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Let first state that I understand natural selection. I am not asking if evolution happened. I see evolution as a fact, but I do not assume the current theory of natural selection as fact.

I wonder if there has been enough "time", or number of generations, needed to create enough mutations that lead to the known genetic complexity of all species today (or even just until dinosaurs), since the Last Universal Ancestor.

Is it possible to prove, or estimate this time?

Note: There was obviously enough time for evolution to occur. My question is if, the known mechanisms of mutation and theory of natural selection, are enough to justify the evolution in this amount of time.

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The evolution to the current state of life on earth has occurred through some 3.8 billion years. During this time it has gone from the most basic forms of life, simple self-replicating units, to the complex beings we see today. Evolution, the process of change within a collection of units, is caused by 4 factors, mutation, selection, drift, and gene flow. So firstly, the current state is not thought to just be the result of natural selection but instead a result of all the mechanisms of evolution.

Selection can itself be subdivided in to two types, natural and sexual selection. Therefore "natural selection" does not even contain all types of selection. Selection is not a simple process, but occurs in a very complex manner, simultaneously affecting the many levels upon which selection can act (nucleotide, gene, organelle, cell, organs, organism, population, species, ecosystem etc.).

There are a number of things to consider when discussing whether enough time has elapsed for the mechanisms of evolution to produce the variation we see today, a primary concern is quantifying how much variation there is in the world that has evolved. Here are some other factors which would determine the likelihood at arriving at that level of genetic variation:

  • Mutation rates (per generation)
  • Generation times
  • Offspring per generation (affects the number of potentially new lineages per generation)
  • Genome size (number of potential sites)
  • Complexity and strength of selection
  • Population size (affecting drift and the efficacy of selection)
  • Genetic admixture/inbreeding/potential gene flow
  • Recombination rates
  • Social structure
  • Environmental variation

These all vary wildly in contemporary populations and would also have varied in ancestral lineages too, this makes it, in my opinion, near impossible to even get a rough estimate of how likely our current state of variation evolved via the known mechanisms of evolution. But there is a simple answer, all variation you see today arose from simple life and evolved in the last 4 billion years via the four known mechanisms of evolution - which, in part, includes natural selection. The proof is in its existence and the absence of other possible (plausible) mechanisms.

To illustrate the complexity of the problem and the high likelihood of these mechanisms leading to substantial genetic variation (this is highly unscientific):

I'd suggest a very conservative estimate of just mutation rates and time since life began (3.8 billion years, Last universal common ancestor [LUCA]), using approximate human mutation rates (175 per generation and 25 years per generation = 7 bp mutations per year), would suggest a single lineage from LUCA to now could have had some 26 billion mutations, an average of 8 mutations per site in the human genome (this would assume constant mutation and generation rates, and starting genome size of 3 billion BP in LUCA - obviously completely ridiculous, but it's just an illustration and assumes evolution purely by drift and mutation).

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In terms of the literal question asked, I do not believe anyone could provide a satisfactory answer. There are too many variables involved in terms of the likelihood of mutation, and the likely effect of that mutation.

However, you may wish to consider that the "genetic complexity", as you put it, of all species alive today is actually astonishingly low.

For starters, all living organisms use the same basic system of encoding and replicating their genetic material because mutations that affect these essential biological systems are almost always lethal.

The same logic applies to other fundamental biological process such as metabolism. For instance there's incredibly homology between the proteins involves in making bacterial flagella spin and those used in mammalian cell membrane transport.

Given this level of conservation, your question may well be moot.

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What's your average contemporary DNA pol error rate? Something like 10^-9 errors per bp? Your average prokaryote generation time is maybe something like 10 days. LUCA is thought to be about 3.5 billion years old. However, it would be expected that DNA pol error rates were far higher in the past. In fact, if RNA + protein world existed (I think a strong case can be made for it), we're looking at multiple orders of magnitude faster change. Eukaryotes with their longer generation times don't pose much problems to the calculations, since the vast majority of domains in Eukaryote proteins were prokaryotic inventions and Eukaryote proteins are mostly just prokaryotic domains shuffled around. I agree with the above answer of there being way too many variables involved (that we would basically have to guess) for robust calculations..

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