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1. Living creatures are defined by a set of blueprints--genes--configured precisely enough to specify how a living creature grows from a single egg cell into an adult. At least tens of thousands of those genes are required to specify how an elephant sustains, grows and reproduces itself.
2. Genes are complicated molecules subject, like most complicated functional structures in this world, to spontaneous decay. A characteristic of such decay is, the great majority of the changes that make any functional difference will be harmful.
3. Occasionally, just by the laws of chance, an instance of the decay will actually be beneficial and be available to processes of evolution.
4. Genes are selected for independently one by one, so natural selection can eliminate all those that are harmful while retaining all those that are beneficial. The net result in each generation will be a net benefit.
5. As a result of each beneficial genes being selected for in every generation over many thousands of years, it will spread to become its gene’s dominant allele.
6. Once enough of these genes have accumulated they can be further selected to code for a new feature such as an elephant’s trunk.
7. Once they do, all these genes get selected together for the benefit this major new feature brings.
Did you notice “the flaw.” In case you didn’t, I point it out below
Genes are either selected for individually, or they are not. Step 7 says that once a number of mutations begin coding for something new, such as an elephant’s trunk, they get selected together without fail or else few elephants would have all the genes needed for a functional trunk. If gene selection is not random, though, then step 4 won’t work. And we know selection is not always random, that many genes are essential and "conserved"--protected from recombination etc. If those may not be mutated and selected for at random then maybe there's no purely random mutation at all.
Step 3 assumes that periods of mere millions of years are enough to guarantee the beneficial genes needed for the coding of an elephant's trunk appearing through random decay. But that is not guaranteed. No matter how great a finite number of monkeys you have typing at random, mathematicians express doubts that you would get improvements in a Shakespeare sonnet in a time less than the lifetime of the universe. So step 3 cannot be accepted without proof that the hundreds or thousands of beneficial mutations required for construction of a trunk are likely to appear within, say, 10 million years. And even if random decay of genes could generate improvements among simple creatures with few genes and no very advanced functions, wouldn’t this process slow down greatly as creatures’ genomes got more complex, and honed to greater perfection through longer periods of evolution. Yet more complex creatures seem to evolve complex new functions relatively rapidly (without horizontal gene flow, as in microbes). Evolution does not seem to be paced according to the likelihood of all the beneficial genes needed for a complex 3D-organ having to be produced by random decay of chromosomes.
Step 4 assumes natural selection is 100% efficient. Suppose each generation begins with 1000 times as many harmful as beneficial mutations entering it, and natural selection is 50% efficient. Then 500 times as many harmful as beneficial genes enter the gene pool in each generation, and extinction swiftly ensues. Yet natural selection is usually quoted as having an efficiency of from 1-3%. Step 3 isn’t just flawed, it’s purely wishful thinking, along the lines of Jack getting back down to the Earth without being caught by the giant.
Step 4 assumes that same 100% efficiency. If instead it’s nearer 1%, and in each generation there are 100 times as many progeny conceived as survive to adulthood, any slightly beneficial gene has only a slightly better than 1% chance of appearing in the next generation. You’d need 50 instances of this identical mutation occurring in one generation for one instance to survive into a second generation, with similar odds preventing its appearance for quite a few generations.
Step 5 makes demands on plausibility greater than Jack’s getting back safely home, beyond the point I made above (all the genes involved in the creation of an elephant’s truck all getting selected for together in every meiosis). Somehow, hundreds of genes have to come to collaborate to not only fashion a trunk in the adult but conspire to collaborate on every stage of its development in the embryo. How likely is that! And does the process of working on this collaboration have to wait until the last one required is generated at random and selected until it becomes the major allele at its location?
One way of the other, from the existence of elephants with trunks we know that, if the Modern Synthesis is valid, there must be in the cell sufficient engineering talent for all those beneficial mutations to be retooled so they no longer code for the benefits for which they were originally selected but now work together to code for the development of a trunk. If that much engineering talent is available, why does the cell need to wait for all the genes to be damaged at random? If they have to be damaged first why can’t it damage the required genes itself, all at once, so work of making a trunk can begin immediately? Of course the cell doesn't need the genes to be damaged first! It could work with the same genes the way they are before they got damaged. Mutation would not be required for evolution to proceed. And even if it were, natural selection doesn't have the horse-power to change a great predominance of harmful mutations to a total predominance of beneficial mutations.
Ergo, only steps 1 and 2 as not flawed. Step 3 may not in practice be true. The rest are wrong. There is precious little of the Modern Synthesis left; it is not merely flawed, it is a fairy story along the lines of Jack and Beanstalk.
Did you get that right?