conv_mov: Calculate movement matrix for all age classes

In multiSA: Multi-Stock Assessment

Calculate movement matrix for all age classes

Description

Movement matrices are calculated for all age classes from a base matrix and a gravity model formulation (Carruthers et al. 2016).

Usage

conv_mov(x, g, v, na = dim(x)[1], nr = dim(x)[2], aref = ceiling(0.5 * na))

Arguments

x	Base log-movement parameters. See details. Array ⁠[a, r, r]⁠
g	Gravity model attractivity term. Tendency to move to region r. Matrix ⁠[a, r]⁠
v	Gravity model viscosity term. Tendency to stay in same region. Vector by a
na	Integer, number of ages
nr	Integer, number of regions
aref	Integer, reference age class

Details

Rows index region of origin and columns denote region of destination.

In log space, the movement matrix m_a for age class a from region r to r' is the sum of base matrix x and gravity matrix G:

m_{a,r,r'} = x_{a,r,r'} + G_{a,r,r'}

To essentially exclude movement from r to r', set x_{a,r,r'} = -1000.

Gravity matrix G includes an attractivity term g and viscosity term v:

G_{a,r,r'} = \begin{cases} g'_{a,r'} + v_a \quad & r = r'\\ g'_{a,r'} \quad & \textrm{otherwise} \end{cases}

Vector g' are offset terms relative to the value for the reference age class:

g'_{a,r'} = \begin{cases} g_{a,r} \quad & a = a_{ref}\\ g_{a,r} + g_{a=aref,r} \quad & \textrm{otherwise} \end{cases}

The movement matrix in normal space is obtained by the softmax transformation:

M_{a,r,r'} = \dfrac{\exp(m_{a,r,r'})}{\sum_{r'}\exp(m_{a,r,r'})}

If x and v are zero, then the movement matrix simply distributes the total stock abundance into the various regions as specified in g'.

Value

Movement array ⁠[a, r, r]⁠

References

Carruthers, T.R., et al. 2015. Modelling age-dependent movement: an application to red and gag groupers in the Gulf of Mexico. CJFAS 72: 1159-1176. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1139/cjfas-2014-0471")}

multiSA documentation built on March 21, 2026, 1:06 a.m.