Calculate a stability metric from the multivariate s-map estimated Jacobian

## Source

Ushio, M., Hsieh, Ch., Masuda, R. et al. (2018) Fluctuating interaction network and time-varying stability of a natural fish community. Nature 554, 360–363.

## Arguments

- data
Numeric matrix with time in first column and species abundances in other columns

- 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 covering `0:8` is provided.

- scale
Boolean. Should data be scaled within each window 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 third community prior to the transition
pre_simTransComms <- subset(simTransComms$community3,time < inflection_pt)
#Estimate the stability index for the third community
#(trimmed for speed)
egJI <- multiJI(data = pre_simTransComms[1:10,2:5],
winsize = 75)
```