BEGINNINGS OF CO-OPERATION 75 



with goldfish, the growth-accelerating principle seems 

 to be associated with the protein fraction of the ex- 

 tract. When the whole extract is used, it is said to 

 be growth-inhibiting and to produce the same re- 

 sults as overcrowding. The point I have made is 

 that with the sea-urchin eggs, under the conditions 

 of our experiments, there is also an ill effect of un- 

 dercrowding, and that there is an optimum popula- 

 tion size for speedy development which is neither 

 too crowded nor too scattered. 



Much similar work has been done with the ef- 

 fects of numbers on the rate of multiplication with 

 various protozoans. Again I shall have to select re- 

 sults from the mass of available evidence. The late 

 T. Brailsford Robertson (107) of Australia an- 

 nounced back in 1921 that when two protozoans of 

 a certain species were placed together, the rate of 

 division was considerably more than double that 

 which resulted with only one present. It should be 

 noted that during the time of these experiments and 

 in all these protozoa which we are considering re- 

 production was entirely asexual, by self-division of 

 the original animal. I subjected the data in Robert- 

 son's original paper to statistical analysis and found 

 that there were only thirteen chances in a thousand 

 of getting as great a difference by random sampling. 

 Such results must be taken seriously (Figure 10). 



