Problems of Heterogeneity 185 



binations are made and how transmutations may arise. The census-taker and 

 field naturalist will see one side of the problem, the laboratory student another ; 

 both are right in their frequently hostile utterances, but both partly wrong. 



In the making of a census in any population these main facts are desired : the 

 number showing a particular character; the amount and permanency of the 

 characteristic shown; the minimum, maximum and mean deviation presented; 

 the direction and, if possible, the cause of the condition. 



An entirely false conception of the nature and role of small fluctuations has 

 arisen through the uncritical use of biometric methods, and while it is undoubt- 

 edly true that many characters, as for example the variation in any meristic 

 series, do follow the law of probable error in their measured dimensions, is it 

 certain that the differences in number or dimension are the essential features of 

 the heterogeneity ? These numerical differences, after all, are but the result of 

 operations not discoverable or measured by the methods of the census-taker. 

 Moreover, in color-patterns in animals or plants the amount of the color present 

 may be measured in terms of the area exposed, and from this data the biometri- 

 cian then proceeds to an exhaustive mathematical analysis in which the result, if 

 any at all, is mathematical and not biological. 



The biological facts of the arrangement of the character in the organism, the 

 relation of this to surrounding conditions, and its effects as it varies upon the 

 welfare of the individual, are points which may be of paramount importance; 

 but with these the statistical method does not and can not deal. 



PROBLEMS OF HETEROGENEITY. 



In the literature on " variation " confusion reigns supreme — dogmatic defini- 

 tions, anticipatory assertions, arguments without point ; it is small fluctuations 

 with preservations per utility and described a la biometrics, or it is disconti- 

 nuity per saltum preserved by Mendelian recessiveness or dominance, or it is 

 determinate variation ever in line conditioned by organic growth or by ortho- 

 genesis repeating ancestral states and adding new ones, which are held in line by 

 internal automatic regulating and determining tendencies; or again, it is an 

 inherent tendency to vary determinately, indeterminately, or per saltum, and so 

 on ad infinitum. In reality there are many processes that are involved in this 

 confusing mass of phenomena which are called variation. 



In any population two general sets of operations are interacting. There is the 

 action of the total population as it encounters the conditions of existence, the 

 way in which it responds to its environment and in divers ways meets incident 

 physical conditions and reacts to social relations of the society of which it is a 

 member by population responses. Opposed to this is individual action tending 

 to diversity, frequently to extremes. Both are but parts of the same process; 

 only in the mass action of the population there is obtained a view of what the 

 final effect of the innumerable processes which went on among the individuals in 

 the production of the generation is upon the population in each generation. 

 From the individual is obtained an idea of the methods of interaction, but this 

 could never give complete knowledge, even in a limited and simple population. 

 So, therefore, for the present at least, the general action of the population must 

 be considered until it is known more completely what the mass effects may or 

 may not accomplish in organic evolution. 

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