We develop a general data-driven methodology that yields network representations of agricultural flows pertaining to the spread of invasive species. The methodology synthesizes sparse, diverse, noisy and incomplete data that is typically available to build realistic spatiotemporal network representations. We illustrate the methodology by modeling the seasonal flow of the tomato crop in Nepal between major domestic markets. Through dynamical analysis of the network, we study its role in the spread of a major pest of tomato, Tuta absoluta, an emerging outbreak in this country. In the absence of high-resolution pest distribution data, we apply a novel ranking-based inference approach to establish that tomato trade is a driving factor in the rapid spread of this pest.