grwdd

Lorenzen natural mortality relationship where M is a function of weight, modified to explicitly included M as a function of numbers in a cohort, i.e. density dependence

# S4 method for FLQuant,FLPar
grwdd(age, params, scale, k = 1, fn = vonB)

Arguments

age

mass at which length is to be predicted

params

an FLPar with two values; i.e. a equal to M at unit mass and b a power term; defaults are a=0.3 and b=-0.288

scale

reference

k

rate of change in density dependence

fn

function with growth model, with args age params

...

other arguments, such as scale, e.g. stock numbers now relative to a reference level, e.g. at virgin biomass and k steepness of relationship

Details

@details

The Lorenzen natural mortality relationship is a function of mass-at-age i.e. M=a*wt^b

The relationship can be explained by population density, since as fish grow they also die and so there is potentially less competition for resources between larger and older fish. Density dependence can be modelled by a logistic function, a sigmoid curve (or S shaped) curve, with equation

f(x)=L/(1+exp(-k(x-x0)))

where e is the natural logarithm base (also known as Euler's number), x0 is the x-value of the sigmoid's midpoint, L is the curve's maximum value, and k the steepness of the curve.

Combining the two functions gives

M=aL/(1+exp(-k(n-ref)))*wt^b;

See also

vonB

Examples

if (FALSE) {
library(FLBRP)
library(FLife)

data(teleost)
par=teleost[,"Hucho hucho"]
par=lhPar(par)
hutchen=lhEql(par)

scale=stock.n(hutchen)[,25]%*%stock.wt(hutchen)
scale=(stock.n(hutchen)%*%stock.wt(hutchen)%-%scale)%/%scale

grw=grwdd(wt2len(stock.wt(hutchen),par),params=par,scale,k=.2) 
 
ggplot(as.data.frame(grw))+
   geom_line(aes(age,data,col=factor(year)))+
   theme(legend.position="none")+
   scale_x_continuous(limits=c(0,15))
}