Replication across space and time must be weak in the social and environmental sciences

Replicability takes on special meaning when researching phenomena that are embedded in space and time, including phenomena distributed on the surface and near surface of the Earth. Two principles, spatial dependence and spatial heterogeneity, are generally characteristic of such phenomena. Various practices have evolved in dealing with spatial heterogeneity, including the use of place-based models. We review the rapidly emerging applications of artificial intelligence to phenomena distributed in space and time and speculate on how the principle of spatial heterogeneity might be addressed. We introduce a concept of weak replicability and discuss possible approaches to its measurement.