I wrote, in reply to Alan Kleinman
because I didn't write the comment that you are replying to me.
Thar final “me” is an editing mistake I made. For some reason the PS software displays a pencil icon for editing my comment, buf when I try to use that it, announces that this thread is in “Slow” mode and that such edits aren’t allowed.
I apologize for confusing Joe with Witchdoc.
It’s been a while since I watched Joe’s Fisher Memorial lecture where he was trying to connect thermodynamics with evolution, so I decided to watch it again.
Fisher Memorial lecture 2018 by Joe Felsenstein
Since my major field for my PhD in Mechanical Engineering was thermodynamics, perhaps I can help you understand that connection. So as a starting point, your basic model is correct, that is, energy in minus energy out equal energy stored. But then you have to ask yourself, what exactly are you modeling? Are you modeling evolutionary competition, are you modeling evolutionary adaptation, or are you modeling both? I understand that you are trying to work in the theoretical realm but experimental evidence gives you clues in how to answer this question. When you study the Lenski experiment, you find that he limits energy (the amount of glucose), and in this limited carrying capacity environment, he is setting up a competition between the different variants in his population for that limited amount of energy. Ultimately, the variant that is the most effective user of that limited amount of energy becomes fixed in the population while the other variants are driven to extinction. But fixation is not an adaptive step. Some member of that fixed population needs to get another beneficial mutation which pits that new most fit variant against the rest of the population. If we define an increase in information as an improvement in fitness, that beneficial mutation is the increase in information. Fixation of the most fit variant doesn’t increase information, it is the removal of the less fit variants from the population that had been taking some of the available energy for replication that could have been used for the random trial (replication) for the next beneficial mutation by the variant that ultimately fixes and has a chance to increase in information (fitness) in that variant. So what you have is an evolutionary adaptive process being carried out in a highly competitive low carrying capacity environment.
So, in answer to Witchdoc’s enquiry whether fixation of the beneficial mutation is the answer to my problem, my answer is sometimes. In the case of the Lenski experiment it is. But consider the other experiment I constantly harp on in these discussions, the Kishony experiment.
Consider what the major differences are between the Lenski and Kishony experiment are. The selection pressures are starvation and an antimicrobial agent respectively. The carrying capacity of Lenski experiment is much smaller but it is an open system with daily additions of glucose (energy) than the large carrying capacity with a set amount of energy (food) available in the Kishony experiment. This large carrying capacity of the Kishony experiments allows for much larger population sizes which means more random trials (replications) for the beneficial mutation. Fixation of any beneficial mutation in the Kishony experiment is not required for the next adaptive step in that experiment. Unlike the Lenski experiment, extinction of the less fit variants is required to allow the more fit variant to have sufficient resources to do the random trials (replications) necessary to have an increase in information (improved fitness). In the Kishony experiment, the less fit variants are still alive in the lower drug concentration regions.
The correct theoretical model evolutionary adaptation is the Markov chain model but the correct transition matrix must be formulated. The problem with the Jukes-Cantor model is that the transition matrix easily reaches equilibrium. Real evolutionary processes operate far from any Markov chain equilibrium. This math can also be done using the “at least one” rule from probability theory and will give analogous predictions.
So, in summary, evolutionary competition is a first law of thermodynamics process and evolutionary adaptation is a second law of thernodynamics process. These are distinct processes with different mathematical behaviors. The evolutionary adaptation process can occur in competitive or non-competitive environments. If the evolutionary adaptation process is occurring in a competitive environment, it will slow the adaptation process
Just a back of the envelope calculation, the haploid human genome is 3 billion bases and there are 3 possible substitution mutations at each base, so that’s 9 billion possible substitution mutations. On the low side, each human is born with 50 mutations. If all mutations have an equal chance of occurring, then that’s 60 million births to produce all possible substitution mutations in the human genome. This is a really simple model that doesn’t take into account mutational biases, genetic backgrounds (i.e. epistasis), and other factors, but we can see that with 7 billion people it doesn’t take long to get beneficial mutations.
Neutral mutations still account for the vast majority of differences between the chimp and human lineages.
First, we could be generous and say that 10% of the human genome is under selective pressure which would mean 90% of mutations are probably neutral. In functional DNA we see sequence conservation which means an even larger percentage of mutations are found in non-functional DNA and are neutral. We are still going to have many neutral mutations for those that occur in functional DNA, as shown by the higher rate of fixation of synonymous mutations. Beneficial mutations (and detrimental mutations) make up a rather small percentage of all mutations.
Beneficial mutations can occur in different individuals in parallel and then be combined later on by sexual reproduction and recombination. Asexual species can be useful in modeling evolution, but they have their limitations when they are used to model evolution in sexual species.
A useful benchmark: For an event with probability 1/N, the probability this event will occur at least once in N trials is approximately 0.632 (converges to 1-1/e as N goes to infinity).
This may be the only useful expertise I can contribute to this discussion, so I will retire to the peanut gallery. Some related math in this thread.
I did the math for him earlier in the thread, he rejected it. What can you do?
I don’t think we can use population sizes as a way to directly compare fitness across different environments. Humans have the capacity to make tools and learn techniques to manipulate the environment to their advantage, creating fitness multipliers that have nothing to do with genetics. Put a group of unequipped and unprepared humans out in the jungle environment with the chimpanzees and the differences in fitness will be much smaller.
And particularly not between genetically isolated populations.
If the population of polar bears in the Arctic is declining, that tells us little about the population genetics of squirrels in Japan.
(But things aren’t looking too good for the Japanese squirrel, either. 
)
Based on recent comments, I fail to see the flaw. Neutral mutations are, by definition, neutral, but other factors such as environment also affect fitness. No one is saying there have been no beneficial mutations as well, just relatively few compared to likely neutral mutations.
That’s my conclusion as well. The E. coli population in my large intestine has more individuals than the cumulative human population throughout history. Also, being adapted for a small range in no way makes you less fit.
I may be repeating what others said here, but anyway… There must be a great many neutral differences between humans and chimpanzees, when we look at their genomes. But probably most of the differences in anatomy, and many of the differences in biochemistry, are not neutral and occurred in the small fraction of the genome that has an effect on the structure and function of the organism. I get very frustrated when I hear that because most of the changes are neutral, we can presume that anatomical, physiological, neural, developmental, or behavioral differences occurred by neutral evolution. It is a fallacy, like this one: If we count differences between your car and mine, most of them are small blemishes in the exterior paint. Therefore whatever caused those also caused the engines to be different.
You are assuming a mutation rate of 1.67e-8 which some might say is a little high but ok, let’s run with your number. 1.67e-8*3e9=50 mutations/genome replication. But you are not taking into account correctly the possible base substitutions in your math. 60 million replications of the genome will give a mutation at every possible site in the genome but you have to multiply that number by 3 to get every possible base substitution which gives 1.8e8 replications of that genome. But since humans are diploid, 90 million replications will give the approximate number of descendants needed to get every possible base substitution at every site in the genome somewhere in the population. So, somewhere in those 7 billion people, you are going to have about 33 new sickle cell traits, 33 Tay-Sachs, etc., possibly some beneficial mutations for some selection conditions, and neutral mutations.
In the first post, I gave a link to a page that gives the human population over time. That link states that there have been about 100 billion humans in all history and that 99% lived in the last 10 thousand years which gives about a population of 1 billion to explain the reproductive fitness advantage that humans have over chimpanzees. So, let’s do a thought experiment. Let’s say there are some “agriculture mutations” that give humans the capability of learning and doing large-scale agriculture and it only takes two particular mutations and some member of the population has to have both those mutations to have the understanding to do farming. In that pre 10k period, those billion replications will give about 5 members with one of those beneficial mutations and 5 members with the other agriculture mutation. How many replications are needed for either of those 5 members sets to get the second mutation so that they can improve fitness? When you answer that, explain why the chimpanzee population didn’t do it.
What if one of the beneficial mutations occurs in an Eskimo and the other in an aboriginal Australian? What’s the probability of that recombination event occurring? Remember, you only have 5 members with one of the agricultural mutations and 5 members with the other agricultural mutation in that pre-10k billion replications. Those two mutations must also exist in the same generation for there to be any chance of that recombination event occurring.
An important concept is niches.
There are many more bacteria than humans.
But we don’t say bacteria are more fit than humans, or humans are more fit than bacteria - because they occupy different niches.
Chimpanzees are well adapted to their particular niche.
If we had to live in trees, for fight physically hand to hand with a chimpanzee - we would get destroyed - because the chimpanzee is better adapted to their niche than we are.
Now, if chimpanzees tried to compete with humans in our niche, they would lose.
Humans found a particular niche and carved out and extended that particular niche for themselves.
So much wrong with this. 1) You forget recombination. 2) There is no such thing as a “farming mutation”. 3) The “fitness advantage” you posit doesn’t have to be very large at all to explain the difference in population sizes. 4) Population size is a silly measure of comparative fitness between two species, for reasons that several people have explained to you already. 5) You assume that what is advantageous in one species will also be advantageous in another species, with a different environment and a different genetic background. 6) The major differences between humans and chimps arose over a long period of time. 7) Anatomically and, as far as we can tell, behaviorally modern humans are in the neighborhood of 300,000 years old. 8) You’re still assuming the Texas Sharpshooter fallacy.
I understood the term “neutral” to be purely in regard to selection, and not regarding whether it has an effect on structure of function. So a mutation that effects structure and function, but in such away that presents that presents no selective advantage or disadvantage, would still be considered neutral.
Have I been wrong all this time?
So much wrong even a statistician can see it.
Dr. @kleinman, you have ignored multiple responses questioning the premise that population size is an effective measure of fitness. This might be true in a petri dish, but clearly not in a real world environment. Others, with relevant expertise have responded about the sort of mutations that might be considered neutral (such as regulatory changes). It’s hard to have any serious continuing discussion on the OP topic when you ignore serious questions.
My emphasis. Your premise of a flaw is itself flawed in both measure and application (population size and non-neutral agricultural ??? mutations, respectively). It’s not fair to other participants if you ignore these issues. At a minimum, clarification of exactly what you think is flawed is needed.
No, you haven’t been wrong. You’re right. But the question is: what is the chance that a change in junk DNA has a selective advantage or disadvantage large enough to be selected for or against by natural selection? The criterion is (to close approximation) that the absolute value of the selection coefficient is less than 1/4Ne, where Ne is the effective population size. Which is usually a factor of 2 or 3 less than the population size. If N is 1,000,000, then the absolute value of the selection coefficient should be less than about 0.0000005 for the change to be neutral. The condition is not that it-seems-pretty-small-to-me, or that I-didn’t-notice-any-difference-in-survival or the-animal-looked-healthy-to-me. A “functional” region of the genome will have many of its changes noticed by selection, a junk region many more which are neutral. A change in a visible phenotype – well, forget the idea that it is neutral. (Although in a tradeoff of gain in fitness from one character versus loss from change in another, there will be certain directions that are neutral).
Thanks. I think I’ll have to read that a few times to make sure I get it.