What causes about 1 in 10,000 clovers to have four instead of three leaves? Will progeny(?) grown from its flower's seeds have a higher probability than that of also having four leaves?
From the Wired article The Mysterious Genetics of the Four-Leaf Clover
A clover’s lucky fourth leaf is presumably specified in its DNA. But the clover genome is surprisingly complicated, and finding the genes responsible—and under what conditions—for the four-leaf mutation is a still-unsolved biological puzzle.
From the Wikipedia's Four-leaf clover: Cause (emphasis mine):
It is debated whether the fourth leaf is caused genetically or environmentally. Its relative rarity (1 in 10,000 clovers[ref]) suggests a possible recessive gene appearing at a low frequency. Alternatively, four-leaf clovers could be caused by somatic mutation or a developmental error of environmental causes. They could also be caused by the interaction of several genes that happen to segregate in the individual plant. It is possible all four explanations could apply to individual cases. This means that multiple four-leaf clovers could be found in the same clover plant.[citation needed] (emphasis added)
Answer
A recessive gene for four leaves has been identified (Tashiro et al., 2010). The clover is a tetraploid species and together with the fact that environmental conditions may also suppress the development of the fourth leaf, it indeed takes a lot of luck to find one. If it will bring you any is another question though.
In fact they are aiming at making a four-leaved cultivar (source: New Scientist).
Reference
- Tashiro et al., Crop Sci (2010); 50: 1260–8
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