Extended Data Fig. 1: Graphical model associated with VAR(1) estimation.

\({L}_{t}\) is IID stimulation at time step t, effect on source population is immediate and mediated by linear transformation \({W}_{l,x}\). Effect of \({X}_{t-1}\) on \({X}_{t}\) and \({Y}_{t}\) (target, unstimulated population) is mediated respectively by linear transformation \({W}_{x}\) and \({W}_{x,y}\). Interacting unobserved confounds can add arbitrary correlated noise (\({Z}_{t}\)).