Mmethods {FSA}R Documentation

Estimate natural mortality from a variety of empirical methods.


Several methods can be used to estimated natural mortality (M) from other types of data, including parameters from the von Bertalanffy growth equation, maximum age, and temperature. These relationships have been developed from meta-analyses of a large number of populations. Several of these methods are implemented in this function.


Mmethods(what = c("all", "tmax", "K", "Hoenig", "Pauly"))

  method = Mmethods(),
  justM = TRUE,
  tmax = NULL,
  K = NULL,
  Linf = NULL,
  t0 = NULL,
  b = NULL,
  L = NULL,
  Temp = NULL,
  t50 = NULL,
  Winf = NULL

## S3 method for class 'metaM'
print(x, digits = 4, ...)



A string that indicates what grouping of methods to return. Defaults to returning all methods.


A string that indicates which method or equation to use. See details.


A logical that indicates whether just the estimate of M (TRUE; Default) or a more descriptive list should be returned.


The maximum age for the population of fish.


The Brody growth coefficient from the fit of the von Bertalanffy growth function.


The asymptotic mean length (cm) from the fit of the von Bertalanffy growth function.


The x-intercept from the fit of the von Bertalanffy growth function.


The exponent from the weight-length relationship (slope from the logW-logL relationship).


The body length of the fish (cm).


The temperature experienced by the fish (C).


The age (time) when half the fish in the population are mature.


The asymptotic mean weight (g) from the fit of the von Bertalanffy growth function.


A metaM object returned from metaM when justM=FALSE.


A numeric that controls the number of digits printed for the estimate of M.


Additional arguments for methods. Not implemented.


One of several methods is chosen with method. The available methods can be seen with Mmethods() and are listed below with a brief description of where the equation came from. The sources (listed below) should be consulted for more specific information.


Mmethods returns a character vector with a list of methods. If only one method is chosen then metaM returns a single numeric if justM=TRUE or, otherwise, a metaM object that is a list with the following items:

If multiple methods are chosen then a data.frame is returned with the method name abbreviation in the method variable and the associated estimated M in the M variable.


Kenchington (2014) provided life history parameters for several stocks and used many models to estimate M. I checked the calculations for the PaulyL, PaulyW, HoenigO for Hgroup="all" and Hgroup="fish", HoenigO2 for Hgroup="all" and Hgroup="fish", "JensenK1", "Gislason", "AlversonCarney", "Charnov", "ZhangMegrey", "RikhterEfanov1", and "RikhterEfanov2" methods for three stocks. All results perfectly matched Kenchington's results for Chesapeake Bay Anchovy and Rio Formosa Seahorse. For the Norwegian Fjord Lanternfish, all results perfectly matched Kenchington's results except for when Hgroup="fish" for both HoenigO and HoenigO2.

Results for the Rio Formosa Seahorse data were also tested against results from M.empirical from fishmethods for the PaulyL, PaulyW, HoenigO for Hgroup="all" and Hgroup="fish", "Gislason", and "AlversonCarney" methods (the only methods in common between the two packages). All results matched perfectly.

IFAR Chapter



Derek H. Ogle,


Ogle, D.H. 2016. Introductory Fisheries Analyses with R. Chapman & Hall/CRC, Boca Raton, FL.

Alverson, D.L. and M.J. Carney. 1975. A graphic review of the growth and decay of population cohorts. Journal du Conseil International pour l'Exploration de la Mer. 36:133-143.

Charnov, E.L., H. Gislason, and J.G. Pope. 2013. Evolutionary assembly rules for fish life histories. Fish and Fisheries. 14:213-224.

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.

Hewitt, D.A. and J.M. Hoenig. 2005. Comparison of two approaches for estimating natural mortality based on longevity. Fishery Bulletin. 103:433-437. [Was (is?) from]

Hoenig, J.M. 1983. Empirical use of longevity data to estimate mortality rates. Fishery Bulletin. 82:898-903. [Was (is?) from]

Jensen, A.L. 1996. Beverton and Holt life history invariants result from optimal trade-off of reproduction and survival. Canadian Journal of Fisheries and Aquatic Sciences. 53:820-822. [Was (is?) from .]

Jensen, A.L. 2001. Comparison of theoretical derivations, simple linear regressions, multiple linear regression and principal components for analysis of fish mortality, growth and environmental temperature data. Environometrics. 12:591-598. [Was (is?) from]

Kenchington, T.J. 2014. Natural mortality estimators for information-limited fisheries. Fish and Fisheries. 14:533-562.

Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. Journal du Conseil International pour l'Exploration de la Mer. 39:175-192. [Was (is?) from]

Rikhter, V.A., and V.N. Efanov. 1976. On one of the approaches for estimating natural mortality in fish populations (in Russian). ICNAF Research Document 76/IV/8, 12pp.

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

Zhang, C-I and B.A. Megrey. 2006. A revised Alverson and Carney model for estimating the instantaneous rate of natural mortality. Transactions of the American Fisheries Society. 135-620-633. [Was (is?) from]

See Also

See M.empirical in fishmethods for similar functionality.


## List names for available methods

## Simple Examples
## Example Patagonian Sprat ... from Table 2 in Cerna et al. (2014)
Temp <- 11
Linf <- 17.71
K <- 0.78
t0 <- -0.46
tmax <- t0+3/K
t50 <- t0-(1/K)*log(1-13.5/Linf)

## Example of multiple calculations

## Example of multiple methods using Mmethods
# select some methods
# select just the Hoenig methods

[Package FSA version Index]