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Author Topic:   Interweaving Evolution & Hybrid Vigor
RAZD
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Message 1 of 19 (771179)
09-30-2015 1:14 PM


Heterosis defined
I was rereading the Peter & Rosemary Grant, Darwin's Finches and Evolution thread and in particular noted this passage from the initial quote (Message 1):

quote:
(The People Who Saw Evolution)

... It looked a lot like a fortis, but also like a scandens. Genetic analysis showed 5110 to be a cross between a fortis and a fortis-scandens hybrid. They called it “the Big Bird.”

The Big Bird had a unique song and, when mature, shiny black plumage that was different from the indigenous Daphne birds. It also was extremely “fit” in the Darwinian sense — and promiscuous, surviving another 13 years and mating with six females, producing 18 offspring. It mated with several fortis-fortis-scandens hybrids, then with fortis females, and began a new line of Big Birds that sang the song of the original immigrant.


And I also recall the discussion on New Species of Homo Discovered: Homo naledi of a "braided" history ... from the article:

quote:
This Face Changes the Human Story. But How?

Berger himself thinks the right metaphor for human evolution, instead of a tree branching from a single root, is a braided stream: a river that divides into channels, only to merge again downstream. Similarly, the various hominin types that inhabited the landscapes of Africa must at some point have diverged from a common ancestor. But then farther down the river of time they may have coalesced again, so that we, at the river’s mouth, carry in us today a bit of East Africa, a bit of South Africa, and a whole lot of history we have no notion of whatsoever. ...


Because Homo naledi is a mosaic of features some modern derived features and some preserved ancestral features, and that applies to other species, such that there is some mixing and matching going on, this suggests some hybridization in the past. We also know from DNA analysis that there was some hybridization with Homo neanderthalus (alt Homo sapiens neanderthalus )

Wikipedia defines Heterosis as:

quote:
Heterosis, hybrid vigor, or outbreeding enhancement, is the improved or increased function of any biological quality in a hybrid offspring. The adjective derived from heterosis is heterotic.

An offspring exhibits heterosis if its traits are enhanced as a result of mixing the genetic contributions of its parents. These effects can be due to Mendelian or non-Mendelian inheritance.

Heterosis is often discussed as the opposite of inbreeding depression although differences in these two concepts can be seen in evolutionary considerations such as the role of genetic variation or the effects of genetic drift in small populations on these concepts. Inbreeding depression occurs when related parents have children with traits that negatively influence their fitness largely due to homozygosity. In such instances, outcrossing should result in heterosis.

Not all outcrosses result in heterosis. For example, when a hybrid inherits traits from its parents that are not fully compatible, fitness can be reduced. This is a form of outbreeding depression.


An example of outbreeding depression would be horses, donkeys and mules, where reproductive isolation is not complete but usually results in sterility.

So outbreeding can result in hybrids that are more fit, equally fit or less fit, at which point natural selection would favor the more fit (heterotic) varieties becoming dominant in the population/s, leading to a new species group.

Crossbreeding is done a lot in animal husbandry and agriculture to develop improved stock, so it should not come as a surprise that it can occur naturally when daughter populations regain contact after undergoing different evolutionary experiences, but before they have evolved reproductive isolation.

The amount of independent evolution could vary a lot, as it is the development of reproductive isolation that would stop such interbreeding. Certainly when we see that hybrids can be made between lions and tiger or between lamas and camels after long periods of separation.

We also see this between European invaders and Native peoples of the Americas.

So the tree became a bush becomes an interlinked\braided bush.

         A
         |
         |
        / \
       /   \
      |     |
     / \   / \
    |   \ /   |
    |    |    |
    |    |    |
    B    C    D

Where C is not the same as A, but is a braided mosaic of B and D. Note that A, B, C and D still form a clade descended from A.

This does not mean that evolution does not happen, just that the process is not a cut-and-dried cookie-cutter proposition. This also means that the definition of "species" is a little muddier than before ... and it was muddied before.

Enjoy

Edited by RAZD, : subt

Edited by RAZD, : ..

Edited by RAZD, : fix code

Edited by RAZD, : .


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RAZD
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Message 2 of 19 (771180)
09-30-2015 2:52 PM
Reply to: Message 1 by RAZD
09-30-2015 1:14 PM


... and dogs (and cows and pigs ... )
Another application of this to the debate is when we look at animal husbandry, agriculture and breeding programs.

So outbreeding can result in hybrids that are more fit, equally fit or less fit, at which point natural selection would favor the more fit (heterotic) varieties becoming dominant in the population/s, leading to a new species group.

Now we can see in dog breeding that some dogs are bred to create an extremely inbred population in order to maintain the "breed" and that these types of breeds often exhibit inbreeding depression. These are the "show" dogs, but they are not the only breeds.

Another class of dog breeds are "working" dogs, where the appearance of the dog is not as important as the function. The sheep herding dogs come to mind. To my view they seem to exhibit Heterosis and not exhibit any of the inbreeding symptoms.

We can also look at cow and pig breeding, where the purpose is not some aesthetically "pretty" animal but one that fills a function (more milk, more meat).

From the Wikipedia definition of Heterosis again:

quote:
In proposing the term heterosis to replace the older term heterozygosis, G.H. Shull aimed to avoid limiting the term to the effects that can be explained by heterozygosity in Mendelian inheritance.[1]

The physiological vigor of an organism as manifested in its rapidity of growth, its height and general robustness, is positively correlated with the degree of dissimilarity in the gametes by whose union the organism was formed … The more numerous the differences between the uniting gametes — at least within certain limits — the greater on the whole is the amount of stimulation … These differences need not be Mendelian in their inheritance … To avoid the implication that all the genotypic differences which stimulate cell-division, growth and other physiological activities of an organism are Mendelian in their inheritance and also to gain brevity of expression I suggest … that the word 'heterosis' be adopted.

When the aspects of rapid growth, size and robust health are considered it is easy to see why this is pursued in husbandry.

Again, we can see how (properly applied) artificial husbandry practices offer a window into how natural evolution (mutation and selection) can operate.

Enjoy


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RAZD
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Message 3 of 19 (771181)
10-20-2015 12:03 PM
Reply to: Message 2 by RAZD
09-30-2015 2:52 PM


Revisiting Punctuated Equilibrium ...
https://en.wikipedia.org/wiki/Punctuated_equilibrium

quote:
Punctuated equilibrium (also called punctuated equilibria) is a theory in evolutionary biology which proposes that once species appear in the fossil record they will become stable, showing little net evolutionary change for most of their geological history. This state is called stasis. When significant evolutionary change occurs, the theory proposes that it is generally restricted to rare and geologically rapid events of branching speciation called cladogenesis. Cladogenesis is the process by which a species splits into two distinct species, rather than one species gradually transforming into another.[1] Punctuated equilibrium is commonly contrasted against phyletic gradualism, the belief that evolution generally occurs uniformly and by the steady and gradual transformation of whole lineages (called anagenesis). In this view, evolution is seen as generally smooth and continuous.

In 1972, paleontologists Niles Eldredge and Stephen Jay Gould published a landmark paper developing their theory and called it punctuated equilibria.[2] Their paper built upon Ernst Mayr's model of geographic speciation,[3] I. Michael Lerner's theories of developmental and genetic homeostasis,[4] as well as their own empirical research.[5][6] Eldredge and Gould proposed that the degree of gradualism commonly attributed to Charles Darwin is virtually nonexistent in the fossil record, and that stasis dominates the history of most fossil species.

... Punctuated equilibrium differs from Mayr's theory mainly in that Eldredge and Gould placed considerably greater emphasis on stasis, whereas Mayr was generally concerned with explaining the morphological discontinuity (or "sudden jumps")[10] found in the fossil record.[7] Mayr later complimented Eldredge and Gould's paper, stating that evolutionary stasis had been "unexpected by most evolutionary biologists" and that punctuated equilibrium "had a major impact on paleontology and evolutionary biology". ...


The standard view iirc, is that a small subpopulation evolves in isolation, and then returns to the habitat of the parent population and displaces it with their better adapted phenotypes.

With the emerging thoughts on "braided" beginnings to new species and hybrid interactions during the early stages of new species formation, it seems more logical to me that the returning subpopulation interbreeds with the parent population and the hybrid offspring inherit traits from both populations, which are then selected for fitness, leaving a new population with hybrid vigor and a mosaic of traits.

This has the benefit of mixing the best of both populations within a larger breeding population.

Enjoy


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Message 4 of 19 (771182)
10-21-2015 8:40 AM


Moderator Question
Is this a topic you wanted to discuss, or information you'd like placed over at Links and Information. If this is a discussion topic, how does it tie in with creation/evolution?

Also, I think punctuated equilibria when a population experiences a period of rapid evolution, as opposed to relative stasis. The population could subsequently return to displace the original parent population, but I think that's just competition, not punctuated equilibrium.


--Percy
EvC Forum Director

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RAZD
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Message 5 of 19 (771183)
10-21-2015 9:40 AM
Reply to: Message 4 by Admin
10-21-2015 8:40 AM


Re: Moderator Question -- the basic question for debate
Discussion, on how evolution works in regards to speciation. It's not always straight line process of speciation, but a little tangled, a little messy.

Also, I think punctuated equilibria when a population experiences a period of rapid evolution, as opposed to relative stasis. The population could subsequently return to displace the original parent population, but I think that's just competition, not punctuated equilibrium.

The basic idea behind punctuated equilibria, as I understand it, is that a smaller relatively isolated population undergoes rapid evolution, possibly to adapt it to a slightly different ecology. Then it returns to the parent ecology which has been in stasis (continually readapting to a static ecology) and has an advantage for survival or breeding, and then it takes over and displaces the parent population.

The question I am raising on this is whether full speciation of this daughter population is necessary, or would not a new varietal phenotype that can interbreed and form hybrids that join the best features in a mosaic of phenotypic traits be a valid or better explanation.

We have evidence of such mosaic evolution, the braided stream pattern noted on the Homo naledi thread for instance, and the Darwin Finch hybrid "big Bird" as another.

Enjoy


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Message 6 of 19 (771184)
10-21-2015 1:09 PM
Reply to: Message 5 by RAZD
10-21-2015 9:40 AM


Re: Moderator Question -- the basic question for debate
RAZD writes:

The basic idea behind punctuated equilibria, as I understand it, is that a smaller relatively isolated population undergoes rapid evolution, possibly to adapt it to a slightly different ecology.

Right.

Then it returns to the parent ecology...

Possibly. Or it might migrate somewhere else. Or nowhere else. Or it might return to the parent ecology and co-exist with the parent. Or it might return to the parent ecology and find that there is no longer any parent population to compete against because it's gone extinct.

I thought what was novel about the punctuated equilibria idea was that the episodic nature of the fossil record wasn't necessarily just an artifact of an incomplete fossil record, that it could also be real.


--Percy
EvC Forum Director

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RAZD
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Message 7 of 19 (771185)
10-21-2015 2:33 PM
Reply to: Message 6 by Admin
10-21-2015 1:09 PM


Re: Moderator Question -- the basic question for debate
Possibly. Or it might migrate somewhere else. Or nowhere else. Or it might return to the parent ecology and co-exist with the parent. Or it might return to the parent ecology and find that there is no longer any parent population to compete against because it's gone extinct.

True.

Part of the reason I want to open this to debate with others, particularly those that know more about this than I do.

I thought what was novel about the punctuated equilibria idea was that the episodic nature of the fossil record wasn't necessarily just an artifact of an incomplete fossil record, that it could also be real.

Indeed, but for my argument ("the part I want to focus on" ... ), especially in those areas where successive fossil layers show noticeably different forms.

Now, I would like to credit Faith for leading me to think in this direction while formulating responses to her argument and her questions on this phenomenon in the fossil record.

And I have another example that I am working on, which I will save till after promotion and some confirmation from others that I am not just blowing smoke.

Enjoy


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Message 8 of 19 (771187)
10-21-2015 8:46 PM


Thread Copied from Proposed New Topics Forum
Thread copied here from the Interweaving Evolution & Hybrid Vigor thread in the Proposed New Topics forum.
    
RAZD
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Message 9 of 19 (771282)
10-23-2015 1:17 PM
Reply to: Message 7 by RAZD
10-21-2015 2:33 PM


Greenish Warbler Ring Species and Interwoven Evolution
In Why Evolution is True, There are no ring species Jerry Coyne argues that there are no "ring species in the classic sense" ... and then goes on to describe what he feels the "classic sense" is:

quote:
But first, what is a ring species? Ring species constitute one big and supposedly continuous population in which the attainment of biological speciation (to people like me, that means the evolution of two populations to the point that they cannot produce fertile hybrids were they to live in the same place in nature) does not require full geographic isolation of those populations. Rather, speciation in that continuous population occurs through a gradual spread of the range of the animals, coupled with selection in different places that causes their genetic divergence.

The idea is that classic ring species demonstrate evolution in a horizontal space continuum as opposed to "traditional" evolution in a vertical time continuum, and thus we can look at the intermediate stages between initial division of a population until fully independent species are developed, which in the classic ring species would mean that the two end points don't interbreed.

He further describes this classic ring species as a continuous gradualistic development:

quote:
It works like this: a species expands its range and encounters a roughly round geographic barrier like a valley, the Arctic ice cap, or an uninhabitable plateau. It divides and spreads around the edges of the barrier, so that its range becomes circular as it expands. And as the range begins to form a circle, the populations within it begin to become genetically different as they respond to local selection pressures. But the circle is never interrupted, so while each part of the expanding species becomes genetically different, it still exchanges genes with adjacent populations.

He then cites why the classic ring species does not exist:

quote:
... Because genetic studies, done by both Dick Highton at Maryland and then by Wake and his colleagues themselves (references below) also showed that in places around the ring there were sharp genetic breaks, suggesting not a process of continuous gene flow ...

... everyone has now concluded that the formation of this “ring” involved sporadic and important episodes of geographic isolation between populations, so it’s not the classic “continuous gene flow” scenario involved in making a ring species. ...

... gulls in the genus Larus encircling the Arctic, also fell victim to genetic studies, showing that it was very unlikely that they were ever a continuous ring that was geographically uninterrupted. ...

That left the greenish warbler, ...

... Now, however, genetic analysis of 95 birds and more than 2,000 sites throughout the genome (not just in the mitochondrion), has revealed four genetic clusters around the ring with a sharp intergradation between them (there’s another cluster in the Caucasus, not around the ring). ...


So not a classic continuous gene flow ring species ... and all these examples show lumpy evolution with some isolation and rejoining of the ring variety populations. Messy.

Here's another graphic from the Genomic divergence in a ring species complex paper that Jerry cites:

When I look at these diagrams I see four genetic groups, P.t.nitidus (purple, the western-most, isolated group that may have been the parent population), P.t.viridanus (blue, perhaps the founder of the western clade), P.t.trochiloides (yellow, the first described "type" of P.trochiloides?) and P.t.plumbeitarsus (red, perhaps the founder of the eastern clade) that are pretty much homogenous, and that P.t.ludlowi appears to be a hybrid between P.t.viridanus and P.t.trochiloides that has evolved some distinctive traits (green patches) not shared with either parent population, and likewise that P.t.obscuratus appears to be a hybrid between P.t.trochiloides and P.t.plumbeitarsus that has also evolved some distinctive traits (orange patches) not shared with either parent population. It also looks like a hybrid population may emerge in the north where the ring ends meet and some interbreeding occurs ... or the eastern variety will increasingly become a hybrid with the introgression of the western variety and the loss of gene flow from the south due to habitat destruction. Only time will tell.

Jerry concludes:

quote:
Nevertheless, the results do show a “ring species” of a sort: isolation of two “end” populations of a ring that makes them look like two species, even though all through the ring you don’t see reproductive isolation of adjacent areas. And it shows that speciation can occur despite there having been some gene flow at some times. In nature, populations that form new species must often sometimes exchange genes if they’re not completely isolated by geography (i.e. the finch species that colonized the Galápago), so the dichotomy between “no gene flow” and “pervasive gene flow” may be artificial.

Indeed, "species" is a matter of definition, and if we apply the definition of species discussed on How do you tell one species of turtle from another? where the two populations show distinct genomes and interbreeding is not considered a deal killing element, then it looks to me that we have four species:

  1. P.t.nitidus (becomes P.nitidus?)
  2. P.t.viridanus (becomes P.viridanus?)
  3. P.t.trochiloides (becomes P.trochiloides?) and
  4. P.t.plumbeitarsus (becomes P.plumbeitarsus?)

... if we use the "genetically distinct" definition for species.

How does this fit in with the "Interweaving Evolution and Hybrid Vigor" argument?

Well, we now have two large populations of hybridization that have evolved some distinct traits not found in the neighboring populations:

  1. P.t.ludlowi (viridanus\trochiloides hybrids) and
  2. P.t.obscuratus (trochiloides\plumbeitarsus hybrids)

... with further small hybrid zones between them and their neighboring populations through geography that tends to isolate these two large hybrid populations. The small zones appear have waxed and waned, but they also seem to allow some gene flow when they active, so the two large hybid populations can have limited interactions with the neighboring genetically distinct populations.

These two populations show exactly the intermingling and then later differentiation evolution posited in Message 1.

So the tree became a bush becomes an interlinked\braided bush.

         A
         |
         |
        / \
       /   \
      |     |
     / \   / \
    |   \ /   |
    |    |    |
    |    |    |
    B    C    D

Where C is not the same as A, but is a braided mosaic of B and D. Note that A, B, C and D still form a clade descended from A.

So, not a "classic ring species" but an example of horizontal braided mosaic mixing before species are reproductively isolated.

Enjoy

Edited by RAZD, : clrty


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Faith
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Message 10 of 19 (771360)
10-25-2015 1:08 AM
Reply to: Message 9 by RAZD
10-23-2015 1:17 PM


Re: Greenish Warbler Ring Species and Interwoven Evolution
I wish there was a way I could get my argument onto this thread since it is touching on so many areas of interest to my point of view, but I can't think of a way as it is currently written.
This message is a reply to:
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RAZD
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(1)
Message 11 of 19 (771373)
10-25-2015 12:30 PM
Reply to: Message 10 by Faith
10-25-2015 1:08 AM


Re: Greenish Warbler Ring Species and Interwoven Evolution
I wish there was a way I could get my argument onto this thread since it is touching on so many areas of interest to my point of view, but I can't think of a way as it is currently written.

Well I would like to finish making sure you understand that I understand your argument by finishing the discussion on A New Run at the End of Evolution by Genetic Processes Argument (see Message 209 latest post).

Then we can see how it applies or doesn't apply here.

Enjoy


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herebedragons
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Message 12 of 19 (771793)
10-30-2015 12:05 AM
Reply to: Message 5 by RAZD
10-21-2015 9:40 AM


Re: Moderator Question -- the basic question for debate
The basic idea behind punctuated equilibria, as I understand it, is that a smaller relatively isolated population undergoes rapid evolution, possibly to adapt it to a slightly different ecology. Then it returns to the parent ecology which has been in stasis (continually readapting to a static ecology) and has an advantage for survival or breeding, and then it takes over and displaces the parent population.

I think you may have a slight misconception about punctuated equilibrium. The basic idea behind PE is that organisms remain relatively stable for long periods of time and then make a sudden evolutionary leap. The idea was proposed to help explain why the fossil record looks the way it does, with organism appearing suddenly, hanging around a while virtually unchanged and then disappearing from the fossil record to be replaced by a derived version. It is often thought of as being in opposition to gradualism, but in reality it is a form of gradualism.

I like the way Allen Orr describes it. The image below is a model that Fisher developed and Orr expanded on.

Travelling towards the center of the sphere is adaptation toward an optima. The red line is the fitness path a hypothetical organism might follow. Sometimes the path doesn't lead directly to a most optimal level, but makes a big change not directly towards the center. Some changes are quite small, but others (one in particular) are rather large. The large step (the third layer in from the outside) is what Gould would have identified as punctuated evolution. Another observation Fisher/Orr made was that as the fitness gets closer to optimum, the steps begin to get smaller. So, there is not likely to be large leaps when the population is close to optimal fitness. I think Orr has a good balance between PE and pure gradualism (including neutral theory).

The question I am raising on this is whether full speciation of this daughter population is necessary, or would not a new varietal phenotype that can interbreed and form hybrids that join the best features in a mosaic of phenotypic traits be a valid or better explanation.

The phenomenon you are describing is called reinforcement.

This appears to be an excerpt from Jerry Coyne's book "Why Evolution is True" and is a good article about reinforcement.

HBD


Whoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca

"Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem.

Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.


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RAZD
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Message 13 of 19 (771845)
10-30-2015 7:51 PM
Reply to: Message 12 by herebedragons
10-30-2015 12:05 AM


punk eek and interwoven evolution \ hybrids
I think you may have a slight misconception about punctuated equilibrium. The basic idea behind PE is that organisms remain relatively stable for long periods of time and then make a sudden evolutionary leap. ...

Where that sudden leap occurs in a small population, partially to totally isolated from the main static population -- that small(er) population can evolve faster due to the smaller gene pool where an advantageous mutation\adaptation to a secondary ecology can spread relatively quickly.

... and then disappearing from the fossil record to be replaced by a derived version. ...

Yes, that came in from the periphery ...

... but was the old population replaced or is it a hybrid population, mixing the best adaptations from the isolated population and the static population? Certainly the derived new population is a mosaic evolution from the static parent population with some new traits and some old traits,

... It is often thought of as being in opposition to gradualism, but in reality it is a form of gradualism.

Or we see a range of evolutionary rates and selection pressures. Certainly when we look at foraminifera the record is one of classic gradualism occurring over generations, and certainly when we look at pelycodus we see a general gradualistic overall trend from small to larger, and then at the point of speciation there is a 'sudden' (eg quicker) trend back to small in the one branch to provide 'distance' from the other branch (and resulting reduction of competition) ...

... and there were other earlier branches that failed and either died out or were reabsorbed into the main population. Doesn't that have the potential to introduce new traits back into the main population?

For instance here are a pair of different interpretations of pelycodus and copelemur evolution:


(http://www.mun.ca/biology/scarr/Pelycodus_gradual.htm & http://www.mun.ca/biology/scarr/Pelycodus_punctuated.htm)

In both interpretations the first branch appears to die out or get reabsorbed, and I (not surprisingly) favor the reabsorbed with new mutations added back into the main population. Also I see that the whole population shifted to the left as this occurred, which is another reason why I see reabsorbtion as a viable option here.

Side note: Copelemur is named for Edward Drinker Cope of COPE's Rule that species over time will tend to increase in size, a trend we definitely see running up the right side in both images.

Travelling towards the center of the sphere is adaptation toward an optima. The red line is the fitness path a hypothetical organism might follow. Sometimes the path doesn't lead directly to a most optimal level, but makes a big change not directly towards the center. Some changes are quite small, but others (one in particular) are rather large. The large step (the third layer in from the outside) is what Gould would have identified as punctuated evolution. Another observation Fisher/Orr made was that as the fitness gets closer to optimum, the steps begin to get smaller. So, there is not likely to be large leaps when the population is close to optimal fitness. I think Orr has a good balance between PE and pure gradualism (including neutral theory).

As long as the ecology stays static the selection pressures will be static, and large populations will tend to select towards the centers of their ranges of variations -- ie for stasis. The evolution of variations will be more tolerated at the edges where less viable individuals are pushed into marginal habitats, and if the population is large enough it will cover multiple habitat\ecologies and you can get population subdivision with anomalously high proportions of homozygotes compared to completely homogeneous populations. or one could say ... evolution happens.

The phenomenon you are describing is called reinforcement.

This appears to be an excerpt from Jerry Coyne's book "Why Evolution is True" and is a good article about reinforcement.

Super nice links, I spent a couple hours perusing the first back to the A-Z links and all the items listed. Sad to see it did not list 'mosaic' but not surprised. One of my dad's pet comments was that evolution in general and human evolution in particular displayed mosaic evolution, essentially where parts evolve rather than the whole individual. He thought it was underplayed in the field.

But no, not reinforcement -- as that leads to speciation, but rather an interweave where different populations rejoin and form viable hybrids that exhibit hybrid vigor and how does that occur in natural systems\selection.

Consider the level where populations rejoin, there are genetic differences due to isolated mutation selections, but now they are interbreeding -- cross breeding -- and re-fertilizing the static parent population with new fitness traits that take over. This introduces new traits into the population with a wave effect.

Or am I smoking some kind of crack?

Enjoy

Edited by RAZD, : added


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 Message 16 by herebedragons, posted 10-31-2015 11:47 PM RAZD has responded

  
RAZD
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Posts: 18867
From: the other end of the sidewalk
Joined: 03-14-2004
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Message 14 of 19 (771913)
10-31-2015 6:44 PM
Reply to: Message 12 by herebedragons
10-30-2015 12:05 AM


The Hardy-Weinberg ratio
Again thanks for the links, the http://www.blackwellpublishing.com/ridley/a-z/ link in particular is an excellent resource and should probably be posted in Links and Information.

The Hardy-Weinberg ratio explains quite easily why mutations or rare alleles are more likely to be spread in a small population than a large one:

quote:

The Hardy-Weinberg ratio is the starting point for much of the theory of population genetics. It is the ratio of genotype frequencies that evolve when mating is random and neither selection nor drift are operating. For two alleles (A and a) with frequencies p and q, the Hardy-Weinberg frequencies are

Genotype AA : Aa : aa
Frequency p^2 : 2pq : q^2

These frequencies are reached after a single generation of random mating from any initial genotype frequencies. The Hardy-Weinberg ratio can be understood in terms of simple combinatorial probability.


Now I was a little confused at first by the "reached after a single generation" comment, until I realized that this applies to each generation and changes with selection acting on the relative fitness of p and q.

This also assumes equality between male and female viability and distributions, as the probability of the offspring combinations is the probability of male (p,q) mating with female (p,q) and hence the pxp + pxq + pxq + qxq probabilities. Or in table form

pq
ppppq
qqpqq

But certainly for a new mutation allele the q will be necessarily small, and thus it's relative proportion within the population will be overwhelmingly swamped by p in very large populations but not so much in very small populations.

Enjoy

Edited by RAZD, : table


we are limited in our ability to understand
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RebelAmerican☆Zen☯Deist
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This message is a reply to:
 Message 12 by herebedragons, posted 10-30-2015 12:05 AM herebedragons has responded

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 Message 15 by herebedragons, posted 10-31-2015 11:25 PM RAZD has responded

  
herebedragons
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Posts: 1375
From: Michigan
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(2)
Message 15 of 19 (771919)
10-31-2015 11:25 PM
Reply to: Message 14 by RAZD
10-31-2015 6:44 PM


Re: The Hardy-Weinberg ratio
The Hardy-Weinberg ratio explains quite easily why mutations or rare alleles are more likely to be spread in a small population than a large one:

H-W is one of the most basic principles in population genetics and yet is one of the most often misunderstood. H-W by itself does not address changes in allele frequency but describes what genotypes will be present at any given allele frequencies after one round of mating.

Let's say we have an allele with a frequency of q = 0.10 so that p = 1 - q = 0.90. What H-W says the genotypes would be AA = 0.81, Aa = 0.18, aa = .01. But notice that p still equals 0.90 and q still equals 0.10, no change in allele frequency. Without some force that changes the allele frequency, the frequency will remain q = 0.10.

Here's where H-W gets useful; let's say we find the population has an allele proportion of q = 0.10 and p = 0.90 but the measured genotype frequency is AA = 0.828, Aa = .162, aa = 0.028. We recognize this to be out of H-W equilibrium and so one of the 5 assumptions must not be valid

1. mating is random
2. population is infinitely large
3. no migration
4. no mutation
5. no selection

In this case, mating is not random but shows signs of inbreeding (the proportion of heterozygotes is reduced). We can estimate the inbreeding coefficient by F = (HO-HE)/HO where HO is heterozygotes observed and HE is heterozygotes expected. In this case F = 0.10 which means 10% of the population is autozygous.

Now I was a little confused at first by the "reached after a single generation" comment, until I realized that this applies to each generation and changes with selection acting on the relative fitness of p and q.

Right, so we start with an allele frequency and determine the genotype. The population may then be subjected to selection which will remove an uneven proportion of alleles, ie. one allele will increase in frequency, the other will decrease. Selection models are kinda involved and I won't take time on it here, but let's say that the genotype aa is advantageous and the allele q increases from 0.10 to 0.15 because of selection. We now need to do the H-W calculation again to determine the genotypes of the next generation AA = 0.723, Aa = 0.255, aa = 0.022. So, an increase of 50% in allele frequency resulted in a 120% increase in 'aa' genotype frequency.

But certainly for a new mutation allele the q will be necessarily small, and thus it's relative proportion within the population will be overwhelmingly swamped by p in very large populations but not so much in very small populations.

Definitely true. Unless q confers a large fitness advantage, I would expect drift would be the primary process that would increase its frequency in a small population. Mutations can move to fixation in small populations rather rapidly, especialy when they have even a small fitness advantage.

If you are interested in a really good, easy to understand book on population genetics, I highly recommend A Primer of Population Genetics. We used it in my Evolutionary Biology course and it is an excellent introduction to population genetics. Even if you have a more advanced understanding of the material, it is still a really good book.

HBD


Whoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca

"Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem.

Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.


This message is a reply to:
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