Extended Data Fig. 6: Implementing Structured Causal Modeling (SCM) of Amazon forest drought response using Directed acyclic graphs (DAGs).

a–d, Development of a Directed acyclic graph (DAG) representing the structure of factors influencing tropical forest responses to drought. (a) Initially hypothesized DAG characterizing the causal relationships among climatic, environmental, and forest variables (measured variables depicted as blue nodes, unmeasured rooting depth is depicted in grey) leading to forest drought response (other colour node), with arrows representing the hypothesized causal links. (b) DAG-data consistency tests for initial DAG, with the largest 20 approximated non-linear correlation coefficients (estimated via root mean square error of approximation, RMSEA) between unlinked variables in (a). (Note: unlinked variables in a DAG are hypothesized to have zero correlation or zero conditional correlation; thus, the second row of panel b tests “DR_ | | _DSL | DL” -- whether DR is independent of DSL conditioned on DL, by estimating the non-linear correlation between DR and the residuals of DSL regressed on DL.) Correlations greater than an acceptability threshold (dashed vertical lines at ±0.30) fail the test of conditional independence, addressed by adding to the DAG either a direct causal link (indicated by a green symbol), or links to a common cause (pink symbol) (such added arrows are included in panel c). (c) Final DAG after correcting for conditional independency inconsistencies of the initial DAG in A, in light of ecological considerations. Also illustrates use of the backdoor criterion to determine the causal effect of ‘drought length (DL)’ (the exposed predictor node and associated forward causal paths, in green) on forest drought response (corresponding to the model in Extended Data Fig. 10c), while blocking the confounding variable dry season length, DSL (hypothesized to itself affect DL) and its associated causal backdoor paths (which are considered non-causal paths with respect to the exposed variable DL) (in pink). (d) DAG-Data consistency tests for final DAG (panel c), showing the largest 20 RMSEA values. (e)-(j): GAM regression model predictions (±95% CI shaded region) of causal effects of different variables derived from DAG, employing backdoor criterion, for the Southern Amazon, average across all three droughts: (e) of HAND (no backdoor to be blocked) (f) of PAR (adjusting for back door paths through drought length, dry season length) (g) of Drought length (adjusting for back door path through dry season length) on EVI responses (adjusted EVI prediction); the whole Amazon basin during the 2015 drought: (h) of forest height, categorized by shallow (blue, HAND = 0-10 m) and deep (red, HAND = 20–40 m) water tables (adjusting for back door paths through soil fertility, soil texture and dry season length), (i) of soil fertility (adjusting for back door path through dry season length) (j) of soil texture (no backdoor path to be blocked).