Joe Felsenstein, like other population geneticists, holds a special place in the Creation/Evolution controversy because his works are regarded highly by many creationists who are familiar with genetics. This is a thread for all of us (myself included) to try to learn and understand one of the key concepts in his book Theoretical Evolutionary Genetics, namely absolute fitness. He has generously made his book available on his website (a book of this calibre could sell for hundreds of dollars).
[I will state my best understanding of what is in the book. I welcome technical corrections.]
For me, population genetics seeks to quantify the evolution of genes in a population as they are distributed among genotypes. It seems to me various concepts and definitions such as “absolute fitness” were created in support of that goal. Sometimes there will be usage of the same terms such as “fitness” within population genetics which may intuitively mean something else outside of population genetics. As I was going through the book, I could see some of the motivation for defining things a certain way, but also how it might get misconstrued in contexts outside of population genetics.
The definition of most interest which I got from the book so far is that of absolute fitness (page 50 of the text):
where
is absolute fitness for genotype A.
is the viability or probability that genotype A will become reproductively viable (i.e. alive and able to make offsring)
is the fertility for genotype A.
is absolute fitness for genotype A.
is the fertility for genotype A.
Evolution of the haploid asexual case is not too bad to conceptualize, but it becomes challenging to model the sexual diploid case.
With respect to unicellular micro organisms, I would assume we make 
since to me it seems the notion of a bacteria having several children is not appropriate. Hence 
would be the more important concept for unicellular creatures that reproduce by splitting themselves apart.
In contrast to absolute fitness, there is the additional concept of relative fitness of genotypes in a population, and that is meaningful regarding genotypes of the same species in a population. That was described also in the book.
But getting back to the notion of absolute fitness, it would seem then we can make statements about the mean absolute fitness of all the genotypes in the population. It would seem then we could say the mean absolute fitness of a population can increase or decrease.
I saw all the conditions for the Hardy-Weinberg Law to be valid and appreciate the motivation for making calculations tractable. I have to be careful when the infinite population size idealization is in play and when it is not.
Though relative fitness would seem rather meaningless in comparing individuals between species (like apples and oranges), can absolute fitness not be meaningful between species?
A rat might have 7 offspring per litter, and maybe 3 litters in a lifetime. That’s about 21 rats! Thus the mean absolute fitness of rats is higher than humans if we are talking raw numbers of
But I understand that is probably taking the concept of absolute fitness in population genetics to a domain it was not intended.
Additionally, the viability factor would seem to be not an inherent quality of the genotype but the genotype and environment. Take the same genotype in one environment and the rats will multiply like crazy but in another they won’t.
Thus the absolute fitness is not completely determined genetically but must be related to the environment. Or is there an implicit assumption a population evolves to be more fit in stable environment or at least somehow there is a means of factoring out the effect of environmental effects (like introduction of new predators into the ecosystem). If that is the case, the notion of “absolute fitness” is highly dependent on context. Or again, this is starting to take the notion of absolute fitness in population genetics outside of its intended domain of usage?
Regarding the human population, if the average couple today makes less babies than their ancestors, then are modern humans are less absolutely fit on average? If environmental factors are affecting birth rates, then it would seem mean absolute fitness of a population is most meaningful in a stable environment, and it gets ambiguous when we try to make statements about a populations fitness in environments that are rapidly changing. Or is it correct to say “the environment can change the mean absolute fitness even without the introduction of new alleles or mutations”?
Thanks in advance for thoughtful responses.
NOTES:
1. Lewontin’s paper Santa Fe Winter 2003: Four Problems in Understanding the Evolutionary Process articulated problems in defining “fitness”. He appears to say “fitness” is merely restatement of reproductive statistics. This leads to some complications which I somewhat echo above.
2. Andreas Wagner points out the difficulty in using “fitness” to define complex systems as well as pointing out problems with the definition of “fitness” itself. So what is the accepted strategy for identifying and describing systems? Andreas Wagner in his book Robustness and Evolvability in Living Systems (Princeton Studies in Complexity) describes how in practice the fitness-based, Darwinist world view is supplanted in favor of a more effective methodology:
However, fitness is hard to define rigorously and even more difficult to measure….An examination of fitness and its robustness alone would thus not yield much insight into the opening questions. Instead, it is necessary to analyze, on all levels of organization, the systems that constitute an organism, and that sustain its life. I define such systems loosely as assemblies of parts that carry out well-defined biological functions.
Andreas Wagner
but Wagner’s definition of “system” sounds hauntingly similar to Michael Behe’s definition of Irreducible Complexity:
A single system composed of several well-matched, interacting parts that contribute to the basic function of the system
Alive and able vs actual count of offspring?
It would seem to me that humans have a unique ability to regulate their own reproduction, and that this ability is rather new in human history.
Count of offspring is
1. For many of the species mentioned (rats, humans) the definition of fitness is more complex, since the generations overlap. This gets us into Leslie Matrices of birth and death rates in different years (or months, or whatever), and the “Malthusian parameter”. When you try to have more realism about who mates with who, it gets worse. You can’t always rely, in either case, on the population being in Hardy-Weinberg proportions. So let’s stick with discrete generations — an “annual plant” model — for the purposes of this discussion.
2. The quantity
is for the haploid or asexual case, because then each parent contributes 100% of the genetic material in an offspring. But with diploids, you need to use 
because each parent contributes half the genetic material of each of its offspring, or put another way, two parents get credit for an offspring. This scaling has the nice property that when the average parent that survives has two offspring, the average absolute fitness of the population is 1, and the population size is multiplied by 1 each generation.
3. Although absolute fitnesses are affected by population size (or density), the gene frequencies depend only on the ratios of the absolute fitnesses which are called the relative fitnesses. In the simplest case, where the effect of density-dependent population size regulation falls equally on each genotype, as a multiplier of its absolute fitness, the relative fitnesses then don’t change from one generation to another, even though the absolute fitnesses do change. To follow gene frequencies you then only have to use the relative fitnesses.
Happy to continue to supply some answers, but may be a bit slow over the next few days as it is a busy time (end of academic quarter) and my undergraduate Evolutionary Genetics class takes priority.
Woops, not correct. It’s when the average newborn ends up having two newborn offspring that absolute fitness of 1 implies no change in the size of the population.
I presume because the newborn is multiplied by
, and the parent is represented by the newborn multiplied by 
.
Btw, thanks for taking the time at the end of the semester. This blog can wait, your students are more important.
Your explanation of the S coefficients was the most helpful I’ve seen. I didn’t really get it until I read that section of your book.
Relative fitness does not reduce to individuals, but it does apply to different genotypes within a species. If two competing types have different fitnesses (different expected offspring numbers), the size of that differential conditions the speed and likelihood that one fixes (and renders the other extinct). A vital simplifying assumption here is that the ‘background’ genomes are, in most respects, sufficiently alike for their bearers to be very close ecological competitors. If there is substantial niche partition between them (minimal competition), both can grow without restriction by the other.
Two things happen when you move across species boundaries:
1) Ecological usage tends to diverge more
2) Recombination stops.
The first reduces still further the impact of two genotypes upon each others’ growth. The second removes the applicablity of a ‘constant background’ assumption. The entire genome becomes the genotype, and two genomes not in contact will likely diverge. If both are sexual species, gene flow still occurs with the two divided populations, but not across the boundary. At the boundary (if they are still in the same area) the contest is between entire genomes, not between loci within them. There are different dynamics in play.
It’s an important point in considering sex, for example, because an asexual offshoot has no access to the genes in the ancestral population other than the genome it ‘froze’. It is, properly, a separate species, despite being morphologically and ecologically indistinguishable. This (among many other things) affects the expectation in competition with the ancestor. It’s an interesting subject in itself, and one I really should try and flesh out instead of arguin’ about morality!
The reason none of this has to do with the real world is because no genes in a creature would ever move that far in a spectrum to bring the needed advance that evolution needs to turn bugs into buffalos
Its like counting angels on a pin. The wall against evolutionary change is the impossible probabilities .that are needed endlessly.
I recently rewatched the NOVA show WHAT DARWIN DIDN’T KNOW.
They said it was a surprise to find only 23000 genes etc not much different from other biology. SO they had to say the gene was just SWOTCHED.
Hmmm. I think this changes all this gene stuff period.
its not genetic change but switch change.
Oh brother.
Thanks to Joe for his patience. If had only continued reading the book the definition for the diploid case was on page 60
that is an oversight in the OP, but that’s why I wrote the OP to work out corrections in my understanding. Thanks also to the reader for their forbearance.
Thanks to Joe for his patience. If had only continued reading the book the definition for the diploid case was on page 60
that is an oversight in the OP, but that’s why I wrote the OP to work out corrections in my understanding. Thanks also to the reader for their forbearance.
Robert Byers,
There is no requirement for ‘impossible probabilities’. Mutation occurs at measurable rates, and these are entirely consistent with the genomic differences among taxa.
Switches still occupy a length of genome. They are subject to all the evolutionarty forces that sequence within ‘genes’ is (if you are using, as you seem to be, the molecular biology definition).
Indeed.
That has next to nothing to do with the OP. If you have no inclination to even read and learn a few bits of Joe’s book, you can start your own thread and express your own opinions.
You are welcome to start you own discussion to the effect, “What Robert Byers thinks of population Genetics.”
I and maybe some others want to try to read and learn a few things on this topic, and I’d appreciate if you let the discussion go in the direction of learning the material. Such off-topic comments don’t help toward that goal. If you want to express such dissent, if you want criticize the theory, that’s up to you, but can you at least try to understand Hardy-Weinberg before you opine here again.
I’d request the same of others in this discussion. Please at least become familiar with the basics like Hardy-Weinberg before you start blasting away in the comments.
We’re lucky Joe has even responded at all. I want to make him feel welcome in this discussion and show our appreciation to him.
The significance of Hardy-Weinberg? From the book:
I refrained from quoting the rest because it would be fodder for off topic discussions, and the topic is Absolute Fitness in Theoretical Evolutionary Genetics.
Could it reasonably be said that relative fitness is absolute fitness standardized so that the fitnesses of all genotypes sum to 1?
stcordova,
Hey Sal, who the hell are you? You want to make Joe feel welcome? So what, I want to make Robert feel welcome. You are not the site admin here. What Robert said was entirely relevant to this thread. If you don’t believe in natural selection, then all of this talk about fitness is just obfuscating bullshit.
You can’t even decide if you believe in NS or not, and yet you are convinced you are a creationist who believes in a divine relationship between God and man.
I thought you were kind of an arrogant moderator at UD and you are going to try to do the same here?
This despite the fact that your ideas make no sense whatsoever. How about everyday you quote the bible I tell you to shut up and study more?
The simple fact is there is no way of determining fitness in evolution. Whatever you say is fit beforehand, becomes unfit if that becomes the less prominent allele. Whatever wins is fit. All this talk of “relative fitness” is babble. Is fast fit or not fit? More so than strong?
Discuss all you want with Joe, no one is stopping you. But don’t expect that your theories won’t be criticized.
stcordova,
As far as the hardy Weinberg principle goes, it is an oxymoron.
It says that in the absence of evolutionary elements, the evolutionary elements will remain stable. There can be no such thing, if you believe in evolution.
You’re more than welcome to post a new thread “Sal is full BS”. If you do, I’d encourage the admins to let you post whatever you want and say whatever derogatory things you want to say about me and what I write, etc.
In the mean time, if you don’t have any inclination to understand Hardy-Weinberg, it would seem to me you’re just eager to talk about stuff you have little interest in understanding. Fine. Why do it in this discussion?
If you have author privileges, why don’t you show a little courtesy to those who actual want to read Joe’s work and talk about the specifics.
Nothing stopping for starting your own discussion and creating a love feast for yourself and others.
stcordova,
You don’t get to tell people what they get to talk about Sal, what is so hard for you to get about that?
Does Joe get to criticize Vincent Torley on a topic discussing the Dawkins Weasel program? I guess he does doesn’t he? Where is your outrage over that?
You post whatever you want here, and then when anyone questions your point of view, more than not you just run from justifying your views. You have no moral authority.
Do you believe in NS or not? You can’t even answer that question so how can you talk about Hardy Weinberg? Its an oxymoron.
I wasn’t telling you or Robert to not talk. I actually want you to have a chance to showcase how brilliant and articulate you are in your very own thread. In fact, I’d really like the mods to give you a special indulgence to have your very own howler monkey chamber where what you say is never at risk of going to guano, instead you get to bathe yourself in the guano your write.
As a bonus, I won’t even show up in your discussions to contest anything you say, even if it’s about me. How’s that for a deal?
Standardized somehow. Usually by choosing one genotype and setting its fitness to 1. Could be that the fitnesses of AA, Aa, and aa are 1 : 1-s : 1-t, for example, or in an overdominant case one might standardize on Aa and have 1-s : 1 : 1-t.
Joe,
Regarding equation II-113, genetic variance, it would appear this regarding relative fitness and not absolute fitness.
Fisher’s Fundamental theorem of Natural Selection seems stated in terms of relative fitness, not absolute fitness:
You wrote page 90:
Is that another way of stating Fisher’s Fundamental Theorem of Natural Selection? I did a text search for “Fisher’s Fundamental Theorem” in you book, I got no hits. So is this the same thing? Am I totally not understanding?
Thanks in advance.
Sal, this is a Fisher-like formula, a simplified version of one originally due to Sewall Wright.
I did not discuss the not-so-fundamental Fundamental Theorem of Natural Selection in the book, but I should put in a mention and citation. It turns out to be very hard to find a theorem that comes close to the FNTS and is also provable. There has been a big literature on this, with the most useful recent work by Anthony Edwards and Warren Ewens. You have to make a rather weird theorem to get one that is rigorously true.
The discussion that you found in Chapter II is the place in the book where I cover selection and mean fitness in haploids. See also section II.8 where I cover it for diploids.
I’ve been thinking about this recently and do think a impossible probability issue is in the issue here since dArwins rime.
however it is or probably is off thread on the specific intent of the thread so another time.
Remind’s me of Muller’s Ratchet:
Btw, look who coined the phrase, our very own Joe!
1974! That was 41 years ago. Joe must have been a grade schooler when he wrote that paper.
It was that concept that motivated some of my interest in Joe’s book.
I, for one, admire Sal’s attempts at learning.
When he finally understands population genetics he can apply it to the populations of animals that exited the ark and demonstrate that either population genetics is wrong or that young earth creationism is wrong..
HT to Joe for helping Sal.
[having problems with the editor and latex, comment reposted below]
Reviewing the OP.
I wrote:
Upon re-reading, page 2, seems correct.
I suspect W is used for the number of offspring and is also the symbol for absolute fitness. I don’t think that is an accident. It seems a fair statement for a given genotype:
From the OP:
That is incorrect as Joe pointed out.
stcordova,
Or you could just ask Joe for his email and you and him can have your own little pen-pal party together, where no one can bother you, how’s that? In the meantime if someone is going to post questionable theories here, expect people to comment.
Mung,
Haha.
Or both !
[latex draft test]
The question is how is Absolute Fitness mean in population genetics and theoretical evolutionary genetics. For
Haploids
For diploids with discrete generational schedules like annual plants:
For diploids with overlapping generation schedules like rats and humans, it is more complex.
This should be non-controversial.
As far as the rest of your bloviations phoodoo, these definitions, equations and conventions are used by creationist geneticists who constructed Mendel’s Accountant. You’re now in the position of attacking the basis of important creationist theories. Now don’t you feel stupid for questioning the importance and significance of and credibility of these concepts?
stcordova,
Neither you (nor anyone else) has yet to convincingly demonstrate how fitness in evolution is a before the fact determination, so none of these suppositions means anything.
NOW, if we want to change to a creationist paradigm, then indeed fitness could very well have meaning-since organisms which have goal directed characteristics can be assumed to have more fit and less fit attributes before they have reproduced. Strength, quickness, intelligence, color, size, all of these have the possibility of being “fit” attributes, if an organism strives towards fitness.
If it doesn’t then the only thing that describes fitness, is that which survives. And that can be things which thinking people rightly know are decidingly unfit attributes. Ugliness, slowness, weakness, unhealthiness, these all become possible fitness attributes in an evolution model. That’s why the evolutionist idea of fitness is a pointless one.
Now try to get that, curious one.
Do you believe in natural selection or not Sal? Be brave.
[latex draft]
[latex draft]
[latex draft]
stcordova,
You can find plenty of people who are just as confused as you about their dilemma in reconciling the contradiction of a God with a divine connection to man, and blind evolution (Kenneth Miller comes to mind.)
You think that just because someone puts the word creationist in front of their name, that means I have to believe their ideas?
That sounds more like a problem for you than for me.
Do you believe in natural selection Sal?
phoodoo,
Phoodoo, Sal believes in God. He’s started a decent, technical thread. Your evangelizing is misguided.
The importance of absolute fitness as a concept is that it is a stepping stone to the concept of relative fitness.
If genotype A has an absolute fitness
and genotype a has 
we can say
Creationists Christopher Rupe and John Sanford modeled the well-accepted claim about neutral fixation:
http://en.wikipedia.org/wiki/Fixation_(population_genetics)
and then modeled the fixation rate with various S-coefficients according to Ohta’s criterion for nearly neutral:
NOTE to readers. I can’t preview how Latex will render my equations except by posting them. After I post them I can’t edit them because the editor does something funny and undoes my latex corrections! So there are a lot of dead draft posts above with the contents gutted. Sorry.
No, but one of the creationists who wrote Mendel’s Accountant is John Sanford. He uses the same equations Joe Felsenstein describes. There are chapters in Joe’s book on Multiplicative and Additive Fitness and those are exactly the models creationist Sanford uses.
I’d rather listen and learn from John Sanford than you phoodoo!
John Sanford is an applied geneticist and associate professor of Horticulture at Cornell. His gene gun is in the Smithsonian Museum of American History since at one time many of the intelligently designed genetically modified organisms on the planet were through his gene gun.
Joe’s book is a vital read for anyone seriously wanting to understand genetic evolution as it relates to the creation evolution controversy be they a creationist and IDists or evolutionist.
As for me believing in Natural Selection, the creationist Blyth conceived of it before Darwin and it is made by God to preserve species not originate them.
Now that I answered your question you can answer mine, “don’t you feel stupid for criticizing the foundations of an important creationist theory?” Or are you now going to trash talk the works of John Sanford, one of creationism’s leading thinkers in order that you can save face after looking so willfully ignorant in this discussion? 🙂
stcordova,
I’ve poked around a bit this morning but don’t see any preview option for the LaTeX plugin. Emacs has a previewer, if you’re using that to edit your LaTeX. Otherwise it looks like you’d need to generate a PDF and preview that before cutting and pasting into a comment here. Not the most convenient workflow, I’m afraid.
Patrick,
Thanks for trying to find a solution.
One minor reason that I “prievew by posting” is that every wordpess rendering is slightly different, and I can at least know for sure how it will render.
I may post to an open thread or sand box or something to keep this thread a little cleaner.
The problem is if some minor typo like a backslash is missing, when I try to use the edit feature in the 1 hour window allowed for editing comments, the editor removes the correction! I put a backslash in, and then the editor deletes it when I press “save”.
I suspect some at TSZ don’t have that problem because they somehow managed to configure their editor, which I don’t know how to do.
I, for one, feel stupid for criticizing the foundations of an important creationist theory.
Would that important creationist theory go by the name Genetic Entropy?
stcordova,
First off, Sanford was an atheist until sometime around 2000. So perhaps the theory I am criticizing was created by an atheist.
Secondly, as I have said, there is no way to describe fitness beforehand if one believes in the unguided model of evolution. Luck is fitness in unguided evolution. If smart people chose not to breed because it is detrimental to their lifestyle, then stupidity is fitness in humans.
Thirdly, reconciling a believe in God’s relation with man, with a completely unguided process, which could have made blobs of grey goo instead of conscience humans, is a problem for anyone who believes in both. Perhaps you are a fan of Kenneth Miller.
Finally, what do you feed Tigers on Noah’s ark? Baby lambs?
stcordova,
Yes, I was aware of it, and Joe’s significance with respect to it. If you are invoking it in relation to the ‘reason for sex’ (TM), I am dubious. But sex is probably OT.
phoodoo,
This is like saying that a biased roulette wheel is not biased until after you’ve measured its bias by doing a few spins.
I have to make a correction. This isn’t right:
As Joe pointed out for a genotype for simple non-overlapping populations, 1/2 has to be used as a scaling factor for the diploids number of offspring to get absolute fitness.
For overlapping populations, the representation of absolute fitness isn’t basic algebra but matrix algebra as illustrated here:
https://en.wikipedia.org/wiki/Leslie_matrix