For someone interested in breeding plants, that some plants often don't produce seeds can be a major barrier. A breeder would be limited to looking for selectable mutations, rather than using the more general mixing and segregation of genetics to increase crop diversity.
Many of our common vegetables, fruits, and landscape plants are traditionally propagated by clonal divisions. In some cases (apples, pears, etc.) the complex genetic diversity of the crop means that every seedling would produce a distinct plant. The market demands for consistent production then encourage growers to clone the plants. In other cases, the clonal tradition is enforced by the plants themselves due to their inability to produce seeds. There's also a third category of plants which have such long life-cycles that breeding projects become prohibitive.
Researchers have figured out tricks to get seed and allow breeding to be done with plants that might otherwise prefer not to.
The Trouble with Seeds (1/3): Garlic, Horseradish, Potato Onion, Walking Onion, and Banana.
The Trouble with Seeds (2/3): Pineapple, Lily of the Valley, Potato, and Sweet Potato.
The Trouble with Seeds (3/3): Babington's Leek, Crosnes, and Bur Oak.
Most of this post is an accumulation of information from other sources (in colored quotes below) about how to get seeds from these crops. I've also included my thoughts and experiences where I felt something needed to be clarified or extended.
How to get Babington's leeks (Allium ampeloprasum var. babingtonii) to set seed.
Many alliums have forms which produce clonal bulbils in the flower head along with some flowers, but generally don't produce any viable seed. Research in garlic (A. sativum) has shown that you can often get seeds to mature if you extract the bulbils from the flower head at an early stage. The bulbils seem to draw nutrients away from the flowers and cause them to age too quickly for seeds to mature. When the bulbils are removed, the few flowers then get sufficient energy to grow and mature seeds. This process will probably work for Babington's leaks, or any other allium which produces bulbils and no seeds.
How to get Crosnes (Stachys affinis) to set seed.
Many of our common vegetables, fruits, and landscape plants are traditionally propagated by clonal divisions. In some cases (apples, pears, etc.) the complex genetic diversity of the crop means that every seedling would produce a distinct plant. The market demands for consistent production then encourage growers to clone the plants. In other cases, the clonal tradition is enforced by the plants themselves due to their inability to produce seeds. There's also a third category of plants which have such long life-cycles that breeding projects become prohibitive.
Researchers have figured out tricks to get seed and allow breeding to be done with plants that might otherwise prefer not to.
The Trouble with Seeds (1/3): Garlic, Horseradish, Potato Onion, Walking Onion, and Banana.
The Trouble with Seeds (2/3): Pineapple, Lily of the Valley, Potato, and Sweet Potato.
The Trouble with Seeds (3/3): Babington's Leek, Crosnes, and Bur Oak.
How to get Babington's leeks (Allium ampeloprasum var. babingtonii) to set seed.
Many alliums have forms which produce clonal bulbils in the flower head along with some flowers, but generally don't produce any viable seed. Research in garlic (A. sativum) has shown that you can often get seeds to mature if you extract the bulbils from the flower head at an early stage. The bulbils seem to draw nutrients away from the flowers and cause them to age too quickly for seeds to mature. When the bulbils are removed, the few flowers then get sufficient energy to grow and mature seeds. This process will probably work for Babington's leaks, or any other allium which produces bulbils and no seeds.
How to get Crosnes (Stachys affinis) to set seed.
How to get Bur Oak (Quercus macrocarpus) to set seed, when very young.
Bur Oak trees can live for hundreds of years and generally don't start fruiting until they're 35+ years old. The wild trees produce very large acorns that are relatively sweet, requiring minimal processing to use as a food item. Domestication efforts could readily convert the species into a useful nut crop, but the long life cycle means it will generally have to be considered an intergenerational project.
Grafting methods are routinely used to increase fruit production or control the growth of fruit trees. Such grafting methods might also be applied to the Bur Oaks. When a host oak tree goes into bloom, the hormonal signals flowing through its sap will encourage the grafted Bur Oak to also go into bloom. There are numerous shrub oak species (Q. cornelius-mulleri, Q. dumosa, Q. durata, Q. palmeri, Q. sadleriana, Q. turbinella, Q. vaccinifolia, or Q. wislizeni) that mature much younger than the Bur Oak. One of these might be ideal as a host for grafted seedlings. The shorter life of the host oak would mean that you could plant as many as you need to host whatever number of Bur Oak seedlings you're working with. This process should shorten the 35+ year breeding cycle of the Bur Oak down to 2-3 years, making it a much more reasonable project to take on.
Most of the lovely plant diagrams in this post were derived from public-domain images hosted at botanicalillustrations.org. Some other diagrams are public-domain images from the same era that I found via google. I chose the original images which depicted the plants under discussion in the way I appreciated and then did some coloring or color correction using my favorite image editor (GIMP)