Tell you what. You explain how evolutionary biology accounts for the 1.4 x 10exp-542 probability for the assembly of a small, 900 base-pair human gene, multiplied by 23,000 (the approximate number of genes in the human body, and I'll see what I can come back with-- iff you only answer with your own arguments, not by telling me to read Dawkins, etc. Likewise, no hand-waving Baynesian probability references, unless you do the mathematics.
These numbers are completely wrong and don't apply to a generational model at all, as you have been told before repeatedly mutation doesn't work like that, if you understood how a cell divides to form a haploid cell and then recombines with another beginning the process of meitosis to form a human being and how mutation accumulates, you would no doubt understand why your numbers are way off. Mutation produces tiny changes in the genome so that the next generation is pretty much indistinguishable from the last with perhaps a handful of mutations, if those mutations are viable they will be more likely to become widespread in the population, the fitness these genes confer meaning they are more able to survive and thus more likely to breed. Likewise mutation which are deleterious and enable an animal to be less adaptive will be less prone to be passed on to the next generation, which is called sexual selection, a part of natural selection.
So the gene number of say a rat at a few hundred million genes is changed in the next generation by the mutation coefficient called a dominance coefficient which can be used to model either the likelihood beneficial genes will remain or that deleterious ones will remain. This is used in population models to show the mutation rate which is the likelihood over time of mutation accumulation in a single population and is typically a small fraction.
Of the hundreds of millions of genes then only relatively few have changed. In the 66 or so million of years since mammals became the dominant species on Earth, and hence the vast bulk of the population for millions of years the small burrowing rat like creatures that are thought to be the ancestors of all mammals have over a few trillion generations produced with only a small change in mutation rates a diverse collection of mammals, if you multiply small changes by billions of billions of generations you end up with a large potential for speciation, especially given environments where species are relatively isolated such as Islands and peninsulars where the ingress of animals is relatively small and the breeding population is significant but relatively isolated.
So if you take the number of genes and use logistic model which incorporates a dominance coefficient over time you can show how very small changes to a populations genome can become large and cause speciation given enough time. Most people have the weird idea that suddenly speciation happens and suddenly shazam a rat like ancestor becomes a rat, but typically except in single celled or very simple organisms it is a gradual process over millions of generations, to the extent that if you were to look at it in purely human terms it would seem there was no appreciable change at all.
And no you don't read people's arguments do you. That's why you don't understand enough about anything to advance your numerical sophistry, which bears absolutely no relation to any sort of evolutionary process whatsoever. I have explained in detail how mutation models work, linked them including the logistic progression that model gene expression in science papers over both the short term and more longer term models. It's difficult to model systems over anything more than a few million years though, as the margins of error tend to become large. I've explained this now several times in several different ways providing scientific journal papers which explain it in depth which are freely accessible and what have you done? Ignored them because anything that doesn't fit into your ideas is just plain wrong. And this was before you had me on ignore. Stop ignoring anything to roller coaster on with specious maths that is about as apt to model evolution as it is to model any sort of physical or natural model. Exponential models are useful for physical processes and chemical processes but basically useless in biological models where the rate of change is incredibly small. Exponential models become widely inaccurate with time and the numbers balloon out of all proportion, and do not and can not hence in any way represent population models over time or hence the rate of mutation accumulation or the progression of evolution from single celled organism to simple multicellular organisms, let alone humans. To put it simply you are trying to use a square peg for a round hole, because you don't understand the science on the subject, having never studied it.
Logistic iterative models ftw. A logistic model would progress somewhat more realistically as the iterations are tiny, but will become significant given enough time, significant enough to explain the large diversity of life on Earth, with a few notable mysteries which are slowly being cleared up with time and a more complete picture of the fossil record. It's almost impossible to be sure of things that happened millions of years ago, let alone billions so the models have to by their nature be somewhat hypothetical. Although like with most things we can use speciation as it happens in modern times to infer how it might of happened in pre historic times.
You can waste your time throwing out pointless exponential progressions of gene expression all you like but it is completely impractical, widely unrealistic and shows a remedial understanding of biological systems, evolution, and natural selection as it regards mutation.
To put it simply if you take an insignificant mutation rate and apply it to hundreds of trillions of iterations, the size of mutation accumulation will be relatively large, large enough to explain the diversity of life. What it wont be though is exponential because few if any natural systems work remotely like that and it is meaningless and inappropriate to use such blunt mathematical tools in the reiteration processes that make up evolution.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3296245/
Here's a journal paper detailing a model of mutation so that you can see how it works in science, not that I expect you will read it but meh for reference it shows an actual scientific model. This is the sort of thing you should be attacking, you can't just ignore all the evidence out there and wade in with your own models with no regard where the field is or understanding of biology to any real level. It's frankly pointless and there's no reason anyone should take your maths seriously without knowing what it is you are actually modelling.
Estimation of the distribution of selection coefficients of mutations is a long-standing issue in molecular evolution. In addition to population-based methods, the distribution can be estimated from DNA sequence data by phylogenetic-based models. Previous models have generally found unimodal distributions where the probability mass is concentrated between mildly deleterious and nearly neutral mutations. Here we use a sitewise mutation–selection phylogenetic model to estimate the distribution of selection coefficients among novel and fixed mutations (substitutions) in a data set of 244 mammalian mitochondrial genomes and a set of 401 PB2 proteins from influenza. We find a bimodal distribution of selection coefficients for novel mutations in both the mitochondrial data set and for the influenza protein evolving in its natural reservoir, birds. Most of the mutations are strongly deleterious with the rest of the probability mass concentrated around mildly deleterious to neutral mutations. The distribution of the coefficients among substitutions is unimodal and symmetrical around nearly neutral substitutions for both data sets at adaptive equilibrium. About 0.5% of the nonsynonymous mutations and 14% of the nonsynonymous substitutions in the mitochondrial proteins are advantageous, with 0.5% and 24% observed for the influenza protein. Following a host shift of influenza from birds to humans, however, we find among novel mutations in PB2 a trimodal distribution with a small mode of advantageous mutations.
WHEN a novel mutation appears in the genome of an organism, it may have three different effects on the fitness (w = 1 + s) of its carrier: The mutation may be deleterious (s < 0), reducing fitness through reduced fertility or survival rate. It may be neutral (s ≈ 0), that is, having such a small effect on fitness that the fate of the mutant is mostly determined by random drift. Or the mutation may be advantageous (s > 0), increasing the fitness of its carrier by increasing its fertility or survival in its environment. The frequency distribution of the different types of mutants and their associated selection coefficients (s, also known as fitness effects) is a key issue in population genetics (Bustamante 2005; Eyre-Walker and Keightley 2007). The ultimate fate of a mutation, whether it will become fixed or lost in a population, depends on the strength of selection and on the effect of random drift due to finite population size. In fact, the fitness effect s and the population number N are so closely linked that normally the distribution is expressed in terms of the population scaled coefficient S = 2Ns.
I've only skimmed it to make sure it was related myself but it seems appropriate. You only need an understanding of calculus and of statistical distribution, since you studied engineering you should at least get the gist of this.
http://www.ncbi.nlm.nih.gov/pmc/article ... f/1101.pdf
PDF format link.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3296245/
Journal link.
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