Evolution: The ramfications of mutations And the necessity for Information

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[SX23]

Now, I know for a fact there's a certain research institute that deals entirely with bacteria evolving. There was an article from this institute on how a certain type of bacteria would consistently eventually evolve the ability for photo-synthesis after the 40.000 generation, if I am not mistaken - but bacteria taken from generations previous to that would not necessarilly develop the same kind of ability.
So, if a strand of bacteria is capable of evolving something as complex as photo-synthesis in quite frankly less than a year - it puts a huge stick in the wheels of the claims by your "mathemathicians" that evolution by mutation isn't possible.
Another point here is that even bacteria take numerous generations before they eventually develop a new trait : how can you thus, assume, that even more complex entities than that evolve massive changes to their organisms within just 1 generation? They don't : you keep ignoring the fact evolution is GRADUAL.

Furthermore, if they were true mathemathicians, they would NOT have claimed "It is impossible". What they would have claimed is "Statistically improbable" - two completely different terms.

On an ending point : statements such as "They are smart, how dare you even put forward the idea that they did not take into account multiple generations" are logical fallacies known as arguments of authority.

I did say Impossible, they said "Statistically IMPOSSIBLE", as they took into consideration time factors and the gradual arguments.

To give an example of what is "Statistically IMPOSSIBLE", an easy way to demonstrate would be gravity. As you already know, gravity is a phenomena on which we base our knowledge after repeated observation. Saying: I will go in the street and I will fly ignoring earth's attraction is therefor not impossible, just improbable. However, as all the observation leads to it, we say: "Statistically IMPOSSIBLE". Also, the ideas of the probabilities were brought by Evolutionary scientist, and they were the one who gave the facts to base the calculus onto. It is therefore logic to assume that they do know their matter, isn't it?

[JoCu]

As for the second: Paul S. Moorehead and Martin M. Kaplan, eds., Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution. Read through it, the end point is: The only question was, could mutations serve as the basis—with natural selection—as a mechanism for evolutionary change? The answer of the mathematicians: no. Just plain no!

And some facts that came out from it: The mathematical problem for evolution comes when you want a series of related mutations. The odds of getting two mutations that are related to one another is the product of the separate probabilities: one in 107 x 107, or 1014. That’s a one followed by 14 zeroes, a hundred trillion! Any two mutations might produce no more than a fly with a wavy edge on a bent wing. That’s a long way from producing a truly new structure, and certainly a long way from changing a fly into some new kind of organism. You need more mutations for that. So, what are the odds of getting three mutations in a row? That’s one in a billion trillion (1021). Suddenly, the ocean isn’t big enough to hold enough bacteria to make it likely for you to find a bacterium with three simultaneous or sequential related mutations.

What about trying for four related mutations? One in 1028. Suddenly, the earth isn’t big enough to hold enough organisms to make that very likely. And we’re talking about only four mutations. It would take many more than that to change a fish into a philosopher, or even a fish into a frog. Four mutations don’t even make a start toward any real evolution. But already at this point some evolutionists have given up the classic idea of evolution, because it just plainly doesn’t work.

So, when I looked up this conference I found a lot of creationist websites, but I also found this:
http://pandasthumb.org/archives/2008/02/fisking-dembski-1.html

Also, from the comments to the original poster on that website:

I’m looking at the original monograph (How to Formulate Mathematically Problems of Rate of Evolution? by Dr. Stanislaw M. Ulam) right now, so a few additional quotes are in order. Needless to say, the stuff Dembski does not quote is far more revealing than the stuff he does.

From the very next paragraph (any transcription errors are mine):

“But, I believe that the comments of Professor Eden, in the first five minutes of his talk at least, refer to a random construction of such molecules and even those of us who are in the majority here, the non-mathematicians, realize that this is not the problem at all.

A mathematical treatment of evolution, if it is to be formulated at all, no matter how crudely, must include the mechanism of the advantages that single mutations bring about and the process of how these advantages, no matter how slieght, serve to sieve out parts of the population, which then get additional advantages. It is the process of selection which might produce the more complicated organisms that exist today.

As for myself, I have done a bit of very schematic thinking on the mathematics of such a process and I want to make some remarks to you which certainly are not, as one of the speakers addressed before, correct in a realistic sense but might be relevant for the approach to some quasimathematical discussion at least. The philosophical and general methodological remarks made by various speakers so far can form the basis of what can be, sometime in the future, mathematized. What I am going to do will consist, as it were, of picking out various items from the comments made so far and try to show how, perhaps in some remote future, mathematical schemata can be formulated.”

Did Dembski give an accurate representation? What do you think?

I can't say that I've done my own research into this conference, so I guess take this info as you like.

[Mysthalin]

Lol, and the Wistar conference argument is turned right round against you, SX.

You also avoided my entire post deffering to semantics. Doing so is a logical fallacy - please try typing up a response to that post again.

Also, in you're semantical rave you were not only wrong, but compared apples to oranges.
First off - "Statistically Impossible" and "Statistically Improbable" are two absolutely different terms. Statistical Impossibility means that no matter the circumstances - the chance of something happening is 0. Statistic Improbability means that you're more likely to fail than to succeed - in other words, even a 49 percent success rate could be reffered to as "Mildly Statistically Improbable".

There hasn't been a single observed occurence of somebody defying gravity without the aid of any kind of machinery/technology etc(don't go on a rant of "Somebody in the Bible did!" The Bible is not a piece of scientific proof). So, out of the trillions of jumps performed on Planet Earth 0 have been successful in launching a person off the face of the world. That is Statistical Impossibility(Statistical Impossibility only reffers to CURRENT EXPERIENCE, by the way. If you were to repeat the test enough times to get a positive result - the term would become Statistical Improbability.)
There have literally been millions observed mutations(including complex ones) - particularly in the bacterial realm. Yet, you are not likely to suddenly evolve into something in the next 5 seconds. Neither in the 5 seconds after that. But in the next 40 years - you might(and are almost likely to) get a nice little mutation known as cancer. Or the bacteria living in your tonsils will evolve into something that resists antibiotics and you will die a horrible and painful death as it overflows your organism. Statistically Improbable - but possible, none-the-less.

[SX23]

"QUOTE"

Twenty years ago, evolutionary biologist Richard Lenski of Michigan State University in East Lansing, US, took a single Escherichia coli bacterium and used its descendants to found 12 laboratory populations.
The 12 have been growing ever since, gradually accumulating mutations and evolving for more than 44,000 generations, while Lenski watches what happens.

But sometime around the 31,500th generation, something dramatic happened in just ONE of the populations - the bacteria suddenly acquired the ability to metabolize citrate, a second nutrient in their culture medium that E. coli normally cannot use.

"End of quote"

This means that an organism as simple as a single bacteria do need, more or less, 31,500 thousand generations to evolve an actually useful trait. And that has been observed in only 1 of the 12 population. A simple mathematical calculus should resolve the number of generations required to took in average: 31,500 x 12= 378000. That means we have observed 378,000 generations in a single bacteria before we have something useful. The odds to have beneficial mutations, followed by multiple evolutionary mutations, especially with organism that are incredibly more complex than a bacteria, such as a mammalian, which requires a considerable amount of time with a lot more generations due to their said complexity, are then lowered to an impossibility point. (Not to mention reptilian forms, insects, and etc.)

The mathematical problem for evolution comes when you want a series of related mutations. The odds of getting two mutations that are related to one another is the product of the separate probabilities: one in 10^7 x 10^7, or 10^14. That's a one followed by 14 zeros, a hundred trillion! Any two mutations might produce no more than a fly with a wavy edge on a bent wing. That's a long way from producing a truly new structure, and certainly a long way from changing a fly into some new kind of organism. You need more mutations for that. So, what are the odds of getting three mutations in a row? That's one in a billion trillion (10^21). Suddenly, the ocean isn't big enough to hold enough bacteria to make it likely for you to find a bacterium with three simultaneous or sequential related mutations.

What about trying for four related mutations? One in 10^28. Suddenly, the earth isn't big enough to hold enough organisms to make that very likely. And we're talking about only four mutations. It would take many more than that to change a fish into a philosopher, or even a fish into a frog.

Contrary to popular opinion, drug resistance in bacteria demonstrate natural selection (or a sort of artificial selection, in this case), but only selection among already existing variations within a kind. It also demonstrates that when the odds that a particular process will produce a given effect get too low, good scientists normally look for a better explanation, such as the plasmid explanation for resistance to multiple antibiotics.

If you took the time to read the up above, you will understand that the time required to achieve significant mutations is just above the lapse of what we possess. And that is what I was referring to when saying: It is statistically impossible {in the laps of time alloted.}

As for your source, JoCu, it only indicates that the answer shall be more complicated, as we do not discover "simplifying" facts about genetics. If I allow myself a small quote: "The more we know, the more ignorant we are."
And just like it, your site refers to a pro-evolutionary community, with no real standing as a source.

As for my source:
http://www.sciencemag.org...
http://www.icr.org...
http://openlibrary.org....

You can now rest assured (Unless you discredit three different sources) that a symposium (Academic Conference) has been held in 1966 with this very precise question: Could mutations serve as the basis—with natural selection—as a mechanism for evolutionary change?
The answer of the mathematicians: No. Just plain No!
 

[SX23]

As for my second point, I defy you to find any part in the text taken individually with which you would disagree:

Most of you would agree that this one's needs to be generated by an intelligent organism, both for the encoding mechanism and for the decoding one, along with the fact that plain matter cannot create information.
Then again, most of you would agree to the fact that the DNA possess information which is decoded by ribosomes. However, information cannot be created by matter, and such as, do need an intelligent source. As the sole source on Earth known to be able to do something that might approach some day the DNA complexity and information is the human, and that is impossible that humanity, time's paradoxes forbid, is the source to humanity, or evolution for that matter, we must conclude that a form of intelligence have preceded us.

You can argue that matter might have created randoms patterns over time and somehow DNA. However, DNA do not have any "life" if not decoded by ribosomes. Now, I let you imagine the probabilities to have random matter creating a part of DNA, along, at the very same place, (You'd agree with me that a strain of DNA isn't actually big) Ribosomes that can decode it. Now, considering that with time it might be possible, time such as millions of years, it completely obliterates the fact that DNA deteriorates to an useful state after a few centuries or millennium's, depending on it's conservation.

[Mysthalin]

Read this part :

took a single Escherichia coli bacterium and used its descendants to found 12 laboratory populations

meaning no sexual reproduction

and now this one :

What was really intended was indications from our computations-simple minded as they were-that a process involving only mitosis, in absence of sexual reproduction, would be indeed much too slow

Woop-de-doo.

Most of you would agree that this one's needs to be generated by an intelligent organism, both for the encoding mechanism and for the decoding one, along with the fact that plain matter cannot create information.

No, we wouldn't. This entire statement is a logical fallacy - an argument from consequence. Just because DNA is a kind of information does NOT in any way mean it's something of inteligent design. Atoms - the most basic building block of our universe are also formed by "information" - but it's not decoded by anything, it simply exists. 1 Proton 1 Electron makes a Hydrogen Molecule, 2 Protons, 2 neutrons, 2 Electrons make up a Helium one and so forth.

Now, considering that with time it might be possible, time such as millions of years, it completely obliterates the fact that DNA deteriorates to an useful state after a few centuries or millennium's, depending on it's conservation.

And, yet again - the evolution theory has nothing to do with how life came to exist. It only deals with how life morphed to what it is today.

[SX23]

Recently we discovered that sexual reproduction hinders mutation, and do not promote it, as one of your parent's gene can "overtake" the mutated one. And as you said, those are simple organism. Mammalians, for example, have an incredibly more complex and long DNA strain, thus requiring bigger mutations, and lowering the odds while having an higher number of generations required.

As for your answer: Information can be considered as such only when it is decoded. If you do consider "1 Proton 1 Electron makes a Hydrogen Molecule, 2 Protons, 2 neutrons, 2 Electrons make up a Helium one and so forth." that as information, it's due to an INTELLIGENT being able to decode it so we can understand the matter. Indeed, evolution theory is not in direct relation with abiogenesis, but as you asked a reply for my previous statements, here you are.

[Mysthalin]

Recently we discovered that sexual reproduction hinders mutation, and do not promote it, as one of your parent's gene can "overtake" the mutated one

And vice-versa. On top of there being possible mutations within the new generation while just being a fetus.

And as you said, those are simple organism

Being to digest an entirely new food-group is a very, very major change - even in a bacteria. It's a change, on a smaller scale, equal to a human becoming able to digest unprocessed wood. And, at any rate - by your logic, this should not have been possible, because Evolution is aparently nothing more than a myth.

Mammalians, for example, have an incredibly more complex and long DNA strain, thus requiring bigger mutations, and lowering the odds while having an higher number of generations required.

Or, due to there being more genetic matter to work with - the mutations become more probable. A longer DNA strain means it can break easier, and has to be reformed.

As for your answer: Information can be considered as such only when it is decoded. If you do consider "1 Proton 1 Electron makes a Hydrogen Molecule, 2 Protons, 2 neutrons, 2 Electrons make up a Helium one and so forth." that as information, it's due to an INTELLIGENT being able to decode it so we can understand the matter. Indeed, evolution theory is not in direct relation with abiogenesis, but as you asked a reply for my previous statements, here you are.

Calculators are also quite capable of decoding information. Are they intelligent beings? Hardly.

[JoCu]

This means that an organism as simple as a single bacteria do need, more or less, 31,500 thousand generations to evolve an actually useful trait. And that has been observed in only 1 of the 12 population. A simple mathematical calculus should resolve the number of generations required to took in average: 31,500 x 12= 378000. That means we have observed 378,000 generations in a single bacteria before we have something useful. The odds to have beneficial mutations, followed by multiple evolutionary mutations, especially with organism that are incredibly more complex than a bacteria, such as a mammalian, which requires a considerable amount of time with a lot more generations due to their said complexity, are then lowered to an impossibility point. (Not to mention reptilian forms, insects, and etc.)

The mathematical problem for evolution comes when you want a series of related mutations. The odds of getting two mutations that are related to one another is the product of the separate probabilities: one in 10^7 x 10^7, or 10^14. That's a one followed by 14 zeros, a hundred trillion! Any two mutations might produce no more than a fly with a wavy edge on a bent wing. That's a long way from producing a truly new structure, and certainly a long way from changing a fly into some new kind of organism. You need more mutations for that. So, what are the odds of getting three mutations in a row? That's one in a billion trillion (10^21). Suddenly, the ocean isn't big enough to hold enough bacteria to make it likely for you to find a bacterium with three simultaneous or sequential related mutations.

What about trying for four related mutations? One in 10^28. Suddenly, the earth isn't big enough to hold enough organisms to make that very likely. And we're talking about only four mutations. It would take many more than that to change a fish into a philosopher, or even a fish into a frog.

Contrary to popular opinion, drug resistance in bacteria demonstrate natural selection (or a sort of artificial selection, in this case), but only selection among already existing variations within a kind. It also demonstrates that when the odds that a particular process will produce a given effect get too low, good scientists normally look for a better explanation, such as the plasmid explanation for resistance to multiple antibiotics.

If you took the time to read the up above, you will understand that the time required to achieve significant mutations is just above the lapse of what we possess. And that is what I was referring to when saying: It is statistically impossible {in the laps of time alloted.}

As for your source, JoCu, it only indicates that the answer shall be more complicated, as we do not discover "simplifying" facts about genetics. If I allow myself a small quote: "The more we know, the more ignorant we are."
And just like it, your site refers to a pro-evolutionary community, with no real standing as a source.

As for my source:
http://www.sciencemag.org...
http://www.icr.org...
http://openlibrary.org....

You can now rest assured (Unless you discredit three different sources) that a symposium (Academic Conference) has been held in 1966 with this very precise question: Could mutations serve as the basis—with natural selection—as a mechanism for evolutionary change?
The answer of the mathematicians: No. Just plain No!
 

Your sources just point to the homepages of all those websites. Can you give a real link to the sources, or am I to just take your word on it? If you can, I'd like to read them myself.

http://www.nsf.gov/news/special_reports/darwin/bio.jsp

That is a web site with an interview with Richard Lenski saying how wonderful it's been studying bacteria and evolution. The link is the second to last link on the bottom right. There is also a transcript link.

Also, I'd like to know your thoughts on HeLa cells:
http://en.wikipedia.org/wiki/HeLa

Specifically this portion:

HeLa cells are termed "immortal"  in that they can divide an unlimited number of times in a laboratory cell culture plate as long as fundamental cell survival conditions are met (i.e. being maintained and sustained in a suitable environment). There are many strains of HeLa cells as they continue to evolve by being grown in cell cultures, but all HeLa cells are descended from the same tumor cells removed from Mrs. Lacks. It has been estimated that the total number of HeLa cells that have been propagated in cell culture far exceeds the total number of cells that were in Henrietta Lacks' body.

[SX23]

http://www.sciencemag.org/cgi/content/citation/160/3826/408

http://www.icr.org/article/mathematical-impossibility-evolution/

http://openlibrary.org/books/OL5549167M/Mathematical_challenges_to_the_neo-Darwinian_interpretation_of_evolution.

Sorry for the waiting time and the incomplete sources, mistake while doing ctrl-v ctrl-c. 

As for the HeLa cell's, they're quite interesting, but I doubt we will find anything actually useful and applicable, as they got 82 chromosomes and cannot be paired with human cells, even for comparison (Except for cancer issues).

On a small unrelated side-note, did you ever read the DNI reports on possible immortality?
http://www.dni.gov/nic/confreports_disruptive_tech.html

[Mysthalin]

The icr.org is very clearly and very aggresively pro-creationist. If you want us not to use pro-evolutionist sources, please don't use pro-creationist ones.
The sciencemag.org link is unaccessible.
The openlibrary.org one just advertises the book.

So yeah, why did you even bring them up?

[SX23]

Those are only to assert the fact that this symposium had been made.
I believe this source might be more credible, as it is pro-evolutionary: http://www.evolutionnews.org/2006/07/mathematicians_and_evolution002387.html
It asserts the results of the symposium only, and the answer is the same.

This also brings me to a second point:
Quoting :
http://www.newscientist.com/article/dn14094-bacteria-make-major-evolutionary-shift-in-the-lab.html:

Twenty years ago, evolutionary biologist Richard Lenski of Michigan State University in East Lansing, US, took a single Escherichia coli bacterium and used its descendants to found 12 laboratory populations.
The 12 have been growing ever since, gradually accumulating mutations and evolving for more than 44,000 generations, while Lenski watches what happens.

But sometime around the 31,500th generation, something dramatic happened in just ONE of the populations - the bacteria suddenly acquired the ability to metabolize citrate, a second nutrient in their culture medium that E. coli normally cannot use.
End of quote
This means that an organism as simple as a single bacteria do need, more or less, 31,500 thousand generations to evolve an actually useful trait. And that has been observed in only 1 of the 12 population. A simple mathematical calculus should resolve the number of generations required to took in average: 31,500 x 12= 378000.

This means that we have observed 378,000 generations in a laboratory stance with factors that enhanced the growth of mutations. It is reasonable to assume that a simple animal would need at least a dozen times this number, only due to differences in the length of the DNA strains. A hundred time this number would make 3,780,000 generations before having an actually useful trait. In other words, more or less 4 millions generation. Now, if we look at the fact that most of the animals needs around 5 years to achieve a generation, (And even then I'm being generous) we pass to 18,900,000 years to achieve a SINGLE useful trait. As the passage to one family to another requires at least a thousand (And more, in most of the cases) useful mutations, we go up to 18,900,000,000 years. We've already passed Earth existence (4,500,000,000)... Don't seem that probable to me. Of course, we could continue on with every families (Not even species!) on Earth, and we will go further the creation of our solar system.
And just a small side-note, simple animal forms are believed to be of existence since (only) 600 millions years (1). Now, with luck, it would indeed be possible to slightly lower the year requirement without getting too much off the probability laws. Now, let's compare 18,900,000,000 years (For one new family!) to the best estimates of animal life: 600,000,000 years. I let you compare those odds, and if you have the slightest knowledge in mathematics, you would understand that it's an instance of what we call something impossible.

[Spartan_Marine88]

impossible.

Science, especially under quantum physics, says that nothing, however IMPROBABLE is impossible

[SX23]

Indeed, science don't say it. However, there is a point in mathematics where we CONSIDER it as impossible. By the simple explanation and calculus up above, I believe I clearly demonstrated it.

Oh, and @ Mysthalin:
You also assume that sexual reproduction slows the process of mutation. However, this has been proven false on numerous occasions, for a very specific reason:
It is the advantage of complementation (also known as hybrid vigor, heterosis or MASKING OF MUTATIONS) that happens to occur during sexual reproduction, lowering the odds to pass one on by half on each individuals.
This is not what I would call helpful to the odds.

[Spartan_Marine88]

Indeed, science don't say it. However, there is a point in mathematics where we CONSIDER it as impossible. By the simple explanation and calculus up above, I believe I clearly demonstrated it.

No you proved results discovered in a lab, which ultimatly means nothing as the world is not a lab, and there could be billions of variables over millions of years which would influence everything and we will never know all of them.

[SX23]

I'm aware of that. Under a lab, however, means under beneficial mutations odds as the prerequisite are often forced unto the bacteria.

Now, if you want to compute all factors:
I said a "dozen times this number" while mentioning transition to bacterias to basic animals. However, DNA strains from mammalians are more than a thousand times more complex. You just passed to 18,900,000,000,000 years with accounting more factors. That's more than the supposed creation of our universe. (13,7 billions years only, while we're at 18,900 billions here).
If you mean factors that are beneficial to mutation's conditions, I defy you to find any that occurred since today. Just like that, there has been no recording of Earth massive radiation bombardment due to the Sun, so this argument is excluded.

[Masacree]

Science, especially under quantum physics, says that nothing, however IMPROBABLE is impossible

That's not true.

[Mysthalin]

This means that we have observed 378,000 generations in a laboratory stance with factors that enhanced the growth of mutations. It is reasonable to assume that a simple animal would need at least a dozen times this number, only due to differences in the length of the DNA strains. A hundred time this number would make 3,780,000 generations before having an actually useful trait

First you say a dozen, then you say a hundred, eventually multiplying merely by 10.

So which one is it? Your lack of consistency grants little in the form of credibility.

You have already, at this point, misinterpreted the entire information from the link, failing to take into account the ammount of individuals at each generation, the actual time frame for each generation to pass(bacteria don't take an entire year to pass on to a new generation) and the complexity of something such as DIGESTING AN ENTIRELY NEW FOOD GROUP.
Furthermore - you're assuming something such as that without putting forward any kind of scientific evidence. I could reply by saying "It is reasonable to assume that a complex animal would need at least 1/10th that number, only due to the instability provided by longer DNA strains." - and I'd be just as right (I.e. not right at all) as you are now.

And, due to that - the rest of your calculations are entirely incorrect.

[SX23]

First you say a dozen, then you say a hundred, eventually multiplying merely by 10.

So which one is it? Your lack of consistency grants little in the form of credibility.

You have already, at this point, misinterpreted the entire information from the link, failing to take into account the ammount of individuals at each generation, the actual time frame for each generation to pass(bacteria don't take an entire year to pass on to a new generation) and the complexity of something such as DIGESTING AN ENTIRELY NEW FOOD GROUP.
Furthermore - you're assuming something such as that without putting forward any kind of scientific evidence. I could reply by saying "It is reasonable to assume that a complex animal would need at least 1/10th that number, only due to the instability provided by longer DNA strains." - and I'd be just as right (I.e. not right at all) as you are now.

And, due to that - the rest of your calculations are entirely incorrect.

I meant to put one more zero actually.
A slight mistake from my part, which just increase the chances of the improbability.  If you want scientific evidence, well, let me say first that the number is going to be incredibly bigger, as I only took into account the simplest factor, and even less (You'll notice in the next few calculus).
But as you asked...
Here we go:
First of all, bacteria's did not take a year for a generation indeed. And as such, they do not taken into account for the time part.
But, as we observed 378,000 generations before we had ONE beneficial mutation.
This means that we need, in average, around 378,000 generations of e.coli to get a change. Ok doke, up to there, you should agree.
Now:
The genome is an organism’s complete set of DNA. Genomes vary widely in size: the smallest known genome for a free-living organism (a bacterium) contains about 600,000 DNA base pairs, while human and mouse genomes have some 3 billion. Except for mature red blood cells, all human cells contain a complete genome.
(http://www.ornl.gov/sci/techresources/Human_Genome/project/info.shtml)
Now, let's compare to the human number of DNA pairs in contrast with bacteria: (3,000,000,000/600,000)= 5,000 times more complex. Now, let's give that 5,000 to our lovely generations number: 1,890,000,000. 1 billion and 890 millions. Now, most of mammalians needs a generation length of, more or less, 2 to 10 years in average. So let's go with a safe number and say 5 years. 9,450,000,000. Around 10 billions years. Our solar system is younger. AND animal life exists from only a mere 600,000,000 years. So, we have the fastest mutation recorded, with which if we extrapolate, gives 9,450,000,000 years. Now, did you notice the fact that I didn't take in account 2 mutations? Did you tough I've forgot it? Well, nope. Sadly for you, assuming with need atleast a thousand mutations to pass from one family to another, we just went to 945,000,000,000. 945 billions years to pass from one animal family to another. Now, do you want me to continue with the others family? Or is the required 945 billions years not enough?

[HexaFighter]

But, as we observed 378,000 generations before we had ONE beneficial mutation.

i doubt this very much

for example, in humans
important mutations happen in zygotes (sperm, egg)
 you can have up to 200 mutations in a single spermatozoid.
multiply that by the number of zygotes and multiply that by the number of individuals in the population.
It doesn't take long before new born feature a ton of new mutations.

multiply this reproduction cycle  again with the newborn
and a long time later you end up with...