Heirloom varieties of plants are historical varieties that are not used in commercial agriculture. Typically, they are defined as plant varieties that existed before 1951, when commercial hybridization began. These tend to be sources of genetic diversity, having been left to their own devices and allowed to freely pollinate for long periods of time.
If you have a garden, pick a vegetable you were going to plant anyway, but just try to find an heirloom variety. You could try to plant a few different plants as heirlooms and compare them to the standard varieties you were going to buy.
Try to find seeds or cuttings or starts locally. Go to your local nursery and ask if they have any heirloom plants. If you get ones that have been grown in your region for a while, they will likely grow very well for you because they have evolved to work well in that area.
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