Analysis of Heterogeneity in Some Simplest Charactebs 217 



experiences in their ontogeny, and came into my hands for study from the field 

 in quite heterogeneous states of nourishment, age, and reproductive activity. 



It was thought that the " character " might be of some interest in the study 

 of " variation " phenomena, and in that similar weight determinations had been 

 used in investigations, there was no a priori reason why the same might not be of 

 interest in this material. This first study of the weights as a structural char- 

 acter was so unsatisfactory that I did not follow it further at that time. There 

 were too many obvious sources of error in the set of observations, too little homo- 

 geneity of materials or determinations, even though the statistical method did 

 blend them beautifully in the end ; so that the attempt was abandoned from the 

 point of view of materials taken in nature, even with the greatest care as to 

 location, generation, and conditions of life and stage of development. 



In 1901, 1902, and 1903 I made a different plan of attack upon the problem 

 of weight as a " unit-character," this time breeding from single pairs, obtaining 

 the weight of the progeny at the onset of the breeding-period, and in the next 

 generation breeding only from the individuals that had the same weight as the 

 parents, and so on. Effort was made to have the material as uniformly nour- 

 ished at all times as possible, to give it all the food it would eat, and to weigh at a 

 fully nourished state at the onset of reproduction activities. Other conditions 

 were not controlled or measured and no attention was paid to them, excepting 

 to make them as nearly normal as possible, so as to give the best growing-condi- 

 tions for each group and produce homogeneous materials. These measurements 

 were made in a series of experiments to modify the size of this species by selec- 

 tion, and the measurements here recorded were a part of the measurements 

 made in the course of that study, and serve well in this place to illustrate what 

 one really finds in the variation of characters of this class. 



In the population which I was using for this work, which came from eastern 

 Massachusetts, I weighed both males and females, and the means of the weight 

 at breeding were males 7.5 to females 10. In figure 31 is given the results of the 

 weighings of the males in four generations. At the start three sets of weights 

 were mated — light, average, and heavy — the male being used as the basis of the 

 determinations. They were mated with females whose weight was to the males' 

 weight as 10 : 7.5., thus preserving " statistical equality " in the matings. From 

 the lightest condition mated (a) a line of descent was carried out as shown in 

 figure 31. In the first generation are shown the matings from the different 

 light, average, and heavy pairs, with the male weights alone given, showing that 

 the three conditions of weight gave about the same conditions in the array of the 

 weights in the progeny. In figure 31 are given the results in the line of descent 

 from the light condition (.-1) for four generations. The materials subtended 

 certain weight values, in terms of more and less, and in consequence were at once 

 arranged in a line distribution of plus and minus ; but the array of values showed 

 nothing of any interest, save the shortcomings of statistics and their inability 

 to analyze the condition in the material under investigation. I was interested in 

 this set of determinations for the reason that so many similar determinations 

 had been made with far less care than I had employed, and not infrequently far- 

 reaching conclusions had been drawn, the reason for which I could not discover. 

 The general result is simply that statistically determined weight is not a simple 

 character of the organism, although not infrequently so considered. 

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