IV 



qUANTITATIVE ASPECTS 



607 



declines (Brondsted, 1955). The quality, also, of a regenerate may change with 

 age (Przibram, 1931) probably as a correlate of the decrease in specific growth- 

 rate. Abnormal regenerates in planarians are associated with slow regeneration 

 (Child, 1913, 1921). 



Some degree of correlation between specific regeneration-rate and the specific 



"^ 



3 mm 



O. 



D 



a°a 



n 



o 

 ^1.0 



□ \ nn 



0.5- 





o \ 



□ \ 



dR 



^° 



^ □ 



.\o 



o^a. 





10 c 



5 -H 



Abdomen 



3 mm 



width 



Fig. 3. The relationship between 

 (O) specific growth rate, (n) spe- 

 cific regeneration rate per day, 

 and body-size (abdomen-width) in 

 Asellus aquaticus. Both specific rates 

 expressed as a percentage of body- 

 size. The curves are approximately 

 exponential or hyperboloid. The 

 relative rate of decline, with in- 

 creasing body-size, is at first greater 

 for growth-rate than for regener- 

 ation-rate, and ultiniately it is 

 less. The specific regeneration-rate, 

 throughout, is about ten times the 

 normal growth-rate. In both curves 

 there is an irregularity due to a 

 temporary increase in rate, around 

 the size 1.25 mm abdomen- width 

 for growth-rate, and somewhat later 

 for regeneration-rate. (From results 

 ofNeedham, 1949a.). 



rate of normal growth is to be expected (p. 591). Apart from their age-decline 

 (Fig. 3), their response to other variables is similar (Przibram, 191 7). This is indi- 

 cated by a further analysis of the results ofNeedham (1947b), using individuals 

 of a fairly narrow age (size)-band. When the individual results are grouped accord- 

 ing to the amount of increase in body-size during the stadium following amputa- 

 tion, the amount of regeneration during that time increases approximately linearly 

 from 1.35 mm in individuals making no body-growth, to 1.97 mm in those which 

 grew a maximal amount of 0.27 mm in body-width. The increase in regeneration- 

 rate is therefore about twice that in growth-rate. However, the total excess of 

 regeneration-, over growth-rate depends mainly on the high rate of regeneration 

 pre-empted before there is any body-growth at all. 



Przibram (191 7) considered that his results were adequately fitted by a function 

 which related regeneration-rate to both the normal growth-rate and the amount 

 still to be regenerated (p. 603). The function was clumsier than necessary, but it 

 shares with the work of Du Nouy ( 1 936) the virtue of incorporating, simultaneously, 

 more than one relevant variable into an algebraical definition of regeneration- 

 rate. Paulain (1938) and others also have stressed the complication of trying to 

 measure regeneration-rate when the standard, body-size itself, is changing. In 

 an animal which is not growing, the growth-parameter becomes a constant, and 

 Przibram's relation for regeneration-rate simplifies and integrates to give one 

 reasonably similar to those of Paulain (1938) and Du Noiiy (1936). 



Quantitative studies on regeneration-rate in relation to other variables are 



Literature p. 64g 



