Velslad et al. Estimating dredge catching efficiency for Callinectes sapidus 



413 



Lane 1 



Figure 2 



Schematic diagram of a standard removal experiment conducted m Maryland waters. Each removal from the area (coverage) con- 

 sisted of three parallel tows conducted back and forth at a speed of 3 knots. A maximum of ten removals was completed for each 

 experiment. 



pace width of crabs in the first removals would, on 

 average, be larger than in the final removals. 



We used two models to estimate the dredge effi- 

 ciency for each experiment. Model 1 is a standard 

 Leslie model (Leslie and Davis, 1939) 



y,=q[P,-K,_,]^qP,-qK,_,, (1) 



where _v, = the catch from the ith removal; and 



K'j J = cumulative catch taken before each 

 removal; 

 P,j = the initial population in the area before 

 the depletion experiment. 



The catchability coefficient q = the slope of the linear 

 regression estimated from Equation 1. The basic 

 assumption of this model is that the number of crabs 

 in each removal and the unit of effort is measured 

 without error. An implication of using model 1 is 

 that if the zth removal in a particular depletion expe- 

 riment is zero, then the cumulative catch provides 

 an absolute measure of the initial population P^. 

 Some crabs, however, may remain in the experimen- 

 tal area, even though no crabs are caught in an indi- 

 vidual removal. This results in an underestimate of 

 Pq and an overestimate of g for this site. 



A different technique may be used to estimate 

 dredge efficiency. For each coverage (/) of the expe- 



rimental area, we can assume that a fixed propor- 

 tion (q) of the true population in the area is removed; 

 therefore, the catch (Vj) in the first coverage is q 

 multiplied by P„, the initial population. For the ith 

 coverage, we have 



and 



ln(- 



y =gll-g)'-iPoe 



\n(q)+ ln( Pq l + [ln( 1 - g )]( / - 1) + ln(f ) . ( 2 ) 



In this model, it is assumed (perhaps more realis- 

 tically) that the fraction of the population removed 

 for each unit of effort is estimated with an error 

 f. A simple regression of Iny, against (/-I) provides 

 an estimate of the slope, ln(l-ql. An estimate of 

 the expected value of the catchability coefficient iq) 

 is obtained after a retransformation, following the 

 method of Finney (1941; see also Johnson et al., 

 1994, p. 221). The variance of the slope estimate in 

 model 2 is taken into account in the estimation of 

 ( 1—q). and hence q. An approximation for estimating 

 q for a single experiment is 



q = l-expi(i + sl/2 



where /? = an estimate of the slope in Equation 2, 

 with variance SZ (Gilbert 1987). 



