Curtis (1990) examined the population dynamics related to the recovery of an offshore Lake Trout population near Stannard Rock, Lake Superior. As part of this study, mortality rates were estimated from the relative abundance of Lake Trout longer than 43.2 cm. Relative abundance was recorded as the catch-per-unit-effort (CPE) of each age group in each year expressed as the number of fish caught per 50,000 m of 114.3 mm mesh gillnet. The results are shown in the table below. [Note: (1) the values in the table have been rounded to integers; (2) values recorded as “tr” in the original paper were recorded as “0.5” in this table; and (3) the years of capture are not contiguous (there is a break between 1959 and 1963 and again between 1969 and 1973).]

Year       VI      VII     VIII       IX        X       XI      XII     XIII      XIV
1959 64 219 241 121 33 9 1 0.5 1
1963 129 339 331 192 70 16 0.5 0.5 0.5
1964 149 524 515 201 63 18 2 0.5 0.5
1965 75 379 501 328 133 39 11 1 0.5
1966 149 488 459 172 64 22 5 0.5 0.5
1967 63 368 287 130 55 19 6 0.5 0.5
1968 50 215 259 141 55 18 5 1 0.5
1969 45 150 153 76 23 6 0.5 0.5 0.5
1973 101 759 1268 1116 491 141 40 4 0.5
1974 151 733 1114 1092 571 163 50 9 5
1975 109 901 1517 1606 1076 342 117 12 7
1976 53 604 1204 1560 1146 396 156 18 10
1977 157 867 1343 1410 1031 417 192 17 7
1978 89 735 1307 1623 1150 445 198 18 14
1979 29 299 718 1268 1195 585 300 36 14

Use these results to answer the following questions.

  1. What year-class of fish is represented by the 339 age-VII fish caught in 1963?
  2. Identify the vectors of catches and ages that would be used to estimate the instantaneous total mortality rates for the following situations.
    1. For fish captured in 1963.
    2. For fish of the 1963 year-class.
    3. The earliest year-class that is fully represented for ages IX through XII.
    4. The latest year-class that is fully represented for ages IX through XII.
  3. For the data in each vector created above.
    1. Identify whether these data represent a cross-sectional or longitudinal catch curve?
    2. Identify the descending limb of each catch-curve. Explain your reasoning.
    3. Estimate, with 95% confidence interval, the instantaneous total mortality rate using the regression method. Carefully interpret this result.
    4. Convert the point estimate from above to an annual rate.
    5. Estimate, with 95% confidence interval, the instantaneous total mortality rate using the Chapman-Robson method. Carefully interpret this result.
    6. Convert the point estimate from above to an annual rate.
  4. Determine if the instantaneous mortality rate is significantly different between the earliest and latest year-classes that are fully represented for ages IX through XII.

from Derek H. Ogle , created 21-Jan-16, updated 03-Feb-16, Comments/Suggestions.