312 PRINCIPLES OF EMBRYOLOGY 



competence, that of dominance is an expression of a hydranth individua- 

 tion field which extends outside the hmits of the actual hydranth structure. 



It must be clearly recognised that when we speak in this case of gra- 

 dients or of fields, we are doing no more than describe the phenomena 

 revealed in experiment, and are still far from a satisfying explanation of 

 the mechanisms involved. We can, however, in the case of the hydroids, 

 make some further progress towards this, both in the refinement of the 

 theoretical formulation of the case and in the experimental discovery of 

 new facts about it. 



Let us consider the theoretical aspects first. Both Barth (1940) and 

 Spiegelman (1945) have suggested that the mechanism of the individua- 

 tion field is to be found in a competition between the various regions for 

 physiologically necessary substances. Suppose, for instance, that the pro- 

 duction of a new hydranth involves the transformation of some raw 

 material K into hydranth material R. Then clearly if two hydranths are 

 being formed, and are physiologically connected so that they both utihse 

 a common supply of K, the development of one hydranth will tend to 

 inhibit that of the other. If one hydranth gets some sort of start over the 

 other, or is more effective in drawing supplies of K from the pool, then 

 it will be dominant, and, while being little inhibited itself, will have a 

 strong depressant effect on the other. 



If one makes assumptions about the character of the reactions, one can 

 put the situation into mathematical language. One of the simplest hy- 

 potheses, which is adopted by Spiegelman in his formulation, is that the 

 production of R is (i) proportional to the amount of raw material still 

 available, i.e. to K — R; and (ii) the efficiency of utilising the raw mater- 

 ial is reduced as time goes on and the concentration of R builds up. The 

 second assumption could be expressed, to a first approximation, by sup- 

 posing that the rate of formation of R is proportional to ^ — cR, where 

 c is some constant. 



For a single process of hydranth formation we should then have an 

 equation of the form 



^-{K- R){h - cR). 



If there are two competing sites of hydranth formation, we shall have to 

 consider an R, a I) and a c for each of them, which we may indicate as 

 Rif R2, bi, bz, Ci, c^. Moreover in accordance with the second assumption 

 above, we must expect that the formation of hydranth at one site has an 

 effect on the efficiency of hydranth production not only at that site but 

 at the other one also. We can cater for tliis by including a new term in the 



