Tree configuration and ancestral reconstruction approach
Scientific names were standardized among data sets and brought up to date by querying species names against the International Plant Names Index (http://www.ipni.org/), Tropicos (http://www.tropicos.org/), The Plant List (http://www.theplantlist.org/) and the Angiosperm Phylogeny website (http://www.mobot.org/MOBOT/research/APweb/) for a total of 629 species for root traits and 643 species for vein density information, with 117 species shared between datasets. We based phylogenetic trees on a dated molecular phylogeny using seven genome regions compared among >30000 species (Zanne et al.2014). This phylogenetic tree matched 515 species from the root database and 492 species from the vein density database, which were thus used for statistical analysis and ancestral reconstructions. Finally, we assigned mycorrhizal state to all species in each phylogenetic tree for posterior analyses of coevolution between plant traits and mycorrhizal affiliation. Plants were grouped in five different phylogenetic clades, representing major lineages in the seed plant phylogeny: Gymnosperms, Magnoliids (Magnoliids + Basal Angiosperms), Monocots, Rosids (Rosids + Saxifragales) and Asterids (Asterids + Caryophyllales + Santalales).
First, based on trait information from extant species we illustrate the association between root traits and leaf venation in extant species creating a bivariate correlation (Fig. 1) and calculate the variation in root diameter, SRL and mycorrhizal affiliation among major seed plant clades (Fig. 2). To test hypothesis A) shifts in mycorrhizal state associated with root morphology changes were tested using the maximum possible number of species in each category using a logistic regression (OLR) and a phylogenetic logistic regression (PLR), using the package corHMM (Beaulieu et al. 2013). The PLR incorporates the phylogenetic relatedness among species to maximize the penalized likelihood of the logistic regression (Ives & Garland 2010, Tung, Ho & Ané 2014). Because the AM state is ancestral in seed plants, we compared root morphological traits between AM species to ECM or NM states. Since species classified as AMNM are found either with or without AM fungi based on ecological context (Brundrett 2009; Maherali et al. 2016), AMNM plants can be described as engaging in a facultative mutualism, which is distinct from either the AM or NM states (Moora 2014). Therefore, we also tested whether root morphology changed from the AM to the facultative AMNM state. Finally, because plants in the AMNM state can found in nature without mycorrhizae, we also tested whether root morphology changed with the transition from the AM to the combined AMNM + NM grouping. For all cases, we interpret significant logistic regressions as evidence that a shift in root morphology influenced the likelihood of a switch in mycorrhizal state.
To test hypothesis B, (shifts in root trait correspond with leaf and habit changes but independent from mycorrhizal association), we tested whether the association between leaf and root traits were significant even after accounting for mycorrhizal state and growth habit using phylogenetic generalized least squares models (PGLS) ANOVA models as implemented in the R package ape (version 5.0; Paradis et al.  2004). First, we tested four different evolutionary models (Brownian, Pagel, Martins and Garland, and Orstein-Uhlenbeck) to determine the best fit for the structural error in the model (Paradis and Claude 2002). Once Pagel’s structure was identified as the best fit for the data on the response variables (Diameter, SRL and RTD), we created models with root traits as dependent variables, and leaf vein density, growth habit (herb, shrub and tree) and mycorrhizal state (AM, ECM, AMNM and NM) as independent variables, and the phylogenetic variance-covariance matrix among species as the error structure of the model (101 species for Diameter, 94 species for RTD and SRL). We also calculate ordinary least square (OLS) tests for the same models, in order to determine how the phylogenetic correction influenced the results. For both models (OLS and PGLS), we tested the trend across all seed plants and within Magnoliids, Rosids and Asterids, but not within Monocots or Gymnosperms due to the paucity of leaf venation data for these two groups.
To visualize changes in root and leaf traits over time, we reconstructed ancestral states for each trait using the Zanne et al. (2014) phylogeny for seed plants. To reconstruct ancestral node values for vein density and root traits, we used a maximum likelihood (ML) estimation for continuous variables based on the assumption of Brownian dispersion of each character across the phylogeny (O’Meara et al. 2006, Revell et al. 2012). To do this, we created separate species-level phylogenies for each trait, and then we estimated node means and variances using the Rohlf (2001) recursive re-rooting algorithm as implemented in the function fastAnc in the packagephytools (Revell 2012) for R (ver 3.4.3, R Core Team 2017). For mycorrhizal state, which is a discrete variable, we used a continuous time Markov chain model using the function ace in ape(Paradis et al. 2004). To assign the probability that a particular node was in one of the mycorrhizal states (AM, ECM, NM), we calculated marginal estimations based on asymmetrical rates (“ARD” mode in the function ace ) given the phylogeny and tip states. To illustrate whether changes in root morphology occurred before or after mycorrhizal state transitions, we created scatterplots of node values for diameter and color coded accordingly with the estimated probability of mycorrhizal stages at each node, using a threshold of 75% as the minimum to switch mycorrhizal type from the ancestral AM to a new category (see Table S5) .