February, '10] FISKE : SUPERPARASITISM 93 



suits. The second egg, if deposited in a different caterpillar, brings 

 about a parasitism of 2 per cent, but there is a chance that it will be 

 deposited in the same host. The odds, to be exact, are 1 in 100, so 

 instead of 2 per cent of parasitism, the chances are even that the para- 

 sitism is 1.99 per cent. This is, of course, impossible with only 100 

 hosts, but there is no other way to express the conditions. 



The third egg is much more likely to be deposited in a third cater- 

 pillar than otherwise, but at the same time there is the 1 chance to 100 

 that was mentioned above, which must be taken into consideration, 

 and in addition 2 chances to 100 that it will be deposited in one or the 

 other of the two hosts previoasly attacked. Reduced to percentage, 

 the chances are that instead of 3 per cent of parasitism as the result of 

 the deposition of three eggs, it will be 2.9701 per cent. 



As parasitism progresses, there is, ob\'iously, a rapidly increasing 

 chance that the parasite will select an already parasitized host for 

 attack, and by the time that ten eggs are deposited there is an even 

 cliance that one among them is wasted. When a parasitism of 50 

 per cent has been reached, the chances are even that no less than 10 

 have been similarly wasted, and the chances are against instead of in 

 favor of the selection of an unparasitized host ever after. 



Instead of 100 per cent of parasitism resulting from the deposition 

 of 100 eggs, chance favors a parasitism of about 64 per cent. In other 

 words, out of 100 eggs 36 are likely to be deposited in hosts already 

 attacked. .If the parasite continues oviposition, it is an even chance 

 that 77 out of the next 100 eggs will be injudiciously placed, and 92 

 out of the third hundred. This is a total of 205 out of 300 eggs which 

 have been wasted. It will, in theory, require about 450 eggs to bring 

 about 99 per cent of parasitism, and since the odds are now 100 to 1 

 against the parent selecting the last remaining unparasitized individ- 

 ual, more than 500 eggs in all must be deposited before 100 per cent of 

 parasitism may reasonably be expected. 



In the accompanying diagram, the vertical lines are indicative of the 

 number of parasite eggs deposited, and the horizontal of the hosts at- 

 tacked. The straight line AB, indicates the percentage of parasitism 

 Mhich would result were the female parasite capable of intelligent 

 selection of her host, and the curve, AC, that which would theoretically 

 result under conditions as above outlined. 



That the calculation is not altogether fantastic is indicated by cer- 

 tain experiments which have been carried on in the laboratory, in 

 which conditions not so very different from those prevailing in the 

 imaginary island have been artificially produced. The results have 

 not been exactly in accordance with the curve as shown, but nearly 



