The Tragedy of Group Selectionism

Before 1966, it was not unusual to see serious biologists advocating evolutionary hypotheses that we would now regard as magical thinking.  These muddled notions played an important historical role in the development of later evolutionary theory, error calling forth correction; like the folly of English kings provoking into existence the Magna Carta and constitutional democracy.

As an example of romance, Vero Wynne-Edwards, Warder Allee, and J. L. Brereton, among others, believed that predators would voluntarily restrain their breeding to avoid overpopulating their habitat and exhausting the prey population.

But evolution does not open the floodgates to arbitrary purposes.  You cannot explain a rattlesnake's rattle by saying that it exists to benefit other animals who would otherwise be bitten.  No outside Evolution Fairy decides when a gene ought to be promoted; the gene's effect must somehow directly cause the gene to be more prevalent in the next generation.  It's clear why our human sense of aesthetics, witnessing a population crash of foxes who've eaten all the rabbits, cries "Something should've been done!"  But how would a gene complex for restraining reproduction—of all things!—cause itself to become more frequent in the next generation?

A human being designing a neat little toy ecology—for entertainment purposes, like a model railroad—might be annoyed if their painstakingly constructed fox and rabbit populations self-destructed by the foxes eating all the rabbits and then dying of starvation themselves.  So the human would tinker with the toy ecology—a fox-breeding-restrainer is the obvious solution that leaps to our human minds—until the ecology looked nice and neat.  Nature has no human, of course, but that needn't stop us—now that we know what we want on aesthetic grounds, we just have to come up with a plausible argument that persuades Nature to want the same thing on evolutionary grounds.

Obviously, selection on the level of the individual won't produce individual restraint in breeding.  Individuals who reproduce unrestrainedly will, naturally, produce more offspring than individuals who restrain themselves.

(Addendum:  Individual selection will not produce individual sacrifice of breeding opportunities.  Individual selection can certainly produce individuals who, after acquiring all available resources, use those resources to produce 4 big eggs instead of 8 small eggs—not to conserve social resources, but because that is the individual sweet spot for number of eggs * egg survival probability.  This does not get rid of the commons problem.)

But suppose that the species population was broken up into subpopulations, which were mostly isolated, and only occasionally interbred.  Then, surely, subpopulations that restrained their breeding would be less likely to go extinct, and would send out more messengers, and create new colonies to reinhabit the territories of crashed populations.

The problem with this scenario wasn't that it was mathematically impossible.  The problem was that it was possible but very difficult.

The fundamental problem is that it's not only restrained breeders who reap the benefits of restrained breeding.  If some foxes refrain from spawning cubs who eat rabbits, then the uneaten rabbits don't go to only cubs who carry the restrained-breeding adaptation.  The unrestrained foxes, and their many more cubs, will happily eat any rabbits left unhunted.  The only way the restraining gene can survive against this pressure, is if the benefits of restraint preferentially go to restrainers.

Specifically, the requirement is C/B < FST where C is the cost of altruism to the donor, B is the benefit of altruism to the recipient, and FST is the spatial structure of the population: the average relatedness between a randomly selected organism and its randomly selected neighbor, where a "neighbor" is any other fox who benefits from an altruistic fox's restraint.  (I believe this is a derivation with different symbols, best one I could find online.)

So is the cost of restrained breeding sufficiently small, and the empirical benefit of less famine sufficiently large, compared to the empirical spatial structure of fox populations and rabbit populations, that the group selection argument can work?

The math suggests this is pretty unlikely.  In this simulation, for example, the cost to altruists is 3% of fitness, pure altruist groups have a fitness twice as great as pure selfish groups, the subpopulation size is 25, and 20% of all deaths are replaced with messengers from another group: the result is polymorphic for selfishness and altruism.  If the subpopulation size is doubled to 50, selfishness is fixed; if the cost to altruists is increased to 6%, selfishness is fixed; if the altruistic benefit is decreased by half, selfishness is fixed or in large majority.  Neighborhood-groups must be very small, with only around 5 members, for group selection to operate when the cost of altruism exceeds 10%.  This doesn't seem plausibly true of foxes restraining their breeding.

You can guess by now, I think, that the group selectionists ultimately lost the scientific argument.  The kicker was not the mathematical argument, but empirical observation: foxes didn't restrain their breeding (I forget the exact species of dispute; it wasn't foxes and rabbits), and indeed, predator-prey systems crash all the time.  Group selectionism would later revive, somewhat, in drastically different form—mathematically speaking, there is neighborhood structure, which implies nonzero group selection pressure not necessarily capable of overcoming countervailing individual selection pressure, and if you don't take it into account your math will be wrong, full stop.  And evolved enforcement mechanisms (not originally postulated) change the game entirely.  So why is this now-historical scientific dispute worthy material for Overcoming Bias?

A decade after the controversy, a biologist had a fascinating idea.  The mathematical conditions for group selection overcoming individual selection were too extreme to be found in Nature.  Why not create them artificially, in the laboratory?  Michael J. Wade proceeded to do just that, repeatedly selecting populations of insects for low numbers of adults per subpopulation.  And what was the result?  Did the insects restrain their breeding and live in quiet peace with enough food for all?

No; the adults adapted to cannibalize eggs and larvae, especially female larvae.

Of course selecting for small subpopulation sizes would not select for individuals who restrained their own breeding; it would select for individuals who ate other individuals' children.  Especially the girls.

Once you have that experimental result in hand—and it's massively obvious in retrospect—then it suddenly becomes clear how the original group selectionists allowed romanticism, a human sense of aesthetics, to cloud their predictions of Nature.

This is an archetypal example of a missed Third Alternative, resulting from a rationalization of a predetermined bottom line which produced a fake justification and then motivatedly stopped.  The group selectionists didn't start with clear, fresh minds, happen upon the idea of group selection, and neutrally extrapolate forward the probable outcome.  They started out with the beautiful idea of fox populations voluntarily restraining their reproduction to what the rabbit population would bear, Nature in perfect harmony; then they searched for a reason why this would happen, and came up with the idea of group selection; then, since they knew what they wanted the outcome of group selection to be, they didn't look for any less beautiful and aesthetic adaptations that group selection would be more likely to promote instead.  If they'd really been trying to calmly and neutrally predict the result of selecting for small subpopulation sizes resistant to famine, they would have thought of cannibalizing other organisms' children or some similarly "ugly" outcome—long before they imagined anything so evolutionarily outré as individual restraint in breeding!

This also illustrates the point I was trying to make in Einstein's Arrogance:  With large answer spaces, nearly all of the real work goes into promoting one possible answer to the point of being singled out for attention.  If a hypothesis is improperly promoted to your attention—your sense of aesthetics suggests a beautiful way for Nature to be, and yet natural selection doesn't involve an Evolution Fairy who shares your appreciation—then this alone may seal your doom, unless you can manage to clear your mind entirely and start over.

In principle, the world's stupidest person may say the Sun is shining, but that doesn't make it dark out.  Even if an answer is suggested by a lunatic on LSD, you should be able to neutrally calculate the evidence for and against, and if necessary, un-believe.

In practice, the group selectionists were doomed because their bottom line was originally suggested by their sense of aesthetics, and Nature's bottom line was produced by natural selection.  These two processes had no principled reason for their outputs to correlate, and indeed they didn't.  All the furious argument afterward didn't change that.

If you start with your own desires for what Nature should do, consider Nature's own observed reasons for doing things, and then rationalize an extremely persuasive argument for why Nature should produce your preferred outcome for Nature's own reasons, then Nature, alas, still won't listen.  The universe has no mind and is not subject to clever political persuasion.  You can argue all day why gravity should really make water flow uphill, and the water just ends up in the same place regardless.  It's like the universe plain isn't listening.  J. R. Molloy said:  "Nature is the ultimate bigot, because it is obstinately and intolerantly devoted to its own prejudices and absolutely refuses to yield to the most persuasive rationalizations of humans."

I often recommend evolutionary biology to friends just because the modern field tries to train its students against rationalization, error calling forth correction.  Physicists and electrical engineers don't have to be carefully trained to avoid anthropomorphizing electrons, because electrons don't exhibit mindish behaviors.  Natural selection creates purposefulnesses which are alien to humans, and students of evolutionary theory are warned accordingly.  It's good training for any thinker, but it is especially important if you want to think clearly about other weird mindish processes that do not work like you do.

 

Part of the sequence The Simple Math of Evolution

Next post: "Fake Optimization Criteria"

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Caledonian, delaying reproduction in order to maximize an individual organism's lifetime output is not the same as foregoing reproduction to benefit the chances of other organisms. The latter behavior is altruistic, the former behavior is not. Williams discusses this while showing that observed cases of apparent reproductive restraint match very finely the requirements of individual optimization.

Now I've said before that I can't include all the fillips and caveats in a series of blog posts. If you want to add a fillip in a comment, that's fine, but please don't assume that I'm ignorant.

Wrong. Sometimes quality, not quantity, matters.

Well, actually, it seems to be a case where a simple "ceteris paribus" would have taken care of that. If someone writes something that is easily fixed with a "ceteris paribus" or by some other simple means, I try to avoid saying "wrong".

Dude, trying to gain an evolutionary advantage by "restraint in breeding" is like trying to get rich by overpaying your income tax. Hey, every extra dollar you give the IRS is one dollar removed from the national debt, which should improve the economy... and give you as an individual some utterly microscopic imperceptible benefit, w00t!

Constant, It's group selection because the individual is essentially making a sacrifice to reproduce less, to benefit the group. It happens blindly, through normal evolution of selecting the individual, but how else do you expect it to happen?

As I pointed out, the benefit to the group is a side-effect. In your scenario the fox survives because of a direct benefit to the fox. As for "how else" "I" expect it to happen, it's not about what I expect (since I am not advocating group selection), it's about what group selection is. As Wikipedia explains (and this is consistent with my outside knowledge, I quote it for convenience not authority): group selection is "the idea that alleles can become fixed or spread in a population because of the benefits they bestow on groups, regardless of the fitness of individuals within that group." That is not what is happening in your scenario, because, as you describe it, the individual fox that restrains its reproduction is more fit because it preserves energy. This is a benefit to the individual.

Venu: You definitely can do that in Mathematics, but that's because reasoning about Mathematics has some special properties that most reasoning about the real world does not.

  1. Math is black and white If you find a proof for something, it's true. Until you do, you can't really call your hunch math. However, in the real world, it's very easy to find arguments for things that are false.
  2. Math has monotonicity What this means is, that if you use Lemma A and Lemma B to prove Theorem Z, then whether or not Lemma C is true has nothing to do with whether your proof of Z still stands. The real world isn't like this, in that you can't arbitrarily pick a subset of the things you know to reason from. If A, B, C and Z were causally related events in the world, ignoring C would be cherry-picking your evidence.

The upshot is, if you try to backward chain from a conclusion in our non-monotone probabilistic world, you're quite likely to find a nice sounding but possibly flawed argument starting from cherry-picked premises. In fact, if your conclusion is wrong, you pretty much have to, unless your argument generator is so awesome that it fails to come up with arguments when you try to find one for a wrong conclusion. Sadly, we know from experience that the human argument generator isn't that awesome.

Yudkowsky, is this where your Babyeating aliens from Three Worlds Collide come from?

Eliezer: It's still not at all unusual to see serious biologists advocating magical thinking. Evolutionary theory as conveyed in the undergraduate biology curriculum is extremely elementary, and it's easy to graduate without even mastering what is covered, not to mention without making single step inferences from it. Most biologists know no more about modern evolutionary than that plus the results of reading and for the most part believing either Gould or Dawkins. You can't assume that scientists are familiar with the sub-fields of their discipline, nor that they don't believe themselves to have some special expertise in those subfields due to their working in a related field. Of course, relative to the general population they do have special expertise in the related subfields, just not relative to specialists in those subfields working 50 or 100 years ago.

All: It seems to me that Caledonian is evolving into a troll. He's not there yet, but I suggest that a warning may be in order.

My priors are not what they were a week ago. Thank you for the fascinating posts.

Barkley: The mathematical population geneticists were defending multi-level evolution, at least in principle under the right conditions.

How on earth could a mathematical population geneticist do anything else? In principle under the right conditions, you can create group selection in a laboratory and observe the results. Price's Equation in its various forms is a logical tautology. The question is whether the tautology has nontrivial empirical content: are group selection pressures tiny trivial things easily overwhelmed by individual selection pressures, or are they strong enough that evolutionary reasoning must routinely take them into account, or are they strong enough and persistent enough to create their own complex adaptations, over million-year timescales, involving significant organismal sacrifices of fitness; without any adapted enforcement mechanisms such as reciprocal altruism which make the behavior individually reproductively advantageous; without any adapted group boundaries such as cell walls; and without any enforcement of genetic identity such as in multicellular organisms?

It's the last part that is, to put it mildly, controversial; and it's what I've been referring to as "original" or "old-style" group-selectionist thinking.

It is a good rule of thumb that an amateur should never postulate group selection. Never ever never ever for never, as McCabe says. Somehow it's always an altruistic sacrifice to achieve some aesthetically beautiful consequence, rather than, say, cannibalism. And somehow they never do any math.

Professionals calculating whether spatial structure among self-replicating chemical hypercycles in tide pools could support adaptations leading up to the emergence of cell boundaries is a whole 'nother story.

Recovering: roughly how long did it take to write, how long do you think it would have taken a year ago

Probably at least eight hours. The publication time, just before midnight in California, should be a clue.

A year ago it would have taken months because it would have been part of a much huger document which included all the evolutionary posts into one giant blob, and I would have gone back and tweaked all the pieces instead of writing anything new.

The original plan was for this post on the tragedy of group selectionism to come directly after the post on Fake Justification. Then, when I tried to write the post, I found that I had to explain a whole lot of material on basic principles of reasoning about evolution, which detracted from the main point; so I split that off into "An Alien God". Then I noticed that "The Wonder of Evolution" could be taken out of "An Alien God" and make that post at least a little shorter. Then I figured I might as well do "Evolutions Are Stupid" and "Speed Limit and Complexity Bound" while I was on the topic, because I often have cause to refer to those equations. Then the "Gould" post because I often encounter people whom Gould has misled, and the complexity bound made a good illustrative case (though I'm presently in a state of mistrusting my math, if not Williams's heuristic argument and the observed number of human genes). Then I could finally get back to the original post on group selectionism...

Wiseman, you are not giving an example of group selection. You are imagining one single group (or two if we split the rabbits and foxes apart) over a long period of time. With group selection there are multiple groups, some of which die out on their own or get squashed/absorbed by other groups or the groups increase in size and split apart at different rates. For the rabbits/foxes example we could imagine multiple populations all separated and say that in all instances where breeding was not restrained, they overpopulated and died out, leaving only the ones that did restrain. However, all those populations would be vulnerable to the overbreeding mutation suddenly appearing, so it would not be a good explanation.

Wiseman, you are not describing group selection. You are still describing individual selection, because the causally effective advantage is to the individual. The benefit to the group is a side-effect. Here is your description of the advantage, which you call the key: "because it will spend less energy developing fox fetuses that won't survive anyway." That is an advantage to the individual foxes.

I also have doubts about the specifics of your scenario, but I won't get into that.

Another excellent post.

If you don't mind me asking, roughly how long did it take to write, how long do you think it would have taken a year ago, and (assuming reading is already fast) what do you think are the most important factors that make writing speed go voom with frequent practice?

Eliezer's report of Wade's study is not completely accurate. From the link, emphasis mine:

...some of the B populations [the ones selected for low population] enjoy a higher cannibalism rate while other B populations have a longer mean developmental time or a lower average fecundity relative to the controls.... Thus, the decline in mean population size in the B treatment... is the result of both group selection and individual selection within populations favoring characters responsible for low population size....

In summary, these results indicate (i) that group selection in the opposite direction to individual selection can produce significant genetic change, (ii) that group selection in the same direction as individual selection can produce results very different from individual selection acting alone, and (iii) that a process of random extinctions with recolonization can establish conditions favorable to the operation of group selection.

To get group selection out of this scenario, you would have to have one fox group with a lower-than-optimal breeding rate, which let the rabbit population expand, which lessened the chance of a crash in food supply that would wipe out the population. Then that fox group would survive, and the neighboring groups would perish. But there is no way to enforce this pact of lower-than-optimal breeding rates in the first place.

Enforce? You don't need to enforce something that's build into organism's biology - and in the scenario you describe, their reduced rate would be the 'optimal' solution.

Even if a trait offers serious advantages in between-group competition, if it's a disadvantage in within-group competition, it will often dwindle and die out over time. What matters is whether the trait can make more copies of itself than will be eliminated; if it can't, there's no mechanism for it to persist, but if it can, one way or another, its frequency will increase. There has to be replication on the level of the group, not just on the level of the individual, for group-level benefits to cause traits to persist.

In an environment where new groups are frequently formed from randomly-selected subsets of previous groups, and groups compete with each other, the founder effect can amplify the frequency of traits that benefit the group but are disadvantageous for the individuals carrying them. Now groups are acting as a unit of replication, and so selection forces can maintain traits on this level.

This is why mice don't go extinct even though they're parasitized by the replicator gene. Sure, the gene rapidly dominates any group it's introduced to, and prevents successful reproduction within that group, but there are enough obstacles to divide the total mouse population into smaller groups in the short term. Inside any one group, not having the gene loses out to having it every time. But the constant establishment of new groups, and the temporary limits to gene spread between groups, together make it possible for the gene-absense to persist. If you removed the restrictions on gene flow the parasite gene would spread throughout the entire mouse population and they'd all die out. If there aren't enough distinct groups, group-level selection doesn't 'work' - just as individual-level selection doesn't 'work' when there aren't enough individuals.

Wiseman, you are not describing group selection. You are still describing individual selection, because the causally effective advantage is to the individual.

So repeat the logic, only substitute small, interrelated, relatively isolated groups of foxes for the individuals in the previous examples.

Populations can be the unit of selection just as individual organisms can.

Eliezer, I don't need to make assumptions about what you do and do not know when you make statements like "Obviously, selection on the level of the individual won't produce individual restraint in breeding." Either you've demonstrated your ignorance on the subject, or you've demonstrated that you can't convey your knowledge on the subject. From the perspective of your readers, the two possibilities are functionally equivalent.

Individual-level selection has produced LOTS and LOTS of individual restraint in breeding. This is not only obvious to biologists but to laypeople with everyday knowledge.

If you meant instead that organisms will not make sacrifies for general welfare unless the general welfare benefits the genes of the individual as well, you'd be right - but that is not what you said.

Kaj, fast breeding does not just incur a cost on the cubs, but on the mothers developing the cub fetuses. No matter the dearth of rabbits/food, as long as it's less than the amount needed to sustain the current fox population, the less energy and time spent by a fox mother developing unnecessary fetuses, the less likely she will die before child birth. You can't just calculate the raw probability of cubs surviving by saying "Each cub has X% chance of surviving, therefore the more cubs, the greater total chance that some will survive". A cub is taken care of primarily by it's mother, by nature of non-group selected genes. If each cub has roughly equal capability of aquiring food from the mother, that leaves the same amount of food for a larger number of cubs than the restrained breeding fox families. If 6 cubs have to share the amount of food that can only sustain 1 cub, it's likely no cubs will survive. Even if some cubs manage to horde more food than others, there still can only be so many surviving cubs based on the amount of food available, which will be the same amount as can survive from the restrained-breeder families. That means that the unrestrained breeder-mothers just spent much more energy and time producing the same amount of viable cub offspring as the restrained breeders, leading to a worse long term outlook for the survival of that unrestrained breeding family.

Wiseman, you need to put your scenario into mathematical terms, or write a simulation, or something. It's too easy to imagine some foxes and rabbits breeding and scurrying about, and convince yourself that something is possible. In any case the situation you described is not "group selection", but good old-fashioned gene-level selection. In this case it's selection for genes that lead to an optimal breeding rate.

I thought I made it clear that I knew about the modern revival in multilevel selection. Was this not clear enough?

Group selectionism would later revive, somewhat, in drastically different form - mathematically speaking, there is neighborhood structure, which implies nonzero group selection pressure not necessarily capable of overcoming countervailing individual selection pressure, and if you don't take it into account your math will be wrong, full stop. And evolved enforcement mechanisms (not originally postulated) change the game entirely.

Barkley: got any explanations for why the supportable information in a genome should go as the inverse square of the mutation rate?

[...] and if you don't take it into account your math will be wrong, full stop.

And... I just now realized that "full stop" is functionally equivalent to "period."

[...] and if you don't take it into account your math will be wrong, period.

"Full stop" says the same thing but avoids the negative reaction that "period" brings. Clever. It was bugging me for the last few times I saw it but I didn't figure out why until this article.

EDIT: Haha, this got downvoted? I guess I didn't see that coming. Ah well. It'll probably go back up. And then go back down.

Full stop is just the British English version of period. It took me a while to figure out what period meant in that context in American English. Period generally refers to menstruation in British English.

Period generally refers to menstruation in British English.

I've heard people say this more than once, and each time I always want to say "Come on!" That particular meaning (which of course is just as well known in American English) is nothing but a derivative of the principal meaning of "period" (in all English-speaking countries), which is "length of time" or more generally "interval" -- which also gives rise to the American usage referring to the punctuation mark, as sentences are in some sense regular units of discourse.

Growing up in England I picked up from American TV and movies that saying 'period' at the end of a sentence was a way of emphasizing a statement. I picked up the meaning from context but didn't understand the derivation as 'period' had only two salient meanings for me: an interval or menstruation. As a teenager in high school at the time the latter was probably the strongest association. At some point I discovered that 'period' in American English meant 'full stop' and suddenly the phrase made perfect sense (since in British English we use 'full stop' in the same sense, though it's a somewhat less common phrase).

All the meanings share a fairly obvious association in retrospect. I maintain that for most British English speakers however (at least those my age or older who weren't as steeped in American culture as younger Brits might be) the word period is much more strongly associated with menstruation than with punctuation, even being aware of the latter meaning.

I maintain that for most British English speakers however... the word period is much more strongly associated with menstruation than with punctuation, even being aware of the latter meaning.

Oh, that's undoubtedly true; the punctuation usage is definitely an Americanism. My point was that the most salient meaning is (or certainly ought to be) the general one of "interval". (I've never seen a British mathematician wince when discussing the period of the sine function.)

the punctuation usage is definitely an Americanism

According to various online sources, the first written usage of "period" to mean "dot at the end of a sentence" was in 1609. I can't find mention of a source, but I find it hard to believe it's American. I've been unable to find an origin for "full stop" - some sites try to link it to the telegraph, but inconsistently mention that "full stop" was not used instead of "stop" since it would cost more.

ETA: found the 1609 reference. John Davies) - poem here - grep for "but thy nailes"

Well, a number of modern-day Americanisms aren't American in origin, but rather are the result of the usage in question having become obsolete in Britain. Standard examples include "sick" for "ill" and "fall" for "autumn" ("mad" for "angry" might also be one, though I'm not sure).

The same phenomenon occurs in other widely-distributed languages, notably Portuguese, where in some respects Brazilian usage resembles the old-fashioned language of Portugal more than the modern language of Portugal does.

The word "Americanism" seems to imply that it's some crazy thing the Americans have decided to do, against all sense, as opposed to continuing to use the language in the same fashion it's been used for hundreds of years. For example, I've heard "Authorise is the correct spelling; Americans just spell it 'authorize' because they like to be different" despite the British "authorise" being the common spelling for only about a century and the OED still recommending "authorize".

-ize is something else, but most american spellings (not usage) really are the abrupt decision of Noah Webster. He was a nationalist and the theory that he was trying to create an american identity is poorly-attested but not insane.

In the brief period of time since I last commented two new good posts on group selection, E.O. Wilson and how it does not gel with our aesthetic/moral preferences have appeared.

Once you are dealing with hominids, which may be the most important example, indeed "enforcement" may well be important. There is a growing lit on how reciprocal altruism ultimately depends on punishment of free riders, that is, enforcement.

Really? I'd thought that was generally understood - that was the whole point of Tit for Tat, after all, that it could both reward cooperative behavior and punish defection. One without the other is useless: kindness without cruelty is weak, cruelty without kindness self-destructs.

But the point I'm trying to get across isn't about altruism, but group-friendly behavior in general. Altruism is an important subcategory, certainly, but there's a wider case to be made.

And Eliezer is STILL wrong in his earlier quoted statement. Why am I not surprised?

Rosser: I am not going to get into the debate about the specific math of your model as others have already done so.

There's only one equation in this post and it's a standard one. Were you referring to the Speed Limit post? I already put all original math in that post into abeyance pending further investigation.

I'm reasonably certain the McCabe I was quoting isn't your McCabe.

I suppose I have a unique professional perspective on how tragic the class of warped thinking revealed in old-style group selectionism is likely to be. ("You can get all these wonderfully aesthetic results just by optimizing for criterion X - oops the real result is cannibalism.") Future posts should make this clear.

Everything Wiseman is describing is happening at the level of the gene, not the population.

Imagine there is a gene for breeding rate - different variants of the gene give rise to different breeding rates (1, 2, .... offspring per year, let's say). A fox that has a high-rate allele of the gene will spend more energy on breeding than on caring for existing offspring, while the reverse is true with a fox that has a low-rate allele.

Given the natural fluctuations of food availability over the long term, there is going to be an optimal range of breeding rates. Genes that specify too high a rate will find themselves in bodies that spend too much time breeding to care for their offspring sufficiently, and such genes will not get passed on as frequently. Genes that specify too low a rate will be outcompeted. Caledonian is correct; it's like investing. But the investment pays off directly to the gene involved, so the fact that the vehicles and populations also benefit is an incidental.

To get group selection out of this scenario, you would have to have one fox group with a lower-than-optimal breeding rate, which let the rabbit population expand, which lessened the chance of a crash in food supply that would wipe out the population. Then that fox group would survive, and the neighboring groups would perish. But there is no way to enforce this pact of lower-than-optimal breeding rates in the first place.

Wiseman, you haven't shown that it really is beneficial to reproduce less in the scenario that you are describing. Yes, a smaller group will consume less food - but if there are six foxes, then the probability than at least one of them will survive can very well be higher than if there is only one. The group that reproduces less will still be outbred by the one that reproduces more, so the faster-breeding one could on average have more surviving members.

This might not be the case in situations where food is extremly scarce, but it should be so in situations where there is only enough food for, say, 80% of the population. Without running the numbers, it would intuitively feel that the fast-breeders have an advantage most of the time with the slow-breeders only having an advantage a small portion of the time - so while the exact gene frequencies will fluctuate, they won't give the slow-breeders a decisive advantage.

Eliezer,

Maybe I will get back to you on that point, and maybe I will not. I am about to leave town, and I spend 30 hours a week editing a journal, along with being a full professor of economics. This is why I turned down Robin's invitation to become a co-blogger here. Too damned busy. This is not meant to be a copout or an escape. I already spent a couple of hours I did not have last night digging through Gould again on your other posting.

I will note that the special issue I edited includes a wide variety of views and that there remain sharply contrasting opinions regarding the bottom line. Interestingly, the hardest line defenders of the Dawkins position (he was invited to participate, as were Tooby and Maynard Smith, although they declined), was a paper by GMU's Vernon Smith and Dan Houser, two economists. The political scientist, Axelrod, was also defending that view. The mathematical population geneticists were defending multi-level evolution, at least in principle under the right conditions.

For the record, I think you are a smart guy. If I have the time, I shall get into responding to your specific question. But I gotta go now.

But the error isn't fixable simply by the addition of "all else being equal", because the important concepts that need to be addressed include the reality that some things are grossly unlikely to ever be equal.

There's a reason humans usually have only one child gestating at a time, even though it would be a simple matter biologically to have multiple fertilizations.

There's another reason the mouse gene that causes 90% of mouse sperm to carry a copy of itself in the heterozygous state and certain fetal/infant death in the homozygous doesn't cause mice to go extinct.

Discarding the concept of group selection is foolish. What's important is to recognize what factors are necessary and sufficient to permit group selection to occur.

Suppose an organism of an A genotype emits pheromons depressing development of female reproductive organs in receptive organisms of same population (with an aa genotype), and so gains resources for its own reproduction during a given season, and then during the next season it doesn't emit the pheromon (through some environmental regulation/...) and the homozygotes of the population get a chance to reproduce... Does this count as group selection? It would be still the same species, since the A can receive sperm from any genotype, and use of resources can be regulated. (I'm just trying to apply 'group selection' to anything without a nervous system, and having trouble. It seems to me lately that your 'evolution' is a rather selective concept.)

See my post about an experimental validation of group selection among nightshades.

This is just a nitpick: according to The Other Wiki democratic constitutions are older than English kings, the most egregious example being The Solonian Constitution after reform by Cleisthenes, which codified Athenian "democracy". Yes, I know, semantics.