Interpretation of Canonical Discriminant Functions, Canonical Variates, and Principal Components

1992 ◽  
Vol 46 (3) ◽  
pp. 217 ◽  
Author(s):  
Alvin C. Rencher
Keyword(s):  
Principal Components ◽  
Discriminant Functions ◽  
Canonical Variates

A morphometric analysis of hybrid salamanders (genus Ambystoma) and their progenitors on Kelleys Island in Lake Erie

1989 ◽  
Vol 67 (10) ◽  
pp. 2376-2383 ◽  
Author(s):  
Clifford W. Zeyl ◽  
Leslie A. Lowcock
Keyword(s):  
Morphometric Analysis ◽  
Principal Components ◽  
Lake Erie ◽  
Meristic Character ◽  
Discriminant Functions ◽  
Morphometric Characters ◽  
Size And Shape ◽  
Canonical Variates

Six morphometric characters and one meristic character were measured on 96 adult and 88 juvenile Ambystoma from Kelleys Island, where extensive hybridization involves three species. Canonical variates, discriminant functions, and size-constrained principal components analyses showed that A. laterale (represented only in hybrids on Kelleys Island), A. texanum, A. tigrinum, and A. laterale–texanum–tigrinum are distinguishable from each other and from a complex of hybrids involving A. texanum and A. laterale. Within the latter complex, different ploidies are not distinct morphologically. Introgression may explain isolated atypical individuals. Adults differ from juveniles in both size and shape, demonstrating allometry.

scholarly journals Morphological evaluation of common bean diversity in Bosnia and Herzegovina using the discriminant analysis of principal components (DAPC) multivariate method

Genetika ◽  
2013 ◽  
Vol 45 (3) ◽  
pp. 963-977 ◽  
Author(s):  
Jasmin Grahic ◽  
Fuad Gasi ◽  
Mirsad Kurtovic ◽  
Lutvija Karic ◽  
Mirha Djikic ◽  
...  
Keyword(s):  
Discriminant Analysis ◽  
Common Bean ◽  
Bosnia And Herzegovina ◽  
Principal Components ◽  
Morphological Characteristics ◽  
Principal Component ◽  
Discriminant Functions ◽  
Factor Loadings ◽  
Geographical Regions ◽  
High Level

In order to analyze morphological characteristics of locally cultivated common bean landraces from Bosnia and Herzegovina (B&H), thirteen quantitative and qualitative traits of 40 P. vulgaris accessions, collected from four geographical regions (Northwest B&H, Northeast B&H, Central B&H and Sarajevo) and maintained at the Gene bank of the Faculty of Agriculture and Food Sciences in Sarajevo, were examined. Principal component analysis (PCA) showed that the proportion of variance retained in the first two principal components was 54.35%. The first principal component had high contributing factor loadings from seed width, seed height and seed weight, whilst the second principal component had high contributing factor loadings from the analyzed traits seed per pod and pod length. PCA plot, based on the first two principal components, displayed a high level of variability among the analyzed material. The discriminant analysis of principal components (DAPC) created 3 discriminant functions (DF), whereby the first two discriminant functions accounted for 90.4% of the variance retained. Based on the retained DFs, DAPC provided group membership probabilities which showed that 70% of the accessions examined were correctly classified between the geographically defined groups. Based on the taxonomic distance, 40 common bean accessions analyzed in this study formed two major clusters, whereas two accessions Acc304 and Acc307 didn?t group in any of those. Acc360 and Acc362, as well as Acc324 and Acc371 displayed a high level of similarity and are probably the same landrace. The present diversity of Bosnia and Herzegovina?s common been landraces could be useful in future breeding programs.

Hybridization between northern redbelly dace (Phoxinus eos) and finescale dace (Phoxinus neogaeus) (Osteichthyes: Cyprinidae) in Alberta

1989 ◽  
Vol 67 (3) ◽  
pp. 579-584 ◽  
Author(s):  
Mrinal K. Das ◽  
Joseph S. Nelson
Keyword(s):  
Principal Components ◽  
Parental Species ◽  
Introgressive Hybridization ◽  
Morphological Characters ◽  
Allopatric Populations ◽  
Canonical Variates ◽  
Female Hybrid ◽  
Hybrid Group

Hybridization between northern redbelly dace (Phoxinus eos) and finescale dace (Phoxinus neogaeus) was studied in Upper Pierre Grey Lake, Alberta. Sympatric parental and hybrid populations were compared with allopatric populations from Cameron Lake and Tay Lake, Alberta. Canonical variates and principal components analyses, using 31 morphological characters, revealed that the two parental groups were bridged by an intermediate all-female hybrid group in Upper Pierre Grey Lake. Hybrids made up approximately 33% of the individuals of the sympatic population. Neither backcross nor hybrid F2 individuals could be identified from the analyses, although the majority of hybrids were morphologically more similar to P. neogaeus than to P. eos. No clear evidence of introgressive hybridization was found in either of the sympatric parental species.

Leaf diversity in yellow birch (Betula alleghaniensis)

1974 ◽  
Vol 52 (11) ◽  
pp. 2407-2414 ◽  
Author(s):  
Bruce P. Dancik ◽  
Burton V. Barnes
Keyword(s):  
Principal Components ◽  
Canonical Variate ◽  
Betula Alleghaniensis ◽  
Yellow Birch ◽  
Short Shoot ◽  
Population Comparisons ◽  
Canonical Variates ◽  
Long Shoots

Analysis of leaves from several crown positions of a single yellow birch (Betula alleghaniensis Britton) indicated that particular short-shoot leaves from the middle and lower inside crown were more uniform than those from other crown positions. The short-shoot leaves typically occur in pairs. Each pair consists of two distinctly different leaves, termed here the A and B leaves. The A leaf is consistently larger, with more veins and teeth and a more inequilateral base than the B leaf. Because of their relative uniformity, lower inside crown A leaves would be useful as "standard" leaves for among-tree and among-population comparisons. Late leaves, borne on long shoots in exposed portions of the upper crown, were smaller than the short-shoot leaves in all dimensions. Principal components and canonical variates of the short-shoot leaves from the lower and middle inside crown exhibited the most compact and least variable groupings of all of the leaf types. The first canonical variate separated the leaves of the lower and middle crown from those of the upper crown. The second canonical variate separated A and B leaves. Observations of emerging leaves indicated no systematic differences in position of the A and B leaf.

Determination of the Authenticity of Orange Juice by Discriminant Analysis of near Infrared Spectra

1993 ◽  
Vol 1 (1) ◽  
pp. 33-44 ◽  
Author(s):  
D.G. Evans ◽  
C.N.G. Scotter ◽  
L.Z. Day ◽  
M.N. Hall
Keyword(s):  
Principal Components ◽  
Orange Juice ◽  
Near Infrared ◽  
Principal Component ◽  
Success Rates ◽  
Data Transformations ◽  
Near Infrared Spectra ◽  
Canonical Variates ◽  
Calibration Samples

Near infrared spectroscopy was used to discriminate between three sources of orange juice. Three pretreatments and five data transformations to improve discrimination were compared. Principal components analysis of 92 calibration samples was followed by canonical variates analysis using up to 25 principal components. Success rates were compared across pretreatments and transformations for the calibration and test data (50 samples). 100% prediction success was obtained with 25 principal components following no pretreatment and no transformation. Principal component loadings were interpretable.

Morphometric study of the Pissodes strobi complex (Coleoptera: Curculionidae)

2002 ◽  
Vol 134 (4) ◽  
pp. 447-466 ◽  
Author(s):  
Daryl J.M. Williams ◽  
David W. Langor
Keyword(s):  
Body Size ◽  
Morphological Characters ◽  
Resolving Power ◽  
Morphometric Study ◽  
Stepwise Discriminant Analysis ◽  
Western North America ◽  
Discriminant Functions ◽  
Canonical Variates Analysis ◽  
Pissodes Strobi ◽  
Canonical Variates

AbstractMorphometric data were collected on 15 characters in adults of the species of the Pissodes strobi complex (P. nemorensis (Germar), P. schwarzi Hopkins, P. strobi (Peck), and P. terminalis Hopping). Data were examined using stepwise discriminant analysis to determine if all characters contribute significantly to the diagnosis of taxa, and their relative amounts of resolving power were illuminated using canonical variates analysis. Discriminant functions were generated to diagnose species. Separate discriminant functions were generated for each sex for populations from eastern and western North America. Significant sexual dimorphism and variability in body size decrease the utility of morphological characters for diagnosis, but did not prevent the formulation of useful discriminant functions, particularly when selected ratios that control for body size were added.

Multivariate analysis of hybridizing Cyprinidae from the Kananaskis Reservoirs, Alberta

1980 ◽  
Vol 58 (9) ◽  
pp. 1664-1673 ◽  
Author(s):  
G. A. Butcher
Keyword(s):  
Multivariate Analysis ◽  
Principal Components ◽  
Parental Species ◽  
Morphological Characters ◽  
Rhinichthys Cataractae ◽  
Canonical Variates ◽  
Couesius Plumbeus ◽  
Hybrid Group

Principal components and canonical variates analyses of hybridizing Couesius plumbeus (lake chub) and Rhinichthys cataractae (longnose dace) from Upper and Lower Kananaskis Reservoirs, Alberta, using 21 morphological characters, revealed two parental groups bridged continuously by an intermediate hybrid group. This morphological overlap between the hybrids and the parental species indicates that it is not always possible to positively identify "pure" parental individuals from the Kananaskis. Neither backcross nor hybrid F2 individuals could be identified from the analyses, although the Kananaskis R. cataractae showed effects suggestive of either selection or introgression, relative to known R. cataractae from widespread Alberta localities. Rhinichthys cataractae has also declined in numbers relative to C. plumbeus since last studied in 1961. Couesius plumbeus does not show similar effects suggestive of selection or introgression.

The taxonomy of the Carex pensylvanica complex (Cyperaceae) in North America

1983 ◽  
Vol 61 (6) ◽  
pp. 1692-1717 ◽  
Author(s):  
William J. Crins ◽  
Peter W. Ball
Keyword(s):  
North America ◽  
Principal Components Analysis ◽  
Principal Components ◽  
Morphological Variation ◽  
Discriminant Functions ◽  
Distribution Maps ◽  
Variation Patterns ◽  
Carex Pensylvanica ◽  
Components Analysis ◽  
Eastern Species

The Carex pensylvanica complex consists of four North American taxa. Morphological variation patterns within the complex were examined using principal-components analysis and discriminant-functions analysis. These results indicate that two eastern species, C. lucorum Willdenow ex Link, and C. pensylvanica Lamarck, and one western species, C. inops Bailey, should be recognized. The latter species comprises two subspecies, C. inops subsp. inops and C. inops subsp. heliophila (Mackenzie) Crins, comb. nov. Cytological and geographical evidence lend support to this classification. A key and distribution maps for the taxa are provided.

A multivariate approach to variation in microfilariae: examination of species Wuchereria lewisi and Demes of the species W. bancrofti

1976 ◽  
Vol 24 (1) ◽  
pp. 105 ◽  
Author(s):  
NA Campbell
Keyword(s):  
Principal Components ◽  
Complete Separation ◽  
Canonical Analysis ◽  
Population Differences ◽  
Multivariate Approach ◽  
Population Means ◽  
The Poor ◽  
Canonical Variates ◽  
Morphological Differences ◽  
The Individual

Morphological differences between W. lewisi and demes of W. bancrofti result primarily from differences in the size of the individual microfilaria. A canonical analysis shows complete separation of the species. Because of the poor correlations between the characters, shape differences are not consistent and are not revealed by this analysis. Shape differences may be postulated on the basis of the ratios of the means. However, these ratios tend to be highly variable within populations because of poor correlations between the characters, and there will be considerable overlap of the ratios between the two species. An assumption of high correlations (and hence consistent ratios) between characters results in two canonical variates which may be interpreted as reflecting shape differences. The relatively low correlations between the measurements tend to give a result similar to that by a principal components approach on the population means. Correlations within populations are generally low and therefore have little influence in determining between-population differences. Under these circumstances principal components and the more efficient canonical variates give similar results. The different assumptions implicit in the two approaches are discussed.

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