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).

```
M.empirical(Linf = NULL, Winf = NULL, Kl = NULL, Kw = NULL,
T = NULL, tmax = NULL, tm = NULL, GSI = NULL, Wdry = NULL,
Wwet = NULL, Bl = NULL, method = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11))
```

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. `1`

= Pauly (1980)
length equation - requires Linf, Kl, and T; `2`

= Pauly (1980) weight equation - requires Winf, Kw, and T;
`3`

= Hoenig (1983) joint equation - requires tmax; `4`

= Alverson and Carney (1975) - requires Kl and tmax;
`5`

= Roff (1984) - requires Kl and tm; `6`

= Gunderson and Dygert (1988) - requires GSI; `7`

= Peterson
and Wroblewski (1984) - requires Wdry; `8`

= Lorenzen (1996) - requires Wwet;
`9`

= Gislason et al. (2010) - requires Linf, K and Bl; `10`

= Then et al. (2015) tmax - requires tmax;
`11`

= Then et al. (2015) growth - requires Kl and Linf.

A matrix of M estimates.

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

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.

```
# NOT RUN {
M.empirical(Linf=30.1,Kl=0.31,T=24,method=c(1))
# }
```

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