  Increasing cultivated lands, crop homogenization and global food trade have
fostered the spread of crop pests and diseases. Optimizing crop protection is
urgently needed to ensure food safety. One aspect of crop protection is
surveillance, which focuses on the early detection of a parasite, and control,
aiming to fight and possibly eradicate it. Network theory has been widely used
to model the spread of human and animal infectious diseases in systems
described through nodes and edges. It has been successfully used to optimize
monitoring and immunization campaigns. In crop protection, there is a growing
literature using this theory to describe parasites spread and to conceive
protection strategies. Here we review the use of network theory in crop
protection, from the more descriptive to the more applied approaches aimed to
optimize crop protection. We retrace the logical process that has led
epidemiological models to rely on network theory, and we provide examples of
how the spread of crop parasites has been represented via a network
description. We define the objectives of surveillance and control, and we show
how these have been declined in the network-based epidemiological sphere and
then adapted in the agricultural context. We eventually discuss the discrepancy
between the application of network theory in surveillance and control to
identify culprits and solutions. We find that: i) scientists have successfully
interpreted very different modes of parasitic transmission under the lens of
network theory; ii) while network-based surveillance has progressively
clarified its objectives and sound tools have been proposed, network-based
control has been less studied and applied; iii) network-thinking must address
how to properly define edges and nodes at different geographic scale to broad
its application in crop protection.
