> Here, we built a spatially explicit tropical forest vulnerability index (TFVI) based on observations of forest cover, carbon, and water fluxes to identify areas where rainforests are losing resilience to disturbance and are changing toward an irreversible state, a “tipping point.”
The extended version of the paper (https://www.cell.com/one-earth/pdfExtended/S2590-3322(21)003...) has a lot more detail and math, and the underlying model is described on page 999 (13 in the PDF) under Equation 8. The model is implemented using the rlm function in R (https://www.rdocumentation.org/packages/MASS/versions/7.3-54...), which fits a linear regression model using iterated re-weighted least squares (IWLS). The input and output variables can be seen on page 1022 (35 in the PDF) in Table S1.
As an aside, I really dislike the increasing use of "tipping points" in discussions around climate change. It seems so vague and imprecise, and the claim of irreversibility seems hard to establish. In the context of this paper, if you read the extended version, it seems tipping point here is essentially long-term loss of biomass (not necessarily a climate-related outcome). Additionally, rather than irreversibility, the model they use predicts losses as a 1-month or 1-year lagged outcome based on various input stressor variables. The magnitude of the output index will need to be interpreted to determine how significant the negative outcome is (that is, the model does not actually determine an irreversible 'tipping point'). Here's the relevant text:
> The absolute magnitude of TFVI represents the risk of critical transitions that would result in abrupt decreases (negative values) or increases (positive values) of the response variable given long-term trends in the stressors. The larger the absolute value of TFVI, the greater the risk of a critical transition to either higher or lower value of the ecosystem response.