VARIATION AND CORRELATION IN AßCELLA*. 



By RAYMOND PEARL and FRANCES J. DUNBAR. 



I. Introduction. 



The piirpo.se of thi,s paper is to present the rcsiilts of a quantitative study of 

 the variability of the common shelled rhizopod, Arcella vulgaris. Comparatively 

 little is known regarding the amouut of the individual Variation which exists in 

 the differcnt groups of the Protozoa, and it seem.s highly desirabie that our know- 

 ledge in this field should be extended. Almost the only piece of quantitative work 

 on the variability of theso fornis which has appeared is that of Simpsonf on 

 Paramcecium. It was with the idea of determining the Variation in a still lower 

 form than Parumaicium that the present work was undertaken. The plan foUowed 

 in this work was, however, somewhat different from that of Simpson. Since his 

 primary purpose was the deterniination of the amount of Variation foUowing 

 binary fission, only organisms of known immcdiate ancestry were measured. The 

 labour involved in isolating a particular Paramoocium undergoing division, and in 

 measuring the daughter individuals aftcr fission has been completed, is very con- 

 siderable, and consequently it is not surprising that measurements for but 100 

 pairs were collected. 



Our plan was to determine the amount of Variation in a repräsentative sample 

 of a homogeneous popidation of Arcellae, without reference to the immediate 

 ancestry of the individuals of tlio sample. This is the course which not only 

 usually is, but in most cases niust be, foUowed in studying the Variation in higher 

 forms, sinco the difficulties of getting a sufficiently large number for Statistical 

 purposes of individuals of known ancestry are very great. By working in this way 

 it would seem that we might get values of the Variation coefficients which would 

 be better for the purposes of comparing protozoan with metazoan variability than 

 those of Simpson. The practical difficulties in handling the material in this way 



* Contributions from the Zoological Laboratory of the Uuiversity of Michigan. 

 + Simpson, J. Y., "The Relation of Binary Fission to Variation." Bioinetriku, Vol. i., pj). 400 — 

 •404, 1902. 



Biometrika ii 41 



