TWO FORTRAN II PROGRAMS FOR ANALYSIS OF MORPHOMETRY DATA 



Table 1. — Symbols and Formulae for Statistics Computed by Data Assembly and Analysis (DASAN) 



(x or y = any variate; *see section on statistics) 



Statistics 



Coefficient of relative dispersion from regression of x on y 

 Standard error of D(X.Y) 



Factor for computing a confidence interval of A(YX)* 

 Factor for computing a confidence interval of B(Y)* 

 Factor for computing a confidence interval of A(XY)* 

 Factor for computing a confidence interval of B(X)* 



CONAXY CONBXY 

 CONBX CONAX 



'*, 



CBy 



CA XU 

 CB X 



Basically, the programs are designed to process arrays of 

 data in which rows represent specimens and columns repre- 

 sent measured and computed variables. Alternatively, an in- 

 put array may represent a single organism, for example, a 

 coiled snail or a segmented anthropod, with the rows repre- 

 senting, respectively, individual whorls or segments. A high 

 degree of adaptability to different kinds of problems is 

 achieved because of the numerous control cards which 

 specify input and output format, table headings, and column 

 numbers of variables on which operations are to be 

 performed. 



The first program, referred to here as DASAN (Data 

 Assembly and Analysis), computes the output arrays and all 

 statistics; the second program, referred to as VPLOT 

 (Variable Plotting), plots the bivariate scatter diagrams, 

 using the punched output deck from DASAN as input. 



Background and Acknowledgments. — The initial versions 

 of the programs described here were lengthy and were 

 designed for the author's own research concerned with the 

 morphometric analysis and phylogenetic interpretation of a 

 closely-knit group of species within the Pectinidae (Mol- 

 lusca: Bivalvia) . Interest expressed by others made clear 



the value of revising the programs so that they would be 

 adaptable to a wide variety of problems. 



The reprogramming was carried out at the Smithsonian 

 Institution, Washington, D.C., as part of a continuing proj- 

 ect concerned with the paleobiology of the Pectinidae, which 

 is supported by a grant from the Smithsonian Research 

 Foundation. Use of the IBM 7094 of the Columbia Univer- 

 sity Computer Center was made possible through the gener- 

 osity of Dr. John Imbrie of the Department of Geology. 

 Invaluable assistance in constructing the initial programs, 

 particularly in incorporating the variable plotting routine 

 (Subroutine APLOT), was received from D. M. Vincent 

 Manson of the American Museum of Natural History. The 

 APLOT subroutine originally appeared in a program written 

 by Clarence Bradford and Arthur Gasche of the University 

 of Chicago and has subsequently been adapted to a number 

 of programs by Manson. Constructive suggestions regarding 

 both programs and texts have been gratefully received from 

 Alan Cheetham of the Smithsonian Institution, Stephen Jay 

 Gould of Harvard University, and Niles Eldredge of 

 Columbia University. 



Statistics 



The statistics appearing in the output of DASAN are com- 

 puted by means of the formulae shown in Table 1, all of 

 which have been taken from either Imbrie (1956) or 

 Simpson, Roe, and Lewontin (1960). In addition to their 

 use in summarizing data and in the drawing of regression 

 lines or lines of best fit directly onto the output of VPLOT, 

 the statistics are of use in the construction of modified Dice- 

 Leraas diagrams (Simpson et al., p. 355) and in determining 

 whether differences in the position and slope of reduced 

 major axes are statistically significant (Imbrie, p. 237) . 



Using the factors marked by asterisks in Table 1, confi- 

 dence intervals (CI) for the slopes and intercepts of regres- 

 sion lines may be calculated as follows, where t is the familiar 

 Student's / with N — 2 degrees of freedom and other symbols 

 are the mathematical symbols of Table 1 : 



Ch 



- b vx ± CA ux t 



CI a =a u ±CB„t 

 CI b V =b x ,±CA,J 



XU 



CI a =a x ±CB x t 



