uni_smap_jacobian {EWSmethods}

S-map Inferred Jacobian

Description

Performs the S-map on a univariate time series to infer the Jacobian matrix at different points in time across thetas.

Usage

uni_smap_jacobian(data, theta_seq = NULL, E = 1, tau = NULL, scale = TRUE)

Arguments

data

Numeric matrix with time in first column and species abundance in the second

theta_seq

Numeric vector of thetas (nonlinear tuning parameters) to estimate the Jacobian over. If 'NULL', a default sequence is provided.

E

Numeric. The embedding dimension. Is suggested to be positive.

tau

Numeric. The time-delay offset to use for time delay embedding. Suggested to be positive here, but if not provided, is set to 10% the length of the time series.

scale

Boolean. Should data be scaled prior to estimating the Jacobian.

Value

A list containing three objects:

smap_J

Jacobian matrices across taus. It is recommended to average across these matrices.

eigenJ

Absolute maximum eigenvalue.

reJ

Real component of dominant eigenvalue

imJ

Imaginary component of dominant eigenvalue.

Source

Grziwotz, F., Chang, C.-W., Dakos, V., van Nes, E.H., Schwarzländer, M., Kamps, O., et al. (2023). Anticipating the occurrence and type of critical transitions. Science Advances, 9.

Examples

#Load the multivariate simulated
#dataset `simTransComms`

data("simTransComms")

#Subset the second community prior to the transition

pre_simTransComms <- subset(simTransComms$community2,time < inflection_pt)
winsize <- round(dim(pre_simTransComms)[1] * 50/100)

#Estimate the Jacobian for the first 50 timepoints of the
#second species using s-map
est_jac <- uni_smap_jacobian(pre_simTransComms[1:50,2:3])