76 PROBLEMS OF RELATIVE GROWTH 



together does not curve over downwards at high body-sizes, 

 as with various other holometabolous forms.) If so, then 

 with earwigs within the known range of body-size, those with 

 stunted body will always have larger forceps, though this 

 should not hold if we could produce individuals of a much 

 larger body-size. 



A further peculiarity of the curves is that those for high 

 and low forms taken separately (Fig. 40) both show a pheno- 

 menon the reverse of that found in most holometabolous 

 insects — namely that they are concave upwards at their upper 

 ends ; in addition, they are concave downwards at their 

 lower ends, indicating a rapid growth-coefficient at either 

 end. This may, perhaps, be accounted for if we suppose that 

 growth-ratio is accelerated during the period just before and 

 just after a moult. The high-sloping early portion of the ' low ' 

 curve would be due to the normal initial high growth-ratio 

 of the forceps-rudiment at the first onset of heterogony, and 

 would comprise those individuals which started their forceps- 

 heterogony late in the instar prior to the imago. The high- 

 sloping end portion of the same curve would include those 

 which started their heterogony relatively early in the same 

 instar. But those in which heterogony was initiated towards 

 the middle of the instar would only have one period of accelera- 

 tion at the end of a period of slow growth-ratio, and therefore 

 would show less change of forceps-size for a given increase of 

 body-size. If an extra instar is added, the rapid growth- 

 periods are repeated, with corresponding results on the curve. 

 This is, of course, purely speculative, but may serve as the 

 basis for further work. 1 



The case of Xylotrupes (Huxley, 1927c) has been less 

 thoroughly analysed. It presents various complications, most 

 notable being a tendency to trimodality over a certain range 

 of body-size. 



In Lucanidae (Huxley, 1931c) analysis of Dudich's paper 

 (1923) and other data show several interesting facts. First, 

 that in Cyclommatus the range of male body-length (without 

 mandibles) is much greater than in other stag-beetles, being 

 about as much as the mean body-size, whereas in Lucanus 

 cervus and L. lunifer it is less than half the mean. (The ratio 

 of largest to smallest body-length in Dudich's Cyclommatus 

 specimens is 2-47 ; in Bateson and Brindley's Lucanus cervus, 



1 Most of the suggestions here advanced concerning Forficula 

 modify or extend those put forward in my paper on the subject (1. a). 



