Routines for iteratively solving the Baranov catch equation. More...

#include "statsLib.h"

Functions
double	get_ft (const double &ct, const double &m, const dvector &va, const dvector &ba)
dvector	get_ft (dvector &ct, const double &m, const dmatrix &V, const dvector &ba)
	Solving the Baranov catch equation for multiple fleets.
dvector	get_ft (dvector &ct, const double &m, const dmatrix &V, const dvector &na, const dvector &wa)
	Solving the Baranov catch equation for multiple fleets.

Detailed Description

Routines for iteratively solving the Baranov catch equation.

Author:: Steven Martell

Date:: 2/28/2011

The general form of the Baranov catch equation is given by:

$C = \frac{N F(1-\exp(-F-M))}{F+M}$

where $ C $ is the catch (in either total numbers or total weight) $N$ is the abundance at the start of the time step, $ F$ is the instantaneous fishing mortality rate $M$ is the instantaneous natural mortality rate. The Baranov catch equation is a transcedental equation; here Newtons root finding method is implemented to determine $F$ .

The basic algorithm is as follows:

1) Set initial guess for $F$ based on Popes approximation $F=\frac{C}{N \exp(-0.5M)}$ .

2) Calculate the predicted catch $\acute{C}$ based on initial $F$

3) Calculate the derivative of the catch equation $\frac{\partial{C}}{\partial{F}} ={\frac {N \left( 1-{{\rm e}^{-M-F}} \right) }{M+F}}+{\frac {NF{ {\rm e}^{-M-F}}}{M+F}}-{\frac {NF \left( 1-{{\rm e}^{-M-F}} \right) }{ \left( M+F \right) ^{2}}}$

4) Update estimate of $ F $ using $F_{i+1} = F_i - \frac{\acute{C}-C}{\frac{\partial{C}}{\partial{F}}}$

At present this function is only implemented for data-type variables.

Definition in file baranov.cpp.

Function Documentation

double get_ft	(	const double &	ct,
		const double &	m,
		const dvector &	va,
		const dvector &	ba
	)

Author:: Steven James Dean Martell UBC Fisheries Centre

Date:: 2011-07-12

Parameters:

ct	the observed catch
m	the instantaneous natural mortality rate
va	a vector of age-specific selectivities.
ba	the initial numbers or biomass (same units as the catch) at age.

Returns:: ft the instantaneous fishing mortality rate for fully selected (va=1) individuals.

See also:

Definition at line 51 of file baranov.cpp.

dvector get_ft	(	dvector &	ct,
		const double &	m,
		const dmatrix &	V,
		const dvector &	ba
	)

Solving the Baranov catch equation for multiple fleets.

Author:: Steven James Dean Martell UBC Fisheries Centre

Date:: 2011-07-12

Parameters:

ct	a vector of observed catch for each fleet.
m	the instantaneous natural mortality rate (age-independent).
V	a matrix of age-specific selectivities where each row corresponds to the fleet.
ba	the initial numbers or biomass (same units as the catch) at age.

Returns:: ft a vector of instantaneous fishing mortality rate for fully selected (va=1) individuals for each fishing fleet.

See also:

Definition at line 94 of file baranov.cpp.

dvector get_ft	(	dvector &	ct,
		const double &	m,
		const dmatrix &	V,
		const dvector &	na,
		const dvector &	wa
	)

Solving the Baranov catch equation for multiple fleets.

Author:: Steven James Dean Martell UBC Fisheries Centre

Date:: 2011-07-12

Parameters:

ct	a vector of observed catch for each fleet.
m	the instantaneous natural mortality rate (age-independent).
V	a matrix of age-specific selectivities where each row corresponds to the fleet.
na	a vector of initial numbers or biomass (same units as the catch) at age.
wa	a vector of mean weights-at-age

Returns:: ft a vector of instantaneous fishing mortality rate for fully selected (va=1) individuals for each fishing fleet.

See also:

Definition at line 174 of file baranov.cpp.

Functions

Detailed Description

Function Documentation