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Author Topic:   Tautology and Natural Selection
Peter
Member (Idle past 1497 days)
Posts: 2161
From: Cambridgeshire, UK.
Joined: 02-05-2002


Message 61 of 130 (47849)
07-29-2003 5:35 AM
Reply to: Message 55 by Minnemooseus
07-28-2003 1:40 PM


(2) is what Syamsu seems to have the most trouble with....
apart from general comprehension that is

This message is a reply to:
 Message 55 by Minnemooseus, posted 07-28-2003 1:40 PM Minnemooseus has not replied

  
Quetzal
Member (Idle past 5890 days)
Posts: 3228
Joined: 01-09-2002


Message 62 of 130 (47852)
07-29-2003 6:49 AM
Reply to: Message 60 by JustinC
07-29-2003 4:59 AM


I agree with all of that....I think. Do you think I don't? I'm just wondering so I can articulate what I am saying better in the future.
It's entirely possible I'm not understanding what you're trying to get at (yeah, that's a dangling participle - so sue me.) My principal (and thus far only) objection to what you've written revolves around your attempts to apply engineering terminology to biology. The concept may be useful as an analogy in specific, very limited cases, but overall it can be highly misleading. Especially if you use the analogy with non-biologists who don't understand the distinction. Perhaps I'm just an old fart who has a knee-jerk reaction because of all the creationists who misuse the analogy to push their agendas. Maybe you could take a moment to explain exactly what you're getting at (another dangle) and why you find the engineering analogy so compelling. THEN we can disagree on something substantive that doesn't rest on mutual misunderstanding.
Just out of curiousity, is anyone here an evolutionary biologist or know anybody in the field? I'm majoring in Biology right now, but I want to specifically go into Evolutionary Biology, and even more specifically Paleoanthropology. I'm going to be a sophomore, so either way classes for my specific major haven't been taken yet.
Well, let see. Mammuthus and Taz are molecular biologists (IIRC), SLPx is a biologist/primatologist, Wounded King is a biologist of some ilk or other. There are a couple of other people that I suspect are biologists of one stripe or another but who are "undeclared". Andya is studying to be a zoologist, and my background is ecology (could'a guessed, right?) with most of my field work in conservation biology. I'd say go for evolutionary ecology, but I'm biased. Screw paleoanthropology, there's too many "personalities" dominating the field.
Maybe I wasn't specific enough. I mean better than their immediate ancestors, again barring genetic drift.
And,
I'm still not sure how this is objectionable to my statements. They'd have to be better engineered for reproductive success than their immediate ancestors for them to be here at all, even if they are now in a state of decline due to environmental changes or because of variant populations.
Nyet! And this is where we part company, I think. None of those organisms are better than their immediate ancestors. In every case they are worse off, if anything. In one case at least (Wollemia), they ARE their "immediate ancestors" because of the asexual reproduction strategy it uses (coppicing). Simply because an organism reproduces doesn't make it better than its forebears. Mutation-induced variation might make organisms different, not necessarily better. In fact, mutation probably has an even greater chance of making things worse, especially for an organism near its fitness peak.
Out of curiosity, what do you mean by species exchange? Do you mean being replaced by a closely related species that they share a common ancestor with?
Yes and no. Species exchange is a term used to describe the replacement of one species in a given niche or habitat by another. They may or may not be closely related. It can be seen in modern species when exotics are introduced into an ecosystem and wipe out the indigenous species (competitive exclusion) for instance. Another possibility is where a local extinction (background extinction) event or ecosystem degradation occurs that leaves open a number of niches allowing for ecological release of unrelated organisms. In any case, the net result is that one species replaces another - which may have significant impact on the community - to the point where an entire community changes membership.
The term can also be used to describe what is occasionally observed in the fossil record when one species is replaced by a similar one or even a daughter species. In the record, this looks like one species appearing for the first time in a region at the same time another disappears. Elizabeth Vrba coined the term "turnover pulse" for the phenomenon - "turnover" is the species exchange, "pulse" is the ripple effect down through the ecosystem that changes bunches of other species at the same time in the same community. However, she thinks the proximate cause is climatological. IMO the record isn't fine-grained enough to determine causes at anything less than wide geographical or continental space and millions of years of time. (Q ducks while all the geologists jump on that statement.)
I wasn't referring to the wing in context of an organism, I was actually thinking about jetplanes when I wrote it. I was analogizing the wing situation with the organism situation, i.e. wing=organism, lift=reproductive success, and air=environment. Wings lift and organisms reproduce. So you'd factor in everything that effects lifting or reproduction. In the case of reproduction, wings lift may or may not affect reproduction; that wasn't my point though.
I think you've lost me. Could you clarify your point? Sorry - it's probably just a senior moment...

This message is a reply to:
 Message 60 by JustinC, posted 07-29-2003 4:59 AM JustinC has replied

Replies to this message:
 Message 66 by JustinC, posted 07-29-2003 8:56 AM Quetzal has replied

  
Quetzal
Member (Idle past 5890 days)
Posts: 3228
Joined: 01-09-2002


Message 63 of 130 (47854)
07-29-2003 7:05 AM
Reply to: Message 55 by Minnemooseus
07-28-2003 1:40 PM


Hey Moose!
1) The "survival of the fitest" phrase is widely considered to be merely an approximation - not to be taked too literally.
Yep. Not only an approximation, but a misleading soundbite coined by a journalist to popularize and conceptualize natural selection for the masses. One of several things to take Darwin to task for is that he allowed himself to be convinced to include it in his later writings and even in later editions of Origin.
2) It has been vaguely touched upon, but seemingly not explicitly stated - The "survival of the fitest" is a matter of statistical probability - Not all the "most fit" survive to reproduce, and some of the "less fit" do survive to reproduce.
Yep again. Mammuthus and someone else mentioned it. Thanks for bringing it to the fore. In fact, unless there's some realy drastic change in selection pressures that just happens to coincide with a pre-existing trait, significantly changing the frequency of alleles in a population is a lengthy, multi-generation process. Most times, new variants simply disappear over time. Sometimes they can persist as long as the newcomer can live polymorphically with the other variants. Sometimes, especially in smallish populations, drift causes the frequency to increase or decrease more or less randomly.
3) Concerning the asteroid impact - My impression of things is that the environment of the time was already undergoing a radical, if not as sudden of a change as an asteroid impact. A major extinction event was happening prior to the asteroid showing up. Perhaps a worthy topic would be "How significant was the asteroid impact, in the K-T extinction event?". But I'm not going to start the topic.
I've also read that. I'm not sure how "radical" the change was, but there is certainly indications that dinos were on the decline for at least 10 million years before the Big One. Another topic, tho'. I'd still be curious as to anyone's ideas on whether mass extinction events like that asteroid figure into the fitness landscape for a species.

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JustinC
Member (Idle past 4862 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 64 of 130 (47856)
07-29-2003 7:21 AM
Reply to: Message 59 by Mammuthus
07-29-2003 4:23 AM


quote:
Actually this is not completely true. You can stack the odds in favor of a desired outcome, however, perhaps a bacteria that deletes part of your insert has a fitness advantage or knocks everything out except the promoter and the amp resistance gene has an advantage...then you end up with an unexpected and undesireable result. This actually happens in most of these experiments i.e. there is a substantial fraction of surviving bacteria that do not have what you wanted in or selected for. This will happen under almost any circumstances i.e. fairly homogeneous populations can produce novel variants as well that fall somewhere else in the fitness landscape, better, worse, the same...
I did say with all other factors being equal, so I'm not sure the novel variant scenerio is necessarily a criticism. Also, I've stated before that it should be 'The probable reproductive success of the best engineered for reproductive success', so I'm not saying that reproductive success is definative.
quote:
I would not concede that surival of the fittest is unuseful only that as moose pointed out, due to chance events i.e. boloid collisions etc. less fit organisms can survive and reproduce. Again, it is a probability. The observations is that some alleles, variants, are more predominant than others...that is something you can go out and test. The explanation is that said variants have come to predominate by having more offspring i.e. higher fitness.....
I wouldn't say its an explanation of why they predominate. Isn't reproductive success and predomination essentially the same thing? That is one variant leaves the most offspring, then it will predominate by definition. I think predomination and reproductive success are basically referring to the same thing.
quote:
where survival of the fittest goes a bit astray is that it is a bit all or nothing...a certain trait can be at a high frequency without driving all other variants to extinction. The tough part is to figure out why certain variants predominate in natural populations.
Why would all other variants not be driven to extinction, out of curiousity? Is it because that some variants would be due to recessive traits and because of genetic drift? Why would bacteria have different variations living together besides those variants produced by mutations in the previous generation?
quote:
My problem with using the term engineering is that implies intent i.e. purpose. If you just have an increase in representation of variants that produce more offspring regardless of whether it makes them better or worse from an engineering perpective it is the opposite of engineering. Remember, you can have variants arise that say see worse than other variants but are so fecund that they come to dominate..from an engineering perspective this is crazy..but from natures point of view it makes sense.
An engineering perspective is only relevant to enhancing a process or function. It wouldn't be opposite an engineering perspective to say that if the function is reproductive success then certain features will be conducive for reproductive success while not being conducive towards another function, like optimal vision.
I can sympathize with your objections about using 'function' and 'purpose'. I stated before that they shouldn't be used, but I don't know. When can we say something has a function and does not? Do only human artifacts have functions? Do the wings of an airplane have function but not the wings of an eagle?
Any thoughts about words like function and purpose?
JustinC

This message is a reply to:
 Message 59 by Mammuthus, posted 07-29-2003 4:23 AM Mammuthus has replied

Replies to this message:
 Message 65 by Mammuthus, posted 07-29-2003 8:10 AM JustinC has not replied

  
Mammuthus
Member (Idle past 6493 days)
Posts: 3085
From: Munich, Germany
Joined: 08-09-2002


Message 65 of 130 (47858)
07-29-2003 8:10 AM
Reply to: Message 64 by JustinC
07-29-2003 7:21 AM


quote:
I did say with all other factors being equal, so I'm not sure the novel variant scenerio is necessarily a criticism. Also, I've stated before that it should be 'The probable reproductive success of the best engineered for reproductive success', so I'm not saying that reproductive success is definative.
Ok..and Quetzal also pointed out that once population reaches a relatively high fitness threshold or adaptive peak (note again this does not mean it is particularly good, well engineered etc.) mutation will often introduce less adaptive variants...but they could come to predominate by chance as well i.e. they are the guys who did not get hit by the meteor..or had really big umbrellas
quote:
I wouldn't say its an explanation of why they predominate. Isn't reproductive success and predomination essentially the same thing? That is one variant leaves the most offspring, then it will predominate by definition. I think predomination and reproductive success are basically referring to the same thing.
Yes in general but if you are talking about the fitness contribution of a gene you would likely talk about allelic frequencies or a predominant allele rather than in terms of the genes reproductive success..sorry if I made things less clear.
quote:
Why would all other variants not be driven to extinction, out of curiousity? Is it because that some variants would be due to recessive traits and because of genetic drift? Why would bacteria have different variations living together besides those variants produced by mutations in the previous generation?
Except in clonal populations, we are all variants..you and I are different. We may differ in ways that have no impact on our potential reproductive success now but in a different environment it may. If you look at almost any trait or genetic marker you will find some alleles that appear at high frequency but very often you will find individuals or groups of individuals that share a rare variant...some traits are fixed in the population but even so, mutation will tend to at least produce some variants in every generation. Selection for a trait does not immediately imply extinction of all other variants. In fact most traits vary in such a way to produce a normal distribution..think of height for example. Even in very homogeneous populations there is still variation. It does not mean that a trait cannot become so rare that it becomes extinct..but it is not a requirement.
quote:
An engineering perspective is only relevant to enhancing a process or function. It wouldn't be opposite an engineering perspective to say that if the function is reproductive success then certain features will be conducive for reproductive success while not being conducive towards another function, like optimal vision.
I can sympathize with your objections about using 'function' and 'purpose'. I stated before that they shouldn't be used, but I don't know. When can we say something has a function and does not? Do only human artifacts have functions? Do the wings of an airplane have function but not the wings of an eagle?
Any thoughts about words like function and purpose?
Qutezal covered this in his last post but I don't think either of us object to the word function. A specific enzyme catalyzes a specific chemical reaction..this is different from assigning it an intelligent purpose associated with an enzyme having been engineered to catalyze a specific chemical reaction. It implies a goal oriented process for which there is no evidence in evolutionary science.
When you talk about function as the characteristic of a trait i.e. the function of a MAP kinase or whatever, that is fine as this does not describe how the MAP kinase evolved..only what it currently does.
A birds wing may be functional equivalent to an airplanes wing at some level..however, the development of an airplanes wing was a process of engineering with an explicit goal..the evolution of a birds wing may have started out as something that had absolutely nothing to do with flight i.e. it did not arise out of an intent by the organism to fly or to produce offpring that could fly.
cheers,
M

This message is a reply to:
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JustinC
Member (Idle past 4862 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 66 of 130 (47861)
07-29-2003 8:56 AM
Reply to: Message 62 by Quetzal
07-29-2003 6:49 AM


quote:
Maybe you could take a moment to explain exactly what you're getting at (another dangle) and why you find the engineering analogy so compelling. THEN we can disagree on something substantive that doesn't rest on mutual misunderstanding
I think that natural selection is essentially like engineering. In engineering you have a purpose, for consistency lets say to maximize a wings lift. In natural selection, it's reproductive success. In the wing scenerio, lets say every time a better wing was designed it would replace all other wings. And then they'd modify that wing until they got something better and so on. It would be like natural selection, except surviving would be non sequitir. But if the function is reproductive success, then the organisms will by definition have a higher chance of reproductive success. Also, better engineered for other features may or may not be conducive to this broad function, so they could be expected as well.
I also like the way that they both have the "tautology" problem when describing the principles in general. 'Reproductive success of the better engineered for reproductive success' and 'Better lift by the wing better engineered for better lift'.
I don't know if that is coherent, I pulled an alnighter and have to go to work in the fields in 10 min.
Let the disagreeing begin.

This message is a reply to:
 Message 62 by Quetzal, posted 07-29-2003 6:49 AM Quetzal has replied

Replies to this message:
 Message 67 by Mammuthus, posted 07-29-2003 10:09 AM JustinC has not replied
 Message 72 by Quetzal, posted 07-30-2003 7:05 AM JustinC has replied

  
Mammuthus
Member (Idle past 6493 days)
Posts: 3085
From: Munich, Germany
Joined: 08-09-2002


Message 67 of 130 (47869)
07-29-2003 10:09 AM
Reply to: Message 66 by JustinC
07-29-2003 8:56 AM


quote:
I think that natural selection is essentially like engineering. In engineering you have a purpose, for consistency lets say to maximize a wings lift. In natural selection, it's reproductive success.
In engineering you have a purpose that you set out in advance to achieve. Not in evolution... thus engineering is an extremely poor way of describing natural selection or evolution. As I mentioned in my last post, the process that gave rise to wings could very well have developed in the beginning for a completely different purpose such as to enhance jumping or running without any a priori goal of developing flight capacity...and a lot of birds ditched the ability to fly like kakapos and moas as opposed to refining it as you are proposing...it is a crucial difference to say that you arrive at a specific function as opposed to knowing what you are trying to arrive at beforehand.

This message is a reply to:
 Message 66 by JustinC, posted 07-29-2003 8:56 AM JustinC has not replied

Replies to this message:
 Message 68 by Peter, posted 07-29-2003 11:59 AM Mammuthus has replied

  
Peter
Member (Idle past 1497 days)
Posts: 2161
From: Cambridgeshire, UK.
Joined: 02-05-2002


Message 68 of 130 (47888)
07-29-2003 11:59 AM
Reply to: Message 67 by Mammuthus
07-29-2003 10:09 AM


I think what JustinCy is saying is that natural selection
is operating in a similar way to engineering processes, not
that the evolution of a wing can be viewed to be an engineered
process.
S/He says that with an engineering problem you have a function
to be optimised, and feels that natural selection is optimising
reproductive success.
I don't agree with JustinCy, but I think your disagreement is with
a different view on what JustinCy is saying.
Course I could be the one with the wrong end of the stick.
...and I'm the one who doesn't see why 'survival of the fittest'
is a problem

This message is a reply to:
 Message 67 by Mammuthus, posted 07-29-2003 10:09 AM Mammuthus has replied

Replies to this message:
 Message 69 by Mammuthus, posted 07-30-2003 4:46 AM Peter has replied

  
Mammuthus
Member (Idle past 6493 days)
Posts: 3085
From: Munich, Germany
Joined: 08-09-2002


Message 69 of 130 (47975)
07-30-2003 4:46 AM
Reply to: Message 68 by Peter
07-29-2003 11:59 AM


quote:
I think what JustinCy is saying is that natural selection
is operating in a similar way to engineering processes, not
that the evolution of a wing can be viewed to be an engineered
process.
S/He says that with an engineering problem you have a function
to be optimised, and feels that natural selection is optimising
reproductive success.
Again I re-iterate, an engineer has an explicit a priori goal or desired outcome. Natural selection and evolution do not..so how are they comparable. And natural selection is not optimizing reproductive success...how is it that when a trait becomes more frequent it is "optimized"...what is optimal? Not a single biological system is optimal. Reproductive success can be the difference between producing 10 offpring or 1 in a small population..is this optimized if the related group or species the next mountain range over has a population size of millions? Which one is optimized? How has natural selection optimized reproductive success? Some phenotypes are more abundant because of advantages in transmitting their heritable material from one generation to the next...not because they are the optimized reproducers....

This message is a reply to:
 Message 68 by Peter, posted 07-29-2003 11:59 AM Peter has replied

Replies to this message:
 Message 70 by Peter, posted 07-30-2003 6:02 AM Mammuthus has replied
 Message 77 by JustinC, posted 07-30-2003 11:35 AM Mammuthus has replied

  
Peter
Member (Idle past 1497 days)
Posts: 2161
From: Cambridgeshire, UK.
Joined: 02-05-2002


Message 70 of 130 (47984)
07-30-2003 6:02 AM
Reply to: Message 69 by Mammuthus
07-30-2003 4:46 AM


I don't disagree with you, but I think what JustinCy is saying
is that natural selection is acting to optimise
reproductive success -- not optimise individual traits.
You seem to disagreeing with an engineering analogy, but I think
the analogy is targetted slightly differently to the way
you are looking at it.
I still think it's wrong to say that NS optimises anything,
especially reproductive success -- but then I don't think that
reproductive success is a good definition of fitness either,
unless you define repro.succ. to be about survival of offpsring.

This message is a reply to:
 Message 69 by Mammuthus, posted 07-30-2003 4:46 AM Mammuthus has replied

Replies to this message:
 Message 71 by Mammuthus, posted 07-30-2003 6:13 AM Peter has replied
 Message 73 by Quetzal, posted 07-30-2003 7:27 AM Peter has replied

  
Mammuthus
Member (Idle past 6493 days)
Posts: 3085
From: Munich, Germany
Joined: 08-09-2002


Message 71 of 130 (47985)
07-30-2003 6:13 AM
Reply to: Message 70 by Peter
07-30-2003 6:02 AM


quote:
...but then I don't think that
reproductive success is a good definition of fitness either,
unless you define repro.succ. to be about survival of offpsring.
Then you will have to propose a new more esoteric definition to argue....however, if you look at a population where trait X is very highly represented, you know that all those individuals had parents who passed on trait X to them so thus for the parental generation they had the higher reproductive success and thus higher fitness. Now take the current generation with trait X..you don't know if that it will be the most highly represented trait that it passed on or not...it could be that now trait X is a hinderance to survival/reproduction/ mate choice etc. and individuals with trait Y have the most offspring and in the next generation Y is more highly represented than X...then those with trait Y had the higher fitness...basing your definition on survival is not useful unless you believe that dead or never born individuals contribute to the next generation.

This message is a reply to:
 Message 70 by Peter, posted 07-30-2003 6:02 AM Peter has replied

Replies to this message:
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Quetzal
Member (Idle past 5890 days)
Posts: 3228
Joined: 01-09-2002


Message 72 of 130 (47992)
07-30-2003 7:05 AM
Reply to: Message 66 by JustinC
07-29-2003 8:56 AM


Okay, I think I'm beginning to pierce through the fog, here. It comes down to the way you're using the terminology, I guess. You appear to be using "function" and "purpose" in the sense of "role played by" when discussing engineering and natural selection. This is where I got confused. It's a somewhat idiosyncratic way of looking at it, but if that's what makes you comfortable with conceptualizing the idea, then I really don't have a problem with it. I would caution you that function and purpose are not interchangeable. In biology, a strict definition of purpose is meaningless (nature has no purpose), and function is context-dependent. When you use either one in discussions of biology or biological systems or populations or whatever, you may be opening yourself to misunderstanding. This is apparently where my difficulty with your idea of "best engineered for reproductive success" comes from. Or your phrase "the function of natural selection is reproductive success." I guess you're not wrong conceptually the way you've described it - it's just a very odd way of describing what occurs.
Now I'm gonna go argue with Peter .

This message is a reply to:
 Message 66 by JustinC, posted 07-29-2003 8:56 AM JustinC has replied

Replies to this message:
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Quetzal
Member (Idle past 5890 days)
Posts: 3228
Joined: 01-09-2002


Message 73 of 130 (47994)
07-30-2003 7:27 AM
Reply to: Message 70 by Peter
07-30-2003 6:02 AM


I still think it's wrong to say that NS optimises anything,
especially reproductive success -- but then I don't think that
reproductive success is a good definition of fitness either,
unless you define repro.succ. to be about survival of offpsring.
I don't think reproductive success IS a definition of fitness. It's how we quantitatively measure relative fitness at the organismal level. At the level of a population, however, you have a couple of choices, depending on what you're trying to express. F'rinstance, from a pop gen standpoint as Mammuthus pointed out above, you can talk about how an allele or suite of alleles changes in frequency over multiple generations (increase to fixation of novel or rare alleles, for example) as a measure of the fitness of those alleles. Or you can talk about the persistence of a population over the generations in the face of variable environmental factors or changing selective pressures as a measure of the mean fitness (read adaptability) of the population. The "how" of the frequency change and the "how" of persistence over generations is through reproduction. Reproduction only indirectly bears on fitness in and of itself.
I don't know whether that made any sense.

This message is a reply to:
 Message 70 by Peter, posted 07-30-2003 6:02 AM Peter has replied

Replies to this message:
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John
Inactive Member


Message 74 of 130 (48006)
07-30-2003 9:33 AM
Reply to: Message 45 by JustinC
07-26-2003 5:58 PM


quote:
Whose arguing tautologies are fallacious? I'm not.
Usually, when people complain about tautologies, it is because of a perception that there is something 'wrong' with them.
quote:
But tautologies do not make predictions and are not scientific statements.
Tautologies don't make predictions. Definitions don't predict. They just identify. That is all that is going on when you say that 'survivors survive' -- you are pointing out the relevant subset of creatures. Why this subset? The reason is reproduction. Dead creatures don't reproduce and are hence irrelevant to evolution.
quote:
Saying "Survivors survive" doesn't give any clue as to the direction of evolution.
What direction?
If you mean that 'survivors survive' doesn't tell us which adaptations lead to higher survival rates, then of course it doesn't. You have to examine the survivors to find out. I think you are trying to drag way too much out of the first step of the analysis.
quote:
The statement would be true under any scenerio, i.e. if all organisms survive randomly.
Well, if it is always true, it is a very good place to start. Then you ask, "Why?" "Is there a reason some survive and others do not?"
quote:
I wouldn't even say its an observation, it's a logical necessity.
One hundred critters are born. You tag them and release them. A year later, you find all the tags but only 25 are attached to living animals. This is not observation?
quote:
It's good for a definition, but not good for science.[
I dare you to do science without definitions. Hell, I dare you to think about anything without starting with definitions. Why are you downplaying this? Consider. We want to study light. What is light? Well, you have to define it somehow, otherwise you can't move on to further study. "Light is what illuminates the Earth during the day." "Light is what candles emit." All very circular definitions really. It is unavoidable. You seem to object to this step.
------------------
No webpage found at provided URL: www.hells-handmaiden.com

This message is a reply to:
 Message 45 by JustinC, posted 07-26-2003 5:58 PM JustinC has replied

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Peter
Member (Idle past 1497 days)
Posts: 2161
From: Cambridgeshire, UK.
Joined: 02-05-2002


Message 75 of 130 (48022)
07-30-2003 11:05 AM
Reply to: Message 71 by Mammuthus
07-30-2003 6:13 AM


What if you take a snapshot of a population where
(for arguments sake) all the offpsring were born in
the same season, and no more offspring will be born until
these ones mature.
What determines the extant traits at the beginning of the
reproductive season for the offpsring?
Is it how many with trait X were born (reference to numbers
of parents in previous gen.)
Or number of trait X offspring that have survived to
the breeding season?
It might not be that trait Y individuals have more offspring
so much as more of them survive to maturity.
The same holds iteratively for season-on-season survival rates.
You may have 100 X's born and 50 Y's but all 50 Y's survive
to breed and only 10 X's.
Each X has ten offpsring per season of which one survives
and each Y has one only which survives.

This message is a reply to:
 Message 71 by Mammuthus, posted 07-30-2003 6:13 AM Mammuthus has not replied

  
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