Intrinsic rate of increase from an FLBiol object

Description

For an FLBiol object with the mortality-at-age, fecundity and spwn data present in the object slots, this method calculates the intrinsic rate of increase r for the given population.

It does this using two methods:

(1) Solving the Euler-Lotka equation.

(2) Calculating the logarithm of the real part of the largest/lead eigenvalue of the Leslie transition matrix.

These two methods are not identical but do give similar answers for the same data and parameters

Usage

r(object, ...)

Arguments

Details

To chose the method used to estimate r (Euler-Lotka or Leslie matrix) we supply either 'el' or 'leslie' as the 'method' argument (see below). To calculate r along years or cohorts by supply either 'year' or 'cohort' as the 'by' argument (see below).

The method can handle Monte Carlo samples (i.e. with iterations) in either the fec, m or both slots required to calculate r and the conversion is done internally so that we obtain an FLQuant of the correct dimensions.

Value

An object of class FLQuant-class.

Author(s)

FLR Team

See Also

FLBiol-class

Examples

## Not run: 

# call in the NS herring stock and biol objects

data(nsher.biol)
data(nsher)

# calculate the gradient at the origin from the spawning stock numbers to the recruits

tmp <- nsher.biol
n(tmp) <- stock.n(nsher)
m(tmp) <- harvest(nsher)+m(nsher.biol)

# use nls to calculate gradient of (recruits/spawning stock numbers)
# assuming log-normal errors

dfx <- data.frame(rec=as.vector(n(tmp)[1,]),ssn=as.vector(ssn(tmp)))
res <- nls(log(rec)~log(a)+log(ssn),dfx,start=list(a=mean(n(tmp)[1,]/ssn(tmp))))

# use this value of recruits per spawner times maturity as the birth function for 
# the Leslie transition matrix/Euler-Lotka equation

alpha <- coef(res)[[1]]
fec(tmp)[] <- fec(tmp)[] * alpha

# calculate r assuming only natural mortality and by year
# using both Euler-Lotka (el) and Lesie matrix (leslie) method

m(tmp) <- m(nsh.biol)
r.nsh.el <- r(tmp,by='year',method='el')
r.nsh.lm <- r(tmp,by='year',method='leslie')
## End(Not run)