Description Usage Arguments Details Value Note Author(s) References Examples

The approaches of Pauly (1980), Hoenig (1983), Alverson and Carney (1975), Roff (1984), Gunderson and Dygert (1988), Petersen and Wroblewski (1984), Lorenzen (1996), Gislason et al. (2010) and Then et al. (2015) are encoded for estimation of natural mortality (M).

1 2 3 |

`Linf` |
Length-infinity value from a von Bertalanffy growth curve (total length-cm). |

`Winf` |
Weight-infinity value from a von Bertalanffy growth curve (wet weight-grams). |

`Kl` |
Kl is the growth coefficient (per year) from a von Bertalanffy growth curve for length. |

`Kw` |
Kw is the growth coefficient (per year) from a von Bertalanffy growth curve for weight. |

`T` |
the mean water temperature (Celsius) experienced by the stock. |

`tmax` |
the oldest age observed for the species. |

`tm` |
the age at maturity. |

`GSI` |
gonadosomatic index (wet ovary weight over wet body weight). |

`Wdry` |
total dry weight in grams. |

`Wwet` |
total wet weight at mean length in grams. |

`Bl` |
body length in cm. |

`method` |
vector of method code(s). Any combination of methods can employed. |

Please read the references below for details about equations. Some estimates of M will not be valid for certain fish groups.

A matrix of M estimates.

Original functions for the Pauly (1980) length equation and the Hoenig (1983) fish equation were provided by Michael H. Prager, National Marine Fisheries Service, Beaufort, North Carolina.

Gary A. Nelson, Massachusetts Division of Marine Fisheries [email protected]

Alverson, D. L. and M. J. Carney. 1975. A graphic review of the growth and decay of population cohorts. J. Cons. Int. Explor. Mer 36: 133-143.

Gislason, H., N. Daan, J. C. Rice, and J. G. Pope. 2010. Size, growth, temperature and the natural mortality of marine fish. Fish and Fisheries 11: 149-158.

Gunderson, D. R. and P. H. Dygert. 1988. Reproductive effort as a predictor of natural mortality rate. J. Cons. Int. Explor. Mer 44: 200-209.

Hoenig, J. M. 1983. Empirical use of longevity data to estimate mortality rates. Fish. Bull. 82: 898-903.

Lorenzen, K. 1996. The relationship between body weight and natural mortality in juvenile and adult fish: a comparison of natural ecosystems and aquaculture. J. Fish. Biol. 49: 627-647.

Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. Int. Explor. Mer: 175-192.

Peterson, I. and J. S. Wroblewski. 1984. Mortality rate of fishes in the pelagic ecosystem. Can. J. Fish. Aquat. Sci. 41: 1117-1120.

Roff, D. A. 1984. The evolution of life history parameters in teleosts. Can. J. Fish. Aquat. Sci. 41: 989-1000.

Then, A. Y., J. M. Hoenig, N. G. Hall, D. A. Hewitt. 2015. Evaluating the predictive performance of empirical estimators of natural mortality rate using information on over 200 fish species. ICES J. Mar. Sci. 72: 82-92.

1 | ```
M.empirical(Linf=30.1,Kl=0.31,T=24,method=c(1))
``` |

```
Loading required package: MASS
Loading required package: boot
Loading required package: bootstrap
Loading required package: lme4
Loading required package: Matrix
Loading required package: numDeriv
M
Pauly (1980) - Length Equation 0.772
```

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