Register | Sign In


Understanding through Discussion


EvC Forum active members: 65 (9162 total)
2 online now:
Newest Member: popoi
Post Volume: Total: 915,806 Year: 3,063/9,624 Month: 908/1,588 Week: 91/223 Day: 2/17 Hour: 0/0


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Author Topic:   Fitness: Hueristic or Fundamental to Biology?
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 1 of 47 (391763)
03-27-2007 10:22 AM


The purpose of this thread is to state some of my objections to fitness and hopefully clear up some of my misconceptions about the concept.
I'd like to start with Quetzl's response to me in another thread, and go from there.
Right. I certainly haven't read anywhere that fitness is "just fecundity", so I'm not sure where you got that. Unfortunately, we're coming up to the end of this thread, so a long digression here may be counterproductive. Without getting into a very long discussion, suffice for the purposes of this thread I define fitness as the average lifetime contribution of individuals posessing a particular genotype to the population after one (or more) generations. In other words, not just the numbers of offspring that an individual can pump out, but the number of offspring carrying a particular genotype that themselves live to reproduce. So, simplistically, fitness of a genotype = (average fecundity) X (fraction surviving).
Obviously, there is a lot of detail and nuance (relative vs absolute fitness, for instance) that I'm leaving out, but that's the gist, and probably sufficient for this particular discussion.
Let me isolate his definition
So, simplistically, fitness of a genotype = (average fecundity) X (fraction surviving).
and
In other words, not just the numbers of offspring that an individual can pump out, but the number of offspring carrying a particular genotype that themselves live to reproduce.
Though it is simplistic it's a good starting point to state my objection.
For the opening post, i'll just state that this definition seems to be recursive in nature. In other words fitness is the ability to produce individuals that have the propensity to to produce individuals that have the propensity, etc.
(Fitness of a genotype)= (Average Fecundity)X(Fitness of offspring's genotypes)
The ability of the offspring to themselves produce offspring would have to be in the definition, or else we come to the absurd conclusion that producing a large number of sterile offspring is the "fit" thing to do.

Replies to this message:
 Message 3 by fallacycop, posted 03-27-2007 12:40 PM JustinC has replied
 Message 7 by Modulous, posted 03-27-2007 1:21 PM JustinC has replied
 Message 18 by RAZD, posted 03-28-2007 12:36 AM JustinC has not replied
 Message 20 by RAZD, posted 03-28-2007 8:19 AM JustinC has not replied
 Message 21 by Modulous, posted 03-28-2007 10:07 AM JustinC has replied
 Message 37 by MartinV, posted 03-31-2007 12:57 PM JustinC has not replied

  
AdminWounded
Inactive Member


Message 2 of 47 (391769)
03-27-2007 10:47 AM


Thread moved here from the Proposed New Topics forum.

  
fallacycop
Member (Idle past 5520 days)
Posts: 692
From: Fortaleza-CE Brazil
Joined: 02-18-2006


Message 3 of 47 (391788)
03-27-2007 12:40 PM
Reply to: Message 1 by JustinC
03-27-2007 10:22 AM


(Fitness of a genotype)= (Average Fecundity)X(Fitness of offspring's genotypes)
Sure. And your objection is?

This message is a reply to:
 Message 1 by JustinC, posted 03-27-2007 10:22 AM JustinC has replied

Replies to this message:
 Message 4 by JustinC, posted 03-27-2007 12:55 PM fallacycop has replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 4 of 47 (391792)
03-27-2007 12:55 PM
Reply to: Message 3 by fallacycop
03-27-2007 12:40 PM


quote:
Sure. And your objection is?
By that definition, the fitness of the offsprings genotype would be determined by their offsprings genotype which would be determined by their offsprings genotype, ad infinitim.
The equation would be incalculable even in principle.

This message is a reply to:
 Message 3 by fallacycop, posted 03-27-2007 12:40 PM fallacycop has replied

Replies to this message:
 Message 5 by fallacycop, posted 03-27-2007 1:02 PM JustinC has replied

  
fallacycop
Member (Idle past 5520 days)
Posts: 692
From: Fortaleza-CE Brazil
Joined: 02-18-2006


Message 5 of 47 (391794)
03-27-2007 1:02 PM
Reply to: Message 4 by JustinC
03-27-2007 12:55 PM


recursive equations sometimes can have solutions.
But simpler then that is to introduce an arbitrary cutoff at some point.

This message is a reply to:
 Message 4 by JustinC, posted 03-27-2007 12:55 PM JustinC has replied

Replies to this message:
 Message 6 by JustinC, posted 03-27-2007 1:16 PM fallacycop has replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 6 of 47 (391798)
03-27-2007 1:16 PM
Reply to: Message 5 by fallacycop
03-27-2007 1:02 PM


quote:
recursive equations sometimes can have solutions.
Yes, but in this case the solution to the function fitness F(x) is depending on the function F(x+1), which is dependent on F(x+2), etc. [added by edit]does anyone know is these type of equations have solutions. My "common sense" mathematical intuition says no, but mathematical concepts are very counterintuitive. I still have troube with a zero volume polyhedron.
If F(x+1) was dependent on F(x) then you would simply need to ground it and we'd be on our way.
quote:
But simpler then that is to introduce an arbitrary cutoff at some point.
I don't disagree with this, but if there was an arbitrary cutoff then I'd call it a good hueristic device; I don't think it could be labled as a fundamental truth of evolutionary theory as it would be be based on the arbitariness of the subject using it.
Edited by JustinC, : No reason given.

This message is a reply to:
 Message 5 by fallacycop, posted 03-27-2007 1:02 PM fallacycop has replied

Replies to this message:
 Message 8 by fallacycop, posted 03-27-2007 1:44 PM JustinC has replied

  
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 7 of 47 (391799)
03-27-2007 1:21 PM
Reply to: Message 1 by JustinC
03-27-2007 10:22 AM


The ability of the offspring to themselves produce offspring would have to be in the definition, or else we come to the absurd conclusion that producing a large number of sterile offspring is the "fit" thing to do.
...
(Fitness of a genotype)= (Average Fecundity)X(Fitness of offspring's genotypes)
And we arrive at the logical absuridity that all genotypes have 0 fitness. The last offspring in the lineage has (presumably) 0 fitness, and thus the product of all those fitnesses and fecundities becomes 0. I'd imagine that last of the genotypes has an 'average fecundity' of 0 too.
So indeed - producing a large number of sterile offspring makes you exactly as fit as producing a large number of fertile offspring, if the end result is a single infertile descendant, or a generation of infertile descendants. If some gene came along, that gave genotypes a massive reproductive advantage, but rendered a significant number of the offspring of a certain genome infertile...we could quickly find ourselves with the dilemma of calling the original genotype unfit.
Quetzal's orginal formulation doesn't give us this absurd result fortunately. Our genotype that gives birth to a 10 individuals has an average fecundity of 10 let's say. 5 of them survive to reproduce. Its fitness is thus 10 * .5 = 5. If its offspring's offspring are all infertile, then that reflects badly on their genome, not the grandfather's genotype's fitness.
The issue you raised is a valid one though- a genotype that makes an army of infertile grandchildren is regarded as having a fitness of 5 which could be measured more fit than a genotype that makes only a small gang of very fertile grandchildren.
These are the tough breaks of trying to calculate fitness. Personally I think a time period or generation level should be included in the calculation. The higher the generational level (or longer the time period), the lower the fitness is likely to be (since every lineage goes extinct eventually), naturally fitness will probably fluctuate - sometimes largely so, but it will come to a 0 in the end. The longer that is, perhaps, the fitter.
In some species (such as succesful sexual species) any given genotype is very rare. So its average fecundity will generally be from a sample size of 1 - which means bad luck or good luck can drastically effect how we measure its fitness in any given environment. If it wasn't for some new predator being introduced next door to our family of snuggles by a sequence of happenstance situations resulting in the Henderson's pet dog tearing them to pieces, they might have become the biggest and longest standing history of snuggles in all time. Sure, we can conclude that the fitness of father snuggle's genotype to survive in the environment of the Henderson's was 0 - but how fit was his genotype to survive in its normal environment?
In the above scenario of course - we know that bad luck tainted our calculation, but if we have to go on are the numbers, we'd conclude that the genotype was unfit for its environment (assuming mistakenly that the environment was average). By luck, we realize that father snuggle has an identical twin brother - with exactly the same genotype. Uncle snuggles has an absolute fitness of 8, and lives in an average environnment. Even with this amazing stroke of luck, we would deduce this genotype's fitness wildly incorrectly.
If we pooled all the fitnesses of this generation together we could say that the genotypes with the highest (calculated) fitness were likely to be most actually fit individuals, with some exceptions.
From here could deduce, approximately, how allele frequencies will change in the gene pool of the next generation.
Edited by Modulous, : No reason given.

This message is a reply to:
 Message 1 by JustinC, posted 03-27-2007 10:22 AM JustinC has replied

Replies to this message:
 Message 9 by JustinC, posted 03-27-2007 3:07 PM Modulous has replied

  
fallacycop
Member (Idle past 5520 days)
Posts: 692
From: Fortaleza-CE Brazil
Joined: 02-18-2006


Message 8 of 47 (391801)
03-27-2007 1:44 PM
Reply to: Message 6 by JustinC
03-27-2007 1:16 PM


Even if you can find a solution to the infinite recursion, that solution will not be any better then the cutoff solution because it is not possible to predict the future. What is fit today may be unfit in the future. So, the best you can do is to introduce the cutoff (such is life). Quetzal introduces it after one generation. You might want to introduce more generations in your definition, if you will, but I doubt it would make much of a difference, if at all.
fundamental truth of evolutionary theory
May be you're being too ambitious...

This message is a reply to:
 Message 6 by JustinC, posted 03-27-2007 1:16 PM JustinC has replied

Replies to this message:
 Message 10 by JustinC, posted 03-27-2007 3:10 PM fallacycop has not replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 9 of 47 (391810)
03-27-2007 3:07 PM
Reply to: Message 7 by Modulous
03-27-2007 1:21 PM


quote:
In the above scenario of course - we know that bad luck tainted our calculation, but if we have to go on are the numbers, we'd conclude that the genotype was unfit for its environment (assuming mistakenly that the environment was average). By luck, we realize that father snuggle has an identical twin brother - with exactly the same genotype. Uncle snuggles has an absolute fitness of 8, and lives in an average environnment. Even with this amazing stroke of luck, we would deduce this genotype's fitness wildly incorrectly.
This is kindof my point. 'Fitness' is a tool we use to calculate populational changes, i.e, it isn't intrinsic to organisms or to evolution. Two different genotypes can have wildy different fitnesses and that's ok, as long as we know what the numbers mean and what their use is.
To act like organisms have an intrinsic property called fitness and this is the reason they have reproductive success seems just plain wrong.
Fitness is just our ability to extrapolate from past results to future results. That is, if the environment is relatively stable we can say that, on average, the genotypes which had increased fecundity in the past will have them in the future. Also, since there is a strong hereditary tendency the offspring will likely have the same genotype, and in the same environment, will have increased fecundity.
quote:
From here could deduce, approximately, how allele frequencies will change in the gene pool of the next generation.
So would you agree that fitness is just a tool we use to make predictions about the relative frequencies of traits or genes in future generations, and isn't a profound insight of evolutionary theory.
What I mean by 'isn't a profound insight' is that it has no explanatory power. Organisms don't survive and reproduce because they are 'fit.' To understand their survival and reproduction you have to look at the complex interaction of the phenotype and environment. Since this is a monumental task if done from scratch, we can just take a short cut and say that those that did well in the past will, ceteris paribus, do well in the future.
[edit]Clarification question: Do you think that fitness is an inextricable part in understanding natural selection and evolution?
Edited by JustinC, : No reason given.

This message is a reply to:
 Message 7 by Modulous, posted 03-27-2007 1:21 PM Modulous has replied

Replies to this message:
 Message 19 by Modulous, posted 03-28-2007 2:27 AM JustinC has not replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 10 of 47 (391811)
03-27-2007 3:10 PM
Reply to: Message 8 by fallacycop
03-27-2007 1:44 PM


quote:
May be you're being too ambitious...
Yeah, that wording did seem a little extreme. I just meant that 'fitness' isn't necessary for understanding natural selection or evolution, i.e, it has no explanatory power.

This message is a reply to:
 Message 8 by fallacycop, posted 03-27-2007 1:44 PM fallacycop has not replied

Replies to this message:
 Message 11 by Chiroptera, posted 03-27-2007 3:36 PM JustinC has replied

  
Chiroptera
Inactive Member


Message 11 of 47 (391814)
03-27-2007 3:36 PM
Reply to: Message 10 by JustinC
03-27-2007 3:10 PM


Maybe a population biologist can critique the Wikipedia article on fitness, but it does give the impression that it is an important quantity in population genetics.
Wikipedia gives the definition:
It describes the capability of an individual of certain genotype to reproduce, and usually is equal to the proportion of the individual's genes in all the genes of the next generation.
Anyway, it seems odd that an entire field of biology would use a technical term if it weren't important.

Actually, if their god makes better pancakes, I'm totally switching sides. -- Charley the Australopithecine

This message is a reply to:
 Message 10 by JustinC, posted 03-27-2007 3:10 PM JustinC has replied

Replies to this message:
 Message 12 by JustinC, posted 03-27-2007 3:46 PM Chiroptera has replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 12 of 47 (391815)
03-27-2007 3:46 PM
Reply to: Message 11 by Chiroptera
03-27-2007 3:36 PM


quote:
Anyway, it seems odd that an entire field of biology would use a technical term if it weren't important.
I would agree. To reiterate the spirit of this thread:
The purpose of this thread is to state some of my objections to fitness and hopefully clear up some of my misconceptions about the concept.
My objections aren't necessarily well-thought out or held with any strong convictions. I'm just throwing some problems out there I have with the concept hoping to get vindicated or corrected.
Edited by JustinC, : No reason given.

This message is a reply to:
 Message 11 by Chiroptera, posted 03-27-2007 3:36 PM Chiroptera has replied

Replies to this message:
 Message 13 by AZPaul3, posted 03-27-2007 4:42 PM JustinC has not replied
 Message 14 by Chiroptera, posted 03-27-2007 4:44 PM JustinC has replied

  
AZPaul3
Member
Posts: 8513
From: Phoenix
Joined: 11-06-2006
Member Rating: 5.2


Message 13 of 47 (391830)
03-27-2007 4:42 PM
Reply to: Message 12 by JustinC
03-27-2007 3:46 PM


Fit to be Tied
If "fitness" is an issue for some then maybe drop the term in favor of "success."
Wiki on "Natural Selection"
Natural selection acts on the phenotype, or the observable characteristics of an organism, such that individuals with favorable phenotypes are more likely to survive and reproduce than those with less favorable phenotypes. If these phenotypes have a genetic basis, then the genotype associated with the favorable phenotype will increase in frequency in the next generation.
This is a pretty good defenition. Reproductive success in a single generation seems "fit" to me. Whether the genotype/phenotype of the offspring can also be classified as "fit" remains to be seen.
Edited by AZPaul3, : Minor boo-boo's

This message is a reply to:
 Message 12 by JustinC, posted 03-27-2007 3:46 PM JustinC has not replied

  
Chiroptera
Inactive Member


Message 14 of 47 (391831)
03-27-2007 4:44 PM
Reply to: Message 12 by JustinC
03-27-2007 3:46 PM


I really looked up the word because I wan't certain whether fitness actually had a technical meaning or whether it was a vaguely defined concept used more as an heuristic aid to making a simple explanation and to avoid a forbiddingly technical discussion.

Actually, if their god makes better pancakes, I'm totally switching sides. -- Charley the Australopithecine

This message is a reply to:
 Message 12 by JustinC, posted 03-27-2007 3:46 PM JustinC has replied

Replies to this message:
 Message 15 by JustinC, posted 03-27-2007 5:15 PM Chiroptera has replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 15 of 47 (391840)
03-27-2007 5:15 PM
Reply to: Message 14 by Chiroptera
03-27-2007 4:44 PM


quote:
I really looked up the word because I wan't certain whether fitness actually had a technical meaning or whether it was a vaguely defined concept used more as an heuristic aid to making a simple explanation and to avoid a forbiddingly technical discussion.
Well, I do think the concept is more vague than the wiki article let's on. Dawkin's writes in The Ancestors Tales:
We are used to thinking of individual organisms as striving to maximise a quantity called 'fitness'. Exactly what fitness means is disputed. One favored approximation is 'total number of children'. Another is 'total number of grandchildren', but there is no obvious reason to stop at grandchildren, and many authorities prefer something like, 'total number of descendents alive at some distant date in the future'.
So I think there is room for some discussion about the concept and how best to define what we are talking about.
A reason this is on my mind is because in another thread Quetzl made it seem like it was a failing of the gene-centric view of natural selection because they couldn't define fitness (i'm not agreeing with that, but I think those were the sentiments he conveyed).
But, if its not fundamental to a discription of natural selection then it seems like a moot point wrt the gene- or individualist- centric viewpoint.
So maybe, to clarify the issue, i'm asking is fitness fundamental to the concept of natural selection. I'm not disputing its an important practical concept.
Edited by JustinC, : No reason given.

This message is a reply to:
 Message 14 by Chiroptera, posted 03-27-2007 4:44 PM Chiroptera has replied

Replies to this message:
 Message 16 by Chiroptera, posted 03-27-2007 5:39 PM JustinC has not replied
 Message 17 by AZPaul3, posted 03-27-2007 7:47 PM JustinC has replied

  
Newer Topic | Older Topic
Jump to:


Copyright 2001-2023 by EvC Forum, All Rights Reserved

™ Version 4.2
Innovative software from Qwixotic © 2024