Extended Data Fig. 1: Directed Acyclic Graphs.

Directed Acyclic Graphs (DAGS) allow us to determine the minimal set of covariates in order to estimate the effect of a given variable. DAGS provide a visual representation of cause-and-effects relationships of the processes that generate the data. Specifically, The arrows indicate causal relationships assumed to be occurring. DAGs allow us to determine which variables are needed in a model by identifying possible colliding variables (that is, those we do not want to include), and the minimal set of covariates that are needed to eliminate confounding. This allows to reduce over-controlling. First we define the DAG for all the variables of interest (A.). Then for three variables (Pesticide use, Animal pollinated agriculture, and Honey Bees), we evaluate which variables allow us to estimate each effect. To estimate the effect of Pesticide Use (B.) we need to include Animal pollinated agriculture and Honey Bees in the model. To estimate the effect of Animal Pollinated Agriculture on wild bee occupancy (C.) we need to include climate in the model. Finally, To estimate the effect of Honey Bees (D.) we need to include Animal pollinated agriculture in the model. “Including” a variable here means adding a covariate for that variable to the equation for occupancy in our statistical models.