pimmlawton {primer} | R Documentation |
Used primarily to repeat simulations and analyses of Pimm and Lawton (1977), given a Jacobian matrix. Analyses include eigenanalysis, but also measuring average interaction strength (May 1972), average intraspecific negative density dependence, and the strength of the omnivory interaction, if present.
pimmlawton(mat, N = 1, omni.i = NA, omni.j = NA, omega = NULL)
mat |
a numerical matrix; the "maximum" Jacobian matrix. See details below. |
N |
a scalar for the number of randomizations |
omni.i |
if omnivory is present, the row/col index for the prey. |
omni.j |
if omnivory is present, the row/col index for the predator. |
omega |
if not NULL, a scalar $0<x<1$ indicating the relative weight of omniovory (after McCann et al. (1998)) |
This function simulates a constrained randomization of a Jacobian food web matrix. The matrix it uses mat
is of a special form, which assumes that all non-zero values are drawn from a uniform distribution between zero and a value of some specified magnitude, either positive or negative.
Returns a data frame, where each row corresponds to a single random Jacobian matrix, with the following columns.
DomEig |
the real part of the dominant eigenvalue |
Im |
the imaginary part of the dominant eigenvalue |
IntraDD |
average magnitude, over all species, of the intraspecific negative density dependence; the square root of the sum of the squared diagonal elements of the random Jacobian matrix |
I |
average interaction strength (after May 1972); the square root of, sum of the squared off diagonal elements divided by the number of off diagonal elements. |
I.omni |
average interaction strength for the omnivory interaction; the square root of, sum of the squared omnivory elements effect of predator on prey and prey on predator divided by two. |
Hank Stevens <HStevens@muohio.edu>
R.M. May. Stability and Complexity in Model Ecosystems, volume 6 of Monographs in Population Biology. Princeton University Press, 1973.
K. McCann, A. Hastings, and G.R. Huxel. Weak trophic interactions and the balance of nature. Nature, 395:794–798, 1998.
S.L. Pimm and J.H. Lawton. Number of trophic levels in ecological communities. Nature, 268:329–331, 1977.
M.H.H. Stevens. A Primer of Ecology with R. Use R! Series. Springer. 2009.
### A relevant style of matrix for the first food chain in Pimm and Lawton (1977). Note each non-zero element is the appropriate sign, and the maximum magnitude specified by Pimm and Lawton (1977) Aq = matrix(c( -1, -10, 0, 0, 0.1, 0, -10, 0, 0, 0.1, 0, -10, 0, 0, 0.1, 0), nrow=4, byrow=TRUE) pimmlawton(Aq, N=1) out <- pimmlawton(Aq, N=2000) out <- subset(out, -1/DomEig <150) hist(-1/out$DomEig, main="Frequencies of Return Time")