210 PROBLEMS OF RELATIVE GROWTH 



the ' forms ' are purely arbitrary growth-types, the heterogonic 

 increase of mandible-size with total size being accompanied, 

 as often, by changes in tooth-characters and other morpho- 

 logical alterations. But Dudich states that he is forced to 

 regard them as in some way ' real ' and of taxonomic im- 

 portance, for the following reasons : (i) Because the several 

 ' forms ' are transgressive as regards body-length, the smallest 

 of form 3, for instance, being smaller than the largest of 

 form 2. (2) Because, although the frequency-curve for female 

 body-length is unimodal and approximates to normal type, 

 that for the body-length of the males is irregular, multimodal, 

 and skew. He attaches more importance to (1). 



Analysis (Huxley, 1931c) of his figures by body-size (178 

 specimens grouped into 28 classes) and a plotting of the 

 resultant means showed that when all the ' forms ' were 

 lumped together, a clear approximation to the simple hetero- 

 gony formula (constant growth-partition coefficient of male 

 mandible) was found (with the deviation from it at highest 

 absolute sizes which we previously established as usual in 

 holometabolous insects : see Chapter II). When however the 

 ' forms ' were taken separately, and each subdivided into size- 

 classes, the resultant plot resembled a series of overlapping 

 tiles on a roof, thus giving graphic proof of Dudich's contention 

 that they are transgressive as regards body-size (Figs. 35, 92). 



The type of overlapping, however, at once gives the key 

 to the situation. (1) What we have plotted are the means. 

 (2) But we should expect a definite range of variation in the 

 relative size of mandible for given body-size, whether this be 

 due to variations in growth-partition constant (k) or fractional 

 constant (b). (3) Over the range of size where two ' forms ' 

 overlap (as elsewhere, of course) we should accordingly expect 

 to find some with mandible-size well above the mean for that 

 particular body-size, others with mandible-size well below 

 that mean. (4) But it is a general rule that increasing absolute 

 size of many organs (other Lucanid mandibles — see especially 

 the paper by Griffini, 1912 — deer antlers, etc.) is correlated 

 with morphological changes (Fig. 93). (5) We should there- 

 fore expect that, over each region of the size-range where 

 overlap occurs between two ' forms ', individuals which vary 

 in the direction of high mandible-size should on the whole 

 have the tooth-characters of the form above, those which are 

 low variants as regards mandible-size should on the whole 

 have the tooth-characters of the lower form. (6) The trans- 



