While it's not my area of expertise and I may be wrong in my thinking, but I think some of the confusion may be from your use of terms. Hybrids are not genetically engineered and hybrid animals have been around long before the field of genetic engineering ever began.
For example, you might take the pollen from a red rose bush and use it to fertilize a white rose bush in an effort to create a pink hybrid. You may even take two completely different species of plants and cross fertilize them to form a new species. But this is not genetic engineering.
In both cases, the fertilization process still depends entirely on nature. You are taking the complete and unaltered genetic material from one living organism and giving it the opportunity to fertilize another organism. This will only take place if the two organisms are already very closely related.
You wouldn't be able to perform this procedure on a palm tree and a daisy.
In the animal kingdom, I think it's the horse being mated to a mule that produces a donkey. When dealing with hybrids such as this, they are closely related enough to produce offspring, but are usually too different for that offspring to be able to reproduce. The resulting hybrid is sterile.
Hybrids require that the two organisms share enough genetic information for a successful mating. An organism that has twenty four base gene pairs could never be bred to an organism with sixteen base gene pairs.
In genetic engineering, there is no such restriction. Instead of taking the complete gene code of one organism and mating it to the complete gene code of another, you literally split the gene apart, remove whatever you want, and insert the genetic code you want. That code can come from whatever organism you choose regardless of how closely related they may be.
That doesn't mean that the result will be a viable organism, but it is certainly possible where standard hybrid techniques wouldn't have a chance.
You can also combine genetic material from several different organisms in ways that they have never been combined before in nature.
Again I may be wrong, but I believe you can get a patent on a genetically engineered organism where you can't on a hybrid.
There are dangers regardless of which technique you use. For instance, I believe the Africanized killer bees were created through standard hybrid techniques. But standard hybrid techniques have the advantage of dealing with many more known quantities.
When cross breeding a horse and a mule, you know the result will have the characteristics of one or both of the parent animals but it won't sprout wings and fly away! True hybrids still carry the traits that evolution has built in to the parent organisms. Evolution has provided for their survival (or their lack of ability to survive) as well as providing the rest of it's creatures a defense against these traits.
In the case of the Africanized killer bees, they are no more dangerous than the original African bees that the honey bees were bred with.
With genetic engineering, there is no such test of time.
Mapping the complete gene code of even a simple organism could take a life time. While we are learning a great deal about the genetic makeup of humans, we are still a very long way off from knowing the purpose of every gene that makes us who and what we are.
Gene splicing requires taking a known gene sequence from one organism and inserting it into the proper place in another organism. But not all gene structures are known or fully understood. The result could be a new organism with totally unknown and never before seen traits.
And the technology for gene splicing is not that complicated. It only requires a little knowledge and some simple chemicals. A college kid fooling around in his basement could very easily create the next plague.
But there is also the possibility for tremendous benefit from genetic engineering. Gene therapy could prove to be the next big breakthrough in medicine. Not the least of which could be the eradication of cancer.
Like most things in life, genetic engineering is neither good or evil. It is simply knowledge. If we choose to use that knowledge and/or how we use that knowledge will ultimately be a reflection on us and not on the technology itself.
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