here Pn is the frequency of an allele in a specific generation of your liking, P0 is the frequency of the original gene you are mutating, -n is the generations passed, u is the mutation rate, and e is the mathematical constant, an irrational number of a value of roughly 2.7. The formula accounts for mutations from the wild type allele to the mutant variant, and it accounts for reproduction, assuming the fitness is indiscriminate between the wild type and the new mutant. It's very useful for assessing the changing allele frequency in a population - assuming no natural selection - but when the changing allele does have an impact on fitness, you can integrate the new information in the form of a fitness coefficient (w), which takes into account for the new rate of faster or slower allelic spread into the formula following the mutation rate, u.
So, for example, suppose every 100 wild types develop with no mutant alleles, (or Aa) where out of the individuals that reproduce successfully only 80 of the aa individuals succeed in doing so. The fitness (w) of the recessive phenotype would then be 80% or 0.8. So you would put in a 0.8 at the end and this will correspondingly slow allelic spread.
The formula then becomes Pn=P0e^-nuw
Anyone can try out a calculation on a hypothetical allelic frequency change, although bear in mind mutation rates vary between organism to organism, and even gene to gene. In a human cell, the average mutation rate is something to the tune of 1 mutation in every 30 million base pairs, per generation.
As I've said in previous blog posts, a system contains information by virtue of its relation to another agent or system capable of perceiving, interpreting and responding to that information. The biological substrate he amount of information in a system is quantified by how much it reduces the uncertainty for the receiver.
The genetic algorithms in biology are implicitly part of the whole constraining process; they are informationally connected through interconnected mathematical pathways. You can take any two distinct species and chart their evolutionary relationship through the similarities in their genetic sequence. Differences vary depending on which two species in particular you select, but they all share something in common. Even between the two most distantly related groups, such as between a bacterium and a human cell, you'll find the groundwork for many similar genes and genetic sequences - which play crucial roles in cell maintenance and reproduction - has already been laid out. Genes and regions of DNA responsible for carrying out the process of DNA replication, of coding, regulating, and carrying out the process of creating proteins, are present in both taxonomic groups more or less in nearly the same DNA sequences between groupings.
The genome is suffused with self-replicating elements, known as transposons, which are regions of the gene that are highly mobile elements, often cutting themselves out of a region of the gene, or copying themselves and migrating elsewhere. One class operates by cutting and pasting itself around, with minimal duplicating activity. But in cutting in pasting itself around, it often leaves broken edges of DNA where it comes and goes, which, invariably, is going to be identified and filled by DNA polymerase and its coenzymes. Because DNA polymerase in this instance is working blind, so to speak, it has no idea what nucleotides to use to glue the broken pieces together, so it will use random ones. This chain of events gives transposons of the cutting and pasting class an innate property of causing mutations at the joining sites of wherever they go and leave.
There is second class as well - known as retrotransposons. They are more like 'copy and paste' to the transposons' 'cut and paste' - and they are a large source of new genetic information, because in their very nature they carry genetic regulation sequences responsible for making certain proteins (without which they would be inefficient self-replicators) and regulatory sequences for initiating the production of the aformentioned proteins. They copy themselves, and the translocated copy is carried about by proteins and randomly inserted at a new site on the genome. Since there is no natural selection acting on them - because they don't play a vital role in survival - the copies are free to mutate and mutate successively through generations. And with those promotion factors already in place, whatever the DNA sequence happens to mutate into will engender a new gene. If it turns into something biologically ineffectual, it will just keep mutating until its regulatory sequence is destroyed. If it mutates into something useful for the genotype/phenotype, then voila, here is the new gene. This process plays a big role in the formation of new genes.
Another mechanism of gene duplication comes from what's called 'meiotic recombination', wherein chromosome pairs adjoin to one another and transfer genes between themselves. The net gain of the genes is always zero; there are only two to work with; one per chromosomes, and generally, the recombination yields an equal count of genes between chromosomes when they are done trading. But sometimes an unequal number of genes may be traded; one chromosome may get both genes, and the other none. If the chromosome with both genes becomes a gamete that merges with another gamete to form a new lifeform, then you have a net gain of one gene for every generation following that lifeform to come.
And this is
just one aspect of it in genetics - compound it with other discoveries, with
the observation of gain of function mutations, of emergence of new traits, new
behaviours, homologies in anatomy and physiology, and so on, and there is a picture
so comprehensive that it cannot be denied by a genuine truthseeker.
More to come in Part III
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