CONTINUED SELECTION IN HYDRA 25 



ference found, which means that the true value of the differ- 

 ence could fall so far from the value given by the sample only 

 once in some billions of samples; a certainty that no such differ- 

 ence was produced by selection in this experiment. Even with 

 a strength of heredity of only 0.01, nineteen generations of se- 

 lection result in a diversity of more than 0.2 tentacle which is 

 almost 7 times the probable error so that the chances are more 

 than 400,000 to 1 that no such diversity would be obtained in any 

 given experiment of the same magnitude. If all variations are 

 inherited to the same extent, if selection of every variation con- 

 tributes to evolution in proportion to the extent of the variation 

 from the mean of the race, then the strength of heredity in Hydra 

 must be considerably less than that represented by a coefficient 

 of ancestral inheritance of 0.01. 



If not all variations are inherited, the present experiment may 

 have failed to reveal a greater strength of heredity than this, but 

 if even three-fourths of the variates selected were strictly soma- 

 tic, a regression of 0.05 would almost certainly have been revealed : 

 The inclusion of so many somatic variates would reduce the num- 

 ber of effective selections to one-fourth and a regression of 0.05 

 should result in a diversity of 0.29 tentacle after five selections. 

 If it is assumed that regression is as great as 0.30, which is approx- 

 imately that ascribed to Hydra by Pearson, the percentage of 

 variations which are inherited to this extent must sink below 10 

 per cent to escape detection by this experiment. 



These figures are of interest chiefly for a comparison with the 

 theory of homotyposis and are sufficient to disprove, for Hydra, 

 the theory as advanced by Pearson in 1901 and 1910, ^ and make 

 it possible to state with assurance that if inheritance of varia- 

 tions in number of tentacles occurs within the clone of Hydra it 

 does not follow biometrical laws. For other theories, which hold 

 that continuous variations are inherited but do not define the 

 method or extent of such heredity, it can only be pointed out 

 that if any hereditary variations occur in Hydra they must 



2 On the Principle of Homotyposis. Phil. Trans. Roy. Soc. London, vol. 197, 

 pp. 443-459, 1901. Darwinism, Biometry, and Some Recent Biology. Biomet- 

 rica, vol. 7, pp. 368-385, 1910. 



