Wang and Ellis: Maximum likelihood estimate of mortality and growth from multiple length-frequency data 



387 



Males 



Females 



N 



24 26 20 22 24 



Recruitment length (mm) 



Figure 3 



Parameter estimates against recruitment length l for real tiger prawn 

 {Pcnaeus esculetus) data using quasiperiodic recruitment under model 2. 

 The mean annual total mortality Z is equal to M+0.46F 89 , where F g9 is 

 the fishing mortality in 1989. 



or too large, there is bound to be a violation of those 

 assumptions, leading to high sensitivity of the estimates 

 to changes in / . Therefore, we say the most reasonable 

 value for l is that for which the estimates are most 

 slowly varying in the immediate neighborhood of Z n . 

 On the basis of a t , M and Z for males, / =23.5 would 

 be a reasonable choice. We exclude q from consider- 

 ation because its standard deviation is comparable to 

 its magnitude (see Table 2). In addition we exclude 

 the lag because we expect it to increase approximately 

 monotonically with l , as indeed it does. There is no 

 clear choice for females; therefore we choose / =23.5, 

 the same as for males. This choice is consistent with 

 the consideration that l should be somewhere between 

 20 mm and 30 mm, but in the lower half of the range 

 so that more data can be included in the estimation 

 (because lengths must exceed / I. 



Also shown in Table 2 are jackknife estimates of 

 the standard deviations. The jackknifing is done by 

 dropping the length-frequency record from each occa- 

 sion in turn and re-estimating the parameters. From 

 the over-all estimate 6 and the jackknife estimate 0, 

 from dropping the i tb occasion we obtain a pseudovalue 

 0-(n-l)6Jn, where in our case n=69. The jackknifed 

 standard deviation is simply the standard deviation of 

 these pseudovalues. We also show the jackknifed corre- 

 lation between M and q, which is simply the correlation 

 between the corresponding pseudovalues. In most cases 

 there is a large negative correlation. 



The fishing mortality in 1989 (the year of peak ef- 

 fort), F 89 , is simply proportional to q with constant 

 of proportionality 2865, the number of boat-days of 

 effort in that year. The mean total annual mortality 

 Z is M+0.46F g9 because the mean annual effort was 



