FAMILY PERmmiACEAE 



17 



+ 1.0. Two intergrades were found in these random sam- 

 plings, represented by the two specimens with x- ratios 

 of 0.0. In the symmetrical pattern the critical suture on 

 the left side varied from to 1.6 times as long as the 

 one on the right side; in the asymmetrical pattern the 

 alternate suture varied from to 0.9 times the one on 

 the right side. 



These observations show definitely that p late pat - 

 tern in this group of species is not a stable feature but 

 that there is a variation both in the length of the sutures 

 and in the relative position of the plates, and that be- 

 tween two patterns there is a continuous line of inter- 

 grades. 



Thus, it is evident that the epithecal plate pattern 

 alone cannot be used for the classification of the species 

 related to P. depressum and that it must be used with 

 considerable discretion in other parts of the genus as well. 



The hypothecal pattern is constant throughout the 

 genus, so that it, too, cannot be used. In the present in- 

 vestigations the tabulation of the ventral area was stud- 

 ied. Although it differs greatly in different parts of the 

 genus, it was found to be identical throughout the "For- 

 menkreis P. depressum ." Thus, the plate pattern of no 

 part of the theca is of any value in classifying the units 

 of the group now under consideration. 



For this reason, a new method had to be devised for 

 this purpose. In order to determine whether or not spe- 

 cific and varietal segregations can be made on the basis 

 of body shape, the material in the Carnegie collection 

 related to P. depressum was studied from this stand- 

 point. The results showed that the "Formenkreis P. de- 

 pressum" is made up of several units, some of specific 

 value, others of varietal, and that these are expressed 

 by the shape of the body. 



In order to make proper segregations on the basis 

 of body shape, it is necessary that this feature be de- 

 scribed by numerical expressions so that the frequency 

 of variations can be plotted. In order that the accumu- 

 lated information of the various workers may be com- 

 parable, these numerical expressions must be of a stand- 

 ard nature. For instance, the conclusions in the present 

 work stand partly in opposition to those arrived at by 

 Peters (1928). Even though this is in most part due to 

 the different material used, it is probably also due to the 

 different methods employed in measuring the body pro- 

 portions. For this reason, the proposed standard meth- 

 ods for orienting and measuring the specimen described 

 above (pp. 1, 2, 13) were used in this work. 



When numerical expressions are used, a large num- 

 ber of specimens can be measured, the body proportions 

 computed, the values grouped into convenient classes, 

 and the frequency of these classes plotted. In the inter- 

 pretation of the frequency diagrams, it is necessary to 

 have in mind a standard expression of the species con- 

 cept. The following definitions of the various units have 

 been used in this report. 



It is assumed that a species represents a group of 

 h.uividuals which is morphologically distinct or nearly 

 so in one or more features. The presence of inter- 

 grades in a very small proportion of the specimens is 

 not considered to vitiate the specific segregation. Var- 

 ieties may be considered incipient species which also 

 have a certain morphological distinctness but which are 



connected with the main species by a higher proportion 

 of intergrades. Forms are considered as temporary 

 expressions due either to internal or to environmental 

 causes. They are characterized by rarity of occur- 

 rence. These are the main concepts which have been 

 used in the classification of the Carnegie material given 

 below. 



Example of application of method . The first prob- 

 lem in the "Formenkreis" to be attacked by the statis- 

 tical method was the determination of the validity of P. 

 oceanicum VanhOffen as a specific unit. 



Vanhoffen (1897a) figured P. oceanicum as a spe- 

 cies similar to P. depressum but longer and more slen- 

 der. This was accepted as a valid species by most au- 

 thors. Peters (1928), the only previous investigator to 

 make a numerical study of the body proportions in this 

 group, took exception to this. On the basis of antarctic 

 material and of one sample of North Sea material, he 

 concluded that P. oceanicum represents simply one end 

 of a line of variation which includes both P. depressum 

 and P. oceanicum . although he recognized "broad ' and 

 "slender" forms. 



In the present investigations 170 random specimens 

 of the "Formenkreis" from widely scattered Carnegie 

 stations in the North Atlantic were measured and the 

 h/d ratios computed. The frequencies of the length, 

 width, and h/d classes were plotted as shown in figures 

 11-13. As is apparent from figure 11, this group of 

 specimens was homogeneous so far as length was con- 

 cerned. Some length classes were somewhat more com- 

 mon than others, but they were all connected by numer- 

 ous intergrades. There was no indication of separated 

 variation groups. Similar results were obtained in a 

 study of the frequency of the diameter classes (fig. 12). 

 This indicated an even more unified group except for the 

 small group at the 70-micron and 75-micron classes, 

 which further observation of the material failed to jus- 

 tify as a distinct, unit. 



The diagram of the plotted frequencies of the h/d 

 ratios, however, indicated two variation groups (fig. 13). 

 One centered about the 0.90-unit class, the other around 

 1.35. The extremes of the first group ranged from 0.65 

 to 1.20 and of the second group from 1.20 to 1.75. 



We have here a basis for assigning specific values 

 to two forms: a broad form, P. depressum . in which the 

 h/d ratio is less than 1.20; and a slender form, P. oce - 

 anicum , in which that ratio is more than 1.20. Any spec- 

 imen with an h/d ratio of about 1.20 must be considered 

 a transitional form between the two species. One such 

 was found in the above samplings, as indicated in the 

 diagram. It must also be concluded, therefore, on the 

 basis of the above studies, that these two species are 

 very close. Indeed, more extended studies of other ma- 

 terial may bring them closer than is indicated by the 

 above data. 



It is clear from these studies, however, that we are 

 not dealing here with a single homogeneous group, and 

 that P. oceanicum does not represent simply one end of 

 a line which Includes both P. depressum and P. oceani - 

 cum . as Peters (1928) contended. 



The further application of this statistical method in 

 this group will be taken up in the discussions under the 

 particular species. 



