Understanding how and why certain clades diversify greatly in morphology whereas others do not remains a major theme in evolutionary biology. Projecting families of phylogenies into multivariate morphospaces can distinguish two scenarios potentially leading to unequal morphological diversification: unequal magnitude of change per phylogenetic branch, and unequal efficiency in morphological innovation. This approach is demonstrated using a case study of skulls in sister clades within the South American fish superfamily Anostomoidea. Unequal morphological diversification in this system resulted not from the morphologically diverse clade changing more on each phylogenetic branch, but from that clade distributing an equal amount of change more widely through morphospace and innovating continually. Although substantial morphological evolution occurred throughout the less diverse clade's history, most of that clade's expansion in morphospace occurred in the most basal branches, and more derived portions of that radiation oscillated within previously explored limits. Because simulations revealed that there is a maximum 2.7% probability of generating two clades that differ so greatly in the density of lineages within morphospace under a null Brownian model, the observed difference in pattern likely reflects a difference in the underlying evolutionary process. Clade–specific factors that may have promoted or arrested morphological diversification are discussed.
Empirical methods for identifying differences in the magnitude or mode of morphological change typically require either a phylogeny with branch lengths, ideally in units of time (Garland 1992; Pagel 1999; Harmon et al. 2003; O'Meara et al. 2006) or excellent resolution in the fossil record (Foote 1994, 1996a; Hunt 2007). Although the methods that use branch lengths are undeniably valuable, they cannot be applied readily to phylogenies based on morphological or behavioral data except in rare cases in which exceptional fossil quality can provide lineage durations (e.g., Hunt 2007). Neither can many methods accommodate supertrees unless a fossil-based time-calibration can supply branch lengths (e.g., the 30 fossil calibration points used by Bininda-Emonds et al. 2007). To infer differences in the magnitude and mode of morphological diversification in clades that lack molecular phylogenies or extensive fossil records or at large scales that require the union of multiple phylogenies, additional methods are needed.
By projecting any phylogeny into a multivariate morphospace (hereafter, a phylomorphospace), one can map the history of a clade's morphological diversification and infer the magnitude and direction of shape change along any branch of the phylogeny. The basic idea of projecting phylogenies into two-dimensional morphospaces can be traced at least to Bookstein et al. (1985). Rohlf (2002) formally demonstrated that geometric morphometric variables can be fit to a phylogeny using squared change parsimony, and Stone (2003) presented an alternative multidimensional geometric approach. Previously, phylomorphospaces have been used to investigate the correlation between shifts in morphology, habitat, and diet (Klingenberg and Ekau 1996), the order of morphological transformations (Stone 2003), morphological convergence (Stayton 2005; Macholán 2006), the partitioning of morphological diversity among subclades (Stayton and Ruta 2006), and to visualize adaptive radiations (Clabaut et al. 2007). Here, it is demonstrated that phylomorphospaces including morphologically diverse and depauperate clades can be used to distinguish between two scenarios, one related to magnitude and one related to mode, that can reveal how one clade achieved greater morphological diversity than did another. These two scenarios are: (1) Unequal magnitude of change per phylogenetic branch. Lineages within the clade with high morphological diversity experienced more morphological change per phylogenetic branch on average than did lineages in the clade with low morphological diversity. (Magnitude) (2) Unequal efficiency in morphological innovation. Neither clade experienced more morphological change per phylogenetic branch, but the clade with high morphological diversity explored more novel regions of morphospace. (Mode)
Each of these two scenarios will yield a different pattern when a phylomorphospace is constructed and the positions of the internal nodes are inferred with ancestral state reconstruction methods (reviewed in Cunningham 1998; Martins 1999; Pagel 1999). Scenario one (unequal magnitude of morphological change per branch) predicts that the mean Euclidean distance between adjacent nodes in the phylogeny will be higher in one clade than in the other (Fig. 1). The ability of a null Brownian model of morphological change to generate clades with the observed difference in mean morphometric branch length can be tested via simulation. Rejection of the simulated Brownian null for scenario one implies that the clades being compared either evolved under differing tempos (rates) of morphological evolution or have significantly different crown clade ages. Scenario two (unequal efficiency in morphological innovation) predicts that the branches of the phylogeny will be packed much more densely in morphospace in the clade with low morphological diversity than in the clade with high morphological diversity (Fig. 1). Scenario two is supported when the clade with high morphological diversity distributes an equal amount of morphometric change through a greater volume of morphospace than does the clade with low morphological diversity. This prediction can be tested by determining whether the low diversity clade possesses a much higher lineage density (a new measure defined herein) than does the other, and again, the probability of generating the observed difference in lineage densities at random can be determined through simulation. Rejection of a simulated Brownian null for scenario two implies that at least one of the two clades is evolving under an alternative (non-Brownian) mode of morphological evolution, such as divergent selection, adaptive radiation, or constrained change (Butler and King 2004; Freckleton and Harvey 2006).
The South American characiform fish families Anostomidae, Chilodontidae, Curimatidae, and Prochilodontidae (headstanders, flannel-mouth characins and their relatives, collectively the Anostomoidea of Buckup 1998) provide an excellent case in which a phylomorphospace approach may help reveal the cause of unequal morphological diversification. The clade formed by Anostomidae and Chilodontidae (the Anostomoidea of Sidlauskas 2007, hereafter clade A) contains approximately as many taxa (Vari 1983; Reis et al. 2003) as its sister formed by the union of Curimatidae and Prochilodontidae (the Curimatoidea of Sidlauskas 2007, hereafter, clade C), but clade A is markedly more diverse in skull morphology and trophic ecology (Sidlauskas 2007). Species in clade A may have forwards, downwards, upwards, or backwards facing jaws and eat primarily a variety of plants and invertebrates, whereas species in clade C demonstrate only two distinct skull types and are universally detritivorous (Sidlauskas 2007). Simulations of Brownian evolution on many possible phylogenies in an empirically derived morphospace revealed previously that the rate of morphological change per unit time was unlikely to be equal in the two clades (Sidlauskas 2007), but the lack of a phylogenetic hypothesis of relationships within Anostomidae, the major family in clade A, precluded a more detailed analysis.
A morphology-based phylogeny for Anostomidae has recently become available (Sidlauskas and Vari 2008) and completed the phylogenetic backbone needed to reconstruct the history of diversification in these fishes. In the current study, the phylomorphospace resulting from the combination of a globally-parsimonious phylogeny for Anostomoidea with the morphometric dataset of Sidlauskas (2007) was used to determine which of the two scenarios of unequal diversification outlined above resulted in the remarkable morphological conservatism of Curimatidae and Prochilodontidae and the high morphological disparity of Anostomidae and Chilodontidae. Results indicated strongly that although both of these groups of fishes experienced similar magnitudes of change per phylogenetic branch, lineages within clade A expanded throughout morphospace over the whole course of cladogenesis whereas lineages within clade C oscillated within two tightly defined regions. Once taxon sampling was equalized in the two clades, the Brownian null easily explained the small observed differences in mean morphometric branch length, but pairs of simulated clades rarely differed as greatly in lineage density as did the real clades. This result suggested that the mode and not the magnitude of diversification differed between the major clades in Anostomoidea.
Materials and Methods
This study employed a modified version of the geometric morphometric dataset of Sidlauskas (2007), which described variation in the configuration of 21 landmarks (Fig. 2) distributed around the skull and jaws of 151 members of Anostomidae, Chilodontidae, Curimatidae, and Prochilodontidae. Landmark configurations for five ingroup taxa and the outgroups Parodon suborbitalis and Hemiodus ocellatus (Appendix) were added to the dataset by locating the appropriate landmarks on digital x-rays in tpsDig ver. 2.10 (Rohlf 2006) following Sidlauskas (2007). A few species identifications have also been updated (Appendix). Thirty-seven taxa (mostly in the species-rich genus Leporinus) appear in the morphometric dataset of Sidlauskas (2007) but were not included in the phylogenetic reconstruction for Anostomidae (Sidlauskas and Vari 2008); these taxa were excluded from the morphometric analysis herein. This modified morphometric dataset included 121 species, with 50 of the 149 putatively valid species (34%) in clade A and 69 of the 127 (55%) putatively valid species in clade C represented. Numbers of species in each clade were taken from Reis et al. (2003) and were updated to include recent descriptions.
The modified morphometric dataset was reanalyzed as described previously (Sidlauskas 2007) with a Procrustes fit (Rohlf and Slice 1990) to remove variation among species due to scaling, rotation and translation. A subsequent Relative Warp Analysis (RWA, Rohlf 1993) in tpsRelw ver. 1.45 (Rohlf 2007) yielded a series of orthogonal eigenvectors that describe the major axes of skull shape variation among species. A regression of interspecies distance in relative warp space on interspecies Procrustes distance in tpsSmall ver. 1.20 (Rohlf 2003) was used to verify that the tangent plane projection used in RWA did not significantly distort the distances between specimens in multivariate space. The relative warp scores output by tpsRelw were multiplied by a factor of 100 for ease of visualization in later analyses. Rarefactions were used to calculate the sampling error associated with the consensus configuration for individual species and to confirm that this error was small relative to the typical distances between species.
This study used a set of phylogenies generated from a supermatrix containing 463 morphological characters and 174 taxa. These characters and taxa were assembled from the original data matrices and in-text descriptions from 14 separate studies on the whole Anostomoidea (Vari 1983) or components of it (Winterbottom 1980; Vari 1982, 1984, 1989a,b,c, d, 1991, 1992a,b; Vari et al. 1995; Castro and Vari 2004; Sidlauskas and Vari 2008) and were supplemented with information from species descriptions published after corresponding familial revisions (Vari and Nijssen 1986; Vari and Reis 1995; Vari and Blackledge 1996; Vari and Ortega 1997; Vari and Chang 2006; Scharcansky and Lucena 2007). Analysis was conducted in PAUP* ver. 4.0 b10 (Swofford 2002) using a parsimony ratchet (Nixon 1999) as implemented by PAUPRat (Sikes and Lewis 2001) and yielded a sample of 3235 most-parsimonious trees of length 976. Additional parsimony ratchet searches using the consensus of these trees as a converse constraint (following the example of Catalán et al. 1997) returned no trees of equal or shorter length, suggesting that all tree partitions in the strict consensus are shared by all possible trees of 976 steps in length. Other equally parsimonious trees surely exist, but because each of the 20 iterations of the original parsimony ratchet hit the minimum length many times it is probable that the optima for all tree sectors have been sampled (see discussion in Goloboff 1999: 425–426) and consequently unlikely that the inclusion of additional most parsimonious trees would change the overall strict consensus of relationships. Because a supermatrix of original data (following Nixon and Carpenter 1996; de Queiroz and Gatesy 2007; O'Leary and Gatesy 2007) and not the original phylogenetic topologies was used to form the global reconstruction, each of the trees is a phylogeny with attendant parsimony branch lengths and character optimizations, not a supertree that combines tree topologies (sensu Sanderson et al. 1998). The use of a supermatrix avoids the problems of character duplication and varying quality of source trees that can affect some supertree analyses (Gatesy et al. 2002). The resulting reconstruction provides the best current hypothesis of relationships within the entire Anostomoidea and is largely congruent with the results of the constituent studies. Further details on the morphological characters, the assembly and analysis of the supermatrix, support for the reconstruction, and differences from previous hypotheses of relationships are in preparation for publication elsewhere.
Fifty-three of the 174 species present in the phylogenies are not represented in the morphometric dataset. These 53 taxa were pruned from the most parsimonious trees, yielding 2636 unique topologies, the strict consensus of which appears in Figure 3. These pruned topologies formed the framework for comparative analysis.
ANCESTRAL STATES, MORPHOMETRIC BRANCH LENGTHS, AND PHYLOMORPHOSPACE RECONSTRUCTION
Relative warp values at internal nodes of each most parsimonious phylogeny were estimated from the morphometric tip data using Schluter's et al. (1997) maximum-likelihood algorithm as implemented in the R package APE (Paradis et al. 2004), after setting all branch lengths to unity. This method is mathematically equivalent to unscaled squared change parsimony (Maddison 1991; Martins 1999; Webster and Purvis 2002), and very similar ancestral states were obtained using the squared change parsimony algorithm in Mesquite 1.12 (Maddison and Maddison 2006) on a trial tree. Relative warps are by definition orthogonal and uncorrelated (Rohlf 1993), so the reconstruction of ancestral states for each warp was performed independently of the reconstruction of states on all other warps. Reconstructions of ancestral states were carried out separately for clades A and C on each phylogeny after using the drop.tip function to exclude the outgroups and each clade's sister.
The morphometric change inferred along each branch of a phylogeny equals the Euclidean distance between the nodes or terminals bracketing that branch, calculated along all morphospace axes (warps) simultaneously using the Pythagorean Theorem. These distances are designated as morphometric branch lengths, and are distinct and separate from parsimony branch lengths calculated in PAUP*.
Phylomorphospaces were visualized using the Plot Tree 2D algorithm in the Rhetenor module (Dyreson and Maddison 2003) of Mesquite (Maddison and Maddison 2006). This algorithm reconstructs the ancestral states along any two pairs of morphospace axes, plots all terminal and internal phylogenetic nodes into the morphospace, and draws the branches connecting adjacent nodes. The resulting phylomorphospace illustrates both the magnitude and the direction of morphometric change inferred along each branch. The phylomorphospace visualizations include the branches and nodes connecting clades A and C to each other and the outgroups, but those branches do not figure into the calculations of mean morphometric branch length and lineage density discussed below.
INVESTIGATING THE TWO UNEQUAL MORPHOLOGICAL DIVERSIFICATION SCENARIOS
Each of the two scenarios potentially leading to unequal morphological diversification predicts a different pattern in the distribution of morphometric branch lengths across the phylogeny or throughout morphospace (summarized in Table 1). Scenario one (unequal magnitudes of morphological change per phylogenetic branch) predicts that the mean morphometric branch lengths will be much higher in clade A than in clade C. Whether the observed difference in mean morphometric branch lengths was sufficiently large to indicate a probable shift in evolutionary process was determined by comparison with the expectations of a Brownian null model (see section on simulations below).
Table 1. Possible outcomes and interpretations of tests for differences in phylomorphospaces.
(1) Clade A experienced a higher magnitude of morphological change per phylogenetic branch than did clade C
Comparison of ratio of mean morphometric branch lengths (M) with simulated null
Magnitudes approximately equal, scenario one rejected
Magnitudes unequal, less diverse clade has lower mean morphometric branch length, scenario one maintained
Magnitudes unequal, but less diverse clade has higher mean morphometric branch length, scenario one rejected
(2) Clade A innovated morphologically more efficiently than did clade C
Comparison of ratio of lineage densities (D) with simulated null
Both clades equally efficient at evolving novel morphologies, scenario two rejected
Modes of diversification dissimilar, more diverse clade also more efficient at innovating, scenario two maintained
Modes of diversification dissimilar, but less diverse clade more efficient at innovating, scenario two rejected
Scenario two predicts that clade A was more efficient than clade C at innovating morphologically, even if the amount of morphological change occurring on the branches of each clade was similar. In other words, clade A may have regularly produced species with previously unexplored morphologies, whereas clade C may have regularly produced species that are convergent upon other species in the clade. In such a case, clade C will have folded an equivalent amount of morphometric change into a much smaller region of morphospace than will have the first (Fig. 1), and thus will have a higher lineage density. Lineage density (D) for a clade can be defined generally as
where L is the sum of morphometric branch lengths within a clade, and V is the volume that the clade occupies in morphospace. A variety of volumetric measures are possible (Ciampaglio et al. 2001), such as total range, the volume of a 95% confidence hyperellipsoid, or the volume of a convex hull. This study approximated clade volume as that of the minimum bounding hyperellipsoid, and defined Lineage Density 1 (D1, Fig. 4) for this four-dimensional case as follows:
where ri is the length of the ith semiaxis of the hyperellipsoid. Hyperellipsoid volume was calculated using the R functions ellipsoidhull and volume.ellipsoid, both part of the cluster package (Maechler et al. 2008). Using this method, the major axes of the hyperellipsoid were not forced to align with the four morphospace axes (Fig. 4).
Lineage Density 1 will give misleadingly high values if either clade's distribution is highly restricted on any of the morphospace axes, which can occur if one clade diversifies along a particular axis and the other does not. In such a case, the distribution of a clade can have dimensionality less than that of the whole morphospace, and the volume of the clade and the denominator of the equation can collapse to near zero, giving a misleading picture of morphological diversity (Van Valen 1974). This problem can be avoided using the following alternative definition: Lineage Density 2 (D2, Fig. 4)
The denominator of D2 represents the sum of spans of the major axes of the bounding hyperellipsoid, where n is the number of semiaxes and ri is again the length of the ith semiaxis. In practice, the denominator of D2 was calculated by summing twice the square roots of the eigenvalues of the hyperellipsoid's covariance matrix as returned by ellipsoidhull, and multiplying by the scaling factor d returned by that same script. Taking the nth root of the morphometric branch lengths in the numerator and dividing by the sum of spans preserves the dimensionality of D1 and the concept of a density, in which a low-order measure (the linear, first-order sum of branch lengths) is divided by a higher order measure (e.g., a third-order volume or fourth-order hypervolume).
Comparatively high lineage densities are expected when evolving lineages within a clade oscillated within a limited range of morphologies and comparatively low lineage densities are expected when lineages within a clade frequently explored new regions of morphospace. High lineage densities may be indicative of intrinsic constraints on diversification, such as a lack of genetic variation, low modularity, or developmental canalization (Wagner and Altenberg 1996; Flatt 2005; Erwin 2007). High lineage densities may also indicate the presence of extrinsic barriers in morphospace, which may indicate regions corresponding to implausible or impossible morphologies (Raup 1966; McShea 1994; Foote 1996b; McGhee 1999; Erwin 2007) or ecological incumbency of other groups of organisms (Rosenzweig and McCord 1991; Jablonski 2000; Bambach et al. 2002). Low lineage densities may indicate that a clade was relatively unconstrained in its morphological evolution, or that some process actively drove lineages apart, such as divergent selection (Allender et al. 2003) or adaptive radiation (Schluter 2000).
Both formulations of lineage density were computed for clades A and C on each of the most parsimonious topologies, and means and standard deviations were calculated to determine the sensitivity of the densities to topological uncertainty. The ratio DC/DA for all possible phylogenies was also determined. A DC/DA much higher than 1 for all possible phylogenies would indicate that lineages within clade C are much more densely packed than lineages within clade A and would maintain scenario two as an important potential explanation of unequal morphological diversity. A DC/DA near unity would indicate that the two clades were equally efficient at distributing the available change through morphospace, and DC/DA < 1 would indicate that clade A was less efficient in diversifying, despite its higher overall disparity. Either of the latter patterns would reject scenario two. As with the test of scenario one above, it should be recognized that the raw comparison of lineage densities reveals only whether the observed outcomes of evolution differ between the clades, and does not mandate an underlying difference in process unless comparison with a simulated null model returns a significant result.
The comparison of lineage densities and mean morphometric branch lengths outlined above can reveal whether clade A is more morphologically diverse than clade C because it changed more on each of its branches or because it more frequently invaded new regions of morphospace. To determine whether either potential difference in pattern could be explained as alternative outcomes of a single evolutionary process or whether alternate processes were implicated, the observed differences between the clades were compared to the expectations of a null Brownian model of evolution. A random walk or a Brownian motion process can produce a wide variety of morphological patterns, including unequal morphological diversity, apparent stasis, and clumpiness of morphospace, but some morphological patterns are much more probable than others (Raup and Gould 1974; Raup 1977; Foote 1996b; Pie and Weitz 2005). To determine the probability of randomly generating clades that differ as much in mean morphological branch length and lineage density as do clades A and C, given the available phylogenetic information, random phylomorphospaces were simulated as follows.
First, each of the most parsimonious phylogenies was ultrametricized according to a procedure outlined by Yang and Rannala (1997). This method proceeded by estimating a set of possible divergence times for the phylogeny according to specified level of taxon sampling ρ and rates of speciation λ and extinction μ. The nodes of the phylogeny were then ordered randomly from youngest to oldest under the restriction that all descendant nodes must be younger than the ancestral nodes to which they are connected. The set of divergence times was ordered similarly and assigned to the nodes of the phylogeny. Branch lengths were calculated as the difference in divergence times between adjacent nodes of the phylogeny, and a fully ultrametric tree resulted. All ultrametricized phylogenies were scaled so that the basal split between clades A and C occurred at time t= 1, with the tip species at t= 0. The R scripts that performed this ultrametricization are available upon request.
The level of taxon sampling ρ was known exactly, but the birth/death parameters λ and μ were not. λ and μ were therefore selected randomly for each ultrametric tree. The speciation rate λ varied uniformly between 5 and 15 whereas the extinction rate μ varied uniformly between 0.07 and 10.07. These ranges are centered upon rates of 10 and 5.07, respectively, which were calculated to yield an expected standing diversity of 280 lineages after 100 steps of Δt= 1/100 using equation A25 from Raup (1985) and imply a mean extinction percentage of about 59%. The range of ±5 was chosen to be equivalent for both parameters and ensured that the extinction rate remained positive. This range of simulated values for λ and μ resulted in a wide variety of potential node ages and branch lengths while ensuring that more often than not, the simulated speciation rate exceeded the simulated extinction rate.
Morphological evolution was simulated on each ultrametricized phylogeny under a single-rate Brownian model using the sim.char function in Geiger (Harmon et al. 2008). To ensure that evolution was simulated in a morphospace with dimensionality and variance structure similar to the real data, the relative warp singular values for the Anostomoidea were used to set the expected variance for each simulated morphospace axis. After the simulation of morphological evolution, all branch lengths were set equal to one to mimic the state of knowledge in the real clades, for which the topologies but not the divergence times were known. Ancestral states were reconstructed from the simulated tip data using Schulter's (1997) likelihood algorithm, and the simulated mean morphometric branch length ratios and lineage density ratios were determined.
The resulting null distribution was used to determine the probability of simulating MA/MC or DC/DA ratios as large as those observed in the real clades. These are explicitly one-tailed tests, because the tail of simulations in which MA/MC or DC/DA is unusually low does not falsify the original predictions of higher branch length in clade A or higher lineage density in clade C. The two-tailed alternative would test instead whether the observed ratios were extreme enough to support a conclusion of unequal magnitudes or modes of change in the absence of a priori information about which clade was more morphologically diverse. In the interest of completeness two-tailed tests were also performed, and those results are discussed where the choice of a two-tailed test would alter a conclusion of significance. In the one-tailed case, if 5% or fewer of the simulations differed so greatly in mean morphometric branch length M, then the single rates Brownian process would be rejected in favor of either a two rates model in which the rate of morphological evolution in clade A exceeded that in clade C or a single rate model in which the crown clade age for clade A was forced to be much older than the crown clade age for clade C. Either of those models can yield unequal magnitudes of morphological change (Collar et al. 2005). If fewer than 5% of simulations differed so greatly in lineage density D, then a Brownian model of evolution would likely be a poor fit for either or both clades and a significant difference in the underlying mode of evolution would be indicated. The evolution of clade C might be more constrained than that of clade A, as could be modeled by the erection of boundaries in morphospace (Garland et al. 1993; Diaz-Uriarte and Garland 1996) or by an Ornstein-Uhlenbeck (OU) process in which an attractive force pulls evolving lineages toward optimal morphologies (Hansen 1997; Butler and King 2004). Alternatively, lineages in clade A might have undergone an adaptive radiation, as could be modeled by an early burst/declining rates (Pagel 1997, 1999) or niche filling (Harvey and Rambaut 2000; Freckleton and Harvey 2006) model of change, or might be driven away from previously occupied regions of morphospace by divergent selection.
Because the phylogenies used in this study are based on morphology, mapping the morphometric dataset onto those phylogenies to produce a phylomorphospace may introduce circularities. To circumvent this issue, the phylogenetic supermatrix was reanalyzed with 35 characters removed that describe shape changes in the skull and jaws that would be expected to affect the position of the morphometric landmarks. For example, characters describing the rotation or elongation of jaw elements were removed from the dataset. Conversely, characters describing variation in systems not appearing in the morphometric dataset (teeth, axial skeleton, pharyngeal arches, etc.) as well as cranial variation without influence on the position of the morphometric landmarks (e.g., elaborations of the medial surfaces of the jaw bones, variation in the width of the neurocranium) were retained. This reduced data matrix of 428 characters was analyzed in a manner identical to the treatment of the full supermatrix. All comparative analyses were performed in parallel using separate samples of phylogenies derived from the full and reduced versions of the supermatrix.
The better phylogenetic sampling in clade C (55%) than in clade A (34%), may affect the comparative results by artificially increasing the density of nodes, breaking up phylogenetic branches, and depressing morphometric branch lengths in clade C. To correct for this effect and determine whether it altered the comparative conclusions, a parallel comparative analysis was performed with 27 taxa in clade C pruned from the sample of phylogenies and removed from the morphospace (indicated by asterisks in Figs. 3 and 5). This rarefaction equalized the sampling intensity of both clades at 34%. The rarefied sample of clade C was nonrandom and was designed to mimic the sampling of clade A, in which every genus and subgenus is represented by at least one species in both the phylogenetic and morphometric datasets. Duplicate topologies resulting from the exclusion of these taxa were removed from the phylogenetic samples.
All told, four parallel comparative analyses of the data were performed, using (1) all available taxa and the full phylogenetic supermatrix, (2) all available taxa and the reduced supermatrix, (3) equal taxon sampling in clades A and C and the full supermatrix, and (4) equal taxon sampling in clades A and C and the reduced supermatrix. R scripts performing all analyses are available upon request.
For the first three morphospace axes (relative warps or RWs), the percent of variation explained (50.5%, 16.9%, and 11.1%, respectively), morphological interpretations, and the corresponding distribution of species on those axes are fundamentally similar to those reported in Sidlauskas (2007). The first warp (RW1) described primarily the lower jaw's angle and length and the location of the quadrate-anguloarticular joint relative to the orbit. RW1 is a major axis of diversification for Anostomidae within clade A, and clade A spans a much greater range of values on RW1 than does clade C (Fig. 6). RW2 primarily described the overall aspect ratio of the skull, the rotation of the premaxilla, and the dorsoventral positioning of the orbit. RW3 described further aspects of jaw morphology, particularly the shape of the dentary and the premaxilla but also variation in the position of the cleithra, the length of the opercular series, and the diameter of the orbit. The morphological differences described by RW3 separate the two recognized families in clade C, Prochilodontidae and Curimatidae (Fig. 6). A more detailed description of the morphological changes summarized by RW1–3 appears in Sidlauskas (2007).
The interpretation of the fourth warp differed between the studies. In Sidlauskas (2007) the fourth warp explained 6.2% of the original shape variation and largely described the size of the premaxilla, whereas in this modified dataset the fourth warp explains 4.2% of the original shape variation and described the height of the ascending process of the premaxilla as well as the position and length of the anterior portion of the opercular series, which serves as the site of attachment for the interopercular-mandibular ligament. One taxon in clade A, Gnathodolus bidens, has an extremely short preopercle and interopercle and consequently possesses a much more positive score on this axis than does any other surveyed taxon.
A regression of interspecies distance in relative warp space on interspecies Procrustes distance in tpsSmall ver. 1.20 (Rohlf 2003) verified that the tangent plane projection used in RWA did not significantly distort the distances among the surveyed species (Pearson product-moment correlation = 0.9999). Following Sidlauskas (2007), the four morphospace axes explaining the largest percentage of morphological variation were retained for further analysis.
The sampling error around the species consensuses was confirmed to be small relative to the typical distance between species. For example, the mean Procrustes distance between rarefied consensus configurations for Curimata vittata in clade C was 0.028. The value for Semaprochilodus knerii, also in clade C, was similar (0.027). The mean Procrustes distance between species in clade C was 0.130, and of the 2346 pairwise distances between species in that clade, only 15 are below 0.040. Therefore, the morphometric distances among species are attributable primarily to real morphological differences, and not to sampling error.
PHYLOGENETIC ANALYSIS OF THE REDUCED SUPERMATRIX
Reanalysis using the reduced supermatrix without the 35 phylogenetic characters that describe variation similar to that summarized in the morphometric landmarks yielded 2273 shortest trees of 918 steps (CI = 0.607, RI = 0.935). Nineteen of the heuristic parsimony ratchet searches discovered trees of length 918 within 10 ratchet iterations, whereas one search became stranded on a tree-island of length 956 steps and never escaped. The strict consensus formed after the removal of taxa not represented in the morphometric dataset (Fig. 5) was similar to, but not identical to, the consensus from analysis of the full supermatrix (Fig. 3). Differences primarily concern the monophyly of Pseudanos and the placement of Hypomasticus and Anostomoides within Anostomidae in clade A. Within clade C only a single node in Psectrogaster collapses. Reconstructed relationships within Chilodontidae and Prochilodontidae were unaffected by reduction of the supermatrix. The greater incidence of topological changes in clade A is not surprising given that the characters removed dealt primarily with jaw shape and orientation, and that Anostomidae exhibits more jaw diversity than do the other three ingroup families (Sidlauskas 2007). After pruning of taxa not represented in the morphometric dataset and removal of duplicate topologies, 1795 distinct trees were retained from analysis of the reduced supermatrix.
INVESTIGATING UNEQUAL MORPHOLOGICAL DIVERSIFICATION SCENARIO ONE
Scenario one predicted that the more morphologically diverse clade A experienced more morphometric change on each of its phylogenetic branches that did its sister, clade C (Table 1). Initial comparison of the reconstructed morphometric branch lengths in clades A and C (Table 2) using the full supermatrix and all available taxa suggested that lineages within clade A changed more on each branch of the phylogeny (Fig. 3) than did lineages within clade C (MA= 2.48, MC= 2.07). Analysis using phylogenies drawn from all available taxa and the reduced supermatrix (Fig. 4) also indicated a larger mean morphometric branch length in clade A (MA= 2.56) than in clade C (MC= 2.07). The P values from simulations using all available taxa were significant (P= 0.004, reduced supermatrix) or marginally significant (P= 0.060, full supermatrix), indicating the mean simulated morphometric branch length in clade A exceeded that in clade C more than it did in the real data no more than 6% the time (Table 2). Interestingly, the tests using the two-tailed alternative were not significant, (P= 0.203, full supermatrix and P= 0.215, reduced supermatrix). This lack of significance is due to a tendency for the simulations to generate a slightly higher mean morphological branch length in clade C than in clade A (mean simulated MA/MC= 0.98 ± 0.13, full supermatrix and MA/MC= 0.91 ± 0.12, reduced supermatrix). Taken at face value, these results would implicate scenario one, unequal magnitudes of change, as a strong potential cause of unequal morphological diversification.
Table 2. Outcomes of phylomorphospace tests for scenario one, unequal magnitudes of morphometric change per phylogenetic branch as revealed by comparison of morphometric branch lengths in clade A and clade C. M, mean morphometric branch length; MA/MC, ratio of mean morphometric branch lengths in clades A and C; P, significance level of observed MA/MC as determined from simulation of random phylomorphospaces under a Brownian model of evolution on ultrametricized versions of the most-parsimonious phylogenies. Asterisks indicate significance at P≤0.05. All values except P are given in mean±standard deviation.
However, reanalysis using equal taxon sampling in clades A and C revealed that the significant difference in mean branch lengths between the clades resulted from the initially more thorough taxon sampling in clade C. Using topologies derived from either the full or reduced supermatrices with equal taxon sampling, the reconstructed morphometric branch lengths in the two clades were much more similar (Table 2). In the most conservative test, using equal taxon sampling and the reduced version of the supermatrix, the reconstructed mean branch lengths were almost identical (MA= 2.56, MC= 2.36). Equalizing taxon sampling also corrects the skew toward higher simulated values of MC (mean simulated MA/MC= 1.04 ± 0.15, full supermatrix and MA/MC= 0.99 ± 0.14, reduced supermatrix). In simulated phylomorphospaces based on phylogenies with equal taxon sampling in clades A and C, at least 24% and as many as 44.3% of the random outcomes generated MA/MC ratios greater than the observed ratio. A phylomorphospace projection using equal taxon sampling (Fig. 7) illustrates the approximately equal morphological step size between adjacent nodes of the phylogeny in the two clades. Thus, a constant-variance Brownian motion process could have easily generated the morphometric branch lengths of both clades, and the small observed difference in pattern does not necessarily imply a difference in process.
As a consequence of the insignificant difference in morphometric branch lengths between the major clades in Anostomoidea once unequal taxon sampling was accounted for, scenario one was discarded as a probable explanation for the unequal morphological diversification in this system. Clade A is not hyperdiverse because its magnitude of morphological change per phylogenetic branch was high relative to clade C, nor is clade C morphologically conservative because of a lack of morphological evolution.
INVESTIGATING UNEQUAL MORPHOLOGICAL DIVERSIFICATION SCENARIO TWO
Scenario two predicted that the highly diverse clade A dispersed through morphospace more efficiently than did clade C, as would be revealed by a lower lineage density in clade A than in clade C (Table 1). This prediction was supported strongly by the phylomorphospaces (Figs. 6 and 7). No matter which sampling regime, supermatrix, measure of lineage density or alternate phylogeny was used in the phylomorphospace projection, the lineage density of clade C was notably higher than that of clade A (Table 3). The different densities of the two clades can be seen visually in Figure s 6 and 7, where the projection of clade A indicates a continuous expansion through morphospace and little convergence, whereas the projection of clade C indicates an initial division of morphospace between the families Curimatidae and Prochilodontidae followed by morphological oscillation around the centers of the morphospace distributions for those two families. As a result of repeated convergence of morphologies within Curimatidae and Prochilodontidae, using true hyperellipsoid volume (D1), lineages in clade C were estimated to be between 3.94 and 5.43 times more densely packed than in clade A (Table 3). Using a sum of the spans of the hyperellipsoid axes to estimate volume (D2) lineages in clade C were between 1.39 and 1.55 times as densely packed as those in clade A.
Table 3. Outcomes of phylomorphospace investigation of scenario two, unequal efficiency at morphological innovation as revealed by comparison of lineage densities in clades A and C. D1, lineage density 1 (based on volume of a bounding hyperellipse); D2, lineage density 2 (based on sum of spans of major axes of a bounding hyperellipse). P=significance of observed DC/DA as determined from simulation of random phylomorphospaces under a Brownian model of evolution on ultrametricized versions of the most-parsimonious phylogenies. Asterisks indicate significance at P≤0.05. All values except P are given in mean±standard deviation.
The estimates of density in each clade have low standard deviations, typically 6% or less of the mean density value, and there was no overlap in the ranges of potential densities for clades A and C. The high similarity of density values resulting from analysis of alternative topologies for both clades suggested that both measures of lineage density are robust to moderate levels of uncertainty in the phylogenetic reconstruction. Density values were essentially invariant with respect to the supermatrix used (Table 3), but the taxonomic sampling regime employed did have a modest effect on the lineage density of clade C, suggesting that the 21% more through taxon sampling in clade C inflated the density values (definition 1) of that clade by approximately 35% in the analyses labeled “all available” (Table 3). Even after correcting for that effect with equal sampling, no sampled phylogeny yielded a lineage density for either clade within or close to the range of values that characterized the other. Assuming that the true phylogeny for clades A and C was among those sampled, the lineage densities of the two clades must be quite different.
Comparison of the observed ratios of lineage densities to ratios calculated from the null distribution of phylomorphospaces revealed that the simulated clades rarely differed so greatly in lineage densities. Analyses using all available taxa indicated probabilities less than 1% whereas those using equal taxon sampling indicated probabilities between 1.0% and 2.7% (Table 3). All one-tailed tests reported in Table 3 retain significance at an α level of 0.05 using the two-tailed alternative. Using true volume to calculate density (D1), the expected density ratio for the simulated clades using equal taxon sampling and the reduced supermatrix was only 1.14 ± 0.78 (the value was 1.10 ± 0.78 for all taxa and the full supermatrix), indicating that the observed density ratios of 3.94–5.43 were well out in the tail of the distribution. A similar conclusion was drawn from densities calculated using a sum of spans (D2), where the expected density ratio was 0.99 ± 0.16, and observed values were 1.39 or greater. This was a strong result, particularly in light of the fact that the variance in outcomes of random walks in morphospace tends to be quite high (Raup and Gould 1974; Pie and Weitz 2005).
Scenario two was maintained as a potential explanation for unequal diversification and was the better supported of the two examined scenarios. Clade A appears to have continuously expanded into new regions of morphospace through all stages of cladogenesis whereas clade C evolved the full range of its modern morphologies early in cladogenesis (Figs. 6 and 7). After that initial saturation of its modern morphospace, clade C appears to have repeatedly generated new species that iterated previously explored morphologies. This difference in the outcome of evolution is unlikely to have been generated as two stochastic outcomes of a Brownian evolutionary process. Instead, one or both clades appear to have evolved under an alternate model of evolution.
CONTINUOUS AND ARRESTED DIVERSIFICATION IN CHARACIFORM FISHES
Application of the phylomorphospace approach to the evolution of Anostomoidea indicated that the high morphological diversity of Anostomidae and Chilodontidae (clade A) relative to Curimatidae and Prochilodontidae (clade C) did not result because lineages within clade A changed morphologically more than did lineages within clade C (scenario one). Instead, the average morphometric distance between adjacent nodes in the phylogenies for all of these families was similar (Table 2). Unequal morphological diversification within the Anostomoidea seems to have been driven by a difference in the mode of morphological diversification, revealed by the large difference in lineage densities between clades A and C (Table 3). In other words, it was not the magnitude of change that differed between the clades, but how that change was distributed throughout morphospace.
In clade C, the most profound morphological difference occurred at the initial cladogenetic event separating Curimatidae from Prochilodontidae on the third relative warp (Fig. 5B, E). After that split, both families continued to speciate and lineages continued to shift in morphology, but morphological evolution of the new lineages proceeded within a fairly narrow range of possibilities that were crossed multiple times within each family. Over the course of cladogenesis, the buildup of lineages in two small regions of morphospace resulted in a clade of many anatomically similar species and high lineage density. Early saturation of morphospace has been demonstrated in the fossil record for many other groups of taxa, including arthropods (Briggs et al. 1992), crinoids (Foote 1994, 1996a), inarticulate brachiopods (Smith and Bunje 1999), mammalian carnivores (Wesley-Hunt 2005) and the Ediacaran fauna (Shen et al. 2008) and may be a common evolutionary phenomenon.
Clade A shows a very different pattern, where after the initial stages of cladogenesis and the split between Chilodontidae and Anostomidae, lineages continued to evolve novel morphologies and annex new regions of morphospace. It is the pattern of continuous innovation in clade A, in contrast to the arrested evolution of novel morphologies in clade C that explains unequal morphological diversification within the Anostomoidea.
Why then, did an earlier study on this same system (Sidlauskas 2007) find evidence for an unequal rate (magnitude) of morphological change? That study, like many other recent contributions (Collar et al. 2005; Collar and Wainwright 2006; O'Meara et al. 2006), used an explicitly Brownian model of evolution to infer differences in the rate of morphological change per unit time. Under such a model, morphological variance is expected to increase over time in a diffusive process (Felsenstein 1985; Ricklefs 2006). In the absence of a detailed phylogenetic hypothesis, I assumed that the crown clade ages for the two sister taxa were likely to be approximately equal and, given clade A's nearly twofold greater morphological variance, calculated that the Brownian rate parameter was significantly likely to have been higher in clade A than in clade C, even accounting for the uncertainty inherent in a random walk along an unknown phylogeny.
Now that greater phylogenetic information is available, it is apparent that the Brownian model of evolution fits the evolution of at least one of the major clades in the Anostomoidea poorly (results herein). Rather than indicating a diffusive process, the phylomorphospace pattern for clade C (Figs. 6 and 7) reveals that the Curimatidae and Prochilodontidae each seem to oscillate around a separate point in morphospace, suggesting that a constrained OU model of evolutionary change with multiple optima may fit each of those families much more closely than does an unconstrained Brownian model (Butler and King 2004). It is also possible that lineages in clade A are diverging morphologically in a non-Brownian fashion, perhaps in accord with the predictions of a niche-filling (Harvey and Rambaut 2000) or early burst/declining rates (Pagel 1997, 1999) model. When a time-calibrated phylogeny for the Anostomoidea is available, it may be possible to tease apart which clade is best modeled by non-Brownian evolution by applying hierarchical likelihood tests (Harmon et al. 2008). No matter which clade's evolution is better described by an alternate model, it seems likely that model misspecification may explain the earlier indication of a significant difference in the rate of morphological change in clades A and C (Sidlauskas 2007).
DOES THE WHOLE ANOSTOMOIDEA REPRESENT AN ADAPTIVE RADIATION?
The fact that the four families in clades A and C together partition morphospace with almost no overlap among them (Figs. 6 and 7) is suggestive of a burst of morphological diversification associated with the initial speciation events in the Anostomoidea (adaptive radiation by partitioning morphological diversity among, rather than within subclades in the sense of Harmon et al. 2003), but that pattern is also consistent with more gradual diversification followed by the extinction of intermediate or overlapping forms (Raup and Gould 1974; Foote 1990, 1997; Erwin 2007). Partitioning of morphospace can also be generated by a Brownian random walk with logistic diversification, which models a carrying capacity on the number of lineages in morphospace (Pie and Weitz 2005). Thus, the partitioning of morphospace among the basal lineages in the Anostomoidea alone is an insufficient demonstration of adaptive radiation. An eventual temporal calibration of the phylogeny for the whole Anostomoidea (clades A and C together) based on molecular data may reveal whether the initial splits in the phylogeny are closely packed, and would permit comparison of the increase in lineage diversity and morphological diversity over time following the neontological approach of Harmon et al. (2003). In the absence of that test, there is no particular reason to assume that morphological diversification was linked to an early burst of speciation in the whole Anostomoidea or any portion of it, as would be predicted by an adaptive radiation scenario (Schluter 2000). It is equally possible that the Anostomoidea represent a nonadaptive radiation (Gittenberger 1991; Futuyma 2003; Kozak et al. 2006), in which speciation and the accumulation of ecological and morphological novelties were decoupled.
POSSIBLE UNDERLYING CAUSES
Sidlauskas (2007, 312–314) discussed several clade-specific anatomical or ecological factors that may have promoted morphological innovation in clade A or constrained lineages within clade C to vary only within a small range of morphologies. Explanations for clade C focused on the acquisition of a completely detritivorous ecology (Bowen 1983; Bowen et al. 1984) with attendant loss of teeth affixed to the oral jaws, specialization of the pharyngeal arches, evolution of a complex epibranchial organ used in filtering substrate, and acquisition of a very long intestine (see Vari 1983, 1989a; Castro and Vari 2004 for detailed descriptions of these anatomical features). Together these specializations allow Curimatidae and Prochilodontidae to exploit an ecological niche largely untapped by any other South American member of Characiformes (Bowen 1983; Flecker 1996). In shallow waters detritus is a very abundant resource (Flecker 1996) with a reasonable nutritive value (Bowen 1979; Pieczyńska 1993) that permits members of clade C to reach large body sizes up to 800 mm total length in Ichthyoelephas longirostris (Patiño 1973; Castro and Vari 2003, 2004) and to form enormous migratory schools that can comprise as much as 50% of a region's fish biomass (Bowen 1983) and sustain up to 90% of the commercial fisheries in some regions of Amazonia (Goulding et al. 1988). Experimental removal of the detritivorous species in clade C has been shown to radically alter the carbon cycle (Taylor et al. 2006), sediment accrual, and invertebrate communities (Flecker 1996) of South American rivers, illustrating the importance of detritus and detritivory to the ecology of aquatic systems and the absence of other ecologically equivalent groups of fishes in the Neotropics. It may be that specialization on a superabundant resource has placed the members of clade C on an adaptive peak with little competition for resources or pressure to evolve new ecologies. It may also be that the evolution of the fairly profound suite of morphological changes needed to annex detritus as a food resource, including the loss of teeth affixed to the oral jaws in adults (Vari 1983), acts as an anatomical constraint that closes some evolutionary options, such as durophagy, herbivory, and carnivory to members of clade C. Either or both of these factors may limit the morphological evolution of Curimatidae and Prochilodontidae.
Within clade A, Sidlauskas (2007) hypothesized that evolution of a highly elongate quadrate repositioned the lower jaw joint in advance of the eye and permitted the evolution of upturned jaw morphologies that were inaccessible to fishes with the plesiomorphic position of that joint ventral to the neurocranium. This study revealed that there is a trend toward increasingly negative values of RW1 within clade A (the blue clade in Figs. 6 and 7), which corresponds to the evolution of an increasingly elongate quadrate and a more anteriorly positioned lower jaw joint. The progression of increasingly elongate quadrate morphologies shown from top to bottom in Sidlauskas (2007, Fig. 2) corresponds generally to the leftwards trend in morphospace, with the taxa at the negative extreme of RW1 including members of the genera Anostomus, Gnathodolus, Laemolyta, Petulanos, Pseudanos, Sartor, and Synaptolaemus, which have the most elongate quadrates and most extremely upturned jaws of any examined species (for condition in Sartor, see Sidlauskas 2007, Figure 2D and Sidlauskas and Vari 2008, Figure 3 and 7). The trend toward negative values on RW1 in the Anostomidae persists even when phylogenetic characters correlated with that morphometric change were removed from the supermatrix and new phylogenies were generated (Fig. 6D–F). Thus, recent phylogenetic work confirms that the initial elongation of the quadrate and relocation of the lower jaw joint preceded the evolution of the most morphologically extreme species and may have been an intermediate step necessary for the annexation of the portion of morphospace characterized by the most negative values of RW1.
Developmental and phylogenetic evidence suggests a heterochronic mechanism for that annexation. Members of Rhytiodus and Schizodon, the sister group to the clade containing the seven genera with upturned jaws cited above, change from having upturned jaws as juveniles to forward-facing jaws as adults (Santos 1980; Sidlauskas et al. 2007). Neotenic fixation of that juvenile morphology may explain the origin of the upwards facing jaws that characterize the most morphologically divergent adult members of Anostomidae. Given the findings above, quadrate elongation should be maintained as a potential promoter of the high morphological diversity that characterizes clade A.
Testing which of the clade-specific factors discussed above is most likely to have promoted or restricted morphological diversification will require comparison with other groups of fishes that have independently evolved similar synapomorphies. For example, several other groups of tropical freshwater fishes have independently evolved detritivorous habits and present fertile ground for comparison, including the African characiforms in the family Citharinidae (Daget 1962a,b) and some African cichlids such as Sarotherodon and Tilapia (Bowen 1979, 1981, 1988). Work is ongoing to determine whether the evolution of detritivory is associated with increased lineage density and arrested morphological diversification in the African characiforms as well. In the case studies on both continents, it will also be important to determine whether the detritivorous clade or its sister is unusual in the broader context of characiform evolution, which mandates comparison of linage densities and morphometric branch lengths with immediate outgroups. In the case of Anostomoidea, there is an emerging consensus that either Hemiodontidae or Prochilodontidae, or both together, form the sister taxon (Buckup 1998; Calcagnotto et al. 2005). Phylomorphospace projections for those families will help reveal whether continuous morphological innovation or arrested morphological diversification typifies characiform evolution.
STRENGTHS OF THE PHYLOMORPHOSPACE APPROACH
Clades with high morphological diversity are not necessarily the ones that changed the most; they may simply be the clades that distributed change most widely in morphospace. The major strength of the phylomorphospace approach is its ability to infer which of these two scenarios better explains particular instances of unequal morphological diversification from phylogenies that lack branch lengths. Much recent work in this area has concentrated solely upon the effects on morphological diversity of varying the rate of morphological change (Ackerly and Nyffeler 2004; O'Meara et al. 2006; Sidlauskas 2007) and has not considered variation in the distribution of change through morphospace explicitly. The integration of the concept of lineage density into phylomorphospace analysis is an important advance, as it can reveal discontinuities in the pattern of inferred evolution that may be missed by other methods of analysis. For example, methods that focus exclusively on the absolute rate of change of morphology per unit time or per phylogenetic branch would be unable to distinguish between the extreme cases of lineages within a clade alternating between just two distinct phenotypes separated by a given morphometric distance, and lineages evolving an entirely new phenotype separated from the old by that same distance at each split in the phylogeny. Unequal morphological diversification is not always a result of unequal magnitude or rate of change; it can also result from inequality in the realized directions of change.
The OU approach advocated by Butler and King (2004) also considers the rate of morphological change and its directionality (specifically, the intensity of inferred attraction to one or more phenotypic optima), but that method is designed for one or more univariate characters considered separately, not a multivariate morphospace taken as a whole. The phylomorphospace approach is designed for simultaneous analysis of a dataset of continuously varying and uncorrelated characters (such as the output of a multivariate ordination). The phylomorphospace statistics are also relatively simple and can be calculated for large families of trees, such as a set of most parsimonious topologies, a bootstrap sample or a Bayesian posterior distribution. As the number of available phylogenies and character datasets increases, synthetic approaches to tree building uniting data on hundreds of species are becoming increasingly common (Sanderson et al. 1998; Bininda-Emonds and Sanderson 2001; Bininda-Emonds 2004; Driskell et al. 2004; Bininda-Emonds et al. 2007; O'Leary and Gatesy 2007). Supermatrix and supertree methods frequently return large families of nonultrametric trees, which the phylomorphospace approach can handle as input by simulating possible branch lengths, an approach that could also be adapted profitably to OU and other generalized least squares approaches that require ultrametric phylogenies. Thus, by accommodating multivariate datasets and phylogenetic uncertainty simultaneously, phylomorphospaces can fill a growing niche in comparative phylogenetic analysis.
CAVEATS AND ASSUMPTIONS OF THE PHYLOMORPHOSPACE APPROACH
The major assumption involved in analyzing a phylomorphospace is that the ancestral state reconstruction, and hence the projection of phylogeny into morphospace, approximates the true morphology of the ancestors and history of the clade. For ancestral state reconstruction in a morphospace via squared change parsimony to work effectively, the ancestor represented by a node in a phylogeny must have been likely to possess a morphology intermediate to the morphology of the nodes connected to it. Sparse taxon sampling or the passage of so much time that descendant lineages have moved very far away from the ancestral condition can cause ancestral state reconstruction to founder (Martins 1999; Salisbury and Kim 2001; Erwin 2007). The most likely cause of sparse sampling is significant extinction, particularly of peripheral morphologies, which can erase the evidence of passage through particular regions of morphospace (Ciampaglio et al. 2001). Skewed taxon sampling, such as the omission of large modern subclades could generate a similar pattern. Studies based on exclusively modern taxa assume that there are not so many nodes missing from the phylogeny that the ancestral state reconstruction becomes meaningless, but this assumption is difficult to test and the effect of extinction is a serious concern, particularly for very old lineages. Previous morphospace analyses of lineages with good fossil records have certainly shown that the limits of morphospace explored by a clade can fluctuate over time (Ciampaglio 2002, 2004; McGowan 2004; Villier and Korn 2004). It should also be recognized that unequal extinction is another potential cause of unequal morphological diversification, and that expansion of a clade's morphology due to ecological release following a major extinction has been documented repeatedly in the fossil record (Raup 1994; Foote 1996a; Roy 1996; Jablonski 2000; Ciampaglio 2004). Unfortunately, the effects of mass extinction on the morphological recovery and diversification of clades cannot be tested using only modern taxa. The average rates of speciation and extinction used to generate possible branch lengths in the simulations of morphological evolution implied an average survivorship of about 40%, but without a detailed fossil record for Anostomoidea there is no real way to know whether that rate is accurate. Given that the entire known fossil record for this clade consists of a single whole specimen and a few isolated teeth (Roberts 1975; Lundberg 1997), it is unlikely that a reconstruction of the history of anostomoid extinction will ever be possible.
Ancestral state reconstruction will also work best when the magnitude of morphological change on any given branch is moderate compared to the range of morphologies exhibited by the total clade. If the average step size of morphological change is very large, then the position of the modern species may not be informative as to the morphology of even their recent common ancestors, let alone the morphology of the basal nodes in the phylogeny (Schultz et al. 1996; Losos 1999; Omland 1999). Species will also not resemble their ancestors closely when the rate of attraction toward an adaptive peak in an OU process is very high. Fortunately, the fact that closely related species and genera tend to be proximate in the morphospace for the Anostomoidea, particularly within clade A (Figs. 5 and 6), and that the four families clearly partition the modern morphospace among them suggests that lineages within each of the clades did not cross the whole of morphospace repeatedly and that the strength of attraction to local optima is not sufficient to erase the signal of phylogeny. It is unlikely, but not impossible, that very high rates of morphological change are obscuring the pattern of dispersion of the clades throughout morphospace in this case study.
Care must be taken in interpreting the magnitude of change on each phylogenetic branch as a rate of morphological change. If the ancestral state reconstruction is based on squared-change parsimony, phylomorphospace analysis yields the mean magnitude of morphological change per phylogenetic branch, which is essentially a rate of change per speciation event, not per unit time. These rates are correlated, and higher values of the Brownian rate parameter do tend to produce longer distances between adjacent nodes in simulated phylomorphospaces (results not shown), but they are not equivalent. If a time calibration is available, estimated morphological rates per branch can be converted to rates in years by dividing the morphometric branch lengths calculated in phylomorphospace by the inferred time elapsed along each branch. This will yield a separate estimate of the rate of change per unit time on each branch of the phylogeny. These estimates can be partitioned into subclades with high and low morphological diversity and differences in mean rate between the subclades (scenario one) can again be tested by simulation. The test of scenario two will not vary between phylogenies with and without branch lengths in units of time because the calculation of lineage density depends solely upon total morphometric branch length and the volume of morphospace explored by a clade. Time does not enter into the comparison of lineage densities unless it is used implicitly in the calculation of ancestral states, for example by employing Schluter's (1997) method on an ultrametric, time-calibrated tree.
It should also be recognized that the output of a phylomorphospace study depends critically on which morphologies were used to construct the morphospace. Analysis of different anatomical systems may yield different patterns of morphological diversity. For example, the gill arches of the members of clade C are much more variable than the gill arches of clade A, with 87 characters in the supermatrix describing phylogenetically informative variation in that system in clade C, compared to 22 such characters in clade A (some characters are informative about relationships within both clades). Had a morphospace been constructed using landmarks on the gill arches rather than the remainder of the skull, clade C would likely have been found to have higher morphological variance and to occupy a greater volume of gill morphospace. Disparity is found where one looks for it, and results based on one anatomical system should not be extrapolated to others.
Associate Editor: G. Hunt
Special thanks go to my Ph.D. thesis advisors B. Chernoff and M. Westneat and thesis committee members M. Foote, S. Hackett, L. V. Valen, and R. Vari, who supervised the collection of much of the data underlying this article and its preliminary interpretation. I also thank M. Alfaro, D. Eernisse, L. Harmon, S. Hopkins, G. Hunt, C. Kammerer, B. O'Meara, S. Otto, S. Price, V. L. Roth, C. T. Stayton, D. Swofford, C. Thacker, M. Whitlock, G. Wray, and D. Zwickl for criticisms of various manuscript drafts and/or discussion of the methods used herein. This research, data synthesis, analysis, and writing were supported by a postdoctoral fellowship from the National Evolutionary Synthesis Center, NESCent (NSF EF-0423641). The majority of the morphometric dataset and the phylogeny of Anostomidae employed herein were assembled with the support of EPA STAR Graduate Fellowship 915987, NSF Doctoral Dissertation Improvement Grant #DEB0412364, The Field Museum's Lester Armour Graduate Fellowship, the Herbert R. and Evelyn Axelrod Chair in Systematic Ichthyology in the Division of Fishes of the National Museum of Natural History, Smithsonian Institution, The University of Chicago's Hinds Fund and a Böhlke Award from the Academy of Natural Sciences of Philadelphia. Richard Vari and Sandra Raredon at the National Museum of Natural History provided free time on and gracious technical assistance with their digital x-ray system.
Table Appendix.. Species, lot numbers, and numbers of specimens for newly added or reidentified material used to create the morphospace. Institutional abbreviations are as listed at http://www.asih.org/files/codons.pdf. The remainder of the material appears in table A1 of Sidlauskas (2007). The specimens originally identified as Leporinus desmotes in Sidlauskas (2007) are more properly assigned to L. jatuncochi (Sidlauskas and Vari 2008) and appear herein under that name. Following Sidlauskas and Vari (2008), the specimens originally assigned to L. ecuadorensis have been split into L. ecuadorensis and L. cf. ecuadorensis. The specimens originally identified as L. maculatus appear herein as L. pellegrinii; these two very similar species may be synonymous (see discussion in Géry et al. 1988; Sidlauskas and Vari 2008), but the pigmentation of the cited material matches the description of L. pellegrinii most closely. The material identified as Schizodon sp. A in Sidlauskas (2007) corresponds to the recently described Schizodon scotorhabdotus (Sidlauskas et al. 2007).