http://www.nytimes.com/2009/11/10/science/10qna.html

Q & A
Seedy Lives of Citrus
By C. CLAIBORNE RAY
Published: November 9, 2009

Q. Lemons have lots of seeds, and most oranges, too. But I’ve never encountered a seed in a lime. Why?
A. The Tahiti or Persian lime you usually buy is a species that does not have seeds “because it is what we call a triploid,” said Fred G. Gmitter Jr., professor of citrus genetics and breeding at the University of Florida. It has a number of chromosomes that does not neatly divide in two for the purposes of sexual propagation and seed-making.

Most citrus fruits are diploid, Dr. Gmitter said. That is, their chromosomes come in pairs, like those of humans, which have 46 chromosomes, so that each offspring gets 23 from the mother and 23 from the father.

In citrus fruits, there are usually 18 chromosomes from the pollen parent and 18 from the seed parent, Dr. Gmitter said. What we know as the Key lime, Mexican lime or West Indian lime is diploid and has seeds.

But some kinds of plants, including the seedless lime, have a number of chromosomes that cannot divide exactly in half, but come in groups of threes, like 27. “This leads to confusion in the process of making pollen and eggs,” Dr. Gmitter said, “so they are sterile.”

The seedless lime is a naturally occurring spontaneous mutation. There are also seedless watermelons and of course the banana, Dr. Gmitter said. In fact, he said, citrus breeding programs are working hard to develop seedless triploid lemons.