Calculate a stability metric from the s-map estimated Jacobian of a univariate time series

## 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.

## Arguments

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

- winsize
Numeric. Defines the window size of the rolling window as a percentage of the time series length.

- 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 dataframe where the first column is last time index of the window and the second column is the estimated index value. A value <1.0 indicates stability, a value >1.0 indicates instability.

## 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)
#Estimate the univariate stability index for the first species in
#the second community
egJI <- uniJI(data = pre_simTransComms[1:25,2:3],
winsize = 75, E = 3)
```