76 BULLETIN 16 9, UNITED STATES NATIONAL MUSEUM 



of these were calculated. These new figures furnished a check on the 

 probable taxonomic significance of the grouping. A priori, the range 

 of variation allowed by the graphic grouping appeared too large for 

 single species. Most paleontologists would think it wholly unjustified, 

 for instance, to place a lower premolar measuring 7.0 mm in length in 

 the same species with one measuring 9.1. But the coefficient of 

 variation of the whole group to which these belong is only 5.3, and that 

 is small, rather than large, for a Imear dimension of teeth of a single 

 mammalian species, so that there is no reason to believe that the graphs 

 have permitted confusion of two species. 



These statistical data, furthermore, when considered from a taxo- 

 nomic biological viewpoint, suggested the degree of variation to be 

 expected in species of tliis family and also gave a criterion for judging 

 the greater or less usefulness of certain characters for taxonomic dis- 

 tinction. Thus, in turn, a check was possible on the groups too small 

 for the useful calculation of these derived data. 



After full consideration of all these primary and secondary data, 

 it was clear that of the eight groups finally achieved and checked each 

 represents a variable morphological unit, that the variation in each is 

 not greater than commonly occurs in natural species, but that no two 

 can be combined without producing a unit statistically heterogeneous 

 and morphologically much more variable than a species. The biologi- 

 cal conclusion is thus that eight species are present. 



Eight species of a single family seems a relatively large number to 

 occur at a single horizon and locality ,^^ but there is really nothing 

 extraordinary in this number. The ptilodontids are analogous to small 

 rodents, and there is, for instance, hardly any region of the United 

 States today that does not have more than eight species of Cricetidae. 

 This large number of species clearly is not due to maldng the specific 

 distinctions too small. On the contrary, since we have definite, con- 

 crete statistical data warranting this, allowance has been made for 

 much more variation than is usually granted within a paleontological 

 species. The largest individual of sindairi, for instance, is 48 percent 

 larger than the smallest (length of P4), a much greater variation than 

 the current rule-of-thumb methods permit, although the demon- 

 strable probability that they do belong to one species is very great. 



A few specimens could not be placed in any of these eight species. 

 A Eucosmodon-\ike lower incisor, for instance, probably does not belong 

 with any of them. (It is also from a difterent locality.) Several 

 upper teeth, not of montanus, cannot be associated v/ith lower jaws, 

 and wliile they almost certainly belong among the species based on 



31 All these species occur in the Gidley Quarry. While the specimens from the Gidley Quarry cannot all 

 be exactly contemporaneous, they are practically so. Nevertheless the probability that they represent a 

 succession of years or seasons helps to explain the faunal variety, not by the evolution of new species but by 

 the opportunity for more thorough sampling of a large area. 



