140 



Fishery Bulletin 90(1), 1992 



fishermen's returns and unpublished information 

 supplied by the Victorian Fisheries Division. In- 

 formation on the history of the Victorian abalone 

 fishery was extracted from unpublished records 

 supplied by the Victorian Fisheries Division (Dep. 

 Conserv. Environ., 240 Victoria Pde, Melbourne 

 3002; see also McShane 1990). 



Yield-per-recruit 



Generalised fisheries exploitation models such as 

 yield-per-recruit rely heavily on several assump- 

 tions. For any "unit stock": 



1 Growth rates do not vary with time or density of 

 the exploitable stock. Thus growth can be modeled with 

 one set of parameters, e.g., the von Bertalanffy growth 

 equation (Ricker 1975). Departures from these assump- 

 tions are known for abalone (e.g., Newman 1968, Sloan 

 and Breen 1988, Day and Fleming 1992). However, for 

 stocks of H. rubra the assumptions are reasonable 

 (McShane et al. 1988a). 



2 The rate of natural mortality is known and does not 

 vary with age, time or density of the stock. Natural 

 mortality is an important parameter in yield-per-recruit 

 models, yet it is often the most difficult to estimate ac- 

 curately. Natural mortality of//, rubra is constant with 

 age after the first year (Shepherd et al. 1982, McShane 

 1991, Shepherd and Breen 1992). Estimates of natural 

 mortality are in Table 1. 



3 Fishing (F) and natural (M) mortality are indepen- 

 dent of each other. For abalone fisheries, fishing mor- 

 tality cannot be considered applicable to the entire 

 fishery. Individual exploitation rates are applied to 

 substocks opportunistically according to weather and 

 incentive (Sluczanowski 1984, McShane and Smith 

 1989a). Incidental mortality can be caused by fishing, 

 for example, wounding of undersize individuals (Sloan 

 and Breen 1988, Tegner 1989, Shepherd and Breen 

 1992). 



4 Recruitment is constant. Recruitment measured as 

 the density of post-settlement individuals is highly 

 variable for//, rubra (McShane et al. 1988b, McShane 

 and Smith 1991). However, variation in growth rates 

 of prerecruit individuals within a population acts to 

 smooth out year-to-year variation in those //. rubra 

 reaching harvestable size (McShane 1991). 



5 Individuals of the same age have the same weight 

 and susceptibility to capture. Individual variation in the 

 relationships of weight to length and length to age has 

 been demonstrated for H. rubra, but reasonable 



Table 1 



Estimates of rates of natural mortality (M) for Haliotis rubra. 



Reference 



Location 



M(yr-') 



Beinssen and Powell (1979) 

 Nash (1992) 

 Shepherd et al. (1982) 

 Prince et al. (1988) 



northeast Victoria 0.20 



northern Tasmania 0.24-0.29 



South Australia 0.21-0.36 



southeast Tasmania 0.1-0.7 



generalizations of these relationships can be made for 

 the stock (McShane et al. 1988a, McShane and Smith 

 1992). 



To investigate the effects of various rates of fishing, 

 the yield-per-recruit equation of Ricker (1975:237) was 

 used. The increase in length with age of//, rubra was 

 computed using the von Bertalanffy growth equation 



Lt = L^(l 



-Kt- 



to) 



where Lt is the shell length in mm of H. rubra at age 

 t years, L^ is the hypothetical maximum length, K is 

 the Brody growth constant, and to is the hypothetical 

 age when length is zero. 



In calculating the yield-per-recruit of H. rubra at 

 various ages, I assumed that individuals were recruited 

 in the year corresponding to the minimum length at 

 capture. The biomass of an individual of age t years, 

 Wt (g), was assumed to be 0.00016 Lt"^, where Lt is in 

 mm (McShane et al. 1988a). 



Egg-per-recruit 



A simple age-structured model was used in which the 

 relative abundance of females of age t years (A'^t ) was 

 computed as 



where Z is total mortality (F -i- M). The egg production 

 of a female of age t years (Ej) has a linear relationship 

 with length (Lt) for H. rubra (McShane et al. 1988b) 

 such that 



Et = 0.03 Lt - 2.4 



where E is fecundity in millions of eggs, and L is shell 

 length in mm; Lt is derived from the von Bertalanffy 

 growth equation. 

 Total egg production (Etot) is given by 



t = 25 



Etot = 1 iVt • Et 

 t=o 



where t = 25 years is assumed to be the maximum age 



