Morphometric methods and data collection
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Traditional morphometrics (Marcus 1990) comprises data (linear measurements, angles, areas, etc.) and methods (resemblance functions, ordination, classification) that have been employed in order to capture and summarize information on shape variation by sampling shape in an ad hoc kind of way that has no necessary connection to the objects being analyzed (e.g. the measurements shown in red at right). Examples from Crataegus systematics also include measurements used by Bradshaw (1971), Byatt (1975), Love & Feigen (1978) in documenting hybridization between Crataegus species, and those illustrated by Christensen (1992). It can perhaps be argued that those used by Dickinson & Phipps (1984; width at widest point, and lengths above and below the widest point) are less ad hoc.
Note that ratios of measurements have been used by some workers, either as additional descriptors together with the original or other measurements, or to provide a single index of some aspect of shape that is considered important (e.g. Bradshaw 1971). Experience shows that multivariate analyses of the original measurements are likely to capture as much or more variation than do ratios. Moreover, ratios often have undesirable distributional properties that militate against their use in statistical analyses.
|Leaf measurements used by Love & Feigen (1978) to quantify leaf shape in two Crataegus species and their putative hybrid.|
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Landmarks are defined (Slice et al. 1996) as specific points on a biological structure, or its image or outline, that can be located according to some rule and so can be considered homologous across a sample of the same kind of structure (e.g. hawthorn leaves, skulls, mandibles, etc.). Visit the Morphometrics Website glossary (Slice et al. 1996) for further definitions of Type I, II, and III landmarks. Trusses and triangles (Below left; Strauss & Bookstein 1982; Dickinson et al. 1987) provide measurements that covary as shapes change. More recently much more sophisticated methods for analyzing shape differences based on landmark (x,y[,z]) coordinates have become available (thin-plate splines, relative warps), and these are described in Marcus et al. (1993, 1996) and elsewhere. Landmark-based methods are frequently referred to as "geometric morphometrics" (e.g. Bookstein 1991).
|(Far left) 10 Truss and triangle measurements based on the six landmarks circled in red at right. (Left) PCA of the 10 truss measurements that summarizes leaf shape variation between C. monogyna (left), C. laevigata (right), and their hybrid (center). Data from Bradshaw (1971).|
|Link to Stony Brook Morphometrics Website|
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What is one to do when some or all of the objects under study lack landmarks? Although in the past there have been acrimonious exchanges regarding the value of doing so (briefly reviewed in Dickinson et al. 1987), one can use methods based on the closed outline of objects with considerable success (McLellan & Endler 1998). Probably the single most accessible and useful method is that of elliptic Fourier analysis (EFA). In general terms, Fourier analysis can be thought of as supplying the coefficients of a trigonometric function that reproduces as closely as possible a sample curve. As more terms (harmonics) are added to the function the fit to the sample curve becomes better and better (see below). As the particular values of the EFA coefficients constrain the function to follow a closed outline, they provide descriptors of the outline shape that can be compared with the corresponding coefficients from other outlines; PCA provides an efficient means of doing this (McLellan & Endler 1998). Note also that Fourier analysis has been used to provide a graphic summary of multivariate data (Andrews 1972).
(Left) Outline of the leaf at right, summarized using 1, 5, and 10 harmonics (elliptic Fourier analysis carried out using EFAWIN on outline data obtained with TPSDIG; both programs - and many others - can be downloaded from the Morphometrics Website).
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|Morphometric studies in my lab use the program MorphoSys for data collection, together with a video system comprising camera, frame-grabber, video monitor, and 80386-based personal computer (Meacham & Duncan 1991). In addition to capturing morphometric data from leaves (Young et al. 1995; Talent 1998; McLellan & Endler 1998; Metsger unpubl.; Dickinson et al. 2008) this system has also been used for studies of variation in xylem element diameter (Hoy unpubl.), termite soldier caste mandible shape (Dickinson & Myles 1995), floral apex shape (Evans & Dickinson 1996), and gastropod shell morphology (Stone 1998).||
(Above) MorphoSys setup in 2B05D in the ROM Curatorial Center. (From left to right) Dell 386 and monitor with MorphoSys up and running; Sony video monitor (PC keyboard and mouse in front and to right); copystand with herbarium specimen and Sony video camera. (Far left) the herbarium specimen with one leaf isolated for outline capture. (Left) the same leaf outlined on the video monitor. Digital images © T. A. Dickinson.
Significant features of the MorphoSys system include
|The cursor (+) can be locked onto the outline and used to create landmarks.||Outlines, together with landmarks (and measurements), can be printed on a PostScript® printer, or captured as an interpreted PostScript file for input to a vector-based graphics program.||
camera can also be mounted on a Reichert-Jung Polyvar microscope in order
to digitize microscopic structures (here, vessels in a Crataegus
twig; the largest vessels are approximately 10 µm in diameter).
|Outlines can also be output as the (x,y) coordinates of the corresponding Fourier reconstruction, so that they can be plotted as shown here (using S-Plus) positioned according to ordination results. Data from a project on variation in soldier caste termite mandibles carried out in collaboration with Prof. Tim Myles, U of T Faculty of Forestry.|
Click HERE for the abstract and slides of a presentation on morphometrics for the Ontario Ecology & Ethology Colloquium, held at Guelph University on 29 April 2008 (16 Mb file). This presentation compared results from analyses of traditional, landmark, and outline data sets as part of a discussion of the "revolution in morphometrics" described by Jim Rohlf and Les Marcus in 1993.
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back to "The Crataegus problem" - materials
Andrews, D. F. (1972). "Plots of high-dimensional data." Biometrics 28: 125-136.
Bookstein, F. L. (1991). Morphometric tools for landmark data: Geometry and biology. Cambridge, Cambridge University Press. [the orange book]
Bradshaw, A. D. (1971). The significance of hawthorns. In Hedges and local history. S. C. f. L. History. London, National Council of Social Service: 20-29.
Byatt, J. I. (1975). "Hybridization between Crataegus monogyna Jacq. and C. laevigata (Poiret) DC. in southeastern England." Watsonia 10: 253-264.
Christensen, K. I. (1992). "Revision of Crataegus Sect. Crataegus and Nothosect. Crataeguineae (Rosaceae-Maloideae) in the Old World." Systematic Botany Monographs 35: 1-199.
Dickinson, T. A., W. H. Parker, and R. E. Strauss (1987). "Another approach to leaf shape comparisons ." Taxon 36(1): 1-20.
Dickinson, T. A. and J. B. Phipps (1984). "Studies in Crataegus L. (Rosaceae: Maloideae) IX. Short shoot leaf heteroblasty in Crataegus crus-galli L. sensu lato." Canadian Journal of Botany 62(9): 1775-1780.
Dickinson T. A., E. Y. Y. Lo, N. Talent, and R. M. Love (2008). "[North American black-fruited hawthorns IV.] Black-fruited hawthorns of western North America - one or more agamic complexes?" Botany 86: 846-865.
Evans, R. C. and T. A. Dickinson (1996). "North American black-fruited hawthorns (Crataegus section Douglasii Loud.): II. Floral development of 10- and 20-stamen morphotypes." American Journal of Botany 83(8): 961-978.
Love, R. and M. Feigen (1978). "Interspecific hybridization between native and naturalized Crataegus (Rosaceae) in western Oregon." Madroño 25: 211-217.
Marcus, L. F. (1990). Chapter 4. Traditional morphometrics. In Proceedings of the Michigan Morphometric Workshop. Special Publication No. 2. F. J. Rohlf and F. L. Bookstein. Ann Arbor MI, The University of Michigan Museum of Zoology: 77-122. [the blue book]
Marcus, L. F., E. Bello, and A. García-Valdecasas, Eds. (1993). Contributions to morphometrics. Monografias del Museo Nacional de Ciencias Naturales. Madrid, Museo Nacional de Ciencias Naturales. [the black book]
Marcus, L. F., M. Corti, A. Loy, G. J. P. Naylor, and D. E. Slice, Eds. (1996). Advances in Morphometrics. NATO Advanced Science Institute Series A: Life Sciences, vol. 284. New York, Plenum Press. [the white book]
McLellan, T. and J. A. Endler (1998). "The relative success of some methods for measuring and describing the shape of some complex objects." Syst. Biol. 47(2): 264-281.
Meacham, C. A. and T. Duncan (1991). MorphoSys. Berkeley CA, Regents of the University of California.
Rohlf, F. J. and L. F. Marcus. 1993. "A revolution in morphometrics." Trends in Ecology and Evolution 8:129-132
Stone, J. R. (1998). "Landmark-based thin-plate spline relative warp analysis of gastropod shells." Syst. Biol. 47(2): 254-263.
Strauss, R. E. and F. L. Bookstein (1982). "The truss: body form reconstruction in morphometrics." Systematic Zoology 31: 113-135.
Talent, N. (1998). Quantitative traits from leaf morphology in some North American species and hybrids of Populus sections Aigeiros and Tacamahaca (Salicaceae). M.Sc. thesis, Botany Department. Toronto, University of Toronto: xi+380.
Young, J. P., T. A. Dickinson, and N. G. Dengler (1995). "A morphometric analysis of heterophyllous leaf development in Ranunculus flabellaris." International Journal of Plant Sciences 156(5): 590-602.
| Rosaceae evolution | Crataegus systematics | Morphometrics and numerical taxonomy | Comparative morphology |
© 2016 T. A. DickinsonPlease send your comments to email@example.com; last updated 15-Oct-16