r {FLCore} | R Documentation

## 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

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

### 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)

[Package FLCore version 2.2 Index]