290 
Fishery Bulletin 95(2), 1 997 
Table 3 
True population numbers, observed catch, corrected catch, recorrected catch, and percent bias in population numbers output by 
VPA with the three catch matrices as input for scenario 3. Catch occurred only in December. Years are in columns and ages are in 
rows. 
Catch data for December 
True population numbers 
1,000,000 
2,000,000 
4,000,000 
1,000,000 
3,000,000 
1,000,000 
1,000,000 
563,368 
468,980 
986,837 
2,044,458 
532,809 
15,944,22 
489,054 
288,839 
229,497 
206,672 
459,258 
1,014,679 
263,412 
693,044 
144,699 
95,547 
85,574 
83,737 
205,232 
450,766 
96,185 
77,637 
47,574 
35,453 
34,531 
37,305 
90,887 
163,755 
Observed catch 
140,582 
231,169 
389,959 
75,314 
230,032 
120,048 
137,635 
114,731 
79,510 
142,362 
230,269 
61,058 
280,134 
97,654 
81,495 
54,848 
42,555 
74,950 
168,329 
65,040 
192,120 
41,126 
23,014 
17,764 
13,784 
34,340 
112,163 
26,861 
22,066 
11,459 
7,360 
5,684 
6,242 
22,615 
45,731 
Corrected catch 
184,448 
306,692 
524,132 
97,697 
305,147 
157,007 
180,502 
149,922 
103,228 
186,832 
305,469 
78,960 
373,391 
127,228 
105,848 
70,827 
54,785 
97,218 
221,702 
84,184 
253,787 
52,927 
29,468 
227,09 
17,598 
44,113 
146,503 
34,433 
28,246 
14,619 
9,376 
7,237 
7,949 
28,953 
58,922 
Recorrected catch 
180,390 
296,049 
498,706 
96,173 
293,745 
153,805 
176,580 
148,011 
102,273 
182,738 
294,826 
78,198 
360,493 
125,966 
105,966 
71,003 
54,919 
96,365 
216,452 
84,285 
249,728 
53,491 
29,800 
22,930 
17,726 
44,172 
145,367 
34,941 
28,703 
14,838 
9,500 
7,310 
8,030 
29,319 
59,482 
% bias in population numbers from observed catch 
-22.3 
-22.3 
-22.3 
-22.4 
-22.4 
-21.9 
-21.5 
-22.5 
-22.4 
-22.4 
-22.4 
-22.5 
-22.5 
-21.9 
-22.8 
-22.6 
-22.5 
-22.5 
-22.6 
-22.7 
-22.6 
-22.8 
-22.6 
-22.5 
-22.5 
-22.6 
-22.7 
-22.6 
-22.8 
-22.6 
-22.5 
-22.5 
-22.6 
-22.7 
-22.6 
% bias in population 
numbers from corrected catch 
-0.4 
-0.1 
0.9 
-1.5 
0.6 
-1.3 
-1.1 
-0.6 
-1.2 
-0.9 
0.1 
-1.9 
0.2 
-2.1 
-1.2 
-1.6 
-2.0 
-1.8 
-0.7 
-2.5 
-1.2 
-1.8 
-2.1 
-2.4 
-2.9 
-2.8 
-1.9 
-4.1 
-2.3 
-2.5 
-2.7 
-3.1 
-3.7 
-3.8 
-3.6 
% bias in population numbers from recorrected catch 
0.0 
0.1 
0.0 
0.1 
0.0 
0.0 
0.0 
0.0 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
0.1 
ary and the catch occurs. Larger M will cause a large 
population size to be present at the start of Febru- 
ary, and thus the fishing mortality rate needed to 
generate a given catch will be lower. In contrast, the 
December fishing mortality rates are nearly constant 
over the range of M because the value of M does not 
change the population-size value used in step 2 of 
the algorithm as it did for the January catch. 
These examples assume a constant natural mortal- 
ity rate, which may be false in reality. If M varies dur- 
