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 x 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 35.5 33.6 32.1 29.4 31.0 33.0 35.1 32.7 30.0 33.1 36.8 37.6 35.6 32.7
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 35.2 33.7 28.8 26.8 26.8 27.9 26.4 26.5 26.3 26.5 26.5 23.2 24.2 25.3
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 25.3 21.4 25.1 27.3 29.3 30.7 30.0 30.3 31.6 31.7 29.3 28.3 25.5 26.1
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 29.6 29.8 30.7 26.0 26.9 26.5 26.3 26.6 25.3 26.2 27.0 26.3 28.7 29.8
#> year
#> len 2013 2014 2015 2016 2017
#> all 30.4 28.3 30.8 31.9 32.8
#>
#> units: cm
#>
#> $lmaxy
#> An x 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 60 63 86 57 76 73 81 74 77 33 77 50 55 59
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 72 68 83 56 74 76 42 53 54 68 75 76 39 34
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 37 65 24 32 38 43 56 58 61 47 49 52 31 23
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 31 41 48 42 65 34 73 46 43 51 51 35 47 52
#> year
#> len 2013 2014 2015 2016 2017
#> all 58 69 48 77 59
#>
#> units: cm
#>
indicators.len(ple4, indicators=c('pmega'),
params=FLPar(linf=60, k=2.29e-01, t0=-1.37), metric='catch.n')
#> $pmega
#> An x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
#> all 0.338 0.312 0.242 0.242 0.234 0.246 0.272 0.290 0.182 0.160 0.290 0.388
#> year
#> len 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
#> all 0.394 0.332 0.274 0.318 0.188 0.118 0.118 0.220 0.146 0.136 0.178 0.124
#> year
#> len 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
#> all 0.132 0.112 0.082 0.116 0.128 0.106 0.070 0.138 0.162 0.232 0.190 0.218
#> year
#> len 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
#> all 0.236 0.216 0.238 0.160 0.088 0.088 0.106 0.204 0.246 0.156 0.122 0.130
#> year
#> len 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 0.138 0.134 0.120 0.122 0.158 0.144 0.152 0.180 0.200 0.184 0.218 0.254
#> year
#> len 2017
#> all 0.286
#>
#> 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 x 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 21.5 16.9 22.2 22.0 21.2 22.8 16.1 22.0 21.8 21.1 21.4 20.9 20.4 21.5
#> year
#> len 2010 2011 2012 2013 2014 2015 2016 2017
#> all 21.6 20.9 26.4 24.0 22.3 26.9 25.6 21.3
#>
#> units: cm
#>
#> $lmean
#> An x 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 24.0 23.2 29.6 27.1 24.4 27.3 19.1 24.1 27.9 24.0 24.7 28.6 26.2 27.9
#> year
#> len 2010 2011 2012 2013 2014 2015 2016 2017
#> all 28.7 27.1 30.6 27.3 26.0 29.3 29.1 27.9
#>
#> 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 x 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 40.0 36.0 35.0 35.0 38.0 38.0 35.0 35.0 38.0 40.0 40.0 41.0 36.0
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 38.0 39.0 32.0 33.0 35.0 35.0 33.0 33.0 33.0 35.0 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 33.5 28.0 32.0 36.0 35.0 36.0 35.0 35.0 36.0 37.0 36.0 35.0 33.0 34.0
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 37.0 38.0 36.0 35.0 34.0 34.0 32.0 33.0 32.0 34.0 34.0 32.0 33.0 36.5
#> year
#> len 2013 2014 2015 2016 2017
#> all 36.0 37.0 37.0 37.0 38.0
#>
#> units: NA
lmax5(samps)
#> An x 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 59.9 59.9 57.4 58.2 53.0 56.7 56.1 56.7 54.7 50.5 55.3 56.6 58.1 57.2
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 59.1 59.6 59.8 56.3 53.8 57.2 54.1 54.5 53.5 55.6 55.7 53.8 54.7 47.8
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 54.0 50.9 48.9 51.0 49.0 53.2 54.1 51.8 53.6 55.8 57.8 53.0 55.2 49.3
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 50.7 53.9 53.3 55.8 53.7 52.0 51.3 50.4 49.4 52.2 52.0 52.7 51.2 55.4
#> year
#> len 2013 2014 2015 2016 2017
#> all 55.8 55.3 54.9 55.6 56.6
#>
#> units: cm
l95(samps)
#> An x 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 56.5 57.0 55.0 55.5 49.5 52.0 52.0 52.0 51.5 48.0 52.0 55.0 56.0 55.0
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 57.0 56.0 54.5 51.0 49.5 50.5 51.0 52.0 51.0 53.0 50.5 48.0 49.1 45.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 49.5 49.0 46.1 48.0 47.0 50.0 51.0 49.0 51.0 52.5 51.5 51.0 51.0 45.5
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 47.0 49.0 50.5 52.1 48.5 47.1 49.0 47.0 47.0 49.0 48.0 47.5 48.0 53.0
#> year
#> len 2013 2014 2015 2016 2017
#> all 50.5 52.0 53.0 53.0 53.0
#>
#> units: cm
l25(samps)
#> An x 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 33.0 31.0 29.0 30.0 28.0 33.0 34.0 27.0 31.0 34.0 34.0 32.0 32.0 28.2
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 32.0 32.0 26.0 27.0 29.0 27.2 26.0 26.0 26.2 28.0 28.0 26.0 29.0 27.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 26.0 25.0 28.0 31.0 30.0 30.0 29.0 30.0 30.0 30.0 29.0 30.0 28.0 30.0
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 32.0 31.0 31.0 28.0 30.0 27.0 27.2 27.0 27.0 28.2 28.0 27.0 28.0 32.0
#> year
#> len 2013 2014 2015 2016 2017
#> all 30.0 29.0 30.0 29.0 31.0
#>
#> units: cm
lc50(samps)
#> An x 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 22.0 21.5 18.5 16.0 18.0 20.5 18.0 12.5 15.5 18.5 20.5 21.5 22.5 13.5
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 19.0 21.0 13.0 13.0 18.5 13.5 13.5 12.0 13.0 17.0 16.5 12.0 17.0 14.0
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 13.0 12.5 16.0 18.0 19.0 18.5 21.0 17.0 16.0 20.0 16.5 17.5 13.0 16.0
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 18.5 20.5 17.5 19.0 16.0 17.5 17.0 12.5 13.0 17.5 17.0 13.5 15.5 16.5
#> year
#> len 2013 2014 2015 2016 2017
#> all 18.0 13.5 18.5 19.0 17.0
#>
#> units: cm
lmode(samps)
#> An x 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 43 37 32 36 41 36 25 31 37 41 43 45 27
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 38 42 26 26 37 27 27 24 26 34 33 24 34 28
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 26 25 32 36 38 37 42 34 32 40 33 35 26 32
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 37 41 35 38 32 35 34 25 26 35 34 27 31 33
#> year
#> len 2013 2014 2015 2016 2017
#> all 36 27 37 38 34
#>
#> units: cm
lbar(samps)
#> An x 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 39.3 39.6 37.0 37.0 35.2 38.5 39.3 35.9 36.5 37.7 39.5 39.8 40.5 37.5
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 39.3 39.8 34.9 34.4 34.6 35.4 34.3 34.6 34.2 35.4 34.7 32.9 33.8 33.6
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 33.9 30.6 33.3 36.0 35.2 36.0 36.1 35.7 36.3 36.9 36.6 35.7 34.5 34.3
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 36.1 36.9 36.5 34.9 35.2 34.0 33.5 33.5 33.5 34.9 34.7 33.8 34.3 37.6
#> year
#> len 2013 2014 2015 2016 2017
#> all 36.5 37.0 37.1 36.7 38.1
#>
#> units: cm
lmean(samps)
#> An x 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 51.1 51.0 46.5 43.1 43.6 47.7 44.6 38.2 40.0 42.5 46.6 49.9 51.7 41.6
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 49.0 50.2 39.4 37.4 44.1 39.0 39.5 36.7 37.7 42.4 40.9 34.8 41.3 37.8
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 37.3 34.0 38.9 42.4 43.1 43.9 47.8 42.2 41.3 46.7 42.8 42.8 37.1 38.6
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 42.4 46.1 42.5 45.0 39.4 41.5 41.9 35.9 35.8 42.4 41.7 37.7 39.2 41.9
#> year
#> len 2013 2014 2015 2016 2017
#> all 43.5 40.1 45.2 45.6 44.8
#>
#> units: cm
# Linf(ple4) = 60
lmean(samps) / (0.75 * lc50(samps) + 0.25 * 60) #
#> An x 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 1.62 1.64 1.61 1.60 1.53 1.57 1.56 1.57 1.50 1.47 1.53 1.60 1.62 1.66
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 1.68 1.63 1.59 1.51 1.53 1.55 1.57 1.53 1.52 1.53 1.49 1.45 1.49 1.48
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 1.51 1.39 1.44 1.49 1.47 1.52 1.55 1.52 1.53 1.56 1.56 1.52 1.50 1.43
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 1.47 1.52 1.51 1.54 1.46 1.47 1.51 1.47 1.45 1.51 1.50 1.50 1.47 1.53
#> year
#> len 2013 2014 2015 2016 2017
#> all 1.53 1.60 1.56 1.56 1.61
#>
#> units:
lenwt <- FLPar(a=0.01030, b=2.975)
lmaxy(samps, lenwt)
#> An x 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 56 56 53 44 48 47 46 47 39 41 51 56 49
#> year
#> len 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
#> all 53 56 46 46 37 43 51 50 55 44 41 44 34 43
#> year
#> len 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
#> all 38 50 37 41 43 37 42 48 39 40 45 51 44 32
#> year
#> len 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
#> all 41 41 43 40 37 35 45 40 39 46 44 44 48 45
#> year
#> len 2013 2014 2015 2016 2017
#> all 44 48 44 38 46
#>
#> units: cm
pmega(samps, linf=60)
#> An x 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 0.352 0.264 0.232 0.196 0.284 0.320 0.228 0.196 0.156 0.288 0.348
#> year
#> len 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
#> all 0.436 0.320 0.328 0.356 0.232 0.168 0.128 0.172 0.196 0.204 0.176 0.212
#> year
#> len 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
#> all 0.120 0.124 0.100 0.080 0.148 0.100 0.084 0.152 0.128 0.176 0.220 0.192
#> year
#> len 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
#> all 0.188 0.212 0.240 0.180 0.148 0.084 0.136 0.192 0.204 0.140 0.144 0.096
#> year
#> len 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 0.128 0.128 0.120 0.164 0.156 0.148 0.128 0.236 0.212 0.248 0.260 0.220
#> year
#> len 2017
#> all 0.288
#>
#> 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 x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> len 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
#> all 0.273 0.259 0.284 0.250 0.329 0.273 0.223 0.236 0.256 0.265 0.247 0.253
#> year
#> len 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
#> all 0.249 0.215 0.233 0.245 0.262 0.273 0.360 0.256 0.282 0.258 0.278 0.307
#> year
#> len 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
#> all 0.319 0.298 0.358 0.307 0.285 0.371 0.355 0.306 0.350 0.315 0.364 0.297
#> year
#> len 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
#> all 0.267 0.313 0.266 0.305 0.271 0.322 0.311 0.324 0.283 0.361 0.296 0.360
#> year
#> len 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 0.366 0.289 0.297 0.331 0.327 0.296 0.313 0.244 0.291 0.224 0.282 0.300
#> year
#> len 2017
#> all 0.238
#>
#> units: z