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Correspondence analysis of data Correspondence analysis is a method commonly used in studies of modern ecology and vegetational succession. With this method, multi-dimensional relationships are reduced to show variance within data sets on a series of two-dimensional axis plots. The advantages of CA are that it provides the same scaling of sample (locality) and character (genus) plots, enabling direct comparison, and can accommodate incomplete data matrices where some information is missing, as normally occurs with the fossil record (e.g. my Early Jurassic example, below). The relative position of each locality is defined by its constituent leaf genera; localities sharing many genera plot closest together, those with little in common plot furthest apart. Likewise, the relative position of each genus is defined by its degree of association with other genera.
An initial data matrix (Fig. A), comprising a vertical locality axis and a horizontal taxon (e.g. genus, species) axis, may appear to have no structure, but by re-arranging the locality axis (Fig.B) and then the taxon axis (Fig. C), a pattern emerges. The paleontologist may be faced with a data array like Fig. A (or Fig. B if, for example, the paleolatitude is known for each locality) and the computer effectively rearranges the matrix to produce the Fig. C plot. This could be done by hand of course, but with data matrices containing hundreds of columns and rows, this becomes impractical. Figure C shows a very simple matrix, reflecting perhaps latitude, whereas in reality of course there may be more than one source of variance in the data. CA serves to identify the degree of variance and can ordinate the various influences on the data array but cannot, of course, specify the sources of the variance (examples of which include temperature, precipitation, geography, and ecological succession). This is the job of the ecologist or paleontologist. In my work, I use the physiognomy implicit in the names of individual fossil leaf genera to ultimately enable the determination of global paleoclimates. CA of fossil leaf genera and localities, combined with distributional patterns of climate-sensitive sediments, enable global climate zones (biomes) to be drawn on paleogeographic maps. |
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Correspondence analysis (CA) axis 1/axis 2 plot for 57 Early Jurassic leaf genera from Northern Hemisphere localities. Genera were assigned to the following broad morphological categories: microphyllous cycadophytes, microphyllous conifers and Pachypteris (red squares); macrophyllous cycadophytes (green vertical crosses); ferns, sphenophytes and lycophytes (green diagonal crosses); 'unassigned' conifers (brown squares); macrophyllous conifers and ginkgophytes (blue squares). Numbers refer to the following leaf genera: 1 Zamites, 2 Otozamites, 3 Brachyphyllum, 4 Pachypteris, 5 Ptilophyllum, 6 Pagiophyllum, 7 Pterophyllum, 8 Taeniopteris, 9 Nilssonia, 10 Elatocladus, 11 Ctenis, 12 Podozamites, 13 Baiera, 14 Ginkgo, 15 Pityophyllum, 16 Sphenobaiera, 17 Czekanowskia, 18 Desmiophyllum. |

CA Axis 1/Axis 2 distribution of Early Jurassic plant localities from the northern hemisphere, colored according to paleolatitude: 0 to 40 degrees N (red circles), 40 to 60 degrees N (green crosses), 60 to 90 degrees N (blue circles). The patterns become even clearer when the CA scores for individual localities are plotted on palaeogeographic maps. |
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Jurassic floral gradient, derived from the averaged axis 1 scores of genera common to J1, J2 and J3 floras. Five broad morphological categories ('morphocats') and their constituent genera are highlighted, showing the gradation from microphyllous forms to macrophyllous conifers and ginkgophytes. |
Using the floral gradient, I can compare Early, Middle and Late Jurassic plant localities objectively, observe any spatial and temporal changes, and interpret these in terms of floral provinciality, continental motion and global climate change. The following example is of Jurassic floral localities from one basin in Russia and shows how the floral gradient score increases as a function of increasing paleolatitude through the Jurassic, as the colder and more seasonally adapted plants gradually become more common than the smaller-leafed ones more suited to drier low latitude environments. |
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