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Joseph Kane 



Northeast Fisheries Center Narragansett Laboratory 

 National Marine Fisheries Service, NOAA 

 South Ferry Road, Narragansett, RI 02882. 



ESTIMATION OF EQUILIBRIUM SETTLEMENT 



RATES FOR BENTHIC MARINE 



INVERTEBRATES: ITS APPLICATION TO 



MYA ARENARIA (MOLLUSCA: PELECYPODA) 



It is generally agreed that marine invertebrates 

 possessing planktotrophic larval stages experi- 

 ence extremely high mortality during the early 

 stages of their life history. In the settlement of 

 benthic invertebrates, mortality occurs during 

 three critical phases: 1) fertilization, 2) the free- 

 swimming pelagic stage, and 3) the early post- 

 larval attachment period. Since egg loss, larval 

 recruitment, and early postlarval mortality may 

 often be the limiting steps in the development 

 and maintenance of marine benthic communi- 

 ties, it is of interest to ecologists to be able to 

 make direct estimates of settlement rates in such 

 populations. 

 It is often difficult, however, to obtain reason- 



able estimates of early life history stage mortal- 

 ity rates. The earliest attempt to determine such 

 rates was made by Thorson (1966). Based on the 

 standing crop of a population of Venus (= Mer- 

 cenaries mercenaria, he estimated that approxi- 

 mately 98.6% of the clams died during the post- 

 larval period (stage 3) and that loss prior to this 

 was probably much heavier. More recently, 

 Muus (1973), in a study of 11 species of bivalves 

 in the Oresund, Denmark, found postlarval mor- 

 tality rates (stage 3) of 67-100% for all species; 

 whereas Gledhill (1980) calculated larval mor- 

 tality rates (stage 2) of 99.38% and 99.99% for two 

 populations of Mya arenaria in Gloucester, 

 Mass. None of these estimates, however, take into 

 account the heavy mortality that occurs during 

 stage 1, thereby overlooking the substantial loss 

 occurring during the fertilization process itself. 



In an attempt to overcome the difficulty in 

 estimating early survival parameters empiri- 

 cally, Vaughan and Saila (1976) developed an in- 

 direct method using the Leslie matrix for deter- 

 mining mortality rates during the first year of 

 life for the Atlantic bluefin tuna, Thunnus 

 thynnus, assuming an equilibrium population. 

 By expanding their treatment, as suggested by 

 Van Winkle et al. (1978), it is possible to divide 

 age class 1 into particular stages, thereby mak- 

 ing the model appropriate for cases dealing with 

 animals possessing more complex life cycles (i.e., 

 those which include egg, larvae, postlarval juve- 

 niles, etc.). In the case of benthic invertebrates 

 with free-swimming larval stages, this method 

 can be used to calculate mortality rates during 

 settlement for any species population for which 

 demographic parameters are available. Such 

 theoretical estimates are of special interest for 

 two reasons. First, the equilibrium settlement 

 rate (r. s ) value can be compared with field-deter- 

 mined estimates; second, the value may be useful 

 in the prediction of future age structures in 

 natural populations. 



This paper describes the indirect method for 

 estimating the settlement rate based on age- 

 specific fecundity and survivorship rates and 

 discusses its application to a commercially im- 

 portant species of bivalve, Mya arenaria. 



Results 



Leslie Matrix 



Matrix methods for analyzing age-structured 

 populations were developed by Leslie (1945, 



642 



FISHERY BULLETIN: VOL. 80, NO. 3, 1982. 



