Means to an evolutionary end

[Southwind17]

Why is the Theory of Evolution not incompatible with the phenomenon of regression toward the mean? Surely a population mean has to move over time for evolution to occur, but how does that fit with 'regression', and how does 'regression' reconcile with localised random mutation constantly setting new evolutionary paths?

 

[Wowbagger]

It might help to think of evolutionary paths as more like a saw-toothed edge: There are localizes ups and downs, but a long term trend in some direction can be seen in hindsight.

It might also help to remember that ALL averages are subject to change, over time, not just those in biological evolution. Basketball players with "hot hands" might regress towards their personal mean. But, if you chart their abilities over longer periods of time, there would be distinct trends in the increase and decrease of their performance.

Does that cover it?

 

[AvalonXQ]

Regression towards the mean assumes random variables.

By definition, natural selection involves preference for some traits over others -- hence, not random.

Perhaps this would be more easily understood if you were to list the assumptions under which we see regression towards the mean, and then explain how you believe biological populations fit those assumptions.

 

[Wowbagger]

By definition, natural selection involves preference for some traits over others -- hence, not random.

There might be some element of random drift, at the very local level. Though, you are largely correct: The greater trends of evolution are not random (otherwise they wouldn't be "trends", but would remain random deviations from consistent, central values).

 

[Southwind17]

It might help to think of evolutionary paths as more like a saw-toothed edge: There are localizes ups and downs, but a long term trend in some direction can be seen in hindsight.

Accepted, but doesn't really help in reconciling the two, at least not in my mind.

It might also help to remember that ALL averages are subject to change, over time, not just those in biological evolution. Basketball players with "hot hands" might regress towards their personal mean. But, if you chart their abilities over longer periods of time, there would be distinct trends in the increase and decrease of their performance.

Not sure what you're saying here. Are you saying that we should expect to see a round of professional golf as averaged over all PGA Tour players, say, improve over time (equipment development aside)?

Regression towards the mean assumes random variables.

By definition, natural selection involves preference for some traits over others -- hence, not random.

Random mutations?

 

[AvalonXQ]

Accepted, but doesn't really help in reconciling the two, at least not in my mind.


Not sure what you're saying here. Are you saying that we should expect to see a round of professional golf as averaged over all PGA Tour players, say, improve over time (equipment development aside)?


Random mutations?

But not with symmetrical effects.

Regression to the mean assumes random sampling of a distributed population. That would be the case if mutations had no effect on fitness, so that animals with negative mutations had as many offspring as animals with positive mutations.

But a basic assumption of evolution is that this is false -- some variations result in greater survival and more offspring. Thus, the sampling isn't random. It's biased in a certain direction.

Because regression to the mean depends on random sampling and evolution depends on nonrandom survival, the former does not apply to the latter.

 

[Dymanic]

I'm don't think "regression toward the mean" is a very good way to describe the phenomenon, but stabilizing selection is just what you'd expect to see in a population -- especially a large population -- well adapted to local conditions.

The most ideal conditions tend to exist near the center of the natural range (practically a no-brainer if you really think about it). At the edges of that range you may find organisms struggling to exist, let alone reproduce. Random mutation might provide traits that would enable them to become better suited to the harsher (as in "different") conditions, but it would be hard for those mutations to gain traction as long as there was significant gene flow between those organisms and the main population, because in becoming better suited to conditions at the edges of the range, they would become less suited to conditions near the center, where the main population exists, so those mutations would be swamped in the larger genome. It is when the edge-dwellers become completely cut off reproductively from the main population that you'd see the new traits take off, possibly leading to the emergence of a new species ("allopatric speciation").

 

[Gord_in_Toronto]

Natural Selection works against Regression to the Mean by continually selecting the "fitter" members of the set for the next "cycle" and knocking off the less fit ones.

 

[dogjones]

Yes, and it is the environment which determines how the natural selection plays out. So in a sense it is the environment which forces direction into the random mutation and therefore works against regression to the mean.

If the environment behaved randomly, perhaps regression to the mean would come into play. Which would probably not involve life.

 

[Delvo]

Regression to the mean is not a force compelling everything to move back toward average if it's strayed away from average. It's just the fact that if you compare an extreme observation to some other random observation, the other one will probably be closer to average than the extreme one you're comparing it with... because the one you're comparing it with was extreme in the first place.

There's nothing pushing the "other" observation toward average. It's just likely to look "closer" relatively when you compare it to one that you already knew was extreme. And sometimes you even randomly pick one that's just as extreme or more anyway; regression to the mean does not happen in every case, since it's just a statistical trend.

In a way, there isn't even really any regressing going on because there's no particular data changing toward average with time. The "closer to average" movement only appears that way if you put the more average sample second and the more extreme one first. If you write them in the opposite order, so the one that's closer to average establishes the baseline to which the more extreme one gets compared, then you get progression away from the mean; the data are amazingly "getting" more extreme!!1!!

For example, I'm told that the kids in my class in school around second and third grades were, as a group, unusually tall compared to other classes/ages in the same school. The group will most likely go on to have children who are closer to average height than themselves. That might seem like regression to the mean because height gets closer to average with time. However, we are also just as likely to have had parents who are closer to average height than ourselves. And that's regression to the mean as well, even if it sounds like it's going backward in time. My class at that school is the extreme initial observation; our own children and parents are separate observations which, not having been selected for extremeness in the first place, are most likely not so extreme.

 

[Roboramma]

Thanks for a great post Delvo. Very clear explanation and it seems to clear up any difficulty, at least for me.

 

[jayh]

There is, in the absence of selection pressure, a tendency to regress toward the means. Feral dogs after a few generations tend toward a size of 35-40 lb and brown or grey coloring.

 

[Delvo]

That is neither an absence of selection pressure nor a regression to the mean.

 

[Skeptic Ginger]

Natural Selection works against Regression to the Mean by continually selecting the "fitter" members of the set for the next "cycle" and knocking off the less fit ones.

Perhaps I am not thinking of this in the right way but I can think of some contrary examples. One has to ask, which mean?

Take pathogenic microorganisms, if one is looking at the range of virulence a highly virulent influenza virus will drift toward less virulent because even though the virulent organism will be highly successful at first, eventually the less virulent strain will overtake the virulent ones because the more virulent organisms kill their hosts and that limits spread. Likewise a less virulent strain isn't likely to overtake the more virulent strains that don't kill their hosts.

The population size of a species will equilibrate with the food supply, so if one is taling about mean population size, too large of a population won't be sustained and too small of one cannot be sustained either if the gene pool is not varied enough.

Species become stable with much slower genetic drift when the population is in equilibrium with the environment. At some point a stronger lion being able to control a pride does not result in significant drift toward stronger and stronger lion cubs. Or if it does, the evolutionary drift is very very slow. Instead the gene pool gains an advantage because it contains a lot of variability. If evolutionary drift only moved toward stronger and stronger lions, eventually one would expect that gene pool to be very limited.

 

[WhatRoughBeast]

Surely a population mean has to move over time for evolution to occur

Only for an isolated subgroup. Regression of the mean occurs as the result of random variation in the sampled group. In genetics, this randomness is the distribution of genes within a population, with each individual getting an essentially random assortment from its' parents. Keep in mind that the time scale usually associated with RTM is a generation or two, and at this level random mutations are extremely rare.

and how does 'regression' reconcile with localised random mutation constantly setting new evolutionary paths?

Basically, random mutation, especially successful mutation, is very rare (for common-sense meanings of rare. One in a billion odds is pretty trivial in a bacterial colony.) A population of millions of individuals might go millions of years before generating a daughter species. And note that a rare mutation which opens up or takes advantage of a new ecological niche is not the same sort of random as shuffling the existing genes. The swapping of genes in a population with a constant gene frequency implies that none of the current crop are wildly advantageous. The same cannot be said for a key mutation.

 

[stevea]

Measurements of statistical variables regress to their means.
Regression to the mean isn't causal - it's not some force of nature.
"Populations" aren't a statistical variable.
The OP question is meaningless.

 

[Gord_in_Toronto]

Perhaps I am not thinking of this in the right way but I can think of some contrary examples. One has to ask, which mean?

Take pathogenic microorganisms, if one is looking at the range of virulence a highly virulent influenza virus will drift toward less virulent because even though the virulent organism will be highly successful at first, eventually the less virulent strain will overtake the virulent ones because the more virulent organisms kill their hosts and that limits spread. Likewise a less virulent strain isn't likely to overtake the more virulent strains that don't kill their hosts.

The population size of a species will equilibrate with the food supply, so if one is taling about mean population size, too large of a population won't be sustained and too small of one cannot be sustained either if the gene pool is not varied enough.

Species become stable with much slower genetic drift when the population is in equilibrium with the environment. At some point a stronger lion being able to control a pride does not result in significant drift toward stronger and stronger lion cubs. Or if it does, the evolutionary drift is very very slow. Instead the gene pool gains an advantage because it contains a lot of variability. If evolutionary drift only moved toward stronger and stronger lions, eventually one would expect that gene pool to be very limited.

I was only trying to be succinct and pithy. Natural Selection is Survival of the Fittest but Fittest does necessarily mean the physically strongest.

 

[Bram Kaandorp]

I was only trying to be succinct and pithy. Natural Selection is Survival of the Fittest but Fittest doesn't necessarily mean the physically strongest.

ftfy

 

[Gord_in_Toronto]

ftfy

Tnx! Argh!