Biases with the Generalized Euclidean Distance measure in disparity analyses with high levels of missing data

The Generalized Euclidean Distance (GED) measure has been extensively used to conduct morphological disparity analyses based on palaeontological matrices of discrete characters. This is in part because some implementations allow the use of morphological matrices with high percentages of missing data without needing to prune taxa for a subsequent ordination of the data set. Previous studies have suggested that this way of using the GED may generate a bias in the resulting morphospace, but a detailed study of this possible effect has been lacking. Here, we test whether the percentage of missing data for a taxon artificially influences its position in the morphospace, and if missing data affects pre‐ and post‐ordination disparity measures. We find that this use of the GED creates a systematic bias, whereby taxa with higher percentages of missing data are placed closer to the centre of the morphospace than those with more complete scorings. This bias extends into pre‐ and post‐ordination calculations of disparity measures and can lead to erroneous interpretations of disparity patterns, especially if specimens present in a particular time interval or clade have distinct proportions of missing information. We suggest that this implementation of the GED should be used with caution, especially in cases with high percentages of missing data. Results recovered using an alternative distance measure, Maximum Observed Rescaled Distance (MORD), are more robust to missing data. As a consequence, we suggest that MORD is a more appropriate distance measure than GED when analysing data sets with high amounts of missing data.     

JOINED AT THE HIP: LINKED CHARACTERS AND THE PROBLEM OF MISSING DATA IN STUDIES OF DISPARITY

Paleontological investigations into morphological diversity, or disparity, are often confronted with large amounts of missing data. We illustrate how missing discrete data affect disparity using a novel simulation for removing data based on parameters from published datasets that contain both extinct and extant taxa. We develop an algorithm that assesses the distribution of missing characters in extinct taxa, and simulates data loss by applying that distribution to extant taxa. We term this technique “linkage.” We compare differences in disparity metrics and ordination spaces produced by linkage and random character removal. When we incorporated linkage among characters, disparity metrics declined and ordination spaces shrank at a slower rate with increasing missing data, indicating that correlations among characters govern the sensitivity of disparity analysis. We also present and test a new disparity method that uses the linkage algorithm to correct for the bias caused by missing data. We equalized proportions of missing data among time bins before calculating disparity, and found that estimates of disparity changed when missing data were taken into account. By removing the bias of missing data, we can gain new insights into the morphological evolution of organisms and highlight the detrimental effects of missing data on disparity analysis.     

Mapping cladograms into morphospaces

In cladistic analyses, taxa are grouped hierarchically into clades according to shared apomorphic character states to construct cladograms; cladograms are interpretable as phylogenetic hypotheses. In morphological space analyses, organism forms are represented as points in morphospaces; point proximities in morphospaces represent similarities that might be attributable to phenetic convergence and, consequently, may correspond inaccurately with hypothesized evolutionary relationships. A method for synthesizing phylogenetic results that are interpreted from cladistic analyses with phenetic results that are obtained from morphological space analyses is presented here; in particular, points that represent forms typifying taxa in morphospace are assigned as terminal nodes for appropriate cladograms that are mapped into morphospaces by positioning nonterminal nodes and orienting internodes according to a geometric algorithm. Nonterminal nodes may be interpreted as ancestors in phylogenetic hypotheses and occupy positions that represent particular organism forms in morphospaces. By mapping cladograms into morphospaces, therefore, evolutionary morphologists can reconstruct ancestral morphologies and test historical transformation hypotheses.     

Journeys through discrete‐character morphospace: synthesizing phylogeny,tempo, and disparity

Palaeontologists have long employed discrete categorical data to capture morphological variation in fossil species, using the resulting character–taxon matrices to measure evolutionary tempo, infer phylogenies and capture morphological disparity. However, to date these have been seen as separate approaches despite a common goal of understanding morphological evolution over deep time. Here I argue that there are clear advantages to considering these three lines of enquiry in a single space: the phylomorphospace. Conceptually these high‐dimensional spaces capture how a phylogenetic tree explores morphospace and allow us to consider important process questions around evolutionary rates, constraints, convergence and directional trends. Currently the literature contains fundamentally different approaches used to generate such spaces, with no direct comparison between them, despite the differing evolutionary histories they imply. Here I directly compare five different phylomorphospace approaches, three with direct literature equivalents and two that are novel. I use a single empirical case study of coelurosaurian theropod dinosaurs (152 taxa, 853 characters) to show that under many analyses the literature‐derived approaches tend to reflect introduced phylogenetic (rather than the intended morphological) signal. The two novel approaches, which produce limited ancestral state estimates prior to ordination, are able to minimize this phylogenetic signal and thus exhibit more realistic amounts of phylogenetic signal, rate heterogeneity, and convergent evolution.     

Comparable disparity in the appendicular skeleton across the fish–tetrapod transition,and the morphological gap between fish and tetrapod postcrania

Appendicular skeletal traits are used to quantify changes in morphological disparity and morphospace occupation across the fish–tetrapod transition and to explore the informativeness of different data partitions in phylogeny reconstruction. Anterior appendicular data yield trees that differ little from those built from the full character set, whilst posterior appendicular data result in considerable loss of phylogenetic resolution and tree branch rearrangements. Overall, there is a significant incongruence in the signals associated with pectoral and pelvic data. The appendicular skeletons of fish and tetrapods attain similar levels of morphological disparity (at least when data are rarefied at the maximum sample size for fish in our study) and occupy similarly sized regions of morphospace. However, fish appear more dispersed in morphospace than tetrapods do. All taxa show a heterogeneous distribution in morphospace, and there is a clear separation between fish and tetrapods despite the presence of several evolutionarily intermediate taxa.     

Time for a rethink: time sub‐sampling methods in disparity‐through‐time analyses

Disparity‐through‐time analyses can be used to determine how morphological diversity changes in response to mass extinctions, or to investigate the drivers of morphological change. These analyses are routinely applied to palaeobiological datasets, yet, although there is much discussion about how to best calculate disparity, there has been little consideration of how taxa should be sub‐sampled through time. Standard practice is to group taxa into discrete time bins, often based on stratigraphic periods. However, this can introduce biases when bins are of unequal size, and implicitly assumes a punctuated model of evolution. In addition, many time bins may have few or no taxa, meaning that disparity cannot be calculated for the bin and making it harder to complete downstream analyses. Here we describe a different method to complement the disparity‐through‐time tool‐kit: time‐slicing. This method uses a time‐calibrated phylogenetic tree to sample disparity‐through‐time at any fixed point in time rather than binning taxa. It uses all available data (tips, nodes and branches) to increase the power of the analyses, specifies the implied model of evolution (punctuated or gradual), and is implemented in R. We test the time‐slicing method on four example datasets and compare its performance in common disparity‐through‐time analyses. We find that the way we time sub‐sample taxa can change our interpretations of the results of disparity‐through‐time analyses. We advise using multiple methods for time sub‐sampling taxa, rather than just time binning, to gain a better understanding disparity‐through‐time.     

Dinosaur egg‐laying and nesting: The case of an Upper Maastrichtian site at Rennes‐le‐Chateau (Aude,France)

Variation in longevity of taxa in the fossil record has been recognized, but few studies have tested for correlation between position in morphospace and differential survivorship. A sample of 322 Triassic ammonoid species, each one representing a genus, was studied to test whether longer-lived genera were significantly further from the centre of morphospace than shorter-lived genera. Two empirical morphospaces were constructed from morphological data, and the deviation of each genus from the “average form” (centroid) was calculated. Spearman Rank Correlation and Kruskal-Wallis tests were used to test for any significant relationships between distance from the centre of morphospace and longevity. Some longer-lived taxa tended to plot further from the centre of morphospace, but the amounts of variance in longevity accounted for were small and largely statistically non-significant. Ammonoid clade-level morphological stasis appears to be the product of repeated reoccupation of the centre of morphospaces after taxonomic turnover events.     

Categorical versus geometric morphometric approaches to characterizing the evolution of morphological disparity in Osteostraci (Vertebrata,stem Gnathostomata)

Morphological variation (disparity) is almost invariably characterized by two non-mutually exclusive approaches: (1) quantitatively, through geometric morphometrics; and (2) in terms of discrete, ‘cladistic’, or categorical characters. Uncertainty over the comparability of these approaches diminishes the potential to obtain nomothetic insights into the evolution of morphological disparity and the few benchmarking studies conducted so far show contrasting results. Here, we apply both approaches to characterizing morphology in the stem-gnathostome clade Osteostraci in order to assess congruence between these alternative methods as well as to explore the evolutionary patterns of the group in terms of temporal disparity and the influence of phylogenetic relationships and habitat on morphospace occupation. Our results suggest that both approaches yield similar results in morphospace occupation and clustering, but also some differences indicating that these metrics may capture different aspects of morphology. Phylomorphospaces reveal convergence towards a generalized ‘horseshoe’-shaped cranial morphology and two strong trends involving major groups of osteostracans (benneviaspidids and thyestiids), which probably reflect adaptations to different lifestyles. Temporal patterns of disparity obtained from categorical and morphometric approaches appear congruent, however, disparity maxima occur at different times in the evolutionary history of the group. The results of our analyses indicate that categorical and continuous data sets may characterize different patterns of morphological disparity and that discrepancies could reflect preservational limitations of morphometric data and differences in the potential of each data type for characterizing more or less inclusive aspects of overall phenotype.     

Allometric space and allometric disparity: a developmental perspective in the macroevolutionary analysis of morphological disparity

Here, we advance novel uses of allometric spaces--multidimensional spaces specifically defined by allometric coefficients--with the goal of investigating the focal role of development in shaping the evolution of morphological disparity. From their examination, operational measures of allometric disparity can be derived, complementing standard signals of morphological disparity through an intuitive and process-oriented refinement of established analytical protocols used in disparity studies. Allometric spaces thereby become a promising context to reveal different patterns of evolutionary developmental changes and to assess their relative prevalence and importance. Such spaces offer a novel domain of investigation of phenotypic variation and should help in detecting large-scale trends, thus placing various macroevolutionary phenomena in an explicitly developmental context. Ammonoidea (Cephalopoda) at the Lower-Middle Jurassic transition were chosen as a case study to illustrate this methodological approach. We constructed two phenotypic spaces: a static, adult one (adult morphospace) and a dynamic, developmental one (allometric space). Comparative disparity analyses show a strikingly stable occupation in both spaces, despite extensive change in taxonomic composition. In contrast, disparity analyses of subclades reveal clearly distinct morphological and allometric disparity dynamics. Allometric approaches allow developmental insights into morphological diversification otherwise intractable from the analysis of adult morphospace alone.     

Do cladistic and morphometric data capture common patterns of morphological disparity?

The distinctly non‐random diversity of organismal form manifests itself in discrete clusters of taxa that share a common body plan. As a result, analyses of disparity require a scalable comparative framework. The difficulties of applying geometric morphometrics to disparity analyses of groups with vastly divergent body plans are overcome partly by the use of cladistic characters. Character‐based disparity analyses have become increasingly popular, but it is not clear how they are affected by character coding strategies or revisions of primary homology statements. Indeed, whether cladistic and morphometric data capture similar patterns of morphological variation remains a moot point. To address this issue, we employ both cladistic and geometric morphometric data in an exploratory study of disparity focussing on caecilian amphibians. Our results show no impact on relative intertaxon distances when different coding strategies for cladistic characters were used or when revised concepts of homology were considered. In all instances, we found no statistically significant difference between pairwise Euclidean and Procrustes distances, although the strength of the correlation among distance matrices varied. This suggests that cladistic and geometric morphometric data appear to summarize morphological variation in comparable ways. Our results support the use of cladistic data for characterizing organismal disparity.     

The radiation of cynodonts and the ground plan of mammalian morphological diversity

Cynodont therapsids diversified extensively after the Permo-Triassic mass extinction event, and gave rise to mammals in the Jurassic. We use an enlarged and revised dataset of discrete skeletal characters to build a new phylogeny for all main cynodont clades from the Late Permian to the Early Jurassic, and we analyse models of morphological diversification in the group. Basal taxa and epicynodonts are paraphyletic relative to eucynodonts, and the latter are divided into cynognathians and probainognathians, with tritylodonts and mammals forming sister groups. Disparity analyses reveal a heterogeneous distribution of cynodonts in a morphospace derived from cladistic characters. Pairwise morphological distances are weakly correlated with phylogenetic distances. Comparisons of disparity by groups and through time are non-significant, especially after the data are rarefied. A disparity peak occurs in the Early/Middle Triassic, after which period the mean disparity fluctuates little. Cynognathians were characterized by high evolutionary rates and high diversity early in their history, whereas probainognathian rates were low. Community structure may have been instrumental in imposing different rates on the two clades.     

Do different disparity proxies converge on a common signal? Insights from the cranial morphometrics and evolutionary history of Pterosauria (Diapsida: Archosauria)

Disparity, or morphological diversity, is often quantified by evolutionary biologists investigating the macroevolutionary history of clades over geological timescales. Disparity is typically quantified using proxies for morphology, such as measurements, discrete anatomical characters, or geometric morphometrics. If different proxies produce differing results, then the accurate quantification of disparity in deep time may be problematic. However, despite this, few studies have attempted to examine disparity of a single clade using multiple morphological proxies. Here, as a case study for this question, we examine the disparity of the volant Mesozoic fossil reptile clade Pterosauria, an intensively studied group that achieved substantial morphological, ecological and taxonomic diversity during their 145+ million-year evolutionary history. We characterize broadscale patterns of cranial morphological disparity for pterosaurs for the first time using landmark-based geometric morphometrics and make comparisons to calculations of pterosaur disparity based on alternative metrics. Landmark-based disparity calculations suggest that monofenestratan pterosaurs were more diverse cranially than basal non-monofenestratan pterosaurs (at least when the aberrant anurognathids are excluded), and that peak cranial disparity may have occurred in the Early Cretaceous, relatively late in pterosaur evolution. Significantly, our cranial disparity results are broadly congruent with those based on whole skeleton discrete character and limb proportion data sets, indicating that these divergent approaches document a consistent pattern of pterosaur morphological evolution. Therefore, pterosaurs provide an exemplar case demonstrating that different proxies for morphological form can converge on the same disparity signal, which is encouraging because often only one such proxy is available for extinct clades represented by fossils. Furthermore, mapping phylogeny into cranial morphospace demonstrates that pterosaur cranial morphology is significantly correlated with, and potentially constrained by, phylogenetic relationships.     

Discrete and morphometric traits reveal contrasting patterns and processes in the macroevolutionary history of a clade of scorpions

Many palaeontological studies have investigated the evolution of entire body plans, generally relying on discrete character‐taxon matrices. In contrast, macroevolutionary studies performed by neontologists have mostly focused on morphometric traits. Although these data types are very different, some studies have suggested that they capture common patterns. Nonetheless, the tests employed to support this claim have not explicitly incorporated a phylogenetic framework and may therefore be susceptible to confounding effects due to the presence of common phylogenetic structure. We address this question using the scorpion genus Brachistosternus Pocock 1893 as case study. We make use of a time‐calibrated multilocus molecular phylogeny, and compile discrete and traditional morphometric data sets, both capturing the overall morphology of the organisms. We find that morphospaces derived from these matrices are significantly different, and that the degree of discordance cannot be replicated by simulations of random character evolution. Moreover, we find strong support for contrasting modes of evolution, with discrete characters being congruent with an ‘early burst’ scenario whereas morphometric traits suggest species‐specific adaptations to have driven morphological evolution. The inferred macroevolutionary dynamics are therefore contingent on the choice of character type. Finally, we confirm that metrics of correlation fail to detect these profound differences given common phylogenetic structure in both data sets, and that methods incorporating a phylogenetic framework and accounting for expected covariance should be favoured.     

Morphological disparity in theropod jaws: comparing discrete characters and geometric morphometrics

Disparity, the diversity of form and function of organisms, can be assessed from cladistic or phenetic characters, and from discrete characters or continuous characters such as landmarks, outlines, or ratios. But do these different methods of assessing disparity provide comparable results? Here we provide evidence that all metrics correlate significantly with each other and capture similar patterns of morphological variation. We compare three methods of capturing morphological disparity (discrete characters, geometric morphometric outlines and geometric morphometric landmarks) in coelurosaurian dinosaurs. We standardize our study by focusing all our metrics on the mandible, so avoiding the risk of confounding disparity methods with anatomical coverage of the taxa. The correlation is strongest between the two geometric morphometric methods, and weaker between the morphometric methods and the discrete characters. By using phylogenetic simulations of discrete character and geometric morphometric data sets, we show that the strength of these correlations is significantly greater than expected from the evolution of random data under Brownian motion. All disparity metrics confirm that Maniraptoriformes had the highest disparity of all coelurosaurians, and omnivores and herbivores had higher disparity than carnivores.     

Morphological disparity and evolutionary rates of cranial and postcranial characters in sloths (Mammalia,Pilosa, Folivora)

Sloth morphological evolution has been widely studied qualitatively, with comparative anatomy and morpho-functional approaches, or through quantitative assessments of morphological variation using morphometrics. Only recently, however, have folivoran morphological disparity and evolutionary rates begun to be evaluated using discrete character data. Nonetheless, patterns of morphological evolution in separate character partitions have not been investigated, neither the relative influence of, on the one hand, phylogeny, and on the other, dietary and locomotory adaptations of sloths. Here we evaluate those patterns using a phylomorphospace approach, quantifying morphological disparity and evolutionary rates, and investigating possible drivers of morphological evolution for cranial and postcranial characters in Folivora. The evolution of the morphology in those partitions is associated with distinct patterns of disparity among clades and ecological groups, even though the two partitions do not differ substantially in overall evolutionary tempo. Historical processes shaped the morphological evolution of sloths more consistently than ecological ones, although changes in postcranial characters also seem to be associated with locomotory adaptations, in which morphological convergences were much more common. We also discuss important methodological trade-offs in investigations of partitioned datasets mostly composed of fossil taxa.     

The disparity of priapulid, archaeopriapulid and palaeoscolecid worms in the light of new data

Priapulids and their extinct relatives, the archaeopriapulids and palaeoscolecids, are vermiform, carnivorous ecdysozoans with an armoured, extensible proboscis. These worms were an important component of marine communities during the Palaeozoic, but were especially abundant and diverse in the Cambrian. Today, they comprise just seven genera in four families. Priapulids were among the first groups used to test hypotheses concerning the morphological disparity of Cambrian fossils relative to the extant fauna. A previous study sampled at the generic level, concluding that Cambrian genera embodied marginally less morphological diversity than their extant counterparts. Here, we sample predominantly at the species level and include numerous fossils and some extant forms described in the last fifteen years. Empirical morphospaces for priapulids, archaeopriapulids and palaeoscolecids are relatively insensitive to changes in the taxon or character sample: their overall form has altered little, despite the markedly improved sampling. Cambrian and post-Cambrian genera occupy adjacent rather than broadly overlapping regions of these spaces, and Cambrian species still show lower morphological disparity than their post-Cambrian counterparts. Crucially, the significance of this difference has increased with improved taxon sampling over research time. In contrast with empirical morphospaces, the phylogeny of priapulids, archaeopriapulids and palaeoscolecids derived from morphological characters is extremely sensitive to details of taxon sampling and the manner in which characters are weighted. However, the extant Priapulidae and Halicryptidae invariably resolve as sister families, with this entire clade subsequently being sister group to the Maccabeidae. In our most inclusive trees, the extant Tubiluchidae are separated from these other living taxa by a number of small, intervening fossil clades.