I have very big trees in my garden that covers 85% of the sunlight. I'm in Asia with temperatures around 30 °C. It's dry most of the year and the soil is pretty hard.
What food crops should I plant under the shelter?
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If you check the area where you want to plant, you will be able to see what plants are already growing in these conditions, and that will inform you as to what sort of plants you might be able to grow.
But generally, in low light conditions, you need to plant things for their edible leaves, and roots. And you'll need access to water.
There are fruiting/flowering plants that thrive in the shade but to make flowers and fruit you gotta have sun. Blueberries for example will thrive in partial shade and have some flower/fruit. In the sun, you'd get considerably more lush growth and berries from the same plants. Strawberries if they get a few hours of decent light per day might produce a few berries. Less light means fewer flowers which means fewer pollinators and fewer fruits/nuts/seeds.
In the shade the plant can't support the extra vegetative growth as photosynthesis is hampered, the growth becomes thinner and larger trying to get enough sun to compensate. Even if the plant is able to thrive in low light conditions it doesn't mean there is enough energy to make flowers and fruit.
I'd focus on the sunniest, best soil to produce a garden. The soil beneath large trees is chemically starved as the tree has sequestered the necessary chemicals within its own foliage and roots. All forests and virgin environments exhibit this soil depletion. All the chemicals that need replenishing within the plant are all tied up in the plant material. Until death of leaves, branches, fruit releases these chemicals back to the soil. Only to be sucked up or utilized immediately.
Cultivated vegetable plants like tomatoes, peas, beans...might not produce a single fruit. The soil beneath mature trees is thin, depleted as well combined with poor light, energy sources. Piling soil on top of the surface of the soil beneath your tree will compromise your tree unnecessarily. You'd have to install weather proof grow lights. You would have better luck growing vegetables in pots on a sunny porch! And more fun...Plant leafy plants with leafy plants that need and do well with higher Nitrogen. Grasses (orange sedge) mixed with Rainbow chard, Ipomoea (sweet potato vine) chartreuse and/or purple black, cabbages, kale! Butternut lettuce would be excellent as a beautiful grouping with similar needs (water, sun, fert). Grouping and making sure the pots are similar make more space available in 3-D. Another grouping type; blueberry shrub, strawberries, any color of potato (love more acidic soil)...see what I mean?