You are correct, you wouldn't get a duck randomly mutated from a beaver. You'd just get a more duck-like beaver. The changes to the genetic code would rarely ever be disruptive, just divergent. Large changes to the code would probably produce only non-viable fetuses uncompatable with the mother host.
In the beginning...there was nothing...Chuck Norris roundhouse kicked nothing in the face and told it to get a job. And thus, the universe was created.
"I believe that only scientists can understand the universe. It is not so much that I have confidence in scientists being right, but that I have so much in nonscientists being wrong." - Isaac Asimov
Here is the difference between dogma and axiom. While axiom in science is accepted as the root of a theory, its power is confined within the context of that theory. Therefore axioms are subject to an author's objective. Their validity must be established as a posteriori. Axiom are relative and debatable. Dogma in religions are fixed and absolute. There is no debate, no deductive reasoning. They are considered as facts by the religious mass. Virgin Mary gave birth as a virgin, end of discussion. To challenge this dogma is blasphemous. Newton and Einstein both came up with a theory for gravity. Their theory are both sound, the difference is that Einstein introduced spacetime as an additional axiom. Therefore his version is considered more advanced. Einstein's axiom was test and verified by empirical experiments (and commercial product such as GPS). Even so, if anyone comes up with a better theory with different set of axioms, it will be embraced by science. Science is meant to evolve. Dogma is very different in this regard. Using Christianity as an example, the bible writers were long gone. How can it adepts with the ever-changing world? Who has the authority to instill new dogma into the mass? Who is responsible to ensure new dogma are sound? Base on what criteria. This is a tricky a risky business. The fundamental issue is that outside of the spiritual world, religion is out of its element. Facts and evidences matter in the physical world, religion offers nothing to physics, chemistry, biology, medicine, geology, astronomy. There is only so much to learn from a non-growing source of information. Being fancy with metaphors and translation is just stretching it.
Population growth I think is both a religion AND science thing. Is it population growth? Or decline of death? The more lives you save, the more people there will be living. You can go back to 1600-1800 and let plagues wipe out people, lower live expectancy down 20 years. No more growing old into your 80's. You either gotta let people die quickly, sterilize people, or forcefully have China-type 1 child laws. I think developed nations can figure it out or are already figuring it out already without the forcefulness. Its the lesser developing nations that are the ones clinging to their religions in place of science and logic. They're extending their lives and have less infant deaths with advanced medicines. (But see, Uganda people still have a lower carbon footprint, so its Americans that need to die off...) Who do you say should and shouldnt have children? Practicality will be hard to come by Capitalism, free market and technological advancement together has a negative effect like that. All advancements that makes live easier, better and longer are heavily marketed at consumers. Industries want maximum influence and maximum financial gain, and it doesn't think ahead to see if it SHOULD be offered. Big industries crammed all this crap down the people's throat, and now there's guilting the people for their over-consumption. That rings hollow to me. The best desired outcome early 20th century would be if people bought EVEN MORE of what they already bought. 4 times more cars, more medicine, more plastics, more more everything. While they dump their own factory waste into rivers. While an educated consumer base is highly optimal, big industries want the power and they WANT to be seen as the experts. They want people to be easily manipulated "sheeple". And now all along the sheeple just "should have known" the errors of their ways. I say "they" put us into this mess, so "they" need to put us out. We all hitched a ride onto the technology crazy train for worse and better.
Book review from The Guardian (many others online): http://www.guardian.co.uk/science/2010/sep/12/the-grand-design-stephen-hawking