Donna Frazier wrote:

So they're hybrids? Have they (the limes) been specifically
cultivated to have no seeds? If so, why not do the same with
lemons?

There are two main types of limes which seem to predominate the
market. The best for quantity of jiuce and size of fruit are those
commonly known as 'Persian' or 'Tahiti' limes. They are old hybrids
selected and grown widely over the past 100 - 150 years and have
relatively thin rinds and moderately acid flavour.

Their 'seedless' qualities are either due to them being entirely
sterile or self-sterile. Since the only way to get the same fruit
consistently is to propagate vegetatively using grafting or cuttings.
All trees in a plantation would be clones and being closely
related.they'd be self-incompatible resulting in seedless or near
seedless fruits.

The second type which is widely grown on account of its stronger, more
acid flavour is the 'Key lime', which does have seeds. The rind is
thicker and the fruits are smaller but very freely produced. Even
seeded limes have relatively few seeds, so I doubt if 'seedlessness'
is a determining quality in the selection of a variety for growing
commercially.

There is now a seedless lemon derived from 'Eureka', which is one of
the most widely grown varieties. I seem to remember a bit of a fuss
when it first became available a few years ago. As with limes the
presence of seeds does not impair the quality of the fruit or detract
from it, so I can't see the seedless version ousting the popular
conventional varieties in the near future. I think it was Sainsbury
that first stocked it, claiming that the days of worrying about lemon
pips were now over. But really, is it that much trouble to remove a
few seeds from a lemon? There's little real advantage for the
domestic market, but I suppose there is a point when processing tons
of fruit for juice production.

When I last made lime marmalade the Limes had a few seeds

Strange. I've used about 20 limes over the past month or so
and not one had a seed in it.

Depending upon source and time of year, grocers and supermarkets will
stock either type. Because of their stronger flavour and thicker
rinds, .Key limes make a better marmelade and in my opinion, lime
marmelade is the best.