MICHIGAN ACADEMY OF SCIENCE. 37 



words, the differences within the species may be greater than the differences 

 between species, as de Vries has pointed ont. How then are we to decide 

 whether two inchviduals comparatively different from each other, and yet 

 alike, belong to the same or different species? It has been found that for 

 any given character the variations within the species may be expressed nu- 

 merically by an average with deviations, both above and below that average. 

 For instance the average height of the stem in a given species of plants ma}^ 

 be two feet. Most of the plants composing the species may vary only 

 slightly from this average, say from one to three feet. But the greater 

 the number of individuals examined and measured, the more certain 

 it becomes that we shall find a few individuals which differ far more 

 widely from the average. In our supposed case we might find that the ex- 

 treme limits of size were six inches to ten feet, while the average was only 

 two feet. These deviations from the average of the species are called the 

 fluctuating variations. They are largely determined by the external condi- 

 tions in which the species grows. Prof. George Klebs has shown that when 

 plants are subjected to extremes of variation in the external conditions of 

 light, heat, moisture, and food supply, the deviations from the average of 

 the fluctuating variations become far greater than are usually found in a 

 state of nature. Klebs' results with Semper vivum were truly remarkable. 

 He produced variations that are not found in a state of nature in the species 

 with which he worked, changes in the color, size and shape of the flower, 

 great variations in length of the stem and its mode of branching, the size, 

 shape and arrangement of the leaves. As the result of this kind of work, 

 carried on for a considerable number of years, Klebs has given us a definition 

 of a species which expresses the dependence of the form of the plant upon 

 the environment. According to Klebs we must say: 



"To a species belong all individuals which, propagated vegetatively or 

 by self-fertilization, under like external conditions, show the same characters 

 through many generations." If two plants under these conditions show a 

 noticeable difference, they are to be regarded as belonging to two species, 

 even though they have descended from a common ancestor. Gaston Bon- 

 nier has shown by experiment that plants transplanted from the region of 

 Fountainebleau, near Paris, to Toulon, in the Mediterranean region, show in 

 a few years adaptations both of external form and internal structure which 

 cause them to resemble the species characteristic for the Mediterranean re- 

 gion. The same investigator found similar results on transplanting from 

 the plains to the Alpine regions. Knowing the origin of such widely var- 

 iant forms we do not call them two species, but merely extremes in the fluc- 

 tuating variations of the species. It is conceivable, however, that nature 

 might perform this same experiment on such a scale, and in such ways as to 

 make it difficult or impossible to recognize the common origin of two such 

 different types. In that case the botanical collector or systematist, finding 

 the two types in widel}^ separated regions, would describe them as two species 

 of plants. If the distribution of the species was continuous from one of 

 these extreme regions to the other the connecting intermediate forms would 

 show that we had to do merely with extreme fluctuating variations brought 

 about by extremes in soil, moisture, heat and light. If, however, the geo- 

 graphical continuity of the species had been interrupted in an}^ way, it would 

 be impossible to determine by observation alone that the two extreme types 

 were only fluctuating variations of one species. That could be determined 

 by the experimental method as followed by Klebs and Bonnier. Plant the 

 two types in the same region, grow them under exactly the same conditions, 



