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1981. Growth, reproduction, and food habits of olive rock- 

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 MARGOLIS, L. 



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SEKERAK, A. D. 



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 Alberta, 251 p. 



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Milton S. Love 



kimberly shriner 



Pamela morris 



VANTUNA Research Group 

 Department of Biology 

 Occidental College 

 Los Angeles, C A 90041 



SENSITIVITY OF THE POPULATION GROWTH 



RATE TO CHANGES IN SINGLE LIFE HISTORY 



PARAMETERS: ITS APPLICATION TO 



MYA ARENARIA (MOLLUSCA:PELECYPODA) 



The question of sensitivity analyses in demo- 

 graphic studies was first addressed by Lewontin 

 (1965), and since that time, Hamilton (1966), 

 Demetrius (1969), Emlen (1970), Goodman (1971), 

 Keyfitz (1971), and Mertz (1971) have made con- 

 tributions in the area. More recently, Caswell 

 (1978) has given general formulae for the sensi- 



FISHERY BULLETIN: VOL. 82, NO. 3, 1984. 



tivity of the population growth rate (A) derived 

 from a Leslie model, to changes in single life 

 history parameters written as formulae involving 

 eigenvectors of the Leslie matrix. The application 

 of such analyses to the study of the population 

 dynamics of commercially important species can 

 provide useful information to those interested in 

 resource management. 



The work presented here describes the sensitiv- 

 ity of the population growth rate to changes in 

 the settlement rate (Brousseau et al. 1982) and in 

 the age-specific fecundity and survivorship rates 

 of the soft-shell clam, Mya arenaria, using a mod- 

 ified Leslie matrix model and an extension of the 

 sensitivity formulae derived by Caswell (1978). 

 Predictions concerning the effect that changes in 

 these life history parameters will have on K and 

 the implications of these results to the manage- 

 ment of this species are discussed. 



Results 



Leslie Model 



The population of females is divided into n age 

 classes. The Leslie matrix, M, has the following 

 form: 



M = 







bn 







(1) 



Here, a x is the mean number of female eggs pro- 

 duced annually by a female in class i (age i - 1 

 to i); assuming a one-to-one sex ratio, a ; is one- 

 half the total egg production. The parameter b t 

 is the probability of a clam in class i surviving to 

 class 2, 3, ..., n - 1. The survivorship from age 

 class 1 to age class 2 is divided into 2 factors, r s 

 and bi. The factor r s is the settlement rate or the 

 probability that an egg will survive the plank- 

 tonic larval stage and develop into a clam with a 

 2 mm shell length (0-2 mo of age); 6i is the prob- 

 ability that a clam with a 2 mm shell length will 

 survive the remainder of the year (about 10 mo). 

 If x is a column vector with n components such 

 that Xi is the number of females in age class i 

 immediately following spawning, then Mx rep- 

 resents the population 1 yr from now. 



For benthic marine invertebrates possessing 

 planktotrophic larval stages, the events surround- 

 ing metamorphosis and settlement are extremely 



537 



