Calculate or return the Spawning Stock Biomass
Source:R/genericMethods.R, R/FLStock.R, R/FLBiol.R
ssb.RdThe calculated Spawning Stock Biomass (SSB) of a fish population is returned
by this method. SSB is the combined weight of all individuals in a fish stock
that are capable of reproducing. In some classes this is calculated from
information stored in different slots, while in others ssb() is simply
an slot accessor. When the later is the case, the corresponding replacement
method also exists.
For an object of class FLStock, the calculation of SSB depends
on the value of the 'units' attribute in the harvest slot. If this is
in terms of fishing mortality (units(harvest(object)) == 'f'), and
assuming an object structured by age, then SSB is calculated as
$$SSB_{y} = \sum\nolimits_{a} N_{a,y} \cdot e^{-(F_{a,y} \cdot Hs_{a,y} + M_{a,y} \cdot Ms_{a,y})} \cdot W_{a,y} \cdot T_{a,y} $$
where \(N_{a,y}\) is the abundance in numbers (stock.n) by
age (a) and year (y), \(F_{a,y}\) is the fishing mortality (harvest),
\(Hs_{a,y}\) is the proportion of fishing mortality before spawning
(harvest.spwn),
\(M_{a,y}\) is the natural mortality (m),
\(Ms_{a,y}\) is the proportion of natural mortality before spawning
(m.spwn),
\(W_{a,y}\) is the mean weight at age in the stock (m), and
\(T_{a,y}\) is the proportion mature at age in the stock (mat).
For FLStock objects with other dimensions (area,
unit), the calculation is carried out along those dimensions too. To
obtain a global value please use the corresponding summing method.
If the harvest slot contains estimates in terms of harvest rates
(units(harvest(object)) == "hr"), SSB will be computed as
$$SSB_{y} = \sum\nolimits_{a} N_{a,y} \cdot (1 - H_{a,y} \cdot Hs_{a,y}) \cdot e^{-(M_{a,y} \cdot Ms_{a,y})} \cdot W_{a,y} \cdot T_{a,y} $$
where \(H_{a,y}\) is the harvest rate (proportion of catch in weight
over total biomass).
Usage
ssb(object, ...)
# S4 method for class 'FLStock'
ssb(object, ...)
# S4 method for class 'FLBiol'
ssb(object, ...)Value
An object, generally of class FLQuant.
Details
Objects of the FLBiol class do not contain any information on
catch or fishing mortality, so a call to ssb() will only correct abundances
for natural mortality to the moment of spawning. The method can also take
information on catches or fishing mortality and use them when calculating
abundances at spawning time. An FLQuant named either 'catch.n', 'f', 'hr' or
'harvest' can be used. The first three are self-explanatory, while for the last
units must be either 'f' or 'hr'. The quantities should refer to total yearly
values, as the value in the 'spwn' slot will be used to calculate what fraction
of fishing mortality to apply.
Examples
data(ple4)
# SSB from FLStock
ssb(ple4)
#> An x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> age 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966
#> all 342223 355375 362119 380052 391386 482245 440658 430475 383583 404516
#> year
#> age 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
#> all 473938 458977 402865 370472 361610 366129 302365 298094 301757 328726
#> year
#> age 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
#> all 329116 327544 302271 319090 290780 284211 339238 367251 394666 407972
#> year
#> age 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
#> all 470952 424696 448230 396458 356947 311431 279962 233481 222203 203391
#> year
#> age 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
#> all 204948 237863 219149 230902 234211 221902 248312 233478 253737 284447
#> year
#> age 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 293330 371837 453026 554245 575459 617539 709948 823276 774157 836453
#> year
#> age 2017
#> all 913290
#>
#> units: t
biol <- as(ple4, "FLBiol")
# SSB from FLBiol, abundances corrected only for M
ssb(biol)
#> An x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> age 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966
#> all 342223 355375 362119 380052 391386 482245 440658 430475 383583 404516
#> year
#> age 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
#> all 473938 458977 402865 370472 361610 366129 302365 298094 301757 328726
#> year
#> age 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
#> all 329116 327544 302271 319090 290780 284211 339238 367251 394666 407972
#> year
#> age 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
#> all 470952 424696 448230 396458 356947 311431 279962 233481 222203 203391
#> year
#> age 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
#> all 204948 237863 219149 230902 234211 221902 248312 233478 253737 284447
#> year
#> age 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 293330 371837 453026 554245 575459 617539 709948 823276 774157 836453
#> year
#> age 2017
#> all 913290
#>
#> units: t
# Provide catch-at-age, F or HR to correct N
ssb(biol, catch.n=catch.n(ple4))
#> An x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> age 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966
#> all 342223 355375 362119 380052 391386 482245 440658 430475 383583 404516
#> year
#> age 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
#> all 473938 458977 402865 370472 361610 366129 302365 298094 301757 328726
#> year
#> age 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
#> all 329116 327544 302271 319090 290780 284211 339238 367251 394666 407972
#> year
#> age 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
#> all 470952 424696 448230 396458 356947 311431 279962 233481 222203 203391
#> year
#> age 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
#> all 204948 237863 219149 230902 234211 221902 248312 233478 253737 284447
#> year
#> age 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 293330 371837 453026 554245 575459 617539 709948 823276 774157 836453
#> year
#> age 2017
#> all 913290
#>
#> units: t
ssb(biol, f=harvest(ple4))
#> An x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> age 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966
#> all 342223 355375 362119 380052 391386 482245 440658 430475 383583 404516
#> year
#> age 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
#> all 473938 458977 402865 370472 361610 366129 302365 298094 301757 328726
#> year
#> age 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
#> all 329116 327544 302271 319090 290780 284211 339238 367251 394666 407972
#> year
#> age 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
#> all 470952 424696 448230 396458 356947 311431 279962 233481 222203 203391
#> year
#> age 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
#> all 204948 237863 219149 230902 234211 221902 248312 233478 253737 284447
#> year
#> age 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 293330 371837 453026 554245 575459 617539 709948 823276 774157 836453
#> year
#> age 2017
#> all 913290
#>
#> units: t
ssb(biol, harvest=harvest(ple4))
#> An x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> age 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966
#> all 342223 355375 362119 380052 391386 482245 440658 430475 383583 404516
#> year
#> age 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
#> all 473938 458977 402865 370472 361610 366129 302365 298094 301757 328726
#> year
#> age 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
#> all 329116 327544 302271 319090 290780 284211 339238 367251 394666 407972
#> year
#> age 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
#> all 470952 424696 448230 396458 356947 311431 279962 233481 222203 203391
#> year
#> age 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
#> all 204948 237863 219149 230902 234211 221902 248312 233478 253737 284447
#> year
#> age 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 293330 371837 453026 554245 575459 617539 709948 823276 774157 836453
#> year
#> age 2017
#> all 913290
#>
#> units: t
ssb(biol, hr=catch.n(ple4) / stock.n(ple4))
#> An x of class "FLQuant"
#> , , unit = unique, season = all, area = unique
#>
#> year
#> age 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966
#> all 342223 355375 362119 380052 391386 482245 440658 430475 383583 404516
#> year
#> age 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
#> all 473938 458977 402865 370472 361610 366129 302365 298094 301757 328726
#> year
#> age 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
#> all 329116 327544 302271 319090 290780 284211 339238 367251 394666 407972
#> year
#> age 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
#> all 470952 424696 448230 396458 356947 311431 279962 233481 222203 203391
#> year
#> age 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
#> all 204948 237863 219149 230902 234211 221902 248312 233478 253737 284447
#> year
#> age 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
#> all 293330 371837 453026 554245 575459 617539 709948 823276 774157 836453
#> year
#> age 2017
#> all 913290
#>
#> units: t