The 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.

ssb(object, ...)

# S4 method for FLStock
ssb(object, ...)

# S4 method for FLBiol
ssb(object, ...)

Arguments

object
Object on which ssb is calculated or extracted.

Value

An object, generally of class FLQuant.

Details

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).

For an object of class FLBiol, the calculation of SSB is as follows: $$SSB_{a,y} = \sum\nolimits_{a} N_{a,y} \cdot W_{a,y} \cdot e^{-S_{a,y} \cdot M_{a,y}}$$ where \(S_{a,y}\) is the fraction of natural mortality before spawning (spwn). The method for this class does not correct the estimate, based on abundnaces at the start of the time period, for fishing mortality ocurring between that time and spawning, as the class holds no information on fishing mortality.

See also

FLComp

areaSums

Examples

data(ple4) ssb(ple4)
#> An object of class "FLQuant" #> , , unit = unique, season = all, area = unique #> #> year #> age 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 #> all 274205 288540 296825 308164 321354 372863 370373 363077 344013 361549 #> year #> age 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 #> all 416563 402521 377432 333933 316343 319062 268714 278648 293136 310954 #> year #> age 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 #> all 316929 303433 297122 272416 262061 263998 314021 326341 348675 375392 #> year #> age 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 #> all 445855 391254 408489 368969 335747 269528 228668 193093 174408 173903 #> year #> age 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 #> all 185308 211327 184733 208393 234078 162725 179158 151508 167531 173783 #> year #> age 2007 2008 #> all 166061 206480 #> #> units: t