There is a pretty interesting discussion going on in Noyau regarding the many definitions of “fitness” in evolutionary biology. It would be a shame for it to be lost in that particular venue here at TSZ. At the risk of being censored by the admins for posting too many OPs in one month I thought I’d start this thread.
Here’s my take so far:
Allan Miller was charged by phoodoo with resorting to different definitions of fitness. Allan denied the charge and when asked for a definition of fitness Allan provided one. Allan later stated that his definition only properly applied to asexual species.
Others chimed in to say that the definition of fitness depends on the context, which hardly seems to contradict what phoodoo was saying.
My own position is that fitness has its definition within a particular mathematical framework. My position is also that fitness can be defined generically but that such a definition is tautological. Special definitions of fitness are required to make the concept testable.
Here’s hoping we can move the discussion about fitness out of Noyau.
Should we pretend that Sober is illiterate?
Quoted in The Oxford Handbook of Probability and Philosophy p. 620.
: The Oxford Handbook of Probability and Philosophy
: Chapter 28.1 Introduction
: p. 601
Sorry dazz. Don’t you wonder why no one else here was willing to set you straight? It can’t be because they were ignorant. They knew the facts and willingly held them from you.
so tell me where I went wrong. Enlighten me you almighty parrot
You denied that natural selection is stochastic.
Mung:
You are right. And different mathematical models have different quantities that serve as fitnesses. And in some cases that are only slightly more complicated, you can’t come up with a single number for each genotype that “is fitness”. A simple example in a simple discrete-generations model is when the viabilities of males of genotypes AA, Aa, and aa are 1.0 : 0.7 : 0.5 and the viabilites for females are 0.6 : 0.7 : 0.8. There are other simple cases when fertilities of different matings cannot be predicted from the products of “fertilitiies” of the two genotypes. And when generations overlap, things get even hairier.
So does this show that phoodoo was correct? No, because phoodoo’s point was that was fitness as a concept was vague, or circular, or useless (or something else bad, perhaps you can explain).
One can use either fitnesses of genotypes, or when those are not available, components of fitness such as in the example above, to generate numerical predictions of what happens in the longer term. All the while with phodoo fulminating in the background, unheeded.
Yes, real life is even more complex than these models, but the models are important tools to understand the consequences of that complexity.
Elliott is wrong. Elliott is not a theoretical population geneticist, and is not taking into account all the cases where we can get good results without being able to assign a number to each genotype which “is its fitness”.
Are you saying that there are multiple mathematical models each with their own mathematical definition of fitness? Can you provide two examples?
I can provide two mathematical models for gravity, if you’re interested
So?
The quoted text is not from Sober, it is from Beatty and Finsen (1989). Rethinking the Propensity Interpretation.
Exactly.
OK, then Beatty and Finsen are who’s wrong, not Elliott.
Sure, happy to oblige. Model I: we have organisms that reproduce clonally, in discrete generations. The probability of survival to adulthood of a genotype is V (viability). The expected number of offpsring per survivor is F (fertility). In that case fitness is VF
Model II: Diploid individuals in discrete generations, where each genotype has a viabiliuty V that does not depend on which sex they are. Any mating of two genotypes has a fertility that is the product of F values of those genotypes, where F is a “fertility”. Mating of surviving adults is random. In that case the fitness is (1/2)VF.
(Also, although I’ve ignored it so far, one has to distinguish between absolute fitness and relative fitnesses. One is often assuming that the relative fitnesses of genotypes stay constant, but the absolute fitnesses don’t necessarily. Can explain on request.)
In cases with overlapping generations things are more complex, and one needs to take the survival curve (as a function of time) and the age-specific fertilitiy curves, and use calculations of the intrinsic rate of natural increase (“Malthusian parameter”). And even that does not always yield mathematical tractability.
But what about the short term?
You get equations for the genotype frequencies in generation t+1 as a function of the genotype frequencies in generation t. Then you can either solve for the genotype frequencies in all future generations if the viabilities etc, remain the same, or you can iterate them numerically. So the short term is key to the long term.
Not sure who that is a quote from, but they aren’t thinking about the behavior of our typical theoretical population genetics models, in which understanding the short-term is key to understanding the long term.
Roberta L. Millstein
http://www.rlm.net/
Feel free to contact her and tell her why she is wrong. I’d love to hear her response.
No thanks. She may have some other meaning of fitness, such as survival of the whole species, in mind. If anyone is in touch with her, they can point out this thread.
Let’s not lose sight of the fact that phoodoo is trying to argue that because there are multiple definitions of fitness, that means the whole concept is nonsensical, constantly (and deliberately) changed, and impossible to make sense of and without practical application.
Phoodoo also completely fails to comprehend the concept when it is put in the context of an entity. No seriously. Or a rate of increase(or decrease) of an entity.
Basically phoodoo is entirely unable to think if the subject has to do with evolution. He suffers such a complete and total breakdown of his cognitive abilities that he litterally becomes unable to read or think. Ideas that entities can multiply in number escape him. That multiple factors can contribute to fitness simultaneously renders him completely incapable of working out how anyone can know how, or how much, or when, some factor contributes to fitness.
“My position is also that fitness can be defined generically but that such a definition is tautological.”
Please give an example of someone offering this generical definition of fitness and explain how that offered definition is tautological.
No. No, no, no, no, no. That is not what I said. Here’s the problem with this whole ‘debate’. It’s more about who-said-what (As in: Allan keeps changing his definition of fitness. Allan said this, Allan said that. Then Allan spends half his life trying to deal with a barrage of tosh).
The quibbled version of ‘my definition’ is quibble-free in asexual species, because the genotype is preserved as a whole – genotype and phenotype both travel as one unit, coextensive with ‘the individual’. The quibble is that entire diploid individuals in sexual species are not copied entirely. But ‘my definition’ does not even require that they are. It is simply that that objection is particularly irrelevant in asexual species.
That is not the same as saying that ‘fitness is the rate of increase of a replicating entity’ only applies to asexual species. You need to focus upon what is the replicating entity in the two cases – rather than picking stupid semantic holes over ‘replicating’ vs ‘replicated’, or what it means to ‘increase’ an indivisible entity … this is quite high-level stuff, not readily appreciated if your sole objective is to misunderstand. It goes back to George Williams, and his definiton of an evolutionary allele, which depends entirely upon recombination, which happens every generation in sexuals, not in asexuals. Recombination uncouples segments of the genome. It is then those segments that increase or decrease. But increase or decrease they most assuredly do.
Alleles increase their representation in a population of ‘locus instances’ – slots that can be occupied by one variant or another, much like individuals, but one level down. In asexual species, the entire genome is a singe locus, and different lineages are different alleles. In sexuals, the genome, and hence the extent of ‘locus’ and ‘allele’, is subdivided.
So let’s think of a simple case; we can think of a sexual species with no crossover but two chromosomes. Then, through independent segregation each chromosome functions as a separate unit. Individuals with a particular version of Chromosome A have a mean fitness. Those without that version have another. Same goes for Chromosome B. Each has a contribution to individual fitness of diploids, but perfectly arguably, has a fitness itself, in the population of loci. After all, it gets copied, and the number of copies in the population goes up or down somewhat independently of the other.
The mean number of copies produced is fitness. Diploid individuals have a fitness too; they are not identical, but the concept is clearly held in common between the two levels of analysis; that of increase and decrease of copied elements.
This too. It doesn’t contradict what I say either. I accept that you can find any number of authors defining fitness in any number of ways. Dawkins has a good chapter on this in The Extended Phenotype: “An Agony In Five Fits”, if you can bear to. Orr mentions this too. As I have linked both pieces before, this does not chime with a view that I don’t think anyone ever says anything different.
The original charge, the one that had me bristling my way to Noyau, is that I change it constantly. Whereas I believe I have been consistently discussing the one I understand to be in use in mathematical evolutionary biology, which involves the quantification of evolutionary success in terms of changing frequencies in a gene pool, and must ultimately be mediated by some form of effect upon frequency of replication.
Important though to separate ‘context’ as in the context the author uses it in, and the context-dependence of fitness itself. Fitness itself – for any single definition – is entirely context dependent. Fitness can change, even while one takes a consistent view of what it is that is changing.
And because you didn’t say ‘fitness is the rate of increase [in the number] of [individual] replicating entities’, then it is apparently impossible to simply use one’s brain to figure out that this is what you meant.
Nooo, phoodoo now thinks that a “rate of increase” can refer to the size of the individual entity. Maybe the gene is getting fatter.
Omg Allan you’re such an idiot, why do you think individual entities getting fat is a form of fitness?
ARRRGH HOW CAN ANYONE BE THAT DUMB? HOW?
Rumraket,
Yup, heh heh! (Though dumb I can be – just had a letter published in my local paper about ‘Brexit’, and missed a vital word out of my final paragraph that completely reversed its intent! I’m still crimson).
I just thought of another, more succinct, way of looking at it: in the simple sexual system I mentioned, with just two chromosomes in the haploid and no crossover, the chromosomes are precisely equivalent to asexual individuals . They flood a space of such ‘individuals’, which just happen to spend most of their life paired in diploid harness. With the greater subdivision of crossover, the same logic still applies, albeit at a still lower level.
Which is why I think the idea of ‘allele fitness’ works for both systems. And, incidentally, chimes with my view of sex as being ‘for’ haploids, not for diploids.
That changes nothing, you still are woefully shy of understanding the problem.
If we call all generations of any organism the same thing as its ancestor, then we must claim that a fish is the same fitness as everything that came after it, because, well, its just more numbers of the same thing.
I mean, we are some shrew-like mammal from the Jurassic or something, so that must mean we have the same fitness as it. So which one of these “entities” are we counting its rate of increase, the first shrew from the Jurassic?
But of course, that’s not the case, EVERY new generation is a new combination, a new potential, a new formula. So which one of these “entities” are we counting its rate of increase, the first shrew from the Jurassic?
Some dressing with your word salad phoodoo?
Trying to upload paper…
He’s genuinely just blathering.
phoodoo,
A Word From Our Sponsor:
We are certainly likely to have fitnesses (as defined) in the same ball-park as it. Don’t see the problem here. It’s as if nothing that has been written in any of these threads has in fact been written. Or rather, read.
No, not in the same ball park, exactly the same, because we are the same entity. Just more of them.
One must be careful in such a case not to say that the individual unrecombinable segments are the replicating entities. I think you just did.
For example in haploid discrete-generations models with two loci (between which there is recombination at some known rate) we count absolute fitness as the expected number of two-slot haploid offspring per haploid parent. And we do that irrespective of what alleles are in those slots. That’s how the fitnesses are defined in conventional haploid two-locus theory, where if the relative fitnesses are constant, we can calculate the genotype frequencies in successive generations.
Your statements sound as if you need to take the identities of the alleles into account and assign fitnesses to individual alleles that are in the “slots”. Whereas in this case there is one fitness per haploid genotype.
http://theskepticalzone.com/wp/wp-content/uploads/2017/11/metz-et-al-fitness-tree-1992.pdf
dazz,
Thanks dazz! Don’t know what I did wrong – clicked the upload file button, but…
tl;dr: Lyapunov exponent.
You did nothing wrong as far as I know. That’s the link to your upload. For some reason the link won’t show up in the comments section of the thread, but it does here: http://theskepticalzone.com/wp/wp-admin/edit-comments.php
No. Allan’s definition does not make a fish or any other organism a fitness. And it doesn’t make fish or any other organism a number.
I take it that your objection actually is that since the definition assigns fitnesses to organisms based on much they replicate, if you call all of some replicating offspring by the same (common) name, its fitness may go up or down. Thus, squid at t1 has a fitness of X, but squid at t2 has a fitness of Y. Assuming I’m right about what the definition implies (which is always dangerous with me), what do you think is wrong with it?
BTW, mung what does Elliott Sober actually say about this stuff? (As I’ve said before, I think he’s a pretty good philosopher.)
walto,
No, I am saying if the definition is the rate of increase of an entity, then what is the thing we are calling the entity, one of them, or all of them?
If we have a dog, and it has two offspring, and then they have four offspring, which is the entity that is increasing? All of them are the entity?
As I said you can let entity=dogs at t1, Francis the poodle at t2, pugs between t1 and t7, or dogs at all times. You just have to be clear. What makes you. Think they aren’t?
I have to be clear, who has to be clear? If the entity is dogs at t1, then at t2 the dogs at t1 one are not increasing. If the entity is Francis the poodle at t2, then Francis the poodle is not increasing.
One of the most important definition of fitness, one which John Sanford and the Mendel’s Accountant team, is the one used by Joe Felsenstein and the population geneticists. Before I provide the reasons I criticize the definition, it would be good to see it. Joe was very kind to spend time explaining the definition from his textbook, Theoretical Evolutionary Genetics, which I highly recommend to any creationist studying the topic:
and
an important comment:
From the definition of absolute fitness proceeds the definition of relative fitness.
Joe Felsenstein,
I agree. Selection acts on the whole package — the individual.
To define the terms in Joe Felsenstein’s definition:
W_A is absolute fitness for genotype A.
v_A is the viability or probability that genotype A will become reproductively viable (i.e. alive and able to make offsring)
f_A is the fertility for genotype A
Ok, now some of the problems in the definition. Those mathematical idealizations of fitness are environmentally dependent in many cases, and as Lewontin pointed out, even the proportion of a individuals in a population is an environmental variable.
The eye was something Darwin beheld as a product of selection, he viewed eyes as “more fit” for a given environment.
But the problem of the eye’s fitness changes for blind cave fish and another blind creature Allen Orr mentioned call Gamarus Minus. Blindness is of value to creatures that are in the dark because having a functioning eye comes at a metabolic cost. It seems in some cases these are epigenetic rather than genetic issues, but that is a digression…..
The bottom line is even that precise mathematical definition doesn’t really coincide with the idea of selection constructing complexity as Dennett and Dawkins suggests. Orr was keen to point out selection destroys, and Weins, Salthe, Behe and Sanford, etc. have pointed out selection tends to destroy complexity, not build it. Reductive evolution is the dominant mode of evolution, not constructive!
But even Darwin’s view of differential reproductive success relative to the environment has been bypassed:
When Lewontin said: “quantitative expression of the differential reproductive schedules themselves” that seems exactly in line with the definition used in Textbook Evolutionary Theoretical Genetics:
wA = vA fA
or
wA =(1/2) vA fA
Darwin’s notions have be bypassed, but that’s not really ever highlighted is it? Fitness has thus been redefined. There are perhaps 3 major areas of how fitness is defined:
1. the popular notion of fit, as in the medical notion or the complexity notion of Dawkins and Dennett. An athlete who had a vasectomy is considered fit, that doesn’t agree with the evolutionary notion of fit!
2. the environmentally dependent notion of fit by Darwin ( which is now bypassed)
3. the reproductive schedules and formal math definition of wA in evolutionary genetics
The 3 major definitions don’t exactly agree, and they are equivocated to death. For that reason, I find the study of chemistry and physics more satisfying. There is sooooo much less arguments over the basics. In contrast the basics in evolutionary biology are always contentious by comparison.
Francis the poodle at t1 is not identical to any of his offspring. He’s a reproducing entity and (roughly) the more successfully reproducing offspring he has, the higher HIS fitness. If you’re interested in the fitness of his whole line, you look at the reproductivity of additional generations.
So yeah, YOU have to be clear. And it’s really not that complicated. You’re hunting for obscurities where there actually aren’t any.
Gammarus minus is a species of freshwater shrimp common in the Eastern USA. Whilst some sub-populations are found in caves, they don’t appear to be blind.
Joe Felsenstein,
If I’m contradicting that last statement, I am not aware of it. Viewing things from the perspective of a chromosome, and counting mean copies accruing to ‘variant A’ and ‘variant B’ appears to make no difference that matters if the chromosome is the entirety of a haploid genome or but one part of a multiple-chromosome system that passes through diploidy and hence segregates. We have the extra layer of selection acting in the diploid, of course, but in both cases we surely have a mean fitness of alleles ***, it’s just that the alleles in the sexual can be smaller, delimited by the extent of recombination (in my simple example, represented only by independent segregation).
Am I being fuzzy here? Perhaps. Try this:
Let’s have a chromosome X, with 3 different possible modes of transmission.
A) Haploid chomosome number is 1, and there is no sex. X is the genome, variants of X the alleles. X represents a locus.
B) Haploid chomosome number is 1, but there is sex. X is the haploid genome, variants of X are still alleles which happen to spend a time paired. X still represents a locus.
C) Haploid chromosome number is 2 (let’s say it is a version of ‘chromosome X’ with a break) and there is sex, and so diploidy and segregation of the segments – the alleles are now variants of X1, and variants of X2, competing for their subgenome locus in much the same way as the ‘linked genome’ case competes for that larger locus.
I don’t see the fundamental objection to the argument that fitness in the 1) and 2) is rate of increase (or mean copy number) of Chromosome X as a whole, while the third case, with its incidental subdivision, results in the same, but somewhat independent, rates of increase for the unlinked segments X1 and X2 in the ‘environment’ they colonise – the cells they inhabit.
It may be unconventional – I wonder if the reason for that is taking the diploid stance? But, I don’t see why we are obliged to take the diploid stance, other than for convenience and convention.
[*** eta – perhaps by ‘allele’ I really mean ‘haplotype’?]
Mung, could you explain this part:
I don´t see why a generic fitness definition should necessarily be tautological. Nor do I understand what you mean by testing the concept.
Mung, this is not fair to Allan. Phoodoo accused Allan of personally changing definitions. Other peoples definitions are completely irrelevant to that particular charge.
Perhaps good to emphasize once again that it is the population that is evolving, not the “entities” that compose it. If a group of organisms with a particular adaptation is increasing at the expense of others, the composition of the population is changing.
We need the introduction of novel variants by mutation to keep fueling this process. I hope you will see that the introduction of new competitors will impact the fitness of the resident “entities” so it cannot stay exactly the same.
One of the slightly strange qualities of fitness is its relativity, both to the existing alleles and to the circumstances of the environment.
In a steady state asexual population, the mean fitness of all individuals is 1. It can’t be much else, whatever’s happening inside it.
Add a novel allele which (say) gains 1001 births for carriers to every 1000 for the existing allele (quite a significant differential, in fact), and the existing allele is made less fit (or its bearers are, if one prefers) without anything much happening to them individually. The mean fitness of the entire population is still 1, assuming steady state continues. But relative to each other, there is a differential which is likely to propel the new allele towards fixation. Throughout, we implicitly assume mean fitness of the entire population is 1 if we assume steady state continues. But among carriers and non-carriers of the novel allele, that 1 is partitioned between the slightly greater and the slightly lesser – that is how populations adapt. But in the end, when the whole population is fixed for the new allele, that constant mean of 1 now applies to that allele, instead of its predecessor. Something has increased., but it’s not the mean fitness of individuals in the population.