QPmat: Build a projection matrix from a time series of individuals...

In popbio: Construction and Analysis of Matrix Population Models

Description

This function builds one projection matrix from a time series of number (or densities) of individuals per stage (size classes or life stages) using Wood's quadratic programming method. The matrix model also requires a constraint matrix C, vector b, and vector listing nonzero elements of desired projection matrix.

Usage

QPmat(nout, C, b, nonzero)

Arguments

nout	A time series of population vectors
C	C constraint matrix
b	b vector
nonzero	indices of the non-zero elements of the transition matrix (counting by column)

Value

A projection matrix.

Note

This function required solve.QP in the 'quadprog' package , which should be installed and loaded on the user's system.

Author(s)

Original Matlab code in Caswell (2001: 148). Adapted to R by Patrick Nantel

Source

converted Matlab code from Example 6.3 in Caswell (2001)

References

Caswell, H. 2001. Matrix population models. Construction, Analysis and interpretation. 2nd ed. Sinauer, Sunderland, Massachusetts.

Examples

## Not run: 
data(nematode)
## list nonzero elements
nonzero <- c( 1, 2, 5, 6, 7, 9)
## create C matrix
C <- rbind(diag(-1,6), c(1,1,0,0,0,0), c(0,0,1,1,0,0), c(0,0,0,0,0,1))
## calculate b (transpose is not necessary - either way works)
b <- apply(C, 1, max)
QPmat(nematode, C,b,nonzero)

## End(Not run)

Example output

                 J2     J3+J4      adult
J2    -3.555068e-33 0.0000000 0.01423089
J3+J4  1.000000e+00 0.4613452 0.00000000
adult  0.000000e+00 0.5386548 0.96643504

popbio documentation built on May 4, 2018, 1:04 a.m.