# lk-funcs: powh In ejardim/FLMethLen: Prototype package for size based methods

## Description

Estimates growth and mortality parameters from length frequency data.

For a vector with labels corresponding to intervals i.e. "(0,10]" returns a data.frame with left and right boundaries and mid point.

## Usage

 1 2 3  powh(len, n) unbin(x) 

## Arguments

 len vector with length distribution n vector with numbers in each length bin x; a vector of with intervals as names

## Details

Beverton and Holt (1956) developed a method to estimate population parameters such as total mortality (Z) from length data i.e.

Z=K\frac{L_{∞}-\overline{L}}{\overline{L}-L^\prime}

Powell (1979) then developed a method, extended by Wetherall et al. (1987), to estimate growth and mortality parameters. This assumes that the right hand tail of a length frequency distribution is determined by the asymptotic length L and the ratio between Z and the growth rate K.

The Beverton and Holt methods assumes good estimates for K and $L_\infty$, while the Powell-Wetherall method only requires an estimate of K, since $L_\infty$ is estimated by the method as well as Z/K. These method therefore provide estimates for Z/K, if K is unknown and Z if K is known.

As well as assuming that growth follows the von Bertalanffy growth function, it is also assumed that the population is in a steady state with constant exponential mortality, no changes in selection pattern of the fishery and constant recruitment.

In the Powell-Wetherall method $L^\prime$ can take any value between the smallest and largest sizes. Equation 1 then provides a series of estimates of Z and since

\overline{L}-L{\prime}=a+bL{\prime}

a and b can be estimated by a regression analysis where

b={-K}/{Z+K}

a=-bL_{∞}

Therefore plotting $\overlineL-L^\prime$ against $L^\prime$ provides an estimate of $L_\infty$ and Z/K from

L_{∞}=-a/b

Z/K={-1-b}/{b}

If K is known Z can also be esimated

## Value

a data.frame mn (mean), diff (difference), len (length) and n (frequency)

a data.frame with left and right boundaries and mid points.

## References

R. Beverton and S. Holt. Review of method for estimating mortality rates in exploited fish populations, with special reference to sources of bias in catch sampling. Rapports et Proces-Verbaux., 140(1): 67–83, 1956.

D. G. Powell. Estimation of mortality and growth parameters from the length frequency of a catch [model]. Rapports et Proces-Verbaux des Reunions, 175, 1979.

J. Wetherall, J. Polovina, and S. Ralston. Estimating growth and mortality in steady-state fish stocks from length-frequency data. ICLARM Conf. Proc, pages 53–74, 1987.

## Examples

 1 2 3 x=1 x=summary(cut(runif(100),seq(0,1,.1))) unbin(x) 

ejardim/FLMethLen documentation built on May 13, 2017, 4:06 p.m.