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(method = c("all", "tmax", "K", "Hoenig", "Pauly", "FAMS"))metaM(
method = Mmethods(),
tmax = NULL,
K = NULL,
Linf = NULL,
t0 = NULL,
b = NULL,
L = NULL,
Temp = NULL,
t50 = NULL,
Winf = NULL,
PS = NULL,
verbose = TRUE
)
Mmethods returns a character vector with a list of methods.
metaM returns a data.frame with the following items:
M: The estimated natural mortality rate.
cm: The estimated conditional natural mortality rate (computed directly from M).
method: The name for the method within the function (as given in method).
name: A more descriptive name for the method.
givens: A string that contains the input values required by the method to estimate M.
A string that indicates what grouping of methods to return (defaults to all methods) in Mmethods() or which methods or equations to use in metaM(). See details.
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.
The proportion of the population that survive to tmax. Should usually be around 0.01 or 0.05.
Logical for whether to include method name and given inputs in resultant data.frame. Defaults to TRUE.
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, HoenigOF, HoenigO2, HoenigO2F, "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 HoenigOF and HoenigO2F.
Results for the Rio Formosa Seahorse data were also tested against results from M.empirical from fishmethods for the PaulyL, PaulyW, HoenigO, HoenigOF, "Gislason", and "AlversonCarney" methods (the only methods in common between the two packages). All results matched perfectly.
11-Mortality.
Derek H. Ogle, DerekOgle51@gmail.com
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.
method="HoenigNLS": The “modified Hoenig equation derived with a non-linear model” as described in Then et al. (2015) on the third line of Table 3. This method was the preferred method suggested by Then et al. (2015). Requires only tmax.
method="PaulyLNoT": The “modified Pauly length equation” as described on the sixth line of Table 3 in Then et al. (2015). Then et al. (2015) suggested that this is the preferred method if maximum age (tmax) information was not available. Requires K and Linf.
method="PaulyL": The “Pauly (1980) equation using fish lengths” from his equation 11. This is the most commonly used method in the literature. Note that Pauly used common logarithms as used here but the model is often presented in other sources with natural logarithms. Requires K, Linf, and T.
method="PaulyW": The “Pauly (1980) equation for weights” from his equation 10. Requires K, Winf, and T.
method="HoeingO", method="HoeingOF", method="HoeingOM", method="HoeingOC": The original “Hoenig (1983) composite”, “fish”, “mollusc”, and “cetacean” (fit with OLS) equations from the second column on page 899 of Hoenig (1983). Requires only tmax.
method="HoeingO2", method="HoeingO2F", method="HoeingO2M", method="HoeingO2C": The original “Hoenig (1983) composite”, “fish”, “mollusc”, and “cetacean” (fit with Geometric Mean Regression) equations from the second column on page 537 of Kenchington (2014). Requires only tmax.
method="HoenigLM": The “modified Hoenig equation derived with a linear model” as described in Then et al. (2015) on the second line of Table 3. Requires only tmax.
method="HewittHoenig": The “Hewitt and Hoenig (2005) equation” from their equation 8. Requires only tmax.
method="tmax1": The “one-parameter tmax equation” from the first line of Table 3 in Then et al. (2015). Requires only tmax.
method="K1": The “one-parameter K equation” from the fourth line of Table 3 in Then et al. (2015). Requires only K.
method="K2": The “two-parameter K equation” from the fifth line of Table 3 in Then et al. (2015). Requires only K.
method="JensenK1": The “Jensen (1996) one-parameter K equation”. Requires only K.
method="JensenK2": The “Jensen (2001) two-parameter K equation” from their equation 8. Requires only K.
method="Gislason": The “Gislason et al. (2010) equation” from their equation 2. Requires K, Linf, and L.
method="AlversonCarney": The “Alverson and Carney (1975) equation” as given in equation 10 of Zhang and Megrey (2006). Requires tmax and K.
method="Charnov": The “Charnov et al. (2013) equation” as given in the second column of page 545 of Kenchington (2014). Requires K, Linf, and L.
method="ZhangMegreyD", method="ZhangMegreyP": The “Zhang and Megrey (2006) equation” as given in their equation 8 but modified for demersal or pelagic fish. Thus, the user must choose the fish type with group. Requires tmax, K, t0, t50, and b.
method="RikhterEfanov1": The “Rikhter and Efanov (1976) equation (#2)” as given in the second column of page 541 of Kenchington (2014) and in Table 6.4 of Miranda and Bettoli (2007). Requires only t50.
method="RikhterEfanov2": The “Rikhter and Efanov (1976) equation (#1)” as given in the first column of page 541 of Kenchington (2014). Requires t50, K, t0, and b.
method="QuinnDeriso": The “Quinn & Derison (1999)” equation as given in the FAMS manual as equation 4:18. Requires PS and tmax. Included only for use with rFAMS package.
method="ChenWatanabe": The “Chen & Watanabe (1989)” equation as given in the FAMS manual as equation 4:24. As suggested in FAMS manual used tmax for final time and 1 as initial time. Requires tmax, K, and t0. Included only for use with rFAMS package.
method="PetersonWroblewski": The “Peterson & Wroblewski (1984)” equation as given in the FAMS manual as equation 4:22. As suggested in FAMS manual used Winf for weight. Requires Winf. Included only for use with rFAMS package.
Conditional mortality (cm) is estimated from instantaneous natural mortality (M) with 1-exp(-M). It is returned with M here simply as a courtesy for those using the rFAMS package.
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.
Chen, S. and S. Watanabe. 1989. Age dependence of natural mortality coefficient in fish population dynamics. Nippon Suisan Gakkaishi 55:205-208.
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 http://fishbull.noaa.gov/1032/hewitt.pdf.]
Hoenig, J.M. 1983. Empirical use of longevity data to estimate mortality rates. Fishery Bulletin. 82:898-903. [Was (is?) from http://www.afsc.noaa.gov/REFM/age/Docs/Hoenig_EmpiricalUseOfLongevityData.pdf.]
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 http://deepblue.lib.umich.edu/bitstream/handle/2027.42/35236/487_ftp.pdf.]
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 http://innri.unuftp.is/pauly/On%20the%20interrelationships%20betwe.pdf.]
Peterson, I. and J.S. Wroblewski. 1984. Mortality rate of fishes in the pelagic ecosystem. Canadian Journal of Fisheries and Aquatic Sciences. 41:1117-1120.
Quinn III, T.J. and R.B. Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, New York.
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.
Slipke, J.W. and M.J. Maceina. 2013. Fisheries Analysis and Modeling Simulator (FAMS 1.64). American Fisheries Society.
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 http://www.pmel.noaa.gov/foci/publications/2006/zhan0531.pdf.]
See M.empirical in fishmethods for similar functionality.
## List names for available methods
Mmethods()
Mmethods("tmax")
## Simple Examples
metaM("tmax",tmax=20)
metaM("HoenigNLS",tmax=20)
metaM("HoenigNLS",tmax=20,verbose=FALSE)
## Example Patagonian Sprat ... from Table 2 in Cerna et al. (2014)
## http://www.scielo.cl/pdf/lajar/v42n3/art15.pdf
Temp <- 11
Linf <- 17.71
K <- 0.78
t0 <- -0.46
tmax <- t0+3/K
t50 <- t0-(1/K)*log(1-13.5/Linf)
metaM("RikhterEfanov1",t50=t50)
metaM("PaulyL",K=K,Linf=Linf,Temp=Temp)
metaM("HoenigNLS",tmax=tmax)
metaM("HoenigO",tmax=tmax)
metaM("HewittHoenig",tmax=tmax)
metaM("AlversonCarney",K=K,tmax=tmax)
## Example of multiple calculations
metaM(c("RikhterEfanov1","PaulyL","HoenigO","HewittHoenig","AlversonCarney"),
K=K,Linf=Linf,Temp=Temp,tmax=tmax,t50=t50)
## Example of multiple methods using Mmethods
# select some methods
metaM(Mmethods()[-c(15,20,22:24,26:29)],K=K,Linf=Linf,Temp=Temp,tmax=tmax,t50=t50)
# select just the Hoenig methods
metaM(Mmethods("Hoenig"),K=K,Linf=Linf,Temp=Temp,tmax=tmax,t50=t50)
## Example of computing an average M
# select multiple models used in FAMS (example only, these are not best models)
( res <- metaM(Mmethods("FAMS"),tmax=tmax,K=K,Linf=Linf,t0=t0,
Temp=Temp,PS=0.01,Winf=30) )
( meanM <- mean(res$M) )
( meancm <- mean(res$cm) )
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