When a hybridizer crosses a diploid with a diploid they can only assume that all the seedlings are diploids. When they cross a tetraploid with a tetraploid they can only assume that all the seedlings are tetraploids.
Unfortunately, in diploids very rarely a triploid seedling will be produced usually because of 'accidents' during the development of the male and female gametes (pollen and ovules).
In tetraploids there often are more 'accidents' than in diploids during gamete production. A standard tetraploid daylily would have 4 chromosomes for each of 11 sets or 44 chromosomes in total (4 of chromosome A, 4 of chromosome B, and so on to 4 of chromosome J, and 4 of chromosome K). The gametes, for example the pollen would have 2 chromosomes of each of the 11 sets or 22 in total (2 of chromosome A, and so on to 2 of chromosome K).
Unfortunately, due to errors a tetraploid's gametes might not have the correct number of chromosomes (that is, 22) but might have 23, or 24 or 25 or 26 and so on or might have 16, 17, 18, 19, 20, or 21 and so on. A gamete that has 23 chromosomes might have an extra A chromosome or an extra chromosome of any one of the other 10 sets of chromosomes. When two tetraploids are crossed a pollen grain with 17 chromosomes might join an ovule with 16 chromosomes to produce a seedling with 33 chromosomes (a triploid). But those chromosomes might or might not be three of each of the 11 sets. They might be three of some sets, two of other sets and four of some sets.
There is also another way that triploids can be produced by both diploids and tetraploids. Although natural pollinations do not occur extremely frequently in daylilies they do sometimes happen. Natural pollinations happen often in some cultivars (for example Stella de Oro) and less frequently in others. Hand pollinations made by the hybridizer are normally diploid with diploids and tetraploids with tetraploids but natural pollinations may also be diploid x tetraploid or tetraploid x diploid. Rarely those cross-ploidy natural pollinations will be successful and produce a triploid seedling. And even more rarely a triploid seedling might be registered as a diploid or as a tetraploid.
Sometimes a cultivar is purchased that is mislabelled and that is not only a different name but involves a different ploidy. If the misidentified cultivar is used in hybridizing then all the crosses will be with a different ploidy even though the hybridizer believes them to be with the same ploidy. Any seedlings that are produced are likely to be triploids (excepting those from natural pollinations accidentally of the correct ploidy).
The only way to be certain that a seedling is a triploid (or is any other ploidy) is by measuring the amount of its DNA or by counting its chromosomes.
There are a surprising number of different triploid daylilies that have been collected in natural populations in Asia where there are no tetraploid species to help increase the proportion. Although infrequent they do not seem to be extremely rare so they can be expected to occur in hybridizing gardens.
Surely it is possible to find out why some cultivars are recorded as both tetraploid and triploid in the ATP database?
