48 GENETICS IN RELATION TO AGRICULTURE 
Multimodal Curves.—Thus far we have considered only homogeneous 
populations, which, when examined statistically, exhibit a certain degree 
of approximation to the normal curve of variation. Populations fre- 
quently occur, however, both in nature and among domesticated animals 
and plants, which are found to be heterogeneous for certain characters 
at least when subjected to statistical analysis. Graphically shown the 
data for such a character produces a polygon with more than one mode. 
In general such data indicate either the permanent influence of different 
causes affecting only certain individuals or of the same cause acting 
differently upon a portion of the population. Conditions of bimodal 
curves are more or less familiar to all. Sexual dimorphism and certain 
3 4 5 6 7 8 9 
Fre. 20.—Bimodal polygon plotted from data on the earwig. Mean types (x 34) 
indicated above corresponding modes. Numbers below the base line indicate length of 
pincers in mm. (From Bateson and Johannsen.) 
differences in development which are contingent upon sex, such as height 
of comb in fowls, obviously would result in a “notched” graph if the 
characters were measured and the data plotted. The classic example of 
dimorphism producing a bimodal curve is found in the length of the 
pincers of the common earwig (Forficula auricularia) as reported by 
Bateson. Fig. 20 illustrates the two mean types, each sketch being 
placed directly above its corresponding modal class in the graph. Other 
conditions commonly causing mixed populations such as would result in 
bi- or multimodal curves are the following: 
1. Coexistence of groups of different ages; common in birds at certain 
times of the year. 
2. Overlapping of geographical races of the same species—birds, 
mammals. 
3. Coexistence of different races of the same species, for example, 
many grasses in the wild state and various cultivated grains contain 
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