Thursday, 6 November 2008

Shannon Entropy

I've been challenged by an ID advocate in order to explain away a certain element of information theory in regard to evolution. When most people refer to entropy, it's to do with the second law of thermodynamics. But in the case of this particular person, he refers to Shannon Uncertainty - a system in information theory. Now I was very confused as to just what this had to do with evolution, but DNA is a coding sequence so maybe there needs to be some explanation for how evolution overcomes the problem of a loss of information over a long period of time.


Natural selection is a harsh mistress
Firstly, let's take the assumption that mutations are random. There's no way of knowing what mutations will happen in an individual. If there were no copying errors, there would be no modification through successive generations as our DNA is the only material that is passed down from parents to children. It's also important to note that while mutation happens on an individual level, evolution takes place in a population. All children we have will still be homosapien, it's just that given enough genetic isolation that my descendants may be unable to breed with your descendants and from there homosapien becomes two species.

Our genetic code is passed down through sexual intercourse, 50% comes from the male and 50% from the female. Each baby is born with a mixture of traits and some errors in copying. These mutations can be harmful, but most are neutral. Occasionally some can be advantageous, and the theory of evolution stipulates that these advantageous mutations would mean that descendants of that organism would be better at surviving and thus produce more future offspring, eventuating in those successful traits being passed through the whole population. So what of Shannon Uncertainty?

Let's make a hypothetical gene, call it VENTER1. Now this hypothetical gene is vital to the animal COYNORR. It contains 100 coding characters all of which need to be exact in order for Coynorr to survive. Any change to the code would mean that the baby Coynorr would not develop successfully. Without successful embryological development, the baby Coynorr would not be able to pass on the fatal mutation. So the gene while being subjected to random mutation would pass down generation after generation because any modification to that gene would stop the self-replicating process.

That was a very extreme case, what about a non-fatal hypothetical gene, we'll call this one COLLINS1. Now this gene determines the leg strength of the Coynorr, it's a creature that needs to be able to run fast in order to escape predators. While the weakened form of this gene could be passed down through generations, it giving the Coynorr a slight disadvantage against it's predator means that it's less likely to be carried on than those faster Coynorrs. Over many generations, descendants of Coynorrs that don't mutate would have more successful offspring.

So that covers the slightly negative and the severely negative, but what of positive mutations? Now take the hypothetical gene MILLER1. It has a mutation in copying that allows the individual to have a selection advantage over it's rivals. The advantageous mutated gene will become more frequent in the population over time than the same gene without mutation. The Coynorr population would over time have the superior MILLER1 gene, because any born without would be at a survival disadvantage.

And for the final mutation, a neutral mutation. What if the gene WATSON1 had a mutation that could mutate in certain ways without being detrimental? If the mutation changed the functionality but offered neither survival advantage or detriment, then there's no problem. What does it matter if a species has neutral mutations? Each one of us has hundreds of mutations in our code (it's important to remember that there's over 3 billion base pairs in our genetic code) and most of us walk around fine. Indeed some changes would have no effect at all on the organism given that some amino acids can be coded by multiple sequences. Alanine will be coded by any of GCA, GCU, GCG or GCC, Leucine can be coded by any of 6 combinations.


He's a perfect clone
The more and more I've thought about this question, the less it's made sense to me. There's really no way this could apply to evolution at all. When language is transmitted there is specified meaning. If I were to take this post and put it under a modifier, over time the meaning would get lost as mistakes creep in. This is the loss in information theory, but DNA is not specified information in the way language is. There's no one code for any particular species, and variation through generations is not only inevitable but advantageous!

Each generation any one individual passes on only half of their DNA in a child, the other half coming from their sexual partner. So in two generations, a grandparent will only have 25% of their DNA passed on and in three a great grandparent will only have 12.5% passed on. Over time there's very little chance of anything unique to you being passed on, but that doesn't matter. It's the survival of the genes that matters and we are just one transitional form.

And that we are, an intermediary carrier of genes. There's no such thing as the perfect design that is getting lost in transmission over time, a design is as good as it's ability to survive and reproduce. Species live in an ever-changing environment so variation needs to occur for successful adaptation. This is why sex is such a powerful survival strategy in the animal kingdom, it allows for a greater mix of mutations into an offspring. Species are always in evolutionary arms races, sometimes in the macroscopic world and other times in the microscopic world. Those in the old world became resistant to smallpox, but it's introduction to the new world was devastating for the indigenous population.

Mutations in our DNA is not only inevitable, but it's necessary for evolution to occur. Natural selection weeds out the negative mutations and promotes the good mutations, while over time genetic drift with population isolation leads to speciation. What's lost, what's gained, what changes over time, all these are part of the natural process of life. Life simply exists and in this brutal chaotic struggle for survival, any change that can help with that is more than welcome.

1 comment:

Intelligent Designer said...

Hi Kel,

I think you would benefit from reading Genetics for Dummies. This is the first book I read on genetics and it helped me a lot. I think you’ll like it.