4.5 Billion years is not enough time for evolution to occur. You need 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 etc etc years
The basic theory of evolution is that genes undergo random changes called mutations that produce new and different genes. These new, different genes may produce functional proteins that undergo natural selection to give the organism a distinct survival advantage in its particular environment. The combination of these changes eventually, over time, lead to the development of new species.
Let us examine, mathematically, the time required for the development of a single gene that codes for a functional protein, which is the first step, in order for the evolution process to be considered a viable theory. Let us assume that this gene contains 150 codons each coding for an amino acid thus forming a small protein of 150 amino acids for a bacterial species (bacterial genes usually code for proteins over 330 amino acids). Since each codon on the gene could code for 1 of the 20 different amino acids, the amount of possible proteins that could be formed is 20 150 (1.4 x 10 195).
Current scientific findings have shown that 1 in every 10 77 proteins formed from a 150 amino acid protein molecule is functional (Douglas Axe - Cambridge Biochemist). This would mean that for every 1 x 10 77 mutations, a potential functional 150 amino acid protein could be formed which could then undergo natural selection.
Let us now calculate the total number of mutations that could occur in a dense bacterial colony similar to your intestinal colon environment, (4 x 10 11 bacteria per mm 3) which covers the entire surface of the earth (5 x 10 20 mm 2) and extends 100 kilometers (1 x 10 8 mm) upwards to the point where it is considered that the atmosphere meets outer space (Karman's Line). Let us also say that this colony of bacteria has been around since the beginning of the earth 4.5 billion years ago (4.5 x 10 9 years) and actively multiplying and mutating since. We will also assume that the maximum mutation rate of 150 codons for this gene is occurring with every bacterial division. Bacteria usually divide every 9.8 minutes which is equivalent to 5.37 x 10 4 division per year.
The total number of mutations therefore would be:
4 x 10 11 x 5 x 10 20 x 1 x 10 8 x 4.5 x 10 9 x 150 x 5.37 x 10 4 = 7.2 x 10 56 mutations
Based on our calculation we would still require considerably more time to cover the period necessary to form one functional small protein despite the extremely generous and improbable hypothesis in favor of mutation and evolution.
i.e. 4.5 x 10 9 x 1 x 10 77 / 7.2 x 10 56 = 625 x 10 27 years or 625 billion, billion, billion years.
This process would need to be repeated at least 3200 times for the average bacterial cell to account for its total gene pool. In the case of humans with over 25,000 genes with an average amino acids count per protein of over 1000, the number of years to evolve would be unimaginable.
In my view with this type of data, evolution should not even be referred to as a theory but a myth derived from intellectual pursuit.