z = (k * (linf - lmean)) / (lmean - lc) lmean = sum(naa * len) / sum(naa) lc, length at first capture
Usage
indicators.len(
object,
indicators = "lbar",
model = vonbert,
params,
cv = 0.1,
lmax = 1.25,
bin = 1,
n = 500,
metric = catch.n,
...
)
lenquantile(x, quantile = 0.5)
lmax5(x)
l95(x)
l25(x)
lc50(x)
lmode(x)
lbar(x)
lmean(x)
lmaxy(x, lenwt)
pmega(x, linf, lopt = linf * 2/3)
bheqz(x, linf, k, t0, lc = lc50(x))References
Kell, L.T., Minto, C., Gerritsen, H.D. 2022. Evaluation of the skill of length-based indicators to identify stock status and trends. ICES Journal of Marine Science. doiu: 10.1093/icesjms/fsac043.
ICES. 2015. Report of the Fifth Workshop on the Development of Quantitative Assessment Methodologies based on Life-history Traits, Exploitation Characteristics and other Relevant Parameters for Data-limited Stocks (WKLIFE V), 5–9 October 2015, Lisbon, Portugal. ICES CM 2015/ACOM:56. 157 pp.
ICES. 2020. Tenth Workshop on the Development of Quantitative Assessment Methodologies based on LIFE-history traits, exploitation characteristics, and other relevant parameters for data-limited stocks (WKLIFE X). ICES Scientific Reports. 2:98. 72 pp. http://doi.org/10.17895/ices.pub.5985
Examples
data(ple4)
indicators.len(ple4, indicators=c('lbar', 'lmaxy'),
params=FLPar(linf=132, k=0.080, t0=-0.35), metric='catch.n',
lenwt=FLPar(a=0.01030, b=2.975))
#> $lbar
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 34.9 34.9 30.9 30.6 31.3 31.9 35.7 31.4 30.4 33.8 36.4 37.0 36.7 32.0
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 34.3 35.2 28.5 26.3 27.3 28.8 25.9 26.5 27.6 26.5 27.1 23.7 24.6 25.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 24.6 20.5 24.2 27.2 29.1 30.7 30.1 31.2 30.9 31.8 29.5 28.1 25.1 26.5
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 29.2 30.8 30.3 26.5 26.6 26.2 25.9 27.8 25.8 25.4 26.5 26.3 29.6 30.5
#> year
#> len 2013 2014 2015 2016 2017
#> all 30.5 28.3 30.3 31.6 32.5
#>
#> units: cm
#>
#> $lmaxy
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 79 70 71 63 72 46 69 51 63 31 40 46 50 56
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 70 70 70 62 61 84 43 53 51 74 70 75 75 90
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 71 46 23 31 41 49 48 59 54 58 61 74 33 59
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 32 41 45 48 24 55 71 46 57 55 32 64 51 50
#> year
#> len 2013 2014 2015 2016 2017
#> all 61 38 58 61 77
#>
#> units: cm
#>
indicators.len(ple4, indicators=c('pmega'),
params=FLPar(linf=60, k=2.29e-01, t0=-1.37), metric='catch.n')
#> $pmega
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
#> all 0.298 0.310 0.228 0.210 0.228 0.266 0.280 0.272 0.148 0.210 0.312 0.374
#> year
#> len 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
#> all 0.370 0.298 0.326 0.274 0.190 0.142 0.096 0.150 0.202 0.186 0.138 0.136
#> year
#> len 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
#> all 0.124 0.086 0.082 0.108 0.114 0.100 0.078 0.116 0.162 0.216 0.218 0.210
#> year
#> len 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
#> all 0.224 0.224 0.218 0.128 0.114 0.068 0.124 0.202 0.226 0.186 0.146 0.108
#> year
#> len 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 0.136 0.154 0.132 0.124 0.118 0.132 0.196 0.192 0.194 0.186 0.192 0.246
#> year
#> len 2017
#> all 0.280
#>
#> units: NA
#>
data(ple4.index)
indicators.len(ple4.index, indicators=c('lbar', 'lmean'),
params=FLPar(linf=132, k=0.080, t0=-0.35), metric='index')
#> $lbar
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
#> all 21.6 17.1 21.1 22.4 21.1 22.5 16.5 22.2 22.3 22.2 21.7 19.2 21.3 21.6
#> year
#> len 2010 2011 2012 2013 2014 2015 2016 2017
#> all 22.4 20.3 25.1 24.5 23.1 27.1 25.4 21.8
#>
#> units: cm
#>
#> $lmean
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
#> all 25.6 23.3 27.0 25.3 24.0 25.4 22.3 25.8 28.2 25.1 25.1 25.7 24.2 25.5
#> year
#> len 2010 2011 2012 2013 2014 2015 2016 2017
#> all 30.4 24.3 29.5 27.8 26.7 31.5 29.9 29.5
#>
#> units: cm
#>
#
ialk <- invALK(params=FLPar(linf = 60, k = 2.29e-01, t0 = -1.37e+00),
model=vonbert, age=1:10, lmax=1.2)
samps <- lenSamples(catch.n(ple4), invALK=ialk, n=250)
lenquantile(samps, 0.50)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 39.0 38.5 36.0 35.0 35.0 36.0 39.0 35.5 35.0 38.0 40.0 40.0 39.5 34.0
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 36.0 39.0 34.0 32.0 34.0 37.0 31.0 32.0 33.0 33.0 34.0 31.0 33.0 34.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 33.0 27.5 32.0 35.0 36.0 36.0 37.0 37.0 36.0 36.0 35.0 34.0 33.0 33.0
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 37.0 38.0 37.0 34.0 33.0 34.0 34.0 35.0 33.0 33.0 32.0 33.0 34.0 37.0
#> year
#> len 2013 2014 2015 2016 2017
#> all 36.0 34.0 36.0 38.0 38.0
#>
#> units: NA
lmax5(samps)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 59.1 58.5 58.4 55.5 57.4 57.1 58.8 54.8 55.9 54.5 54.1 57.7 59.6 57.6
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 61.3 60.0 57.0 57.3 51.4 56.8 54.2 53.7 55.6 52.3 52.6 54.1 52.0 54.5
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 53.8 49.8 53.4 50.0 52.8 53.6 52.1 55.0 54.6 54.8 53.7 54.5 49.0 49.3
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 50.8 52.3 52.9 53.8 53.3 50.3 51.7 51.8 50.4 51.1 51.4 51.8 54.5 54.3
#> year
#> len 2013 2014 2015 2016 2017
#> all 53.5 52.5 55.6 55.8 58.0
#>
#> units: cm
l95(samps)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 54.0 54.5 54.5 52.0 55.0 53.0 56.0 51.5 52.0 49.6 51.0 53.5 54.5 54.0
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 56.5 57.0 55.0 54.0 47.0 52.5 51.0 49.0 53.0 49.0 49.0 49.1 49.0 50.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 49.1 46.0 47.5 46.0 50.0 49.5 50.0 52.0 51.0 52.5 49.5 51.0 46.5 44.0
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 48.5 51.0 50.0 49.5 49.0 46.5 48.0 48.5 48.0 47.0 49.0 47.0 48.5 50.5
#> year
#> len 2013 2014 2015 2016 2017
#> all 51.0 48.5 51.5 53.0 53.5
#>
#> units: cm
l25(samps)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 34.0 31.0 30.0 29.0 30.0 32.0 33.0 27.0 31.0 34.0 34.2 34.0 31.0 29.0
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 29.0 33.0 26.0 27.0 29.0 29.0 26.0 27.0 26.0 27.0 28.0 26.0 27.0 27.2
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 27.0 25.0 29.0 29.0 30.0 29.0 30.2 31.0 30.0 30.0 29.0 29.0 26.0 30.2
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 33.0 32.0 31.0 27.0 30.0 26.0 29.0 30.0 27.2 28.0 27.0 27.0 28.0 32.0
#> year
#> len 2013 2014 2015 2016 2017
#> all 30.0 29.0 31.0 31.2 31.0
#>
#> units: cm
lc50(samps)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 17.5 17.5 13.0 17.0 16.5 18.5 19.5 13.0 16.5 19.5 18.5 19.5 22.5 16.0
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 18.5 19.5 12.0 13.0 19.0 19.0 13.0 13.5 12.0 12.5 16.5 12.0 18.5 17.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 12.0 12.5 15.5 18.0 17.0 18.5 21.0 16.0 19.0 18.5 13.5 16.0 18.5 16.0
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 18.5 21.0 16.0 19.0 16.5 16.5 17.5 17.0 13.0 17.5 13.0 12.5 17.0 15.0
#> year
#> len 2013 2014 2015 2016 2017
#> all 22.0 16.0 17.5 19.0 19.5
#>
#> units: cm
lmode(samps)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 35 35 26 34 33 37 39 26 33 39 37 39 45 32
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 37 39 24 26 38 38 26 27 24 25 33 24 37 34
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 24 25 31 36 34 37 42 32 38 37 27 32 37 32
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 37 42 32 38 33 33 35 34 26 35 26 25 34 30
#> year
#> len 2013 2014 2015 2016 2017
#> all 44 32 35 38 39
#>
#> units: cm
lbar(samps)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 39.6 38.7 37.0 36.0 36.5 37.2 40.3 36.0 36.8 38.0 39.4 40.0 39.1 36.3
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 37.9 39.8 35.5 34.2 34.7 36.3 33.0 34.3 34.0 33.6 34.8 32.5 33.3 34.2
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 34.1 30.2 33.5 34.9 36.1 36.1 37.1 37.4 36.0 36.6 35.8 34.5 33.1 34.1
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 37.0 37.8 37.0 34.2 34.5 33.8 34.6 35.2 34.1 33.5 33.7 34.3 34.8 37.6
#> year
#> len 2013 2014 2015 2016 2017
#> all 36.2 34.9 36.8 38.2 38.3
#>
#> units: cm
lmean(samps)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 44.6 45.5 39.6 42.3 42.1 45.1 48.0 39.6 41.2 44.7 44.1 46.6 51.6 43.6
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 48.6 47.9 38.0 37.2 44.3 45.0 37.2 38.1 36.3 36.1 41.2 34.8 44.2 41.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 35.6 33.8 38.0 41.6 42.2 44.4 47.6 42.4 44.9 44.8 38.9 40.1 42.7 38.0
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 41.8 47.0 41.4 44.6 40.0 40.0 41.7 41.3 36.6 41.7 36.5 36.5 41.9 40.1
#> year
#> len 2013 2014 2015 2016 2017
#> all 49.9 40.5 43.1 45.6 47.1
#>
#> units: cm
# Linf(ple4) = 60
lmean(samps) / (0.75 * lc50(samps) + 0.25 * 60) #
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 1.59 1.62 1.60 1.53 1.54 1.56 1.62 1.60 1.51 1.51 1.53 1.57 1.62 1.61
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 1.68 1.62 1.58 1.50 1.51 1.54 1.50 1.52 1.51 1.48 1.51 1.45 1.53 1.48
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 1.48 1.39 1.43 1.46 1.52 1.54 1.55 1.57 1.54 1.55 1.55 1.49 1.48 1.41
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 1.45 1.53 1.53 1.53 1.46 1.46 1.48 1.49 1.48 1.48 1.48 1.50 1.51 1.53
#> year
#> len 2013 2014 2015 2016 2017
#> all 1.58 1.50 1.53 1.56 1.59
#>
#> units:
lenwt <- FLPar(a=0.01030, b=2.975)
lmaxy(samps, lenwt)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970
#> all 51 49 58 41 56 37 52 48 36 39 43 45 45 51
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 56 41 56 42 38 41 41 47 55 43 40 36 37 34
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 38 39 33 39 38 45 42 43 38 46 42 42 37 35
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 38 45 48 38 33 42 35 40 40 35 48 44 34 47
#> year
#> len 2013 2014 2015 2016 2017
#> all 44 41 44 53 47
#>
#> units: cm
pmega(samps, linf=60)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
#> all 0.320 0.332 0.216 0.188 0.196 0.204 0.332 0.276 0.196 0.180 0.276 0.376
#> year
#> len 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
#> all 0.364 0.268 0.284 0.316 0.244 0.156 0.124 0.208 0.152 0.192 0.164 0.132
#> year
#> len 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
#> all 0.144 0.104 0.116 0.128 0.136 0.072 0.084 0.088 0.172 0.208 0.232 0.252
#> year
#> len 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
#> all 0.164 0.224 0.200 0.124 0.084 0.056 0.108 0.276 0.212 0.152 0.136 0.092
#> year
#> len 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 0.120 0.148 0.140 0.104 0.152 0.176 0.152 0.224 0.220 0.136 0.224 0.260
#> year
#> len 2017
#> all 0.320
#>
#> units: NA
linf <- 60
k <- 2.29e-01
t0 <- -1.37e+00
bheqz(samps, linf = 60, k = 2.29e-01, t0 = -1.37e+00)
#> An object of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
#> all 0.211 0.231 0.220 0.290 0.270 0.280 0.218 0.239 0.263 0.273 0.226 0.223
#> year
#> len 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
#> all 0.290 0.268 0.261 0.228 0.238 0.280 0.369 0.314 0.308 0.283 0.270 0.286
#> year
#> len 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
#> all 0.316 0.307 0.411 0.343 0.269 0.386 0.338 0.341 0.288 0.311 0.325 0.242
#> year
#> len 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
#> all 0.322 0.295 0.248 0.315 0.423 0.328 0.285 0.304 0.252 0.387 0.324 0.346
#> year
#> len 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 0.340 0.313 0.282 0.379 0.290 0.270 0.324 0.226 0.382 0.303 0.276 0.260
#> year
#> len 2017
#> all 0.265
#>
#> units: z