Disparity Metrics Research Articles

A morphospace of planktonic marine diatoms. II. Sampling standardization and spatial disparity partitioning

AbstractMorphospace occupation through time provides a view of diversification distinct from the more familiar taxonomic tabulations. However, this view is subject to the same geological biases long recognized in studies of taxonomic diversification, where techniques for correcting secular bias in sampling have become standard practice. In this study, we apply sampling standardization techniques to a morphospace investigation to test whether observed stratigraphic trends in morphospace occupation are artifacts of trends in sampling. When sampling bias is corrected by randomized subsampling, all disparity metrics show stationary patterns, or at most directional changes of small magnitude. Metrics describing the average dispersion of taxa in morphospace are less subject to sampling bias than those describing the total extent of morphospace occupied. We also investigate a measure of disparity that is insensitive to sampling intensity, introducing a geographic component of morphological disparity. By analogy to α and β components of taxonomic diversity, we suggest the notions of α and β disparity, and find that α disparity remains roughly constant through time. Our analysis also allows us to present the first taxonomic diversity curve of diatoms under shareholder quorum subsampling (SQS), showing similar results to previously published subsampling methods: a roughly twofold rise over the Cenozoic, with peak diversity around the Eocene/Oligocene boundary. Tests for methodological bias from choices in ordination method and data culling during morphospace construction indicate that our results are relatively insensitive to both factors: Cenozoic occupation of planktonic diatom morphospace is largely unchanging. We find a similarly stationary pattern when we directly analyze the morphological data, seeing no change in the prevalence of taxa with different sets of morphological characters. More broadly, our results make clear that a complete view of morphological disparity must consider sampling biases, which can be addressed with wellestablished, quantitative methods in morphospaces populated using occurrence-level 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.

Morphological and biomechanical disparity of crocodile-line archosaurs following the end-Triassic extinction

Mesozoic crurotarsans exhibited diverse morphologies and feeding modes, representing considerable ecological diversity, yet macroevolutionary patterns remain unexplored. Here, we use a unique combination of morphological and biomechanical disparity metrics to quantify the ecological diversity and trophic radiations of Mesozoic crurotarsans, using the mandible as a morpho-functional proxy. We recover three major trends. First, the diverse assemblage of Late Triassic crurotarsans was morphologically and biomechanically disparate, implying high levels of ecological variation; but, following the end-Triassic extinction, disparity declined. Second, the Jurassic radiation of marine thalattosuchians resulted in very low morphological disparity but moderate variation in jaw biomechanics, highlighting a hydrodynamic constraint on mandibular form. Third, during the Cretaceous terrestrial radiations of neosuchians and notosuchians, mandibular morphological variation increased considerably. By the Late Cretaceous, crocodylomorphs evolved a range of morphologies equalling Late Triassic crurotarsans. By contrast, biomechanical disparity in the Cretaceous did not increase, essentially decoupling from morphology. This enigmatic result could be attributed to biomechanical evolution in other anatomical regions (e.g. cranium, dentition or postcranium), possibly releasing the mandible from selective pressures. Overall, our analyses reveal a complex relationship between morphological and biomechanical disparity in Mesozoic crurotarsans that culminated in specialized feeding ecologies and associated lifestyles.

Body size and premolar evolution in the early‐middle eocene euprimates of Wyoming

The earliest euprimates to arrive in North America were larger-bodied notharctids and smaller-bodied omomyids. Through the Eocene, notharctids generally continued to increase in body size, whereas omomyids generally radiated within small- and increasingly mid-sized niches in the middle Eocene. This study examines the influence of changing body size and diet on the evolution of the lower fourth premolar in Eocene euprimates. The P4 displays considerable morphological variability in these taxa. Despite the fact that most studies of primate dental morphology have focused on the molars, P4 can also provide important paleoecological insights. We analyzed the P4 from 177 euprimate specimens, representing 35 species (11 notharctids and 24 omomyids), in three time bins of approximately equal duration: early Wasatchian, late Wasatchian, and Bridgerian. Two-dimensional surface landmarks were collected from lingual photographs, capturing important variation in cusp position and tooth shape. Disparity metrics were calculated and compared for the three time bins. In the early Eocene, notharctids have a more molarized P4 than omomyids. During the Bridgerian, expanding body size range of omomyids was accompanied by a significant increase in P4 disparity and convergent evolution of the semimolariform condition in the largest omomyines. P4 morphology relates to diet in early euprimates, although patterns vary between families.

Trends in racial and ethnic disparities in infant mortality rates in the United States, 1989-2006.

We sought to measure overall disparities in pregnancy outcome, incorporating data from the many race and ethnic groups that compose the US population, to improve understanding of how disparities may have changed over time. We used Birth Cohort Linked Birth-Infant Death Data Files from US Vital Statistics from 1989-1990 and 2005-2006 to examine multigroup indices of racial and ethnic disparities in the overall infant mortality rate (IMR), preterm birth rate, and gestational age-specific IMRs. We calculated selected absolute and relative multigroup disparity metrics weighting subgroups equally and by population size. Overall IMR decreased on the absolute scale, but increased on the population-weighted relative scale. Disparities in the preterm birth rate decreased on both the absolute and relative scales, and across equally weighted and population-weighted indices. Disparities in preterm IMR increased on both the absolute and relative scales. Infant mortality is a common bellwether of general and maternal and child health. Despite significant decreases in disparities in the preterm birth rate, relative disparities in overall and preterm IMRs increased significantly over the past 20 years.

EXTINCTION SPACE-A METHOD FOR THE QUANTIFICATION AND CLASSIFICATION OF CHANGES IN MORPHOSPACE ACROSS EXTINCTION BOUNDARIES

Three main modes of extinction are responsible for reductions in morphological disparity: (1) random (caused by a nonselective extinction event); (2) marginal (a symmetric, selective extinction event trimming the margin of morphospace); and (3) lateral (an asymmetric, selective extinction event eliminating one side of the morphospace). These three types of extinction event can be distinguished from one another by comparing changes in three measures of morphospace occupation: (1) the sum of range along the main axes; (2) the sum of variance; and (3) the position of the centroid. Computer simulations of various extinction events demonstrate that the pre-extinction distribution of taxa (random or normal) in the morphospace has little influence on the quantification of disparity changes, whereas the modes of the extinction events play the major role. Together, the three disparity metrics define an "extinction-space" in which different extinction events can be directly compared with one another. Application of this method to selected extinction events (Frasnian-Famennian, Devonian-Carboniferous, and Permian-Triassic) of the Ammonoidea demonstrate the similarity of the Devonian events (selective extinctions) but the striking difference from the end-Permian event (nonselective extinction). These events differ in their mode of extinction despite decreases in taxonomic diversity of similar magnitude.

Geographically Equitable Liver Allocation Using Mathematical Redistricting

Introduction: Geographic equity has proven elusive in the United States liver allocation system. Proposals for broader sharing between donor service areas (DSAs), which are grouped into regions, have not been approved. The regional groupings were not designed for equitable organ sharing. Methods: Mathematical optimization methods have been used to organize voting districts or school districts; here we apply them to design organ sharing regions within the United States. Inputs are donation and waiting list registration rates, as well as distances between DSAs. The resulting regional maps are tested using the Liver Simuated Allocation Model to find median MELD at transplant within each region and DSA, among other metrics. Results: Two alternative regional maps are proposed. Either of these alternative maps would reduce geographic disparities. The variance of median MELD at transplant among the DSAs is significantly lower using either of the alternative maps (by Levene's robust test statistic, p < 0.05). Note that although broader sharing within the existing regions would reduce predicted waitlist deaths from 1658.3 to 1600.8, it would actually worsen geographic disparity as demonstrated by a larger standard deviation of median MELD among DSAs.Figure: [Alternative Map 1]Figure: [Liver simulated allocation model results]Conclusion: Simply offering organs over a broader geographic area will not necessarily reduce geographic inequity in organ allocation. Summary metrics, like the number of people who die on the waiting list, could possibly improve at the same time that disparity metrics like the range of organ availability in different places worsens; allocation changes intended to address disparities must be evaluated using direct disparity metrics that measure variation. Mathematical redistricting may help reduce geographic inequity in allocation.

Measuring health disparities: trends in racial−ethnic and socioeconomic disparities in obesity among 2- to 18-year old youth in the United States, 2001–2010

PurposeAlthough eliminating health disparities by race, ethnicity, and socioeconomic status (SES) is a top public health priority internationally and in the United States, weight-related racial/ethnic and SES disparities persist among adults and children in the United States. Few studies have examined how these disparities have changed over time; these studies are limited by the reliance on rate differences or ratios to measure disparities. We sought to advance existing research by using a set of disparity metrics on both the absolute and relative scales to examine trends in childhood obesity disparities over time. MethodsData from 7066 children, ages 2 to 18 years, in the National Health and Nutrition Examination Surveys were used to explore trends in racial/ethnic and SES disparities in pediatric obesity from 2001 to 2010 using a set of different disparity metrics. ResultsRacial/ethnic and SES-related disparities in pediatric obesity did not change significantly from 2001 to 2010 and remain significant. ConclusionsDisparities in obesity have not improved during the past decade. The use of different disparity metrics may lead to different conclusions with respect to how disparities have changed over time, highlighting the need to evaluate disparities using a variety of metrics.

HOW DO GEOLOGICAL SAMPLING BIASES AFFECT STUDIES OF MORPHOLOGICAL EVOLUTION IN DEEP TIME? A CASE STUDY OF PTEROSAUR (REPTILIA: ARCHOSAURIA) DISPARITY

A fundamental contribution of paleobiology to macroevolutionary theory has been the illumination of deep time patterns of diversification. However, recent work has suggested that taxonomic diversity counts taken from the fossil record may be strongly biased by uneven spatiotemporal sampling. Although morphological diversity (disparity) is also frequently used to examine evolutionary radiations, no empirical work has yet addressed how disparity might be affected by uneven fossil record sampling. Here, we use pterosaurs (Mesozoic flying reptiles) as an exemplar group to address this problem. We calculate multiple disparity metrics based upon a comprehensive anatomical dataset including a novel phylogenetic correction for missing data, statistically compare these metrics to four geological sampling proxies, and use multiple regression modeling to assess the importance of uneven sampling and exceptional fossil deposits (Lagerstätten). We find that range-based disparity metrics are strongly affected by uneven fossil record sampling, and should therefore be interpreted cautiously. The robustness of variance-based metrics to sample size and geological sampling suggests that they can be more confidently interpreted as reflecting true biological signals. In addition, our results highlight the problem of high levels of missing data for disparity analyses, indicating a pressing need for more theoretical and empirical work.

The effects of rarity and abundance distributions on measurements of local morphological disparity

Understanding the relationships between morphological disparity and environment, geography, and scale require examination at the local level. Even with disparity metrics that are inherently sample size independent, the nature of rare species and the segregation of common and rare species within morphospace can create substantial sampling issues. Eight well-sampled, Late Ordovician crinoid assemblages were examined for potential biases in the study of local disparity. Disparity is based on the ordination of discrete characters. The rare and common species within these assemblages contributed equally to disparity. In spite of this pattern, rare species in some localities occupy a different area of morphospace, causing disparity to vary greatly with sampling intensity. Morphological rarefaction based on the number of specimens shows that disparity weighted by abundance is constant past a sample size of approximately 30 individuals. This metric is dependent on the evenness within an assemblage as well as the abundance within subgroups in morphospace. Disparity weighted according to abundance gives a view of the functional disparity of an assemblage, which is more applicable in studies of local disparity, though unweighted disparity is still preferred in regional-scale studies and in investigations of morphospace filling through a clade's history.

Spatial patterns of disparity and diversity of the Recent cuttlefishes (Cephalopoda) across the Old World

AbstractAim Diversity and disparity metrics of all Recent cuttlefishes are studied at the macroevolutionary scale (1) to establish the geographical biodiversity patterns of these cephalopods at the species level and (2) to explore the relationships between these two metrics.Location Sampling uses what is known about these tropical, subtropical and warm temperate cephalopods of the Old World based on a literature review and on measurements of museum specimens. Some 111 species spread across seventeen biogeographical areas serve as basic units for exploring diversity and disparity metrics in space.Methods Landmarks describe the shape of the cuttlebone (the inner shell of the sepiids) and differences between shapes are quantified using relative warp analyses. Relative warps are thus used as the morphological axis for constructing morphospaces whose characteristics are described by disparity indices: total variance, range, and minimum and maximum of relative warps. These are analysed and then compared with the diversity (species richness) metric.Results Results show no significant latitudinal or longitudinal gradients either for diversity or for disparity. Around the coast of southern Africa, disparity is high regardless of whether diversity (species richness) is high or low. In the ‘East Indies’ area disparity is low despite the high diversity.Main conclusions The relationship between diversity and disparity is clearly not linear and no simple adjustment models seem to fit. The number of species in a given area does not predict its disparity level. The particular pattern of southern Africa may be the result of paleogeographical changes since the Eocene, whereas that of the ‘East Indies’ may indicate that this area could act as a centre of origin. However, the lack of any clear phylogenetical hypothesis precludes the study from providing any explanation of the observed patterns.