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F J Rohlf

Publications and source records attributed to F J Rohlf.

12 recordsLinked to original sources
PubMed2001

Comparative methods for the analysis of continuous variables: geometric interpretations.

This study is concerned with statistical methods used for the analysis of comparative data (in which observations are not expected to be independent because they are sampled across phylogenetically related species). The phylogenetically independent contrasts (PIC), phylogenetic generalized least-squares (PGLS), and phylogenetic autocorrelation (PA) methods are compared. Although the independent contrasts are not orthogonal, they are independent if the data conform to the Brownian motion model of evolution on which they are based. It is shown that uncentered correlations and regressions through the origin using the PIC method are identical to those obtained using PGLS with an intercept included in the model. The PIC method is a special case of PGLS. Corrected standard errors are given for estimates of the ancestral states based on the PGLS approach. The treatment of trees with hard polytomies is discussed and is shown to be an algorithmic rather than a statistical problem. Some of the relationships among the methods are shown graphically using the multivariate space in which variables are represented as vectors with respect to OTUs used as coordinate axes. The maximum-likelihood estimate of the autoregressive parameter, p, has not been computed correctly in previous studies (an appendix with MATLAB code provides a corrected algorithm). The importance of the eigenvalues and eigenvectors of the connection matrix, W, for the distribution of p is discussed. The PA method is shown to have several problems that limit its usefulness in comparative studies. Although the PA method is a generalized least-squares procedure, it cannot be made equivalent to the PGLS method using a phylogenetic model.

Evolution, Molecular↗
PubMed2000

A geometric morphometric assessment of change in midline brain structural shape following a first episode of schizophrenia.

BACKGROUND: Previous reports indicate that brain structural abnormalities may be progressive in some patients with schizophrenia. Our study was designed to determine deviations in the shape of midline brain structures at the time of onset of symptoms of schizophrenia and 3-5 years later. METHODS: Eleven landmarks were located on the midsagittal magnetic resonance imagery brain scans of 55 patients with schizophrenia and 22 nonpsychiatric control individuals. Geometric morphometric methods were used for the extraction of shape variables from landmark coordinates. Permutation tests were used to test the effects of gender, diagnosis, time elapsed since illness onset, and age on brain shape. RESULTS: The diagnosis-by-time interaction and the effect of gender were significantly different from zero (p<.027 and p <.039, respectively). The effect of time was significant in patients (p <.002), but not in control subjects. Some anatomical abnormalities in mean patient brain morphology seem to be present both at the time of diagnosis and at follow-up. These are similar to anomalies reported by previous geometric morphometrics studies. CONCLUSIONS: Some previously identified brain abnormalities are detectable at the time of first hospitalization. The rapid change in midline brain morphology in patients with schizophrenia during the subsequent 3-5 years is consistent with either a neurodegenerative disease process or an effect of treatment with psychiatric drugs. There is a sexual dimorphism in brain morphology that might be reduced by schizophrenia.

Adult↗
PubMed2000

Ecological character displacement in Plethodon: biomechanical differences found from a geometric morphometric study.

Ecological character displacement describes a pattern where morphological differences between sympatric species are enhanced through interspecific competition. Although widely considered a pervasive force in evolutionary ecology, few clear-cut examples have been documented. Here we report a case of ecological character displacement between two salamander species, Plethodon cinereus and Plethodon hoffmani. Morphology was quantified by using linear measurements and landmark-based geometric morphometric methods for specimens from allopatric and sympatric populations from two geographic transects in south-central Pennsylvania, and stomach contents were assayed to quantify food resource use. Morphological variation was also assessed in 13 additional allopatric populations. In both transects, we found significant morphological differentiation between sympatric populations that was associated with a reduction in prey consumption in sympatry and a segregation of prey according to prey size. No trophic morphological or resource use differences were found between allopatric populations, and comparisons of sympatric populations with randomly paired allopatric populations revealed that the observed sympatric morphological differentiation was greater than expected by chance. The major trophic anatomical differences between sympatric populations relates to functional and biomechanical differences in jaw closure: sympatric P. hoffmani have a faster closing jaw, whereas sympatric P. cinereus have a slower, stronger jaw. Because salamanders immobilize prey of different sizes in different ways, and because the observed sympatric biomechanical differences in jaw closure are associated with the differences in prey consumption, the observed character displacement has a functional ecological correlate, and we can link changes in form with changes in function in this apparent example of character displacement.

Analysis of Variance↗
PubMed2000

Statistical power comparisons among alternative morphometric methods.

This paper compares the statistical power of various tests that have been proposed to test for equality of shape in two populations. Power surfaces are computed with emphasis on the simplest case of three points in the plane (i.e., landmarks at the vertices of a triangle). Goodall's ([1991] J Roy Stat Soc Serb 53:285-339) F-test was found to have the highest power followed by T(2)-tests using Kendall tangent space coordinates. Power for T(2)-tests using Bookstein shape coordinates was good if the baseline was not the shortest side of the triangle. The Rao and Suryawanshi ([1996] Proc Natl Acad Sci 93:12132-12136 and Rao and Suryawanshi [1998] Proc Natl Acad Sci 95:4121-4125) shape variables had much lower power when triangles were not close to being equilateral. Power surfaces for the EDMA-I T statistic revealed very low power for many shape comparisons including those between very different shapes. Power surface for the EDMA-II Z statistic were also complicated and depended strongly on the choice of baseline used for size scaling. The type I error rate was also often not correct for this method. Results for more than three landmarks are also presented. The implications of the results for practical applications of morphometrics are discussed.

Anthropology, Physical↗
PubMed2000

Use of two-block partial least-squares to study covariation in shape.

The relatively new two-block partial least-squares method for analyzing the covariance between two sets of variables is described and contrasted with the well-known method of canonical correlation analysis. Their statistical properties, type of answers, and visualization techniques are discussed. Examples are given to show its usefulness in comparing two sets of variables--especially when one or both of the sets of variables are shape variables from a geometric morphometric study.

Analysis of Variance↗
PubMed1999

Comparing frontal cranial profiles in archaic and modern homo by morphometric analysis.

Archaic and modern human frontal bones are known to be quite distinct externally, by both conventional visual and metric evaluation. Internally this area of the skull has been considerably less well-studied. Here we present results from a comparison of interior, as well as exterior, frontal bone profiles from CT scans of five mid-Pleistocene and Neanderthal crania and 16 modern humans. Analysis was by a new morphometric method, Procrustes analysis of semi-landmarks, that permits the statistical comparison of curves between landmarks. As expected, we found substantial external differences between archaic and modern samples, differences that are mainly confined to the region around the brow ridge. However, in the inner median-sagittal profile, the shape remained remarkably stable over all 21 specimens. This implies that no significant alteration in this region has taken place over a period of a half-million years or more of evolution, even as considerable external change occurred within the hominid clade spanning several species. This confirms that the forms of the inner and outer aspects of the human frontal bone are determined by entirely independent factors, and further indicates unexpected stability in anterior brain morphology over the period during which modern human cognitive capacities emerged. Anat Rec (New Anat): 257:217-224, 1999.

Biometry↗
PubMed1980

Metaphase chromosome associations: Colcemid distorts the pattern.

The nonrandom pattern of the spatial arrangement of chromosomes in the human metaphase complement has been resolved into separate properties by statistical analysis of matrices of ranks of interchromosomal distances averaged over sets of 25 or 50 metaphases. Assessment of the effect of a mitotic-arresting agent, Colcemid, on each of the properties of the pattern shows that those properties for which a spindle fiber dependence may be postulated are disordered by Colcemid, while the tendency for the acrocentric chromosomes to associate, attributable to their mutual participation in nucleolar organization, is not impaired by Colcemid. Furthermore, this analysis has revealed that chromosomes 21 and 22 display an exceptional propensity to be generally associative, i.e., to be close to all chromosomes; that property is obliterated by Colcemid. Since a mitotic-arresting agent is routinely used in the preparation of cells for cytogenetic analysis, that property has hitherto not been recognized.

Adult↗