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.

- What year-class of fish is represented by the 339 age-VII fish caught in 1963?
- Show the data frame of catches and corresponding ages for the following groups of fish.
- For fish captured in 1963.
- For fish of the 1963 year-class.
- The
*earliest*year-class that is**fully**represented for ages IX through XII. - The
*latest*year-class that is**fully**represented for ages IX through XII.

- For each data frame created above, identify whether the data represent a cross-sectional or longitudinal catch curve.
- For the third data frame created above (
*earliest*year class).- Estimate, with 95% confidence interval, the
**instantaneous**total mortality rate using the catch-curve regression method for ages IX through XII. - Estimate, with 95% confidence interval, the
**annual**total mortality rate using the catch-curve regression method for ages IX through XII. Carefully interpret this result.

- Estimate, with 95% confidence interval, the
- Repeat the previous question for the last data frame created above (
*latest*year class). - 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.

## References

*Salvelinus Namaycush*) population in eastern Lake Superior. Journal of Great Lakes Research 16(2):279–287.