exponential decay constant k (d−1).All k-values and species traits were ln-transformed to fit the normality and variance homogeneity assumptions before analyses. In order to test the relationship between k-values and different species leaf traits, we carried out multiple regressions of k-values against all the species traits and selected the best multiple regression models that described that relationship. The multiple regression analysis was accomplished by using the ‘regsubsets’ function in the ‘leaps’ package (R software, developed by R Development Core Team). Subsequently, we carried out a simple regression of k-values against each single trait, respectively.We used both the Akaike's Information Criterion (AIC) and the AICc to compare different models, where the latter was recommended in studies with small sample size (Symonds and Moussalli ). Several parameters could help us select the best model: (1) the smallest AIC or AICc (i.e., closest to ‘truth’); (2) ▵i, that is, the difference between the AIC value of the best model and the AIC value for each of the other models. The ▵i values less than two were considered to be essentially as good as the best model and ▵i values up to six should not be discounted (Richards ); (3) the evidence ratio (ER), which provided a measure of how much more likely the best model is than other models; (4) the Akaike weight (wi), which could also help us to assess the relative strengths of each candidate model (Burnham and Anderson ). In this article, we mainly used the AICc and the Akaike weight as the criteria of best model selection both in the multiple regression analysis and the phylogenetic analysis below. Note that different criteria of model selection usually provide us consistent results for the best model selection.We used the gene-based phylogeny (“time-tree”) from Zanne et al. (), which included only 39 of 48 species, but has genetic estimates of branch lengths. To get a complete sampling, we estimated the phylogeny of all 48 species using ‘Phylomatic’ software online (; see Appendix S1). The species names and the taxonomic levels followed the APG III (Bremer et al. ). For resolving polytomies, randomization was carried out with the help of the function of ‘multi2di’ in the package of ‘picante’ (Purvis and Garland ; Davies et al. ). Branch length of Phylomatic phylogeny was estimated using the ‘Bladj’ function in the ‘Phylocom’ software. We performed all the phylogenetic analyses across both phylogenies (‘Phylocom’ phylogeny and ‘Gene sequence’ phylogeny). In addition, we explored the effect of a single gymnosperm species (Ginkgo biloba) on the results of phylogenetic analyses (Appendix S2). Those results were similar to what we show in the Results section (see below).Three compatible models were considered in the model fitting procedure: (1) a BM model: a random walk model and also a fundamental model for other evolutionary models; (2) an EB model: its net rate of evolution slows exponentially through time as the radiation proceeds (a BM process with a time-dependent dispersion parameter; Blomberg et al. ; Freckleton and Harvey ); and (3) an OU model: a random walk with a ‘rubber-band’ and the trait values are limited to a certain range (Hansen ; Butler and King ). Statistically, the main difference among those three models was the number of parameters in each model. The BM model includes two main parameters: one represents the ancestral state value for the clade; the other is a ‘net rate’ estimate of trait evolution (Felsenstein ; Ackerly ). Compared to the BM model, the EB model includes one more parameter describing the pattern of rate change through time, whereas the OU model includes two more parameters than BM model: one representing the trait optimum and the other representing the strength of the ‘rubber-band’ values back toward the optimum. However, the OU model also includes BM model as a special case (Butler and King ).Under each model, the trait values follow a multivariate normal distribution and a covariance matrix, which is determined by the model and phylogenetic tree. We modeled the evolution of k-values and species traits with maximum likelihood methods using the ‘fitContinuous’ function in GEIGER (Harmon et al. ). This function can fit various likelihood models for continuous character evolution and returns parameter estimates and the likelihood for univariate data sets (Help file for GEIGER). Two main input data were required in this analysis: phylogeny and each single trait data, and in both data files species names should be listed in the same order. Moreover, several parameters should be included in the ‘fitContinuous’ function: the target model and the bounds for each model, that is, the range to constrain parameter estimates. We used the default values for the bounds of three evolutionary models we studied. In addition, we accounted for the effect of measurement error by adding variation to the diagonal of the expected among-species variance–covariance matrix (O'Meara et al. ), which might cause a significant bias in evolutionary rate reconstruction (Martins ). However, the results of model fitting are very similar with and without accounting for measurement error (See Results and Appendix S3). We compared fits of three different models using the Akaike information criterion (AICc and the Akaike weight). We also calculated “phylogenetic half-life”, the time it takes for the expected trait value to move half the distance from the ancestral state to the primary optimum (Hansen ). It can be estimated as t1/2 = ln(2)/α, in which α represents the “rubber-band” parameter within OU models, which can be estimated using the ‘fitContinuous’ function. […]

Pipeline specifications

Software tools Phylomatic, Picante, Phylocom, GEIGER
Application Phylogenetics
Chemicals Carbon