Geometrica-Group of S.A. Tortoises. 191 



2. DISCUSSION. 

 a. Type of Variation. 



In the foregoing sections we have examined the varying condi- 

 tions presented by certain well-defined external characteristics within 

 the many species of the geometrica-group, embracing practically all 

 those relied upon for diagnostic purposes. We find a series of char- 

 acters, each of which, when traced through different members of 

 the group, can be seen to pass by almost insensible gradations from 

 one extreme condition to another. The group as a whole presents us 

 with innumerable stages in the phyletic process of transformation of 

 individual characters ; everywhere we have chains of forms from one 

 extreme of the structure to the other. The extreme variations are so 

 marked that were almost any one of them to become isolated by the 

 elimination of its transitional stages there could be scarcely any 

 hesitation in according specific rank to the individuals possessing it. 



Taking any one of the characters, we find that all its variations 

 form a continuous series from one extreme to the other ; in every 

 case it has been possible to show that the extreme elaboration of a 

 character is reached by slow transitions from some simpler stage. There 

 is no suggestion that characters have changed suddenly from one 

 phase to another, but the variations have always taken place by inter- 

 mediate stages along one or more direct trends. Even such complex 

 geometrical colour patterns as those exhibited by the carapace and 

 plastron of oculifera can be explained in terms of others less 

 complex. 



The type of variation which the geometric a-gxowp illustrates 

 is that known as the direct, continuous, or determinate method, in 

 contrast with the indirect, indeterminate , or haphazard method. In 

 every instance the evolution of a character consists of a gradual but 

 direct change from one stage to another, without any suggestiveness 

 of the sudden introduction of new characters, or of variation along 

 uncertain lines. The studies therefore lend no support whatever to De 

 Vries' Theory of Mutation, which " assumes that new species are 

 produced from existing forms by sudden leaps," but serve to confirm 

 the more generally accepted view that transformations are mostly 

 brought about by slow, gradual changes. The changes of any one 

 character may be in a single definite direction (orthogenesis), e.g., 

 coloration, axillary and inguinal shields, or in different directions 

 (amphigenesis), e.g., nuchal shield, antebrachial shields. 



h. Fixity and Plasticity of Characters. 



On tracing any one character throughout the various sub-groups, 

 it becomes abundantly manifest that the character in question has 

 attained a certain permanence or fixity in some sub-groups w'hile it is 

 yet plastic or variable in others. To take the nuchal shield as an 

 illustration. Within the tentoria sub-group we find all stages from 

 its practical absence to a length of nearly a centimetre, even among 



