68 PROBLEMS OF RELATIVE GROWTH 



§ 5. Heterogony, Moulting, and Dimorphism 



Finally, certain quite different special problems arise from 

 the interaction of constant differential growth-ratios with the 

 characteristic Arthropod process of moulting. It will be clear, 

 since growth in a typical Arthropod only occurs between the 

 shedding of one exoskeleton and the hardening of the next, 

 that in the life-history of any single specimen the theoretical 

 growth-curve relating organ-size with body-size will never be 

 realized. Instead, growth of both organ and rest-of-body will 

 take place in a series of jumps, but the points thus arrived at 

 will all lie on the theoretical curve. 



Although moulting in Crustacea and some insects tends to 

 take place at each doubling of weight (Przibram, 1930), the 

 large variations encountered, together with the variation in 

 the initial post-larval weight, are often sufficient to obscure 

 any recurrent modality in the sizes at which moulting occurs. 

 In a large population of such species, moulting thus occurs 

 at random at any size, and measurements of a heterogonic 

 organ whose growth-ratio is constant over long periods accord- 

 ingly fall on to a continuous curve when made on such a 

 population. 



The state of affairs, however, is entirely different if (a) the 

 organ's high growth-coefficient is confined to one or a few 

 instars and (b) is initiated in a more or less constant phase 

 of an instar — e.g. always immediately after moulting. As 

 the simplest case, let us take one in which the high growth- 

 ratio lasts but one instar, as occurs with the female abdomen 

 of Inachus (Shaw, 1928). When the data are grouped into 

 classes by body-size, and then simply the means of the various 

 size-classes taken, a curve is obtained which merely indicates 

 two periods of approximate isogony, separated by a short phase 

 of intensive heterogony (Figs. 22, 23). But when frequency- 

 curves for relative abdomen-size are prepared for each body- 

 size class, the true state of affairs is revealed (Fig. 39). All 

 female Inachus are then seen to fall into one or other of two 

 sharply non-overlapping groups as regards relative abdomen- 

 size. Those below a certain absolute body-size all have narrow 

 abdomens, those above another higher body-size all have 

 broad abdomens. The curves for the short intervening range 

 of body-size, however, are all bimodal, some individuals having 

 narrow, others broad abdomens, but none being of intermediate 

 type. When the curves for all the classes are summed, we 



