r: Intrinsic rate of increase from an FLBiol object
In FLCore: Core package of FLR, fisheries modelling in R.

Description Usage Arguments Details Value Author(s) See Also Examples

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

1	r(object, ...)

`object`	An object of type `FLBiol`.
`...`	Extra arguments accepted by each implementation.

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.

An object of class FLQuant.

FLR Team

FLBiol

## 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)