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Pyron & Wiens – Electronic Supplementary Material
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1. Phylogeny and divergence-time estimation
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A detailed description of the primary phylogenetic analysis (maximum likelihood [ML] topology
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estimation) is given in our previous study [1]. The extensive concordance of the ML topology
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with previous estimates of amphibian phylogeny is discussed in that paper [1]. Discordance with
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previous estimates involves a few weakly supported branches, and the majority (64%) of nodes
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are well supported [1]. The final concatenated alignment consisted of up to 12712 bp for each of
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2871 species (2,394 frogs, 436 salamanders, and 176 caecilians), including data from up to 12
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genes (3 mitochondrial, 9 nuclear), 43.7% of the 6576 species in our database (5,817 frogs, 583
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salamanders, and 41 caecilians). The full DNA-sequence matrix is available in DataDryad
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doi:10.5061/dryad.vd0m7.
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In the present study, we estimated divergence times for this tree topology using a C++
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implementation of r8s [2] called "sk8s," recently developed by S.A. Smith (pers. comm.). This
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implementation has been released under the new title “treePL” [3]. Both r8s and sk8s utilize the
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same penalized likelihood (PL) algorithm [2]. This algorithm estimates evolutionary rates and
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divergence dates on a tree given a set of fossil constraints and a smoothing factor determining the
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amount of among-branch rate heterogeneity. Following standard methodology, we determined
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the optimal smoothing factor empirically using cross-validation [2], with the root age fixed (see
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below) due to computational constraints. We tested six values for the smoothing parameter (0.01,
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0.1, 1, 10, 100, and 1000), graduated by orders of magnitude across a reasonable range given
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empirical datasets [2]. The cross-validation analysis yielded an optimal smoothing-parameter
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value of 1. Subsequent analyses were run with fixed-age constraints on the nodes listed below,
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given the computational difficulties of dating trees of this size using minimum and maximum
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ages [4], and the existence of mostly concordant divergence-time estimates for amphibians that
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can be used as an existing framework for analysis [5]. This strategy incorporates a prior on the
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root [2, 6] and a number of other nodes, while estimating ages for other clades of interest.
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Based on previous recommendations [7, 8], we placed a constraint on the Amniote-
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Amphibia divergence (the root of the tree) at 330.4 Ma (million years ago). This is based on the
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oldest known fossils of Lepospondyli, the sister group to either Lissamphibia or Reptiliomorpha
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[6, 9-11], and the youngest Whatcheriidae, a sister group to Tetrapoda [12]. The fossil age-
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estimate for this clade is broadly consistent with several recent estimates based on molecular
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clock analyses [6, 11, 13, 14]. To estimate the ages of internal nodes of interest, we fixed a series
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of nodes above the family level, using dates from a recent study of the origins of the major
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lissamphibian groups [5]. While other studies have looked at broad-scale age estimates in
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amphibians [11, 15-17], they lack wide taxonomic sampling. We confirmed the stratigraphic and
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paleontological fit of these dates with several recent reviews of lissamphibian origins [11, 18].
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We attempted to identify nodes that spanned the temporal and taxonomic breadth of the
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higher-level structure of the tree, but that were not too close together (i.e. we did not choose to
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constrain all possible nodes, nor any direct ancestor-descendant pairs). In some cases, the shape
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of the trees necessitated constraining the stem-group age of the most recent common ancestor
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(MRCA) of some families in order to enforce the necessary constraint. However, all crown-
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group ages and most stem-group ages were freely estimated for the nodes of interest (i.e.
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families). We fixed the following internal nodes using estimated ages from ref. [5] based on the
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results of a PL analysis of a slow-evolving nuclear gene with multiple fossil calibration points:
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i) Cryptobranchoidea
The MRCA of Hynobiidae and Cryptobranchidae: 164.50 Ma.
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ii) Sirenoidea
The MRCA of Sirenidae and the non-cryptobranchoid caudates: 199.59 Ma.
iii) Salamandroidea
The MRCA of Salamandridae and Ambystomatidae: 167.22 Ma.
iv) Plethodontoidea
The MRCA of Rhyacotritonidae, Amphiumidae, and Plethodontidae: 133.03 Ma.
v) Leiopelmatoidea
The MRCA of Ascaphidae and Leiopelmatidae: 202.04 Ma.
vi) Pipoidea
The MRCA of Pipidae and Rhinophrynidae: 190.42 Ma.
vii) Discoglossoidea
The MRCA of Discoglossidae, Alytidae, and Bombinatoridae: 160.07 Ma.
viii) Pelobatoidea
The MRCA of Scaphiopodidae, Pelodytidae, Pelobatidae, and Megophryidae: 155.73 Ma.
ix) Ranoidea
The MRCA of Ranidae and Microhylidae et al.: 111.90 Ma.
x) Hyloidea
The MRCA of Bufonidae, Eleutherodactylidae, Hylidae et al.: 73.53 Ma.
xi) Gymnophiona
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The MRCA of extant caecilians: 108.65 Ma.
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Note that all tree-based analyses use only the single dated chronogram derived from the
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unique ML tree with estimated branch-lengths [1]. This tree has 64% of nodes with "strong"
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support (>70% bootstrap support), and alternative topological arrangements could conceivably
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affect our results. However, it is not computationally feasible at present to run these analyses
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(e.g. GeoSSE, QuaSSE) over a large sample of trees that are of the size that we use here.
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Furthermore a large sample of time-calibrated trees is not available, and generating one would be
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extremely difficult. For example, widely used Bayesian methods (e.g. [19]) for simultaneous
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estimation of divergence times and phylogeny would be too computationally intensive for the
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dataset used here (2,871 taxa). Furthermore, generating multiple time-calibrated trees from sk8s
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would also be challenging, since it would require re-estimating the maximum likelihood
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topology many times (bootstrap trees from RAxML include only topologies and molecular
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branch length estimates are necessary for divergence dating with penalized likelihood).
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The insensitivity of our results to variation in topology and branch lengths is suggested
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by another analysis that utilized this tree and found strong concordance between estimates of
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phylogeny-related parameters (e.g. phylogenetic diversity) generated using our topology and
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alternative trees [20]. Also, a large-scale phylogenetic study similar to ours found that
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incorporating phylogenetic uncertainty into estimates of diversification rates did not show a
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strong effect of topological variance on estimated rates or on geographic patterns in their
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distribution [21].
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Despite the limitations imposed by the large size of our tree, our estimates of topology
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and divergence times are broadly concordant with a large body of literature dealing with higher-
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level amphibian phylogeny [5, 17, 22, 23]. The stability of these estimates suggests that
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topological uncertainty (mostly towards the terminals) is unlikely to substantially affect the
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estimates presented. Notably, our estimates of divergence times are particularly concordant with
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another multi-locus study with extensive taxon sampling that used Bayesian method of
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divergence-time estimation [23], as well as others incorporating fossils directly [11].
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2. Distributional and climatic data
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Species range maps were used to obtain data on species richness and climatic niches. Range
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maps (polygons stored as ESRI shapefiles) were downloaded from the 2008 update of the IUCN
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Global Amphibian Assessment (GAA; http://www.iucnredlist.org/initiatives/amphibians),
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accessed in January, 2009, for the 6119 species of amphibian covered by that database. These
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were matched against our taxonomic database, resulting in range maps for 93% (6117; omitting
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two taxa that are of ambiguous taxonomic status in recent classifications) of the 6576 species in
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our database, 5421 frogs, 546 salamanders, and 150 caecilians, ~87% of the ~7000 total
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currently described species listed by AmphibiaWeb [24]. When necessary, disjunct range
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segments were dissolved into multi-part features to extract the centroid. Polygons representing
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introduced ranges or vagrants (as defined in the IUCN metadata) were removed from the dataset.
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The ranges were then projected using the Cylindrical Equal Area projection, similar to
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previous studies [25]. We then extracted the mean, variance, and range for the selected climatic
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and environmental data using zonal statistics summaries (i.e. means of climatic variables within
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polygons). Zonal statistics were processed using Geospatial Modelling Environment v0.3.4b
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(http://www.spatialecology.com/gme/). To avoid the omission of range-restricted species, we
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resampled the AET data at 2.5 min (~5 km) spatial resolution using nearest-neighbor
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interpolation to match the NPP and BIOCLIM data, so that smaller ranges would intersect fully
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with a point on the data layer. For some species still omitted at that resolution, we obtained data
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by extracting values for the polygon centroid.
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A small number of species occur outside of the limits of the scale of the data projection,
such as endemics on small islands, and had no data values for some of the variables. All 6117
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species had data for the 19 BIOCLIM variables, whereas 333 (5%) were missing entries for AET
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and 30 (0.5%) lacked information for NPP. A total of 356 species (6%) were thus missing data
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for 2 of the 21 variables, 223 of which were represented in the phylogeny (8% of the tips), for a
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total of 0.2% missing data cells among the species in the tree. Rather than remove these species
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due to this small amount of missing data, we imputed the absent values using the maximum-
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likelihood Expectation-Maximization (EM) method [26], which has been shown to perform well
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under empirical conditions, without inflating variance or Type I error [27]. Thus, we have 100%
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data coverage for 6117 species (~90% of ~7000 total species), for 21 climatic and environmental
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variables (AET, NPP, and 19 BIOCLIM variables). Of the 2871 species in the phylogeny, 2794
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had ecological data (missing species lacked range maps entirely in the GAA assessment). Thus,
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all phylogenetic analyses of ecological traits used a pruned tree, representing only those 2794
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species with climatic data.
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This analysis has some potential drawbacks. Primarily, we are integrating across range
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maps without considering variation in presence or absence within the bounded range. For
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example, a species that occurs in several valleys between mountains may have a polygon that
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crosses the mountain tops, and thus our data would include climatic data from higher elevations
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where the species does not occur, potentially biasing estimates for that species. However, there
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are two aspects of this dataset that should help to alleviate this problem. First, the range maps
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were individually drawn by taxonomic experts, and should thus include a minimum of
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extralimital areas. Second, the analyses performed using these data (e.g. QuaSSE) incorporate
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uncertainty in trait measurements (see below), and can thus partially account for these errors.
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We then performed Principal Components Analysis (PCA) on the summary values for
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each species to reduce the 21 environmental variables (AET, NPP, and the 19 climatic variables),
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many of which are expected to be strongly correlated [28]. Given that traditional PCA does not
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account for the phylogenetic non-independence of species, we used the phylogenetically
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corrected PCA method [29], calculated with the dated chronogram described below. Code for
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performing these calculations in R is available from RAP. We extracted the first PC axis (PC1)
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for use in further analyses (see below). The first PC axis explains 33% of the variation in these
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variables (table S1). The variables with the strongest negative loadings (<-0.90) are BIO1 (Mean
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Annual Temperature; -0.96), BIO6 (Minimum Temperature of Coldest Month; -0.97), BIO9
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(Mean Temperature of Driest Quarter; -0.91), and BIO11 (Mean Temperature of Coldest
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Quarter; -0.95). Positive variable loadings were weaker, with BIO7 (Temperature Annual Range;
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0.54) the only factor loading greater than 0.5 (table S2).
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In future analyses, including more PC axes might be beneficial. However, we only used
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PC1 for several reasons. The first is computational complexity. Each QuaSSE analysis required
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several weeks to complete, and this would have been difficult for multiple variables. Ideally, an
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analysis of multiple variables would need to be conducted simultaneously, so that estimated rates
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reflected response curves from all variables. This is theoretically possible using QuaSSE [30],
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but has not been implemented in any currently available packages [31]. More importantly, PC1
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strongly reflects temperature variables that have previously been shown to be important
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correlates of amphibian diversity [32]. Most importantly, the QuaSSE results are strongly
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significant (see below). Thus, including additional PC axes will not overturn our results; PC1
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shows a significant relationship with speciation and extinction rates, regardless of whether or not
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other PC axes are significant (or in which direction). The other major axes (PC2–4) are also
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correlated with latitude (Pearson’s correlation coefficient: rP = 0.25, -0.54, 0.75, all p < 0.00001;
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respectively), and will thus presumably support the same pattern of temperate to tropical
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imbalances in speciation and extinction.
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3. Biogeographic regions
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To allow reconstruction of the timing of colonization and length of occupancy of the various
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temperate and tropical ecoregions, we first assigned all 6576 species in our database (including
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the 2871 species in the tree) to one or more ecoregions in a global set of 12 biogeographic
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provinces, using the GAA range maps. The 12 ecoregions follow from commonly used
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definitions in herpetology and biogeography [33–36]. While some ambiguity about the limits of
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these ecoregions may exist, they correspond closely with both geography and species
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distributions, and represent major areas of amphibian diversity and endemism [33]. They are:
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Tropical South America: Tropical regions of South America, ranging from the Colombia-
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Panama border to the latitudinal level of Buenos Aires, excluding the high-elevation southern
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Altiplano (see below under Temperate South America). We defined the boundary between
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Middle and South America as the Panama/Colombia border.
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Tropical Middle America: Including Central America, Baja California Sur, and tropical
regions of Mexico, including Sonora on the Pacific coast, and Tamaulipas on the Gulf coast.
Temperate South America: Southern South America, including Patagonia, the Pampas of
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Argentina and Uruguay, and the high-elevation Altiplano extending into Bolivia and
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southeastern Peru.
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West Indies: The Caribbean Islands, including the Antilles and the Bahamas. Does
not include coastal islands such as Trinidad, Bonaire, Curacao, Aruba, or Cozumel.
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Nearctic: Temperate North America, including the continental United States, Canada, the
central Mexican Plateau, and the Mexican state of Baja California.
Afrotropical: Sub-Saharan Africa and the southern Arabian Peninsula (i.e. Yemen and
southern Oman).
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Western Palearctic: Europe (i.e. west of the Caspian Sea), North Africa (Mauritania to
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Egypt), the northern portion of the Arabian Peninsula (excluding Yemen and southern Oman),
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and northwestern Iran.
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Eastern Palearctic: Temperate Asia east of the Caspian Sea, excluding the tropical
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provinces of southern China (Yunnan, Guangxi, southern Sichuan, Guangdong, Hainan, Hong
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Kong, Macau, and Fujian) and including the major islands of Japan (but not the southern Ryukyu
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Islands). Includes Afghanistan and southeastern Iran.
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Madagascar: Including Madagascar and adjacent islands (i.e. Mauritius, the Seychelles,
and the Comoros).
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Australasia: includes Australia, New Zealand, New Guinea, and islands to the east (e.g.
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Solomon Islands, Fiji, Vanuatu, New Caledonia). Includes the Maluku Islands. Separated from
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Southeast Asia by Weber's Line [37].
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Southeast Asia: Tropical East Asia, from Myanmar to the Lesser Sunda islands, including
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southeast China (Yunnan, Guangxi, Guangdong, Hainan, Hong Kong, Macau, and Fujian
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provinces), Taiwan, the southern Ryukyu Islands, and the Philippines. Separated from Oceania
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by Weber's Line.
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South Asia: The Indian subcontinent, from Pakistan to Bangladesh, including Sri Lanka,
Nepal, and Bhutan.
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Note that species-accumulation curves are still nearly vertical in many of these areas (e.g.
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the Amazon basin, New Guinea; [33, 38]), and new species are still being discovered even in
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relatively well-known areas such as the eastern United States [39]. While absolute diversity is
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likely underestimated in every ecoregion, the proportional differences (i.e. the latitudinal
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gradient) should be reflected in the existing species counts. Undescribed and cryptic diversity
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could also conceivably affect our analyses of speciation, extinction, and dispersal rates (see
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below). However, two aspects of our analyses alleviate these concerns. First, our rate estimates
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are based on phylogenetic branch-length information, not species counts alone, and should thus
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be relatively robust to missing species. Second, our results show higher speciation rates in
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tropical clades even though these clades are more poorly sampled (see below) and these
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differences in rates would only be magnified by including a large number of undescribed tropical
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species (given the relatively safe assumption that most new species will belong to existing
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families).
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4. Mid-domain effect
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As a first test of potential explanations for the latitudinal gradient in diversity, we tested for the
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mid-domain effect (MDE), a putatively non-biological explanation for richness gradients. The
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MDE is the tendency for multiple overlapping ranges to result in a latitudinal gradient, due solely
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to random shuffling of ranges within a bounded geometric domain [40, 41]. Note that we are not
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interested in addressing the MDE as a neutral model for explaining species assemblages in a
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macroecological context. Instead, we simply confirm that the latitudinal diversity gradient in
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amphibians is statistically significant and presumably has a biological origin (i.e. related to rates
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of speciation, extinction, and dispersal) rather than being explained solely by random range
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shuffling. However, we think that the latitudinal gradient might still have a biological origin,
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even if we were unable to reject the MDE hypothesis.
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We tested for the MDE pattern across all amphibians, and then separately in frogs,
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salamanders, and caecilians. For each analysis, we shuffled the empirical range limits 1000 times
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to generate 95% confidence intervals on the expected latitudinal distribution of species richness
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under the mid-domain model, given the observed latitudinal ranges of the species in our dataset
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(i.e. midpoints were randomly shuffled while the range widths were the same as those observed
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empirically). We compared these confidence intervals to the empirical richness-latitude curve to
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determine if the observed patterns differed significantly from the expected null distribution.
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These calculations were performed using Mid-Domain Null [42], with the observed latitudinal
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ranges from 5421 frog species, 546 salamanders, and 150 caecilians.
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Overall, amphibians show a significant deviation from null expectations under the MDE
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model (Fig. 1). The peak amphibian species richness occurs at 6 degrees north of the equator
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(880 species), significantly more than the 229 species expected under the MDE model.
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Accordingly, there are significantly fewer species than expected above 41 degrees north, and
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below 33 degrees south. Similar patterns of significant tropical peaks and temperate deficiencies
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are observed in frogs (837 species at 6 degrees north, with fewer species than expected above
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and below 33 degrees) and caecilians (37 species at 5 degrees north, with fewer than expected
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beyond 28 degrees north and 30 degrees south). Salamanders also reject the MDE null model, as
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their diversity peak is in temperate latitudes, with a peak of 120 species at 37 degrees north,
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declining significantly beyond expectations at 57 degrees north and 1 degree south. Although
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salamanders exhibit a significant extratropical diversity peak, they still contribute to high tropical
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diversity, as a major tropical radiation occurs in Bolitoglossinae [22, 43, 44].
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5. Tree-based analyses
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Differences in species richness between regions must ultimately be explained in terms of the
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processes of speciation, extinction, and dispersal (the only processes that directly change the
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number of species in a region). Therefore, any sufficient explanation for the higher species
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richness of tropical regions should address the following questions: (i) how do rates of
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speciation, extinction, and dispersal vary between temperate and tropical regions, and (ii) how do
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ecological factors, such as the climatic niche of species, affect rates of diversification (speciation
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– extinction)? These questions can be addressed most powerfully in a large-scale phylogenetic
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framework, using recently developed methods designed to address these questions [30, 45]. We
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used two approaches to determine whether or not rates of speciation, extinction, and dispersal
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varied between temperate and tropical clades, and whether or not these differences were
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influenced by ecological variables such as climate and ecosystem energy. The first considers the
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explicit effects of biogeographic region on rates of speciation, extinction, and dispersal
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(GeoSSE), and the second considers the effects of a quantitative trait, climatic niche (PC1) in
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this case, on rates of speciation and extinction (QuaSSE). Simulations using the framework these
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algorithms are based on (BiSSE) suggest that a minimum of 300 tips and 10% sampling of each
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state is necessary to detect significance [46]; our dataset vastly exceeds these parameters (see
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below). We tested these hypotheses as follows:
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(a) Biogeographic analysis
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To test for differences in rates of speciation, extinction, and dispersal between temperate and
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tropical areas, we used the recently developed Geographic-state Speciation and Extinction
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method (GeoSSE) [45] as implemented in the R package 'diversitree' [30]. The GeoSSE method
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is an extension of the BiSSE (Binary-State Speciation and Extinction) method [47], which tests
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whether speciation and extinction rates vary as a function of a binary character. In contrast to
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BiSSE, however, GeoSSE interprets the binary character in an explicitly biogeographic context,
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where a species can occur in one of two regions, A (tropical) or B (temperate), or both regions
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simultaneously (AB). Thus, there are parameters for speciation rate in states A, B, and AB (sA,
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sB, and sAB,), extinction rate in states A and B (xA and xB), and dispersal from A to B and vice
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versa (dA and dB), for a total of seven parameters. All of these parameters are of interest, as all
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may contribute to latitudinal variation in species richness [48–50].
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The primary question addressed in this analysis is whether or not rates of speciation,
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extinction, and dispersal vary between temperate and tropical zones (where all temperate
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ecoregions are considered to be one region and all tropical ecoregions are considered another).
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As there are parameters estimated for each of these rates for each region, some, all, or none of
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these parameters may be significantly different between regions. Thus, we tested a set of 10
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distinct models using the time-calibrated tree described above. We first tested a model in which
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all parameters were free to vary (7 parameters). We then compared this model to a set of
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constrained submodels, in which one or more rates were set to be equal between regions. We
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also tested submodels in which there were no speciation events unique to species that spanned
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both regions (called “intermediate speciation” for brevity below), such that species in the AB
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region had speciation rates of zero. This yields a total of 10 models:
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1) sA, sB, sAB, xA, xB, dA, dB (7 parameters)
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2) sAB = 0 (no intermediate speciation, 6 parameters)
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3) sA = sB (speciation equal between regions, 6 parameters)
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4) xA = xB (extinction equal between regions, 6 parameters)
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5) dA = dB (dispersal symmetric between areas, 6 parameters)
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6) sA = sB, xA = xB (speciation and extinction equal between areas, 5 parameters)
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7) sA = sB, dA = dB (speciation and dispersal equal between areas, 5 parameters)
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8) dA = dB, xA = xB (dispersal and extinction equal between areas, 5 parameters)
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9) sA = sB, xA = xB, dA = dB (equal speciation, extinction, and dispersal, 4 parameters)
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10) sA = sB, xA = xB, dA = dB, sAB = 0 (no intermediate speciation, 3 parameters)
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We coded each species as AB, A, or B based on the ecoregions in which it is found. We
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considered Tropical South America, Tropical Middle America, West Indies, Afrotropics,
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Madagascar, South Asia, Southeast Asia, and Oceania as tropical, and Temperate South
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America, Nearctic, Western Palearctic, and Eastern Palearctic as temperate. The GeoSSE model
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also accounts for incomplete taxon sampling by taking into account the proportion of taxa in
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each state (e.g. A, B, or AB) included in the phylogeny, using essentially the same algorithm as
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BiSSE and QuaSSE [30, 51]. As we had already categorized all 6576 species into one of those
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states, we were able to calculate this directly: the 2871-species phylogeny contains 75% of
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species that occur in both areas (84 of 112), 39% of tropical species (2257 of 5802), and 80% of
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temperate species (530 of 662). We used AIC to discriminate between models, choosing the
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lowest delta AIC score (dAIC hereafter). Of the ten possible models, the best-fit was one in
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which all seven parameters were free to vary, with a dAIC of 4 and an AIC weight (wAIC
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hereafter) of 0.88, indicating that this model is 7.3 times more likely than the next most-likely
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model in which extinction rates are equal between the two areas (wAIC = 0.12; Table S3).
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(b) Climatic-niche analysis
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The second major question in our tree-based analyses is whether or not climate drives the higher
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rates of species accumulation (net diversification) in the tropics revealed by the GeoSSE
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analyses. We tested the hypothesis that environmental variables drive higher rates of net
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diversification in tropical regions compared to temperate areas [50, 52, 53]. To examine the
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potential impact of climate on diversification, speciation, and extinction rates, we tested for trait-
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dependent diversification related to the climatic niche (PC1, as described above), using the
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recently developed Quantitative State Speciation and Extinction (QuaSSE) algorithm [30]
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implemented in the R package 'diversitree.' This algorithm takes a phylogeny and set of trait
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measurements for the tip species in the tree and fits a series of birth-death models in which the
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speciation and extinction probabilities along branches vary as a function of the trait values. This
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allows for a comparison of models in which diversification and trait evolution are independent to
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those in which rates of diversification are related to trait values. Simulations have shown that this
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method can accurately estimate rates using a large-scale phylogeny such as ours [30].
Due to computational and other constraints (see main text), we were unable to test a wide
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range of variables using QuaSSE, and therefore focused on the first principal component axis
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(PC1) from the analysis of 21 environmental variables. PC1 accounted for 33% of the variation
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in climatic variables among the species included (table S1). The starting values for model-fitting
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were the maximum-likelihood estimates of initial rates and parameters estimated in QuaSSE and
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the mean value of PC1 across all species (the mean of species means). We used a generic
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variance for all species' standard deviations (1 / 20), following the author's recommendations
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[30].
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We ran two sets of tests, one in which extinction rates were constant and only speciation
rates varied as a function of trait values, and one in which both rates varied with traits. We fit
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models in which speciation and extinction rates were constant with respect to climatic niche (e.g.
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rate is invariant with respect to trait value, the null expectation), versus those in which they were
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sigmoidal (positive or negative logistic relationship between rate and trait value) or hump-shaped
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(rate peaks at intermediate trait values). We chose sigmoidal and hump-shaped models as they
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present the clearest biological interpretation, where rates are a monotonic (sigmoidal) or normal
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(hump-shaped) function of the trait. We did not compare linear models (e.g. rates are linear
349
functions of the trait) since they do not asymptote, and linear models are subsumed by the
350
sigmoidal model [30]. Models were compared using the AIC calculated by QuaSSE, choosing
351
the model with the lowest dAIC. As with GeoSSE, QuaSSE accounts for missing taxa by
352
including a parameter for the proportion of species that are included in the phylogeny [30].
353
However, we recognize that this approach does not incorporate information about either the
354
biogeographic location (e.g. temperate vs. tropical) or the trait values of the missing species. The
355
proportion used was 0.42 (2794/6576), based on the total number of described amphibian species
356
in our taxonomic database, though as noted above this is likely an underestimate given the slope
357
of species-accumulation curves in the tropics.
358
The best-fit model indicates that both speciation and extinction rates exhibit sigmoidal
359
responses to climatic niche (PC1; table S4), significantly (dAIC > 20; wAIC = 1.0) better than
360
models in which only speciation rates varied. Speciation rates show a negative response to PC1
361
(PC scores ranging from -12.03159 to 45.36072), and a sigmoidal response-curve midpoint at
362
16.67742627 with a slope of 1.1825652. In contrast, extinction rates exhibit a positive
363
relationship with PC1, with a midpoint at 16.95949574 and a slope of 1.3188807. The BM
364
diffusion rate is 1.146715125. PC1 exhibits a significant positive latitudinal gradient (table 1),
365
indicating an increase in speciation rates and decrease in extinction rates in tropical regions.
366
Given the mathematical functions for the sigmoidal response curve [30], we were able to
367
estimate per-lineage speciation and extinction rates for all 6117 species.
368
We note that GeoSSE and QuaSSE provide similar estimates of minimum and maximum
369
speciation rates (GeoSSE: 0.038–0.057 lineages * my-1; QuaSSE: 0.049–0.058) and
370
diversification rates (GeoSSE: 0.030–0.057; QuaSSE: 0.028-0.055), but estimated extinction
371
rates differ somewhat (GeoSSE: 0.00001–0.008; QuaSSE: 0.0023–0.021). Nevertheless, both
372
methods estimate minimal (tropical) extinction rates close to zero, and extinction rates in the
373
temperate zone that are 1–2 orders of magnitude higher. We think tropical extinction rate
374
estimates for GeoSSE may be more accurate, given that it includes all species (both in the
375
phylogeny and not) and explicitly accounts for character states in unsampled species. In contrast,
376
QuaSSE accounts for all sampled and unsampled species in the phylogeny, but does not
377
incorporate trait values of unsampled species, and assumes random placement of unsampled
378
species on the tree. In addition, the correlation between PC1 and latitude is strong but not perfect
379
(R2 = 0.59); temperate species with more “tropical” niches may be obscuring estimates of tropical
380
extinction for QuaSSE. Finally, QuaSSE estimates the response of speciation and extinction to
381
the observed range of variation in a particular trait, and not necessarily the full range of that trait
382
that is inhabited by the species (values for each species are summaries only, not the full range of
383
conditions).
384
385
6. Clade-based analyses
386
To test similar hypotheses about variation in rates of speciation and extinction between
387
temperate and tropical clades using an alternative approach, we estimated evolutionary rates for a
388
set of 66 family level clades, accounting for virtually all known, extant amphibians. This allowed
389
us to test whether or not rates of speciation and extinction varied latitudinally among clades, and
390
whether this variation was related to environmental variables (i.e. climate, energy). We also
391
investigated the possibility that there were diversity-dependent effects on diversification (not
392
explicitly addressed by GeoSSE or QuaSSE), and whether or not these were related to
393
environmental variables. We tested these hypotheses within clades as follows:
394
395
(a) Evolutionary rates and species richness
396
To further test the results from GeoSSE and QuaSSE, we next asked whether or not variation in
397
species richness among clades was related to variation in evolutionary rates (i.e. speciation and
398
extinction), and whether or not these rates varied with environmental variables. We identified 66
399
non-nested, family-level lineages to which we could confidently assign species not included in
400
the phylogeny (all known amphibian species are assigned to genera, and almost all genera are
401
assigned to families, regardless of whether they are included in our analysis). This allowed us to
402
include almost all species of amphibians in our analyses. We used a recent family-level
403
classification derived from the same phylogeny used here [1].
404
For each clade, we estimated ecological, evolutionary, and temporal variables that are
405
potentially relevant for explaining richness patterns. Relevant data for each family are provided
406
in table S14. One particularly important variable is the ages of clades. In theory, the crown-group
407
ages of clades (i.e. oldest split within the group) may be underestimated if not all species are
408
included in the phylogeny, as in our case. However, most families contain multiple genera, and
409
so including all (or most) known genera in a family should usually ensure that the oldest split
410
within the family is included in our tree (monotypic families were excluded from analyses using
411
crown-group ages). Given that the genus-level sampling in this tree is 86% complete, the crown-
412
group age estimates for families should not generally be biased by the incompleteness of the
413
phylogeny. In contrast, the stem-group ages (i.e. the split between the clade and its sister group)
414
should be included for every family of amphibians, since only one species in the family needs to
415
be included to span the stem-group age.
416
Using the geographic range data for all species in each clade (family), we calculated the
417
mean latitudinal midpoint of the clade range as the absolute value of the mean of the latitudinal
418
midpoints of the species in that clade. We estimated the latitudinal range of the clade as the
419
difference between the minimum and maximum latitude occupied across all species in that clade.
420
We calculated the geographic range area for all clades, generating polygons covering the
421
geographic extent of each clade (see above), and measuring area in km2. For all 21 climatic and
422
environmental variables (e.g. 19 variables from the WorldClim database [28], AET, NPP), we
423
estimated clade means from the values of the species in each family as described above. From
424
the dated chronogram, we obtained both the stem and crown-group ages for each clade. We
425
determined the total number of species in each clade based on both species included in the
426
phylogeny and those assigned to the clade based on previous taxonomy (our database).
427
We estimated net diversification rates for each clade from the phylogeny (as all families
428
were represented in the tree) using phylogenetic estimators from Nee et al. [54], with their
429
modifications for incomplete sampling. These algorithms (eq. 20 and 21, as modified by eq. 33
430
and 34) yield estimates of birth-death diversification rates (r = speciation – extinction;  =
431
speciation / extinction) based on the distribution of branching times. These estimators appear to
432
be powerful and broadly applicable for estimating rates with well-sampled phylogenies [55, 56].
433
As the family-level assignment of almost all species is known from previous classifications [1],
434
we were able to calculate the sampling proportion for each clade, and adjust estimates of net
435
diversification rate accordingly as described by Nee et al. [54]. Code for these analyses in R is
436
available from RAP. We removed the family Telmatobiidae from all further clade-based
437
analyses, given that it was a clear outlier in net diversification rate (r = 0.28 vs. an average of
438
0.04), presumably indicating that the crown-group age was not correctly estimated with the given
439
taxon sampling in the phylogeny. Unlike most other anuran families, this species-rich family
440
consists of only one genus, and so extensive species sampling within the genus would be needed
441
to ensure that the earliest split (crown group) was included. However, we acknowledge that
442
another possibility is that the group has extraordinarily high diversification rates due to recent
443
diversification in the high Andes, or that both factors (rapid diversification, incomplete
444
sampling) may be involved.
445
The sampling proportion (percent of described species in family included in our tree)
446
ranges from 11% to 100%, with 17 families being 100% sampled (table S14). To determine if
447
incompleteness in sampling was affecting our rate estimates, we used multiple regression to
448
determine if net diversification rate (r) or relative extinction fraction () were related to sampling
449
proportion, while controlling for the number of species in the clade. When clade size is
450
accounted for using multiple regression, sampling proportion is not a significant contributor to
451
either r (p = 0.749) or  (p = 0.740).
452
Note that there are many potential sources of error in estimating these rates (e.g. clade
453
ages, species numbers), and that this uncertainty could potentially affect the power of the results.
454
However, it is not clear how to incorporate this error in a straightforward manner. Fortunately,
455
given the strength of the significance of our results (see below), it appears that our study has not
456
been strongly impacted by reduced power from such random errors. Furthermore, a recent study
457
incorporating topology-based variability in rate estimation did not find a strong effect [21].
458
In addition to diversification rates, we calculated the rate of climatic-niche evolution for
459
PC1 for each clade based on the Brownian Motion (BM) model (following [25]), using the
460
fitContinuous command in the GEIGER package [57]. We also reconstructed ancestral values of
461
PC1 at internal nodes using the BM model. It is possible that other models (e.g. Ornstein-
462
Uhlenbeck) may represent the best-fit for some of these clades, but both models incorporate the
463
same rate parameter (2), and it is unclear how to incorporate the additional parameters (e.g. )
464
of more complex models. These estimates of rates are based only on those species included in
465
the tree (for 62 clades with >1 species), but previous analyses suggest that there is no clear
466
relationship between rate estimates and completeness of taxon sampling [25]. Using our data
467
from 62 clades, we also find no relationship between sampling proportion and climatic-niche rate
468
(p = 0.072), accounting for clade size using multiple regression.
469
Another potential problem is that these analyses of rates are based on only PC1, which is
470
strongly related to latitude and is strongly influenced by temperature variables (but not
471
precipitation variables; table S2). Thus, important climatic variation may not be included (e.g.
472
major climatic variation within tropical and temperate regions, not simply between them). We
473
acknowledge that studies incorporating additional PCs may find stronger relationships between
474
climatic niche rates and other variables (e.g. diversification; [25]).
475
In a few clades, near zero-length terminal branches linking species pairs appeared to
476
corrupt calculations of rates (i.e. very high rates due to very short branches, where the short
477
branches may be related to recent mitochondrial introgression). Therefore, several species with
478
near-zero length branches were pruned from the tree for these analyses, which were chosen
479
arbitrarily as the first species in the tree for that species pair. We removed Dicamptodon
480
aterrimus, Necturus maculosus, Pelobates varaldii, Leptobrachium hasseltii, Occidozyga
481
borealis, Pseudacris maculata, Melanophryniscus stelzneri, Atelopus bomolochos, Bufo
482
houstonensis, and Bufo bankorensis.
483
For all family-level clades, we thus obtained estimates of eleven variables: species
484
richness, stem and crown age, area, energy proxies (AET, NPP, and BIO1; taken as the average
485
across all species in the family from the range-map estimates described above), net
486
diversification rate, relative extinction fraction, and climatic-niche rate as described above (table
487
S14). We first tested for latitudinal gradients in these variables (table 1). We then constructed
488
multiple regression models in R linking species richness, diversification rate, and climatic-niche
489
rate to age, area, and energy (AET, NPP, and BIO1), which represent potential causal factors or
490
ecological correlates (see below for specific sets of variables tested). Our latitudinal gradient
491
analysis (table 1) includes multiple correlations of important variables (e.g. species richness,
492
diversification rate) against latitude, potentially inviting use of a correction such as a sequential
493
Bonferroni [58]. However, the use of this correction has several mathematical and logical
494
problems for ecological studies [59], though we note that all results in table 1 would still be
495
significant under such a correction.
496
For the clade-based analyses, we first tested for a correlative relationship between species
497
richness within clades and the environmental factors of area and three variables that may be
498
related to energy (AET, NPP, and BIO1). We find significant positive species-area and species-
499
energy relationships (NPP), with BIO1 as a non-significant factor (table S5). However, variation
500
in richness among clades can only be attributed directly to the effects of age and diversification
501
rates. We therefore tested models relating species richness to independent factors including stem-
502
and crown-age, net diversification rate, and relative extinction fraction (table S6). We then
503
attempted to determine which ecological factors influence net diversification rate and relative
504
extinction fraction. We tested the total area occupied by the clade, proxies for energy (AET,
505
NPP, and BIO1), and rates of climatic-niche evolution (Brownian Motion [BM] model for PC1)
506
(tables 7, 8). Climatic-niche rate was not significantly related to net diversification rate (unlike
507
previous analyses of some amphibian subclades; [25]), and we did not test this variable further.
508
509
(b) Diversity dependence
510
Complex interactions between evolutionary rates, species richness, and ecological variables may
511
also affect the latitudinal diversity gradient [60-63]. We tested whether or not estimated carrying
512
capacities vary latitudinally, and whether this potential relationship provides a possible
513
mechanism relating latitudinal environmental variation to speciation and extinction. To test for
514
the potential effects of diversity dependence, we compared the fit of birth-death, monotonic
515
decay (i.e. decreasing speciation rate without diversity dependence), linear diversity dependence
516
(DDL), and exponential diversity dependence (DDX) models [64] in the R package LASER [65].
517
We tested these LASER models first, which do not account for missing species or consider
518
extinction, as a preliminary test for diversity dependence. We used them because the model of
519
monotonic decay of speciation rate, which is the correct null hypothesis for testing against
520
diversity dependence [64], has only been developed (code available from RAP) to be equivalent
521
to the DDL/DDX models in LASER (i.e. 0 extinction and no missing species).
522
We were only able to fit this suite of models to larger clades (>6 species), and some
523
likelihood optimizations failed, resulting in a set of 33 clades (including all clades with >50
524
species) for which comparisons could be made. Of these, linear diversity dependence (DDL) was
525
the best-fit model (dAIC = 0) for all but three (Scaphiopodidae [birth-death], Bufonidae
526
[monotonic decay], and Ranidae [monotonic decay]) of the 33 clades. Estimates for initial
527
diversification rates under DDL (i.e. the starting rates before diversity dependence takes effect)
528
were similar to those from the birth-death models (not shown). Preliminary analyses showed that
529
DDL was the best-fit model for most clades. We then estimated parameters using more
530
sophisticated models [66] accounting for both extinction and missing species (see below).
531
These models also provide an estimate of the total carrying capacity (K) for the clade, an
532
estimate that we can use to test for relationships with ecological variables. This approach make
533
several assumptions that are difficult to test, including: (i) that species interactions can be
534
recovered from phylogenetic data alone, (ii) that only species interactions within clades are
535
relevant and (iii) that diversity dependence can be estimated solely from within-clade diversity
536
[64, 67]. However, it provides at least a preliminary test of the potential effects of ecological
537
factors on interspecific interactions and interspecific interactions on diversification.
538
Given the uniformly high support for DDL against the null hypothesis [64] of diversity
539
independent decreases in speciation rate, we estimated values of K for all family-level clades
540
under the DDL model. However, the implementation of the DDL model in LASER, while well-
541
suited for direct comparison to exponential diversity dependence, monotonic decay, and birth-
542
death models, does not account for incomplete sampling. As incomplete phylogenies may affect
543
parameter estimates, particularly carrying capacity [64], we used the DDL+E model (linear
544
diversity dependence in speciation rate and constant extinction) implemented in the R package
545
DDD [66], which accounts for incomplete sampling.
546
We were able to fit this implementation of the linear diversity-dependence model to 61 of
547
those 63 clades with >1 species. However, we again excluded estimates for Telmatobiidae, and
548
optimizations converged on an infinite K (i.e. a birth-death model without diversity dependence
549
in speciation) for Hyperoliidae and Megophryidae. We estimated K, lam0 (initial speciation
550
rate), and mu (extinction rate). We then calculated K’ (equilibrium species-richness in the
551
absence of extinction; [66]) as (lam0 * K) / (lam0 – mu), which we used in subsequent analyses.
552
Summing the estimates of K’ across families suggests a global K’ of ~10700 species for the 60
553
clades tested (Table S14), or approximately 70% saturation at current diversity levels (~7000
554
species), though we caution that these estimates are based on many assumptions (see above).
555
We first tested for a latitudinal gradient in K’, lam0, mu, and saturation (N / K’). We
556
found significant latitudinal gradients in K’ (Table 1) and saturation (N / K’), but none for lam0
557
and mu. As with the estimated speciation, extinction, and climatic-niche rates above, we then
558
determined if clade-level carrying capacity under DDL+E (log-transformed) was related to area
559
or energy (AET, NPP, and BIO1; Table S9), both with the raw data and the PICs (Table S13).
560
We did not repeat the climate and area analyses for lam0 and mu, as we did not want to compare
561
current ecological factors (e.g. temperature and precipitation) to rate estimates for the early
562
history of the clade (initial speciation rate), and the estimates of constant extinction (mu) would
563
be redundant with the previous analysis, and possibly confounded by diversity dependence in
564
extinction rate, which we did not assess, but which typically receives little support [66].
565
Additionally, we did not implement the diversity dependent extinction model, as there
566
would likely be issues with parameter interpretation (as there is no simple way to compare
567
models with and without extinction). We acknowledge a diversity-dependent estimator of
568
extinction rates might (in theory) provide somewhat different estimated values relative to the
569
other methods that we use. However, it seems likely that diversity-dependent estimates of
570
extinction will also show lower rates in the tropics, where there is little evidence of saturation.
571
572
Note that while the clades we have defined (i.e. reciprocally monophyletic families) are
statistically independent (i.e. non-nested on the phylogeny), certain traits such as diversification
573
rate may not be phylogenetically independent if they are inherited from a common ancestor (i.e.
574
temporally and phylogenetically auto-correlated). To test if this was affecting our results, we
575
repeated the multiple regression analyses involving evolutionary rates described above using the
576
phylogenetically independent contrasts (PICs) of those variables [68], which are then suitable for
577
analysis using ordinary methods such as multiple regression [69]. We estimated PICs for each
578
variable using the dated, 2871-taxon tree pruned to include only a single representative per
579
family (66 tips) in the R package 'APE [70].' For net diversification rate, relative extinction
580
fraction, and carrying capacity, we tested the impact of area and NPP (tables S10–12). The
581
results are highly similar to the non-phylogenetic analyses (tables S7–9).
582
583
7. Ecoregion-based analyses
584
To determine the time of colonization (and time for speciation) in each of the multiple global
585
ecoregions, we reconstructed ancestral areas on the chronogram using two primary methods: the
586
likelihood-based Dispersal-Extinction-Cladogenesis (DEC) model implemented in the program
587
lagrange [71, 72], and maximum-likelihood reconstructions of ecoregions as discrete states using
588
an Mk1 transition model. Use of both approaches was necessary for several reasons. Ancestral-
589
area reconstruction presents several challenges, and explicit methods such as lagrange are
590
typically favored over simply treating areas as character states [71-73]. However, current
591
implementations of lagrange can only include a limited number of taxa and areas. A new C++
592
implementation (S.A. Smith, pers. comm.) considerably improves speed, but cannot process
593
more than 6 areas within a reasonable timeframe, especially given the large number of taxa used
594
here. Thus, for lagrange, we reduced the 12 areas to 6: Neotropics (Tropical South America,
595
Tropical Middle America, West Indies, Temperate South America), Nearctic, Afrotropics
596
(Afrotropics, Indian Ocean), Palearctic (Eastern Palearctic, Western, Palearctic), Tropical Asia
597
(South Asia, Southeast Asia), and Oceania. Given the reduced geographic resolution, we use this
598
analysis primarily to evaluate the robustness of the ML reconstructions under the Mk1 model.
599
We then reconstructed ancestral areas using maximum likelihood in Mesquite 2.72 [74],
600
using all 12 regions described above. We used a single rate for all transitions among states
601
(effectively the only option available for characters with many states in Mesquite). Likelihood
602
analysis in Mesquite does not tolerate polymorphisms or ambiguities in state codings. Therefore,
603
174 species with ranges that included two or more ecoregions were coded as occurring in the
604
ecoregion containing the largest part of their range, determined using the GAA-IUCN range-map
605
polygons (see above). For each branch, the reconstruction of a given state was considered
606
unambiguously supported if the difference in log-likelihood units between that state and the next
607
most likely state was 2 or greater (when the branch was fixed to each state). The results from the
608
Mesquite analysis were then compared to those from lagrange to assess consistency between the
609
methods, and the robustness of the likelihood reconstructions. We found that ancestral area
610
reconstructions for the major nodes of interest (e.g. families) were similar between the two
611
analyses, despite differences in coding (e.g. "Palearctic" from lagrange and "Eastern Palearctic"
612
from Mesquite). The area classifications for the species used in the lagrange and Mesquite
613
analyses are provided in Supplemental Data File 1.
614
The biogeographic reconstructions from lagrange and Mesquite are overall broadly
615
concordant in reconstructing lineages in tropical versus temperate regions through time (based on
616
the combined areas in the lagrange analysis). Both methods yield ambiguous reconstructions
617
towards the root of the tree. Thus, there is no clear signal for a single ecoregion (as currently
618
defined) of origin for the extant amphibians, which may be a consequence of most major
619
landmasses being adjacent or accreted during the late Paleozoic [34], the time period when our
620
results and others suggest that crown-group amphibians first arose. The most ancient crown-
621
group amphibian fossils are distributed in both temperate and tropical regions [35], and a
622
previous phylogenetic analysis of extant taxa supported a Pangaean origin for amphibians [75].
623
Thus, it may not be possible to reconstruct the origin of amphibians in a single, clearly defined
624
modern ecoregion, not due to limits in reconstruction methods and the fossil record, but simply
625
because the region of origin was not clearly homologous to modern ecoregions. Nevertheless, we
626
found that 63 of 66 families had unambiguous reconstructions in a single ecoregion (using
627
Mesquite). These are generally concordant with previous analyses of subsets of these taxa, such
628
as ranoid [76, 77], microhylid [78], bufonid [79], and hylid frogs [80], and salamanders [15].
629
We used the likelihood reconstructions from Mesquite to determine the ancestral
630
ecoregion of the 66 clades (families) used in the clade-based analyses (see below), as well as to
631
determine the timing of initial colonization of the 12 ecoregions for the ecoregion-based
632
analyses. The metric for the timing of colonization was the age of the oldest colonization event
633
for a crown-group clade (i.e. one for which both daughter branches were unambiguously
634
reconstructed in the same area). However, we excluded colonization events involving a single
635
species, given that the timing of dispersal along a single branch is uncertain. This general
636
approach (focusing on the oldest colonization event only) has been shown to yield similar results
637
regarding the time-for-speciation effect (relative to using all colonization events for each region)
638
in empirical studies [44, 77, 80] and has been shown to be accurate in simulations [81].
639
For a final perspective on species richness, we assessed diversity within regions as a
640
function of ecological variation among areas (to test for the well-known species-area and
641
species-energy relationships), and timing of colonization (i.e. time-for-speciation). We
642
performed a series of analyses examining the correlates of richness in each of the 12 global
643
ecoregions defined above. We first circumscribed polygons encompassing the extent of each
644
region, allowing us to calculate mean values (across pixels) for AET, NPP and BIO1 as
645
described above for clades (the mean of those variables within each region). Area was calculated
646
by summing up the total land area of the countries and territories occurring in each ecoregion,
647
taken from the 2007 United Nations Demographic Yearbook
648
(http://unstats.un.org/unsd/demographic/products/dyb/dyb2007.htm).
649
Using the range-map data for the 6576 species, we calculated the total number of species
650
in each area as described above. We also had estimates of the approximate first time of
651
colonization of each region by any extant crown-group amphibian clade based on ancestral area
652
reconstructions on the phylogeny, using maximum likelihood in Mesquite (see above). For these
653
analyses, all variables other than time were ln-transformed. We again employed a multiple-
654
regression strategy to analyze the importance of these variables. We did not include interaction
655
terms, given the large number of parameters this would produce, and the difficulty of interpreting
656
them. The region-based data are given in table S15. As with the clade-based analyses above, we
657
first tested for a relationship between species richness in regions and the ecological variables
658
area, AET, NPP, and BIO1 (table S13). However, the effect of these variables must be to
659
mediate diversification rates, and only age and diversification rate can directly change the
660
number of species in an area [48, 49]. We found that timing of first colonization is not
661
significantly related to species richness within regions (r = 0.12, P = 0.72), indicating that time-
662
for-speciation is not the major driver of the global patterns of richness examined here (consistent
663
with our other results showing the importance of variation in diversification rates instead).
664
665
666
Tables
667
Table S1. Percent variance (%) in ecological variables explained by each principal component
668
(PC) axis. These axes are uncorrelated phylogenetically [29].
Axis
PC1
PC2
PC3
PC4
PC5
PC6
PC7
PC8
PC9
PC10
PC11
PC12
PC13
PC14
PC15
PC16
PC17
PC18
PC19
PC20
669
670
671
672
673
674
675
676
677
% Variance
0.336285
0.199951
0.157879
0.112004
0.062801
0.047690
0.031085
0.021801
0.009433
0.007291
0.006504
0.003943
0.001594
0.000838
0.000306
0.000232
0.000204
0.000144
0.000014
0.000003
678
Table S2. Variable loadings on the first principal component axis (PC1) for the 21 ecological
679
variables (AET, NPP, and BIOCLIM) used to characterize climatic niche.
Variable
AET
NPP
BIO1 = Annual Mean Temperature
BIO2 = Mean Diurnal Range (Mean of monthly (max temp - min temp))
BIO3 = Isothermality (BIO2/BIO7) (* 100)
BIO4 = Temperature Seasonality (standard deviation *100)
BIO5 = Max Temperature of Warmest Month
BIO6 = Min Temperature of Coldest Month
BIO7 = Temperature Annual Range (BIO5-BIO6)
BIO8 = Mean Temperature of Wettest Quarter
BIO9 = Mean Temperature of Driest Quarter
BIO10 = Mean Temperature of Warmest Quarter
BIO11 = Mean Temperature of Coldest Quarter
BIO12 = Annual Precipitation
BIO13 = Precipitation of Wettest Month
BIO14 = Precipitation of Driest Month
BIO15 = Precipitation Seasonality (Coefficient of Variation)
BIO16 = Precipitation of Wettest Quarter
BIO17 = Precipitation of Driest Quarter
BIO18 = Precipitation of Warmest Quarter
BIO19 = Precipitation of Coldest Quarter
680
681
682
683
684
685
686
687
Loading
-0.06
-0.39
-0.96
0.21
-0.22
0.42
-0.80
-0.97
0.55
-0.83
-0.91
-0.82
-0.95
-0.26
-0.41
0.15
-0.50
-0.41
0.13
-0.26
-0.04
688
Table S3. Results from analysis of diversification and dispersal across the entire tree using the
689
GeoSSE model, where sAB is speciation rate for species in both areas, sA and sB and xA and xB
690
the speciation (s) and extinction rates (x) for species in A (tropics) or B (temperate regions),
691
respectively, and dA and dB are the dispersal rates from A to B and B to A, respectively. Models
692
are denoted by parameters fixed to be equal between regions. The best-fitting model is chosen by
693
dAIC, the difference between the AIC for each model and the best-fit AIC, and is boldfaced. The
694
AIC weights (wAIC; model probabilities given the data) indicate that the full model (speciation,
695
extinction, and dispersal estimated separately for each region) is 7.3 times more likely than the
696
next most likely model, the equal extinction (xA = xB) model (0.88/0.12).
Model
Full
sAB = 0
sA = Sb
xA = xB
dA = dB
sA = sB, xA = xB
sA = sB, dA = dB
xA = xB, dA = dB
sA = sB, xA = xB, dA = dB
All Equal
dAIC
DF -lnL
AIC
7 -13062 26137
0
6 -13073 26158
21
6 -13080 26173
36
6 -13065 26141
4
6 -13078 26167
30
5 -13133 26277
140
5 -13088 26185
48
5 -13087 26184
47
4 -13159 26325
188
3 -13168 26343
206
wAIC
0.88
0.00
0.00
0.12
0.00
0.00
0.00
0.00
0.00
0.00
697
698
Table S4. Results from analysis of speciation and extinction using the QuaSSE model and PC1.
699
Results from the best fitting model are in italics and boldface.
Model
Both Rates Constant
Speciation Rates Variable:
Sigmoidal
Hump
Both Rates Variable:
Sigmoidal
Hump
Df lnLik
AIC
3
-18903
37812
dAIC
278
wAIC
0.00
6
6
-18771
-18777
37554
37566
20
32
0.00
0.00
9
9
-18758
-18776
37534
37569
0
35
1.00
0.00
700
Table S5. Best-fit non-phylogenetic multiple regression model (R2 = 0.58) for ecological
701
correlates of species richness among clades (using the 66 family-level clades), showing
702
significantly positive species-area and species-energy relationships [see 82]. Significant variables
703
are boldfaced.
Variable
Area
AET
NPP
BIO1

0.69
0.26
0.41
-0.31
P
<0.00001
0.17
0.0024
0.041
704
705
Table S6. Best-fit non-phylogenetic multiple regression model (R2 = 0.79) for evolutionary
706
determinants of variation in species richness among clades (families), showing significant
707
influences of age and diversification rate. Significant variables are boldfaced.
Variable
Net Diversification Rate
Relative Extinction Fraction
Stem Age
Crown Age

0.63
-0.014
-0.19
0.49
P
<0.00001
0.85
0.018
<0.00001
708
709
Table S7. Best-fit non-phylogenetic multiple regression model (R2 = 0.54) for ecological
710
correlates of net diversification rate within clades, showing positive influences of area, NPP, and
711
climatic-niche rate. Significant variables are boldfaced.
Variable
Area
AET
NPP
BIO1
Climatic-Niche Rate
712

0.59
-0.17
0.65
0.0020
0.20
P
<0.00001
0.43
0.00003
0.99
0.061
713
Table S8. Best-fit non-phylogenetic multiple regression model (R2 = 0.17) for ecological
714
correlates of relative extinction fraction within clades, showing significantly negative influences
715
of area and NPP. Significant variables are boldfaced.

Variable
Area
AET
NPP
BIO1
P
-0.40
0.33
-0.54
-0.13
0.0057
0.24
0.0061
0.59
716
717
Table S9. Best-fit non-phylogenetic multiple regression model (R2 = 0.70) for ecological
718
correlates of clade-level carrying capacity, showing positive influence of area and NPP.
719
Significant variables are boldfaced.

Variable
Area
AET
NPP
BIO1
0.72
0.050
0.50
-0.0054
P
<0.00001
0.77
0.00008
0.97
720
721
Table S10. Best-fit multiple regression model (R2 = 0.55) for ecological correlates of net
722
diversification rate within clades, showing significantly positive influences of area and NPP after
723
correcting for phylogenetic relatedness using independent contrasts. Significant variables are
724
boldfaced.
Variable
Area
NPP
725
726
727

P
0.71 <0.00001
0.39 0.00007
728
Table S11. Best-fit multiple regression model (R2 = 0.16) for ecological correlates of relative
729
extinction fraction within clades, showing significantly negative extinction-area and extinction-
730
energy relationships after correcting for phylogenetic relatedness using independent contrasts.
731
Significant variables are boldfaced.
Variable
Area
NPP

P
-0.36 0.0052
-0.30
0.020
732
733
Table S12. Best-fit multiple regression model (R2 = 0.64) for ecological correlates of clade-level
734
carrying capacity (K'; see above), when phylogenetic relatedness is accounted for using
735
independent contrasts. Significant variables are boldfaced.

Variable
Area
NPP
P
0.79 <0.00001
0.37 0.00004
736
737
Table S13. Best-fit multiple regression model (R2 = 0.85) for ecological correlates of species
738
richness within regions, showing significantly positive species-area and species-energy
739
relationships. Significant variables are boldfaced.
Variable
Area
AET
NPP
BIO1
740
741
742
743

0.91
1.36
-0.23
0.024
P
0.00095
0.0028
0.51
0.91
744
Table S14. Data for family level clades: latitudinal midpoint (absolute value), area (km2), stem
745
and crown age (millions of years), AET, NPP, BIO1, climatic-niche rate, net diversification rate
746
(r), relative extinction fraction (), species richness (log-transformed), sampling proportion (f), K
747
(carrying capacity), lam0 (initial speciation), and mu (extinction rate).
Family
Allophrynidae
Alsodidae
Latitude
Area (km2)
Stem Age
Crown Age
AET
NPP
BIO1
1.708048955
3054770
55.423073
--
1427.79645
9359.1082
26.11196
39.0134965
702329
62.49096
56.50453
578.0942489
10517.96724
8.581705
Alytidae
39.37191376
1145280
119.75406
42.46776
503.2056812
6097.84866
13.32491
Ambystomatidae
29.31390866
10609300
126.97708
42.92458
760.9171384
7455.622604
13.44145
Amphiumidae
31.61858016
903821
126.8701
15.7661
1062.468607
8136.217567
18.55341
Arthroleptidae
0.681079231
11527300
92.04685
80.18015
1163.450727
9702.042959
21.86635
Ascaphidae
46.80502754
543262
202.03997
11.74297
386.063425
4625.1394
5.312665
Batrachylidae
43.37864657
127382
55.95189
39.11489
518.3006258
4642.933475
6.398711
Bombinatoridae
31.84995208
4861160
160.06996
87.32926
892.3341933
7642.399543
14.01735
Brachycephalidae
22.04491914
1026730
68.74202
62.70259
1189.402763
10867.67193
19.46046
Brevicipitidae
18.55704947
4765400
78.69315
59.22915
692.6634036
8402.579836
17.87506
Bufonidae
2.754689333
86131000
70.435323
65.733853
1086.994432
9066.882739
19.47988
Caeciliidae
1.481315079
13346800
98.1577
89.07718
1251.338152
10082.27031
23.40632
Calyptocephalellidae
37.94448008
35586.7
119.30052
31.80992
534.828535
11666.0861
9.887431
Centrolenidae
1.114887764
4259640
55.423073
38.890373
1337.060574
11450.98505
20.26565
Ceratobatrachidae
1.128205496
783113
96.311794
75.009894
1607.182874
11648.90245
24.00661
Ceratophryidae
15.53846889
7558290
69.75387
28.21127
939.7821033
6353.7271
22.67025
Ceuthomantidae
1.281806818
71.45282
--
1615.5
10992.57145
23.69896
Conrauidae
5.579418118
1024600
103.154947
48.286447
1208.697057
8757.963717
23.77739
Craugastoridae
1.623196121
9595850
68.091562
65.717732
1257.886948
11130.43886
18.60515
Cryptobranchidae
34.46217679
1056430
164.49997
67.12057
862.5694767
6759.819333
13.07452
Cycloramphidae
23.57713058
565616
64.38866
56.16665
1171.935337
11863.64847
18.3428
Dendrobatidae
1.244877396
8931430
70.435323
49.389623
1353.044726
10695.21412
21.89496
Dicamptodontidae
43.77335883
244148
126.97708
9.24608
405.8086125
6850.568025
8.33606
Dicroglossidae
15.33846085
21106600
98.872017
92.458197
1167.370007
8855.359253
21.00269
Discoglossidae
37.86148097
917278
119.75406
37.49696
435.3441157
5909.947357
14.72945
Eleutherodactylidae
--
18.1858437
2419080
68.091562
62.702602
1269.954392
12564.38278
22.62622
Heleophrynidae
32.81714244
143473
151.98853
47.92853
471.20806
7457.220217
15.17427
Hemiphractidae
3.205364163
2469070
73.185893
67.743273
1257.15619
11118.48948
18.15616
Hemisotidae
6.379905093
11250700
78.69315
78.69315
967.8521033
8601.842578
22.26207
Hylidae
4.310516022
45634900
72.461674
71.133654
1206.700854
9920.911263
21.08679
Hylodidae
22.0584317
225929
62.49096
49.45676
1142.931679
10867.73023
18.82896
Hynobiidae
33.85252693
13635200
164.49997
134.71527
806.3870882
6868.202576
11.04531
Hyperoliidae
3.654319824
15748700
92.04685
68.81195
1126.404965
9324.52068
22.72454
Ichthyophiidae
8.731444357
1201920
98.1577
63.5134
1349.987835
11344.98526
23.7339
Leiopelmatidae
39.21913921
10305.9
202.03997
90.35597
954.6089658
13944.68428
12.77552
Leptodactylidae
12.78351417
17546000
69.877873
66.192843
1157.030075
8602.637671
22.21294
Mantellidae
18.97448731
557655
97.263287
87.094987
1148.562849
12336.24642
20.47939
Megophryidae
19.59610731
4877100
124.86943
92.73453
1127.14437
8339.72475
17.25454
Micrixalidae
11.70818393
35776.8
104.28619
30.00119
1078.950622
9907.614809
22.746
Microhylidae
4.257846693
37077800
109.4253
86.8813
1415.956901
10718.3403
21.65068
Myobatrachidae
26.36109604
7570810
119.30052
105.40262
693.6177311
7861.446625
19.41503
Nasikabatrachidae
9.788699486
96.5758
--
1194
8337
22.64167
Nyctibatrachidae
11.83066906
39287.2
96.311794
79.978194
1060.893792
9340.14932
23.48055
Odontophrynidae
21.73269696
5251310
68.28657
35.28907
1031.816091
8166.806534
20.38296
Pelobatidae
41.55799478
5490140
124.86943
27.56163
423.6303525
4544.15565
12.64199
Pelodytidae
41.509026
873413
140.99143
35.44643
508.7723067
6235.621833
12.27037
Petropedetidae
1.804446306
344766
96.580878
51.588278
1175.720863
10095.45226
22.28509
Phrynobatrachidae
0.480971813
13697200
103.651358
84.512758
1152.115929
9326.367456
22.62773
Pipidae
0.597835917
20908000
190.41993
149.50213
1212.980575
9663.343406
22.76219
Plethodontidae
22.35436002
7092150
126.8701
103.4176
992.5755401
9756.839175
16.44523
Proteidae
36.95004522
2466430
162.44138
121.84908
860.8276983
6604.354117
14.26737
Ptychadenidae
0.695974365
15839300
105.40068
77.00898
977.7152597
7983.386071
22.35819
Pyxicephalidae
19.15089094
16954100
96.580878
87.696748
709.7968707
6849.949498
17.69063
Ranidae
21.03169771
69290100
100.273057
88.651157
1044.220584
8567.307151
18.29907
12.2322055
64424.1
98.872017
34.690117
1031.515594
9161.57939
24.29849
Rhacophoridae
12.73833888
16031900
97.263287
87.885287
1327.579498
9930.408425
21.37113
Rhinatrematidae
1.480344256
330185
108.6498
95.9791
1414.667428
12475.67478
22.26478
Rhinodermatidae
38.91106503
115360
61.25148
55.95189
533.0475838
11248.3304
11.42209
Rhinophrynidae
17.82898568
342083
190.41993
--
1165.62956
10208.8799
25.38003
Rhyacotritonidae
45.30373874
101940
133.03008
19.09708
440.5110075
8187.09515
8.470833
Salamandridae
35.21462952
14784900
167.21998
116.81398
667.329293
6716.640295
14.20702
Scaphiopodidae
34.89148491
6383670
155.73003
60.83633
546.2378729
4115.269343
14.3578
Sirenidae
30.95968644
1193150
199.58998
55.71798
1070.335575
8419.67185
19.32794
Sooglossidae
4.587194669
96.5758
32.4823
1463.988281
9043.25
24.88854
Telmatobiidae
16.28410915
61.25148
11.92058
655.2036744
5646.657433
9.40336
Ranixalidae
748
749
750
751
752
753
754
--
-371935
Niche Rate
r

ln(Species)
--
0
0
0
Alsodidae
1.13225183
0.0533448
2.21806E-09
Alytidae
0.66823715
1.53E-09
Ambystomatidae
1.82022249
0.0544466
Amphiumidae
0.22950561
Arthroleptidae
Family
f
k
lam0
mu
1.00
--
--
--
3.465735903
0.63
35.691768
0.130878
0.042211
0.999999972
1.609437912
1.00
5
0.221346
0.036891
1.50838E-08
3.465735903
0.53
32
0.208264
0.030669
0.0245544
4.63696E-07
1.098612289
1.00
3
0.227912
0.000032
0.46266979
0.056833
1.99376E-06
4.941642423
0.30
285.45314
0.072708
0.000264
Ascaphidae
1.00709412
0
0
0.693147181
1.00
2
0.090206
0
Batrachylidae
1.62803388
3.38E-07
0.999996331
2.48490665
0.25
12.741595
0.107514
0
Bombinatoridae
2.02532592
7.90E-09
0.999999846
2.302585093
1.00
10
0.05709
0.025341
0.1412021
0.0445375
1.15886E-07
3.737669618
0.14
42.498393
0.128594
0
Brevicipitidae
0.69898965
0.0391363
0.252764934
3.295836866
0.33
27.313833
0.1625
0.060211
Bufonidae
2.02848252
0.069764
1.69088E-07
6.29156914
0.38
620.554105
0.160969
0.053444
Caeciliidae
0.25295469
0.0392936
1.00953E-07
4.787491743
0.26
137.447024
0.072157
0
Calyptocephalellidae
0.43510103
0.0159077
4.49739E-06
1.386294361
0.75
4
0.127069
0.000173
Centrolenidae
1.49384111
0.0938246
6.14122E-07
5.017279837
0.50
199.00615
0.157375
0
Ceratobatrachidae
0.38540556
0.0524407
0.030201464
4.430816799
0.21
90.107807
0.154931
0.066351
Ceratophryidae
2.05597238
0.0533011
2.34019E-05
2.48490665
0.42
12
0.190016
0.003543
--
--
--
1.386294361
0.25
--
--
--
0.00494817
0.0140929
3.2341E-07
1.791759469
0.50
27.079506
0.02282
0
1.1342591
0.0733182
8.22658E-06
6.51174533
0.28
1230.475128
0.095478
0
Cryptobranchidae
0.10932929
2.68E-08
0.999996496
1.098612289
1.00
3
0.031369
0.001864
Cycloramphidae
0.05720611
0.0249241
0.638069
3.496507561
0.12
33.01816
0.133982
0
Dendrobatidae
1.19937442
0.0942092
8.33372E-07
5.590986981
0.44
508.313466
0.145093
0.035761
Dicamptodontidae
0.54308967
0.0434385
9.21495E-06
1.386294361
1.00
4.020132
0.271981
0.010442
Dicroglossidae
0.95976369
0.0419322
3.17104E-07
5.159055299
0.55
236.5171
0.069075
0
Discoglossidae
0.15839619
0.0185364
0.552480346
1.945910149
0.71
7
0.111063
0.000122
Eleutherodactylidae
Allophrynidae
Brachycephalidae
Ceuthomantidae
Conrauidae
Craugastoridae
0.29675548
0.0688
9.40539E-08
5.303304908
0.72
273.527787
0.118205
0
Heleophrynidae
0.0600188
1.25E-08
0.999999537
1.791759469
0.50
6
0.078703
0.00008
Hemiphractidae
1.14266902
0.0594541
8.19255E-07
4.532599493
0.47
155.640419
0.084842
0
Hemisotidae
0.64645807
0.026063
0.839725384
2.197224577
0.11
18
0.104636
0.03582
Hylidae
1.89082748
0.0704031
4.72568E-07
6.777646594
0.49
1523.469808
0.097463
0
Hylodidae
0.10625494
0.0541416
1.54443E-07
3.713572067
0.22
41
0.19642
0.000003
Hynobiidae
0.84067141
0.0260824
1.06134E-08
3.951243719
0.88
64.394992
0.052086
0
Hyperoliidae
1.58101922
0.0674945
0.41850353
5.361292166
0.31
--
0.086048
0.000903
Ichthyophiidae
0.9879679
0.0414827
0.34817299
3.850147602
0.15
48.695515
0.170088
0.072954
Leiopelmatidae
0.03394467
1.79E-09
0.999999898
1.386294361
1.00
4
0.148003
0.063709
Leptodactylidae
0.96709694
0.0662892
8.48714E-06
5.18178355
0.36
280.262426
0.094697
0
0.4451028
0.0408346
5.28098E-08
5.159055299
0.53
188.415875
0.101261
0.015072
Megophryidae
1.66966366
0.0479015
0.502555674
4.94875989
0.40
--
0.072375
0.003999
Micrixalidae
0.15741745
0
0
2.397895273
0.18
11
0.264889
0.0016
Mantellidae
Microhylidae
0.45881602
0.049134
5.58653E-08
6.109247583
0.30
596.274261
0.077343
0
Myobatrachidae
1.16380834
0.0388363
0.273484002
4.852030264
0.35
231.444976
0.08128
0.036218
--
0.00E+00
0
0
1.00
--
--
--
Nasikabatrachidae
Nyctibatrachidae
0.01692385
2.69E-09
0.999999936
2.833213344
0.18
17
0.076736
0
Odontophrynidae
1.11000455
0.0721556
7.58392E-08
3.465735903
0.59
33.205029
0.204338
0.003461
Pelobatidae
1.1416151
0.0136362
2.54051E-07
1.386294361
1.00
4
0.205837
0.013757
Pelodytidae
1.43537263
2.02E-09
0.999999905
1.098612289
1.00
3
0.051614
0.003013
Petropedetidae
1.65041128
1.25E-08
0.999999844
2.302585093
0.60
11.377117
0.070793
0
0.2217805
0.0455307
3.55169E-07
4.356708827
0.15
94.533918
0.085778
0.014398
Pipidae
0.50741581
0.0153707
0.556006679
3.465735903
0.72
33.686817
0.064807
0.035785
Plethodontidae
0.73453596
0.0459554
0.00293846
5.976350909
0.71
1158.331824
0.055276
0
Proteidae
0.15984014
4.58E-08
0.999997585
1.791759469
1.00
6
0.077204
0.019084
Ptychadenidae
0.50153646
0.0427373
8.55995E-07
3.931825633
0.29
58.194203
0.082714
0
Pyxicephalidae
0.54884488
0.0370666
6.47033E-06
4.158883083
0.50
70.880882
0.093505
0.031807
Ranidae
1.65392953
0.0391422
1.75463E-08
5.880532986
0.61
490.386742
0.064919
0
Ranixalidae
0.10651597
0
0
2.302585093
0.20
28.896242
0.052568
0
Rhacophoridae
0.69744173
0.0500376
1.08215E-07
5.765191103
0.34
540.251676
0.068224
0
Rhinatrematidae
0.03362227
0.0093402
1.18401E-07
2.197224577
0.33
9
0.093329
0.000526
Rhinodermatidae
1.13240374
0.0203455
2.71023E-05
1.098612289
0.67
6
0.152699
0.01657
Phrynobatrachidae
Rhinophrynidae
--
0
0
0
1.00
--
--
--
Rhyacotritonidae
0.06970384
0.0337841
3.67591E-07
1.386294361
1.00
4
0.175469
0
Salamandridae
1.03795783
0.0336356
1.88722E-07
4.394449155
0.88
119.279933
0.055062
0
Scaphiopodidae
1.04006654
0.0003
0.992648075
1.945910149
1.00
11.771672
0.002692
0.00002
Sirenidae
0.27064682
0.0128829
0.000845492
1.386294361
1.00
4
0.054746
0.000691
Sooglossidae
0.00070148
0.0202032
8.06935E-08
1.386294361
1.00
4
0.116007
0.000401
--
--
--
4.127134385
0.27
--
--
--
Telmatobiidae
755
756
757
758
759
760
761
762
763
Table S15. Data gathered for 12 global ecoregions. Age is the age of the first extant clade to
764
colonize the region, and calculation of area, AET, NPP, BIO1, and species are described above.
Ecoregion
769
770
771
772
773
774
775
776
777
778
BIO1
Species
1210.526517
7683.729803
23.823743
2306
Nearctic
22754303
199.59
380.919375
3348.183738
1.213184
294
Afrotropical
22028506
151.99
793.765639
5771.137987
23.839337
777
25063848.39
119.75
257.753169
4171.996764
14.816934
132
28977228
134.72
275.816647
2430.872595
-2.272218
233
594275
87.09
1016.191346
8060.398258
22.786441
258
Oceania
9166661
105.4
543.114396
4008.354365
21.368206
612
Southeast Asia
4569153
102.07
1217.395216
8785.118255
22.149457
823
South Asia
4478841
79.98
686.95976
4410.420381
22.42621
359
Tropical Middle America
1512593
87.86
1051.222282
9738.45895
22.884766
695
Temperate South America
3010345
61.25
409.51902
3874.110077
10.487769
128
228881
49.89
1294.942115
10827.98257
24.822695
188
West Indies
768
NPP
95.98
Madagascar
767
AET
13699190
Eastern Palearctic
766
Age
Tropical South America
Western Palearctic
765
Area (km2)
779
References:
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
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