REGENERATION 313 



last bracket of the equation as given above. Thus for two competing 

 hydranths, we shall have to consider equations of the form 



^^ = iK-R,)ib,-c,R,-d,,R,) 



and 



dR 

 --- -{K- R,){b, - c,R, - d,,R,). 



One can see, in a general way, the results which processes of this kind 

 would produce, by considering the situation which would arise when 

 the processes had gone to completion, by which time no further change 

 would be occurring, and the [dRldt)s would be zero. Then we shall have 



and 



From the first of these equations, we see that, in this final state 

 D K duRi 



Ki = — — 



Since if there had been no competition (i.e. if ^12 were zero), Ri would 



have been — , it is obvious that the competition has led to some degree of 



inhibition of Ri; and the same is of course true of i^2- Also dominance 

 wHl occur when either Ri or R^ is larger than the other ; and this may hap- 

 pen either because of the relations between the intrinsic efficiency con- 

 stants b or on account of the 'interaction' coefficients c and d, or from cer- 

 tain combinations of these. For instance, if the interaction coefficients are 

 the same for all sites, but there is a gradient in intrinsic efficiencies we 

 shall have cR^ = bi — dR^ and cR^ = b^ — dRi, whence it is easy to 

 show that 



h — 62 



R^-R 



c-d 



so that if l>i is greater than b^, Ri will be larger than R2» and there will be 

 dominance of the site with greater efficiency over that with less. It is 

 clear, without our going into the details of the other possible cases (see 

 Spiegelman 1945), that the assumption of physiological competition does 

 provide a mechanism by which gradients in efficiencies of synthesis 

 or interaction would give rise to phenomena such as dominance. It thus 

 makes it possible to envisage field phenomena in a form in which they 

 become amenable to physiological analysis, aimed for instance at 



