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      Sharing is caring? Measurement error and the issues arising from combining 3D morphometric datasets

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          Abstract

          Geometric morphometrics is routinely used in ecology and evolution and morphometric datasets are increasingly shared among researchers, allowing for more comprehensive studies and higher statistical power (as a consequence of increased sample size). However, sharing of morphometric data opens up the question of how much nonbiologically relevant variation (i.e., measurement error) is introduced in the resulting datasets and how this variation affects analyses. We perform a set of analyses based on an empirical 3D geometric morphometric dataset. In particular, we quantify the amount of error associated with combining data from multiple devices and digitized by multiple operators and test for the presence of bias. We also extend these analyses to a dataset obtained with a recently developed automated method, which does not require human‐digitized landmarks. Further, we analyze how measurement error affects estimates of phylogenetic signal and how its effect compares with the effect of phylogenetic uncertainty. We show that measurement error can be substantial when combining surface models produced by different devices and even more among landmarks digitized by different operators. We also document the presence of small, but significant, amounts of nonrandom error (i.e., bias). Measurement error is heavily reduced by excluding landmarks that are difficult to digitize. The automated method we tested had low levels of error, if used in combination with a procedure for dimensionality reduction. Estimates of phylogenetic signal can be more affected by measurement error than by phylogenetic uncertainty. Our results generally highlight the importance of landmark choice and the usefulness of estimating measurement error. Further, measurement error may limit comparisons of estimates of phylogenetic signal across studies if these have been performed using different devices or by different operators. Finally, we also show how widely held assumptions do not always hold true, particularly that measurement error affects inference more at a shallower phylogenetic scale and that automated methods perform worse than human digitization.

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          Testing for phylogenetic signal in comparative data: behavioral traits are more labile.

          The primary rationale for the use of phylogenetically based statistical methods is that phylogenetic signal, the tendency for related species to resemble each other, is ubiquitous. Whether this assertion is true for a given trait in a given lineage is an empirical question, but general tools for detecting and quantifying phylogenetic signal are inadequately developed. We present new methods for continuous-valued characters that can be implemented with either phylogenetically independent contrasts or generalized least-squares models. First, a simple randomization procedure allows one to test the null hypothesis of no pattern of similarity among relatives. The test demonstrates correct Type I error rate at a nominal alpha = 0.05 and good power (0.8) for simulated datasets with 20 or more species. Second, we derive a descriptive statistic, K, which allows valid comparisons of the amount of phylogenetic signal across traits and trees. Third, we provide two biologically motivated branch-length transformations, one based on the Ornstein-Uhlenbeck (OU) model of stabilizing selection, the other based on a new model in which character evolution can accelerate or decelerate (ACDC) in rate (e.g., as may occur during or after an adaptive radiation). Maximum likelihood estimation of the OU (d) and ACDC (g) parameters can serve as tests for phylogenetic signal because an estimate of d or g near zero implies that a phylogeny with little hierarchical structure (a star) offers a good fit to the data. Transformations that improve the fit of a tree to comparative data will increase power to detect phylogenetic signal and may also be preferable for further comparative analyses, such as of correlated character evolution. Application of the methods to data from the literature revealed that, for trees with 20 or more species, 92% of traits exhibited significant phylogenetic signal (randomization test), including behavioral and ecological ones that are thought to be relatively evolutionarily malleable (e.g., highly adaptive) and/or subject to relatively strong environmental (nongenetic) effects or high levels of measurement error. Irrespective of sample size, most traits (but not body size, on average) showed less signal than expected given the topology, branch lengths, and a Brownian motion model of evolution (i.e., K was less than one), which may be attributed to adaptation and/or measurement error in the broad sense (including errors in estimates of phenotypes, branch lengths, and topology). Analysis of variance of log K for all 121 traits (from 35 trees) indicated that behavioral traits exhibit lower signal than body size, morphological, life-history, or physiological traits. In addition, physiological traits (corrected for body size) showed less signal than did body size itself. For trees with 20 or more species, the estimated OU (25% of traits) and/or ACDC (40%) transformation parameter differed significantly from both zero and unity, indicating that a hierarchical tree with less (or occasionally more) structure than the original better fit the data and so could be preferred for comparative analyses.
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            A generalized K statistic for estimating phylogenetic signal from shape and other high-dimensional multivariate data.

            Phylogenetic signal is the tendency for closely related species to display similar trait values due to their common ancestry. Several methods have been developed for quantifying phylogenetic signal in univariate traits and for sets of traits treated simultaneously, and the statistical properties of these approaches have been extensively studied. However, methods for assessing phylogenetic signal in high-dimensional multivariate traits like shape are less well developed, and their statistical performance is not well characterized. In this article, I describe a generalization of the K statistic of Blomberg et al. that is useful for quantifying and evaluating phylogenetic signal in highly dimensional multivariate data. The method (K(mult)) is found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices. Using computer simulations based on Brownian motion, I demonstrate that the expected value of K(mult) remains at 1.0 as trait variation among species is increased or decreased, and as the number of trait dimensions is increased. By contrast, estimates of phylogenetic signal found with a squared-change parsimony procedure for multivariate data change with increasing trait variation among species and with increasing numbers of trait dimensions, confounding biological interpretations. I also evaluate the statistical performance of hypothesis testing procedures based on K(mult) and find that the method displays appropriate Type I error and high statistical power for detecting phylogenetic signal in high-dimensional data. Statistical properties of K(mult) were consistent for simulations using bifurcating and random phylogenies, for simulations using different numbers of species, for simulations that varied the number of trait dimensions, and for different underlying models of trait covariance structure. Overall these findings demonstrate that K(mult) provides a useful means of evaluating phylogenetic signal in high-dimensional multivariate traits. Finally, I illustrate the utility of the new approach by evaluating the strength of phylogenetic signal for head shape in a lineage of Plethodon salamanders.
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              Within-species variation and measurement error in phylogenetic comparative methods.

              Most phylogenetically based statistical methods for the analysis of quantitative or continuously varying phenotypic traits assume that variation within species is absent or at least negligible, which is unrealistic for many traits. Within-species variation has several components. Differences among populations of the same species may represent either phylogenetic divergence or direct effects of environmental factors that differ among populations (phenotypic plasticity). Within-population variation also contributes to within-species variation and includes sampling variation, instrument-related error, low repeatability caused by fluctuations in behavioral or physiological state, variation related to age, sex, season, or time of day, and individual variation within such categories. Here we develop techniques for analyzing phylogenetically correlated data to include within-species variation, or "measurement error" as it is often termed in the statistical literature. We derive methods for (i) univariate analyses, including measurement of "phylogenetic signal," (ii) correlation and principal components analysis for multiple traits, (iii) multiple regression, and (iv) inference of "functional relations," such as reduced major axis (RMA) regression. The methods are capable of incorporating measurement error that differs for each data point (mean value for a species or population), but they can be modified for special cases in which less is known about measurement error (e.g., when one is willing to assume something about the ratio of measurement error in two traits). We show that failure to incorporate measurement error can lead to both biased and imprecise (unduly uncertain) parameter estimates. Even previous methods that are thought to account for measurement error, such as conventional RMA regression, can be improved by explicitly incorporating measurement error and phylogenetic correlation. We illustrate these methods with examples and simulations and provide Matlab programs.
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                Author and article information

                Contributors
                carmelo.fruciano@qut.edu.au
                Journal
                Ecol Evol
                Ecol Evol
                10.1002/(ISSN)2045-7758
                ECE3
                Ecology and Evolution
                John Wiley and Sons Inc. (Hoboken )
                2045-7758
                31 July 2017
                September 2017
                : 7
                : 17 ( doiID: 10.1002/ece3.2017.7.issue-17 )
                : 7034-7046
                Affiliations
                [ 1 ] School of Earth, Environmental and Biological Sciences Queensland University of Technology Brisbane Qld Australia
                [ 2 ] School of Earth and Environmental Sciences University of Queensland St. Lucia Qld Australia
                [ 3 ] School of Biological Sciences University of Queensland St. Lucia Qld Australia
                Author notes
                [*] [* ] Correspondence

                Carmelo Fruciano, School of Earth, Environmental and Biological Sciences, Queensland University of Technology, Brisbane, Qld, Australia.

                Email: carmelo.fruciano@ 123456qut.edu.au

                c.fruciano@ 123456unict.it

                Author information
                http://orcid.org/0000-0002-1659-9746
                Article
                ECE33256
                10.1002/ece3.3256
                5587461
                28904781
                9e489329-df16-434b-9159-d063257bf9c6
                © 2017 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.

                This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

                History
                : 09 January 2017
                : 03 May 2017
                : 28 June 2017
                Page count
                Figures: 5, Tables: 4, Pages: 13, Words: 9524
                Funding
                Funded by: Australian Research Council
                Award ID: DP150104659
                Award ID: DP170103227
                Funded by: Australian Government Research Training Program Scholarship
                Categories
                Original Research
                Original Research
                Custom metadata
                2.0
                ece33256
                September 2017
                Converter:WILEY_ML3GV2_TO_NLMPMC version:5.1.9 mode:remove_FC converted:06.09.2017

                Evolutionary Biology
                geometric morphometrics,measurement error,photogrammetry,phylogenetic signal

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