The central hypothesis of agroforestry is the complementarity between crops and trees (Cannell 1996). So ideally trees and crops should use ressources at a different times (e.g. winter crops and deciduous trees in temperate regions, another interesting example is Faidherbia albida in the Sahel, a tree that sheds its leaves during the rainy season, allowing full light to reach the crops) or in different locations (e.g. deep-rooted trees with annual crops). So the important characteristics to look at are phenology and morphology, to maximize complementarity.
But other characteristics are also important, such as trees that can be pruned (to reduce light competition when needed, and/or to feed animals), trees that are able to fix nitrogen from the athmosphere, and thus fertilize crops. For crops, the most desirable trait is tolerance to shade (unfortunately, all modern cultivars have been selected for full sun conditions). For both, absence of allepopathic effect seem desirable, however this is not mandatory: walnut -a tree species known to have an allelopathic effect through the production of juglone- are often used in agroforestry.
Cannell, M. G. R., M. Van Noordwijk, et C. K. Ong. 1996. « The Central Agroforestry Hypothesis: The Trees Must Acquire Resources That the Crop Would Not Otherwise Acquire ». Agroforestry Systems 34: 27‑31. https://doi.org/10.1007/BF00129630.
