Description Usage Arguments Details Value Source References Examples
Functions to calculate the instantaneous natural mortality rate (M) according to 12 different empirical formulas.
1 2 3 
Linf 
infinite total length (TL) from a von Bertalanffy growth curve in cm. 
Winf 
infinite weight form a von Bertalanffy growth curve in wet weightgrams. 
K_l 
is the growth coefficient (per year) from a von Bertalanffy growth curve for length. 
K_w 
is the growth coefficient (per year) from a von Bertalanffy growth curve for weight. 
temp 
average annual temperature at the surface in degrees centigrade. 
tmax 
the oldest age observed for the species. 
tm50 
age when 50% of the population is mature [year] ("age of massive maturation"). 
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 
vector with body lengths in cm for size dependent mortality estimates (method = "Gislason") 
schooling 
logical; if TRUE it is accounted for the schooling behaviour of the species, only for Pauly's methods. Default is FALSE. 
method 
vector of method names. Any combination of following methods can be employed: "AlversonCarney", "Gislason" (size dependent mortality estimates), "GundersonDygert", "Hoenig", "Lorenzen", "Pauly_Linf", "Pauly_Winf", "PetersonWroblewski", "RikhterEfanov", "Roff", "Then_growth", or "Then_tmax". Please refer to Details to see which input parameters are required by each method. 
Function adapted from the mortality function of the fishmethods package by Gary A. Nelson (https://cran.rproject.org/web/packages/fishmethods/index.html).
Depending on the method different input parameters are required:
"AlversonCarney"
requires K_l
and tmax
,
"Gislason"
requires Linf
, K_l
and Bl
,
"GundersonDygert"
requires GSI
,
"Hoenig"
requires tmax
,
"Lorenzen"
requires Wwet
,
"Pauly_Linf"
requires Linf
, K_l
and temp
,
"Pauly_Winf"
requires Winf
, K_w
and temp
,
"PetersonWroblewski"
requires Wdry
,
"RikhterEfanov"
requires tm50
,
"Roff"
requires K_l
and tm50
,
"Then_tmax"
requires tmax
,
"Then_growth"
requires Linf
and K_l
.
If accounting for schooling behaviour M is multiplied by 0.8 according to Pauly (1983).
A matrix of M estimates.
https://cran.rproject.org/web/packages/fishmethods/index.html
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: 133143.
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: 149158.
Gunderson, D. R. and P. H. Dygert. 1988. Reproductive effort as a predictor of natural mortality rate. J. Cons. Int. Explor. Mer 44: 200209.
Hoenig, J. M. 1983. Empirical use of longevity data to estimate mortality rates. Fish. Bull. 82: 898903.
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: 627647.
Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. Int. Explor. Mer: 175192.
Pauly, D., 1983. Some simple methods for the assessment of tropical fish stocks. FAO Fish.Tech.Pap., (234): 52p. Issued also in French and Spanish
Peterson, I. and J. S. Wroblewski. 1984. Mortality rate of fishes in the pelagic ecosystem. Can. J. Fish. Aquat. Sci. 41: 11171120.
Rikhter, V.A., and V.N. Efanov, 1976. On one of the approaches to estimation of natural mortality of fish populations. ICNAF Res.Doc., 76/VI/8: 12p.
Roff, D. A. 1984. The evolution of life history parameters in teleosts. Can. J. Fish. Aquat. Sci. 41: 9891000.
Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.
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: 8292.
1 2  M_empirical(Linf = 80, K_l = 0.5, temp = 25, tmax = 30,
method = c("Pauly_Linf","Hoenig"))

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