APPENDIX I 207 



with 54 degrees of freedom, tliis is far more than is necessary for significance, 

 even at the o-ooi probabihty level. 



The significance could also be assessed by inspection, for die probability of 

 fourteen consecutive differences being all in the same direction by chance is 

 neghgible. 



(^) A Method of Calculating the Minimum Tadpole Mortality 

 FROM THE Observed Rate of Infestation by Polystoma ititcqerrimum 



This method depends on the truth of a number of assumptions, and it is not 

 claimed to be accurate. The assumptions would have to be very far wrong to 

 give a general picture much different from that suggested, and any errors are 

 probably minus. 



The parasite lays fewer eggs than its host. The mature fluke lays 400 to 800 

 eggs, and is hermaphrodite. A female frog lays, say, 1,500 to 3,000 eggs, that 

 is an average of 1,125 per frog, but its parasite lays 600. Since the host and its 

 parasite start life at the same time, such a state of affairs must result in extinction 

 of the parasite unless either the parasite has a mortality less than that of the 

 frog, or there is a multiplying form that functions at an early stage, because 

 by the usual axiom, if the population of frogs is stable, the number of its eggs 

 just balances the mortality of the frogs. Now, a parasite that dies with its host 

 must have a higher mortality, for its own causes of death must be added those 

 of its host. The exact figure is unknown. In the face of this uncertainty, let 

 us make the extreme assumption that the mortality of the parasite up to the 

 moment that it enters the tadpole is nil. The multiplying form does not func- 

 tion until late in tadpole life. Galhen considers that 25 per cent of frogs carry 

 an adult fluke. The parasites would therefore lay about 150 eggs per frog. If 

 all the tadpoles survived to the age at wliich infestation begins, there would be 

 1,125 tadpoles for 150 larvae, that is, 0-13 per tadpole. This was about the 

 number in Lower Parkfield in 1947, and, at Dagger Lane in 1947, the number 

 was lower. It will be recalled that, in those ponds in that year, tadpole mortality 

 was exceptionally low, so that the calciilation, theoretical as it is, holds so far. 

 In all other cases, the number has been higher, and sometimes not even of the 

 same order. For example, the number was 26 in Upper Parkfield and 6-4 in 

 Cat Hill in 1948. It is therefore clear that there are sometimes a hundred times 

 as many parasites as the hypothesis suggests, and there does not seem room for 

 an error of this size in the numbers of parasites. It is probably the mortality 

 among tadpoles that accounts for the high figures of infestation. This mortahty 

 can be calculated as follows — 



Divide the number of parasites found by the calculated infestation, 0-13. 

 The result is the reciprocal of the fraction of the original number of frog's eggs 

 that survive to be tadpoles at the age when they are infested. For example, at 

 Dagger Lane in 1948, the numberof larvae was 26. 26 -^ 0-13 = 200. Therefore 



