I don't think there are many experts on crucian hybrids and what follows is based on my own limited experience as well as plenty of reading. What really matters as far as this website is concerned is be able to distinguish the "true cru" from lookalikes and there is bound to be some over-simplification in what is written here. I hope that some of you will share with us photographs of doubtful looking "crucians" from which we can all learn.
(1) The crucian x common carp hybrid or "F1"
Most fishermen know about the F1, common in many commercial fisheries. It occurs naturally in the wild wherever crucians and common carp swim together but is now artificially bred on quite a large scale.
There is little danger of confusing this fish with the true crucian, because it takes after the common carp in general shape. It looks more like a rather strange common carp than a rather strange crucian. Where it first noticeably differs from the common carp is in the barbules, which are smaller than in the carp. Sometimes there are only 2, rather than 4. In small fish it is sometimes very difficult to see them at all but the body shape should be a giveaway. The second difference from the crucian lies in the number of lateral line scales, which are more numerous than in the crucian, 35 or 36 rather than the usual 32 - 34. The oblique count is usually 6, lower than the crucian's 7 or 8.
However, it's probable that many F1s are in fact goldfish x common carp hybrids, perhaps because breeders haven't always been able to distinguish between brown goldfish and crucians. In this hybrid the lateral line scales are fewer, as you would expect because a goldfish usually numbers 29 to a crucian's 32 - 34. It's difficult otherwise to tell these two hybrids apart, but - really - neither looks much like a crucian.
(2) The crucian x goldfish hybrid
When two species hybridize, the offspring take on some of the characteristics of both parents, sometimes favouring one more than the other. This means that some of these hybrids can look quite like crucians, but most don't. The variations are numerous!
Usually, the lateral line count or the oblique count will warn you that something is not quite right. In the ones I have seen, the lateral line count is usually 30 or 31, as in the photos below, occasionally 32. The oblique count (front of dorsal fin to lateral line, omitting the slotted scale) is usually 6 full scales, with one or more tiny scales at the top.
Sometimes, though, you have to rely on other signs because the scale counts are borderline. The coloration may give a clue. Usually the fish is a nondescript brown or olive or grey, quite unlike the rich and complex colouring of a crucian. If the fish is gold-ish, the patina is often over the whole fish instead of intensifying towards the cheeks and throat as in the true crucian. Again, exceptions occur!
Perhaps the lower fins are very pale rather than orange or brown. Sometimes they have darker tips, like the crucian often does. Perhaps the dorsal is straight or concave. Perhaps the pelvics and/or the caudal is longer than you would expect, hinting at goldfish ancestry.
Once you become familiar with what makes a true crucian you are unlikely to be fooled by a hybrid. I think that all of the following are cru x goldfish hybrids.
(3) Back crosses
This is a very shady area, one where you can help widen our knowledge with your own experience and photographs. A back cross is where a hybrid breeds with one or other original species - I don't think that hybrid x hybrid is very common. So you could have a crucian x carp x carp (or crucian), similarly with the goldfish hybrids. There is, however, a huge amount to learn about this and anglers' contributions could be very useful, so please send in your hybrid pics.
There is some evidence that back-cross fry are weak and seldom make it to adulthood in the wild, almost as if nature has a built-in defense mechanism against losing species. However, though you are very unlikely to meet such a specimen, it is just possible, especially in, for example, a commercial water stocked from heaven knows where.
I can offer no guidance on this because it is outside my experience but a gallery of oddities might be a good idea. If a fertile crucian x goldfish, for example, were to back-cross with a crucian it would seem likely that any surviving offspring would look quite like a true crucian. We need to investigate this, so photographs, please!
It must be possible that koi and crucians or goldfish inter-breed, possibly with similar characteristics to the F1. Are ghost carp (themselves a hybrid between koi and common carp) capable of cross-breeding with crucians and goldfish? The mind boggles! For the last three decades, fish have been moved around far more than ever before and, particularly in "commercials", all sorts of hybridization must have been inadvertently encouraged.
If you have any photographs of strange hybrids, please let's have them for the galleries.
The so-called gibel carp or silver crucian does not occur in this country as far as is known. Fish in the UK with those names have been genetically tested and found to be crucian x goldfish hybrids.