POLYMORPHISM IN NEUTER INSECTS 61 



limitation of raw material due to the system being a closed 

 one, we should expect, from a certain absolute size upwards, 

 the actual values for the size of the heterogonic organ to fall 

 progressively more and more below the theoretically expected 

 value. And this is what we actually find. When organ-size 

 is plotted against total size on a double logarithmic grid, the 

 first part of the curve is a good approximation to a straight 

 line, but the end portion curves over so as to be concave to 

 the x-axis. This is so for all cases so far investigated, includ- 

 ing the mandibles of three species of two genera of stag-beetles, 

 the horn of Xylotrupes, the heads of polymorphic neuter ants, 

 etc. 1 ; Figs. 35, 37, 92. 



§ 4. Heterogony and Polymorphism in Neuter Social 



Insects 



We shall later note some further complications introduced 

 into the situation by the fact of moulting. Here we may refer 

 to the particularly interesting case, just mentioned, of poly- 

 morphic neuter ants. It is well known that in what are 

 apparently the more primitive examples of such polymorphism, 

 there is an unbroken array from smallest to largest neuters, 

 the continuous series being quite arbitrarily divided up into 

 ' worker minimae ', ' worker mediae ', and so on up to ' soldier 

 mediae ' and ' soldier maximae ' ; and some myrmecologists 

 have introduced even more elaborate terms (see Wheeler, 

 1920). Now these series are invariably characterized by a 

 relative increase of head- and especially mandible-size with 

 an absolute increase of total size. Measurements of the 

 weights of head and rest-of-body in species of two genera 

 (the huge Camponotus gigas, from Borneo ; and a driver ant 

 of the genus Anomma from Africa) show that, over the major 

 portion of the size-range, the formula for constant growth- 

 partition coefficient is nicely adhered to 2 (Huxley, 1927 ; 

 Huxley and Bush unpublished) (Table IVa and Fig. 37). 



1 Teissier, 193 1 (p. 97), using weight and not linear measure, shows 

 in his Fig. 20 no curving over of this type for the mandibles of Lucanus 

 cervus. This might mean that my interpretation is wrong, and that 

 mechanical reasons are interfering with great growth in length rather 

 than nutritive reasons with growth in mass. On the other hand, the 

 curvature in my material does not begin until elytron-length 33 mm., 

 and Teissier has hardly any specimens as large as this. 



2 The Anomma curve bends over at high sizes, as described for stag- 

 beetle mandibles, etc. This may presumably be accounted for as 

 suggested earlier in this chapter. But the formula is also not obeyed 



