a, Comparison of causal connectivity strength with location tuning correlation measured during multidirectional reaching behavior (Methods). Top, Location-tuning correlations versus causal connectivity strength. Real data (‘Data’, red); distance-preserved shuffled control distribution (‘Distance shuffled’, gray) represents shuffling of the correlation for all neurons residing in the same distance from the target neuron (Methods). Bottom, Residual tuning correlations versus causal connectivity strength. Residual tuning correlation (‘Residual’, blue) is obtained by subtracting the ‘Distance shuffled’ from ‘Data’ (top; Methods), and represents the residual relationship that remains between connection strength and correlation in location tuning, beyond what is explained by mutual distance dependency. b-c, Comparison of causal connectivity strength measured during rest, with ‘noise correlations’ (sometimes referred to as ‘functional connectivity’) and ‘residual noise correlations’ (Methods) measured for the same neurons during rest (b) or multidirectional reaching behavior (c). Top, Noise correlations versus causal connectivity strength. Noise correlations are measured during rest (b) or multidirectional reaching behavior (c), for the same neurons. Causal connectivity is measured in an independent rest session epoch. Real data (‘Data’, red); distance-preserved shuffled control distribution (‘Distance shuffled’, gray) represents shuffling of the correlation for all neurons residing in the same distance from the target neuron (Methods). Bottom, Residual noise correlations versus causal connectivity strength. Residual noise correlation (‘Residual’, blue) is obtained by subtracting the ‘Distance shuffled’ from ‘Data’ (top; Methods), and represents the residual relationship that remains between connection strength and noise correlations, beyond what is explained by mutual distance dependency. Causal connectivity could accurately predict noise correlations across states. d-e Same in b-c, but for the opposite relationship, i.e., causal connectivity strength versus noise correlations. This indicates to what extent noise correlation can predict, on average, the strength of causal connectivity in the motor cortex. Data in all panels is displayed as mean ± s.e.m. across sessions.