There have been quite a few threads here in the past concerning koi/goldfish hybrids, and since recently I found myself the new owner of a hybrid, I thought I would share my research into the topic.
First of all let me introduce my own young hybrid. He was sold to me as a "black comet" by a well-known vendor. I suspect the foreign wholesaler was not entirely honest with the vendor and I place no blame upon the vendor, who is well-known and has an excellent reputation. Either way, when the fish came to me I photographed it, as I generally do with new fish, and noticed while examining the photos that the fish had tiny barbels. This was my first clue. More on that later. Here is a photo first.
His name is Sygnus, by the way.

First of all, a bit about the...
Viability & Genetics of Hybrids
Koi carp (Cyprinus carpio) and goldfish (Carassius auratus) can hybridize in the average backyard fish pond, and while it is somewhat common, the hybrids are often sterile and do not reproduce themselves. In the wild, hybrids may or may not be sterile depending on the subspecies of carp involved. There are dozens of carp subspecies that may hybridize with introduced goldfish. For example:
So depending on which subspecies is involved, the hybrids can be sterile or reproduce as easily as if they were full-blooded. As documented here:
Additionally, some crosses may produce fertile hybrids of one gender but not the other. See the end of the first paragraph here:
http://www.wdc-jp.biz/pdf_store/isj/publication/pdf/16/163/16304.pdf
A bit more about the viability of hybrids between goldfish and carp subspecies here:
http://www.cababstractsplus.org/abstracts/Abstract.aspx?AcNo=20053041051
So my fish may or may not be sterile - we have yet to see.
Anyway, I wanted to figure out precisely how to identify him as a hybrid...
Identification Using Meristics
First I noticed the barbels, and so I set upon researching the meristic (physical) differences between goldfish, koi, and hybrids.
The most easily identified features include barbels, lateral line scales, and fin rays. An experienced goldfish or koi keeper will also notice body shape, mouth position, and fin shape, but these are highly variable between individuals and can't really be counted on for a solid ID. The best way is to use the shape and number of the pharyngeal teeth, those bony ridges in the jaws that help to grind up food. However, it's impossible to use those unless you kill the fish. So understandably, I wanted something a little less... uh, lethal.
Lateral line scale count is one of the more reliable ways to ID a hybrid.
Sygnus has 33 lateral line scales and 20 dorsal fin rays. He fits right into the hybrid range - on the low end for koi, too many for goldfish.
Another marker is the presence of barbels. Koi have two pairs of barbels - one set just up and back from the mouth, another at the corners of the mouth.
See here for photos: http://www.koiquest.co.uk/Anatomy.htm
Goldfish have no barbels whatsoever, and hybrids either show no barbels or only one set, very small, at the corners of the mouth.
Sygnus has one set of "reduced posterior" barbels, just visible against the rock here:

You can see more photos of possible hybrids with similar small barbels here:
http://www.koiphen.com/forums/showpost.php?p=1442380&postcount=5
You will also notice them in this fish: http://www.tnfish.org/PhotoGalleryF...bridCommonCarpGoldfishMeltonHillNegus_jpg.htm
As I mentioned earlier, an experienced keeper will immediately be able to differentiate between a koi and goldfish by body shape, mouth position and fin shape. These were the first features that tipped me off to the possibility that Sygnus was a hybrid. These are, of course, only to be used as...
Informal Identification Keys
Notice the differences in shape between him and one of the midnight shubunkins:

Right away you should see that the hybrid has a much flatter belly line than the shubunkin's, which curves upward. The hybrid's mouth is set at the bottom of his head, while the shub's is midway between the bottom and top. The hybrid has round fins, the shub has pointed fins. This fin difference is even obvious between the hybrid and my common goldfish.
Here you can see more details:

See the rounded fins? Also notice those sensory nubs around the eyes - koi have them, goldfish do not. They are visible on the photo of koi eyes at the anatomy page I referenced earlier. I have seen them on some hybrids, but others do not have them. It may be another difference between subspecies hybrids.
Other features that stand out to me were the thick, strong caudal peduncle - the muscle that connects his caudal (tail) fin to his body. Notice how much more muscled it is than that of the goldfish. The top photo shows this well. Also the lack of a V-shaped tail. The hybrid has a nearly solid triangle for a tail fin.
In this photo you can just barely make out a very subtle hump between the end of his head and his dorsal fin. This hump may become more prominent as he grows older and larger. Some goldfish will develop a hump like this, and you will see it in many large koi. It seems to be a common characteristic among domestic hybrids.
This website has dozens of photos of domestic hybrids: http://www.shortypen.com/koi/hybrid/index.htm
This is a very quick and dirty look at hybrids and how to identify them, but you can find much more information by exploring the links I provided. Questions and comments are welcome!
First of all let me introduce my own young hybrid. He was sold to me as a "black comet" by a well-known vendor. I suspect the foreign wholesaler was not entirely honest with the vendor and I place no blame upon the vendor, who is well-known and has an excellent reputation. Either way, when the fish came to me I photographed it, as I generally do with new fish, and noticed while examining the photos that the fish had tiny barbels. This was my first clue. More on that later. Here is a photo first.
His name is Sygnus, by the way.

First of all, a bit about the...
Viability & Genetics of Hybrids
Koi carp (Cyprinus carpio) and goldfish (Carassius auratus) can hybridize in the average backyard fish pond, and while it is somewhat common, the hybrids are often sterile and do not reproduce themselves. In the wild, hybrids may or may not be sterile depending on the subspecies of carp involved. There are dozens of carp subspecies that may hybridize with introduced goldfish. For example:
Natural hybrids of the wild Common Carp and the Crucian Carp are often found where the two species co-occur (Banarescu, 1964; Berg, 1964; Lin and Peter, 1991; see appendix B for meristics). The Common Carp naturally hybridizes with Goldfish both in native regions, such as Romania (Banarescu, 1964) and the Czech Republic (Prokes and Barus, 1996) and where they are introduced, such as Canada (Taylor and Mahon, 1977), Australia (Hume and others, 1983), and Ohio (Trautman, 1981). Meristics for Common Carp X Goldfish hybrids are given in appendix B. Common Carp has been artificially hybridized with Grass Carp (Makeyeva and Verigin, 1974a; Stanley and Jones, 1976; Avault and Merowsky, 1978), Bighead Carp (Makeyeva, 1968, 1972; Verigin and Makeeva, 1974), Silver Carp (Makeyeva, 1968; Makeyeva and Verigin, 1974b), and Tench (Victorovsky, 1966).
Source: http://fisc.er.usgs.gov/Carp_ID/html/cyprinus_carpio.html
So depending on which subspecies is involved, the hybrids can be sterile or reproduce as easily as if they were full-blooded. As documented here:
The specific conditions which lead to hybridisation are unclear, but mtDNA sequence data indicate that either species can act as the female parent. The hybrids all appeared to be first- generation crosses with simple combinations of carp and goldfish alleles in both this and the previous study (Pullan & Smith 1987). Chromosomal studies of carp–goldfish hybrids in Russia found the hybrids to be triploids (Zelinskij et al. 1992), and by implication the hybrids would be sterile. However, Hume et al. (1983) reported spent male and female carp–goldfish hybrids in Victoria, Australia, indicating that hybrids are reproductively active, although this does not necessarily mean that eggs or sperms or any offspring are viable.
Source: http://www.doc.govt.nz/upload/documents/science-and-technical/drds219.pdf
Additionally, some crosses may produce fertile hybrids of one gender but not the other. See the end of the first paragraph here:
http://www.wdc-jp.biz/pdf_store/isj/publication/pdf/16/163/16304.pdf
A bit more about the viability of hybrids between goldfish and carp subspecies here:
http://www.cababstractsplus.org/abstracts/Abstract.aspx?AcNo=20053041051
So my fish may or may not be sterile - we have yet to see.
Anyway, I wanted to figure out precisely how to identify him as a hybrid...
Identification Using Meristics
First I noticed the barbels, and so I set upon researching the meristic (physical) differences between goldfish, koi, and hybrids.
The most easily identified features include barbels, lateral line scales, and fin rays. An experienced goldfish or koi keeper will also notice body shape, mouth position, and fin shape, but these are highly variable between individuals and can't really be counted on for a solid ID. The best way is to use the shape and number of the pharyngeal teeth, those bony ridges in the jaws that help to grind up food. However, it's impossible to use those unless you kill the fish. So understandably, I wanted something a little less... uh, lethal.
Lateral line scale count is one of the more reliable ways to ID a hybrid.
The meristics are different between common carp, including koi (Cyprinus carpio) and gibbel carp, including goldfish (Carassius auratus). Paraphrased from Fishes of Tennessee: Typical common carp have 32-41 lateral line scales and 15-23 dorsal fin soft rays. Typical goldfish have 25-31 lateral line scales and 15-18 dorsal fin soft rays.
Source: http://forum.nanfa.org/index.php?s=&showtopic=6877&view=findpost&p=52788
Sygnus has 33 lateral line scales and 20 dorsal fin rays. He fits right into the hybrid range - on the low end for koi, too many for goldfish.
Another marker is the presence of barbels. Koi have two pairs of barbels - one set just up and back from the mouth, another at the corners of the mouth.
See here for photos: http://www.koiquest.co.uk/Anatomy.htm
Goldfish have no barbels whatsoever, and hybrids either show no barbels or only one set, very small, at the corners of the mouth.
The hybrids were intermediate between koi and goldfish for the number of lateral line scales, the shape of the pharyn-geal teeth, and the presence of a pair of reduced posterior barbels.
Source: http://www.royalsociety.org.nz/site/publish/journals/nzjmfr/1987/5.aspx
Sygnus has one set of "reduced posterior" barbels, just visible against the rock here:

You can see more photos of possible hybrids with similar small barbels here:
http://www.koiphen.com/forums/showpost.php?p=1442380&postcount=5
You will also notice them in this fish: http://www.tnfish.org/PhotoGalleryF...bridCommonCarpGoldfishMeltonHillNegus_jpg.htm
As I mentioned earlier, an experienced keeper will immediately be able to differentiate between a koi and goldfish by body shape, mouth position and fin shape. These were the first features that tipped me off to the possibility that Sygnus was a hybrid. These are, of course, only to be used as...
Informal Identification Keys
Notice the differences in shape between him and one of the midnight shubunkins:


Right away you should see that the hybrid has a much flatter belly line than the shubunkin's, which curves upward. The hybrid's mouth is set at the bottom of his head, while the shub's is midway between the bottom and top. The hybrid has round fins, the shub has pointed fins. This fin difference is even obvious between the hybrid and my common goldfish.
Here you can see more details:

See the rounded fins? Also notice those sensory nubs around the eyes - koi have them, goldfish do not. They are visible on the photo of koi eyes at the anatomy page I referenced earlier. I have seen them on some hybrids, but others do not have them. It may be another difference between subspecies hybrids.
Other features that stand out to me were the thick, strong caudal peduncle - the muscle that connects his caudal (tail) fin to his body. Notice how much more muscled it is than that of the goldfish. The top photo shows this well. Also the lack of a V-shaped tail. The hybrid has a nearly solid triangle for a tail fin.
In this photo you can just barely make out a very subtle hump between the end of his head and his dorsal fin. This hump may become more prominent as he grows older and larger. Some goldfish will develop a hump like this, and you will see it in many large koi. It seems to be a common characteristic among domestic hybrids.
This website has dozens of photos of domestic hybrids: http://www.shortypen.com/koi/hybrid/index.htm
This is a very quick and dirty look at hybrids and how to identify them, but you can find much more information by exploring the links I provided. Questions and comments are welcome!
