578 



Fishery Bulletin 91(3), 1993 



Table 1 



Sample sizes and body sizes of sevenspine bay shrimp and flounder prey for laboratory experi- 

 ments. Sample size refers to the number of individual predator-prey trials. Pearson correlation 

 coefficients (r) are given for correlations of predator size with prey size to indicate random 

 allocation of predator and prey sizes. 



Prey 



Size range (C.V.) 



Temperature Sample 



(°C) size Predator (TL) 



Prey(SL) 



Pleuronectes 

 americanus 



18 



60 51-59mm (4.2%) 9-46mm (37.4% ) 0.15 0.24 



Paralichthys 9-12 135 27-65 mm (17.5%) ll-16mm (7.1%) 0.03 0.70 



dentatus 



used large shrimp to minimize the predator size effect, 

 thereby concentrating on prey size to determine if there 

 was a size refuge for winter flounder. In trials involv- 

 ing summer flounder, we used a large range of preda- 

 tor sizes, but a narrow range of flounder sizes (those 

 in the last stage of eye migration) because of the greater 

 availability of the latter. This combination of predator 

 and prey sizes was used to establish the relationship 

 between shrimp size and their ability to successfully 

 prey upon small summer flounder. In all trials, we 

 randomly allocated predators and prey to the bowls to 

 avoid deliberate or inadvertent size biases. 



We used logistic regression analysis (SAS/STAT 

 Users guide, Release 6.03 Edition 1988), which uses 

 maximum likelihood analysis of the natural logarithm 

 of the ratio of these response frequencies (logits) to 

 estimate parameters of a linear model. Because the 

 response is a frequency response rather than a con- 

 tinuous response, a chi-square value is calculated to 

 test for the significance of the treatment variables. 

 Once parameter estimates of the linear model have 

 been made, expected logits can be generated. Expected 

 probabilities of mortality can then be calculated using 

 the following relationship: 



l+e L 



where m is the probability of mortality from preda- 

 tion, e is the root of natural logarithm and L is the 

 logit predicted by the linear model. This relationship 

 is obtained by solving the following simultaneous equa- 

 tions for m: 



m+s=l 



and 



" (f)- L 



where s is the probability of survival. 



Results 



Sevenspine bay shrimp consumed both flounder spe- 

 cies under laboratory conditions, and size effects were 

 important in all interactions. In summer flounder 

 trials, both prey and predator size significantly af- 

 fected the outcome of prey-predator interactions 

 (predator size x 2 =24.07, P<0.0001, prey size x 2 =7.75, 

 P<0.01). Summer flounder matched with larger 

 shrimp experienced generally greater mortality than 

 those matched with smaller shrimp (Fig. 1A). Logis- 

 tic regression of these data produced a positive rela- 

 tionship between probability of predation and shrimp 

 size (Fig. IB) which was stronger when the effect of 

 flounder size was controlled using linear regression 

 and the residuals were plotted against predator size 

 (Fig 1C). Smaller summer flounder experienced 

 higher mortality (Fig. 2A); however, probabilities 

 from logistic regression show no clear pattern (Fig. 

 2B) because of the confounding effect of predator 

 size. When we controlled the predator-size effect, a 

 clear negative relationship was revealed between 

 summer flounder size and probability of predation 

 (Fig. 2C). 



For winter flounder, the effect of flounder size on 

 the probability of predation was significant (\ 2 =4.03, 

 P<0.05), but no significant predator size effect occurred 

 (X 2 =0.04, P>0.8) presumably because we deliberately 

 selected large shrimp in these trials in order to mini- 

 mize this effect. Only the smallest individuals (<17 mm 

 SL) were preyed upon (Fig. 3A). Logistic regression 

 analysis demonstrated that the highest probability of 

 predation was on the smallest individuals (>60% for 

 9mm SL). This probability declined to zero at flounder 

 lengths of approximately >17mm SL (Fig. 3B). Param- 

 eter estimates of the prey size effect for both summer 

 and winter flounder were similar (-0.4 ± 0.2 for winter 

 and -0.6 ± 0.2 for summer), implying a similar size 

 relationship for both species. 



