384 



Fishery Bulletin 103(2) 



F is negatively biased, but once again the standard 

 deviation is reduced. 



Application to tiger prawns (P. semisulcatus) 



The data for this application consist of a six-year 

 sequence of experimental length-frequency data from 

 the trawling region around Albatross Bay in the east- 

 ern Gulf of Carpentaria, Australia. The data consist of 

 catches of tiger prawns from 11 mm to 59 mm (carapace 

 length) for each of 69 times ranging from March 1986 to 

 March 1992. The catches from several stations covering 

 the trawling region at each time (over a few consecutive 

 days) are aggregated. Sampling was done roughly every 

 lunar month. 



We use the catch data for the smaller size classes to 

 obtain two types of recruitment patterns: the aperiodic 

 pattern and the quasiperiodic pattern. The aperiodic 

 pattern is constructed by summing over all individuals 

 with length 21 mm or less for each occasion. The result- 

 ing sequence of plotted time points is then joined up by 

 straight lines. The quasiperiodic pattern is generated 

 from the aperiodic pattern by averaging corresponding 

 points across years to give a single annual pattern. The 

 pattern for all six years is generated from the annual 

 pattern by applying, for each biological year, a scale 

 factor that is found by averaging the catch over all size 

 classes within the year. The start of the biological year 

 is defined as the time when the annual pattern reaches 

 its minimum (see Fig. 2). 



The effort pattern comes from commercial log books 

 collected from fishermen for the period from 1986 to 

 1992 in the area. Effort is measured in boat-days (see 

 Fig. 2). There is substantial contrast in the effort both 

 within years (due to seasonal closures) and across 

 years. This contrast may allow us to separate fishing 

 mortality from natural mortality. 



The instantaneous fishing mortality Fit) is assumed 

 to be qE(t). The mean total mortality Z=M+q E , where 

 E is the mean effort over the study period. Given the 

 results of the simulation study, we expect the parameter 

 Z may be more reliably estimated than either M or q, 

 whose estimates are negatively correlated. 



We further assume that the L y distribution is a trun- 

 cated normal distribution. This choice is based on the 

 shape of the observed length distribution from July to 

 September, the period when this distribution should 

 approximate the asymptotic length distribution. The 

 truncated normal distributions are then reparameter- 

 ized in terms of the mean l x , and variance a\ of this 

 underlying normal distribution. It is more convenient to 

 use these parameters than the mean l a and variance 

 a 2 of the truncated normal distribution. Note that l^ 

 is always larger than l a and a is always less than a*. 

 However, in this application the two sets of parameters 

 are nearly interchangeable because over the range of 

 estimated values Z x exceeds l x * by at most 0.5 mm and 

 o, exceeds a by at most 0.6 mm (see Table 2). 



We define a recruit to be an individual with length l , 

 which can be chosen at discretion. We examine a range 

 of candidate values of /,, between 19.5 mm and 27.5 mm, 

 to find out which values provide the most suitable defi- 

 nition of recruitment for this data set, i.e., that which 

 leads to the least violation of model assumptions. 



In our application the recruitment pattern was de- 

 rived from size classes 21 mm or less. If we use this 

 pattern at say 23.5 mm then we need to shift the pat- 

 tern slightly to later times. It is not apparent to what 

 degree we should shift the pattern; therefore we shall 

 estimate the degree of shift. We call this parameter 

 the lag. We expect the lag to increase with Z . Also note 

 that the derived recruitment pattern is an average over 

 different size classes and hence it is an average over 

 different times. The absolute timing of the pattern is 



