Counterintuitive evolutionary truths

In the Roger Scruton on altruism thread, some commenters have expressed confusion over the evolutionary explanation of altruism in ants.  If workers and soldiers leave no offspring, then how does their altruistic behavior get selected for?

The answer is simple but somewhat counterintuitive. The genes for altruistic behavior are present in both the workers/soldiers and in their parents. Self-sacrificing behavior in the workers and soldiers is bad for their copies of these genes, but it promotes the survival and proliferation of the copies contained in the queen and in her store of sperm. As long as there is a net reproductive benefit to the genes, such altruistic behaviors can be maintained in the population.

Selfish genes, altruistic individuals.

Let’s dedicate this thread to a discussion of other counterintuitive evolutionary truths. Here are some of my favorites:

1. The classic example of sickle-cell trait in humans. Why is a disease-causing mutation maintained in a human population? Shouldn’t selection eliminate the mutants? Not in this case, because only the unfortunate folks who have two copies of the allele get the disease. People with one copy of the allele don’t get the disease, but they do receive a benefit: improved resistance to malaria. In effect, the people with the disease are paying for the improved health of the people with only one copy of the mutation.

(Kinda makes you wonder why the Designer did it that way, doesn’t it?)

2. In utero cannibalism in sharks:

Shark embryos cannibalize their littermates in the womb, with the largest embryo eating all but one of its siblings.

Now, researchers know why: It’s part of a struggle for paternity in utero, where babies of different fathers compete to be born.

The researchers, who detailed their findings today (April 30) in the journal Biology Letters, analyzed shark embryos found in sand tiger sharks (Carcharias taurus) at various stages of gestation and found that the later in pregnancy, the more likely the remaining shark embryos had just one father.

(Kinda makes you wonder why the Designer did it that way, doesn’t it?)

3. Genetic conflict between parents and offspring. Here’s a great example from a 1993 paper by David Haig:

Pregnancy has commonly been viewed as a cooperative interaction between a mother and her fetus. The effects of natural selection on genes expressed in fetuses, however, may be opposed by the effects of natural selection on genes expressed in mothers. In this sense, a genetic conflict can be said to exist between maternal and fetal genes. Fetal genes will be selected to increase the transfer of nutrients to their fetus, and maternal genes will be selected to limit transfers in excess of some maternal optimum. Thus a process of evolutionary escalation is predicted in which fetal actions are opposed by maternal countermeasures. The phenomenon of genomic imprinting means that a similar conflict exists within fetal cells between genes that are expressed when maternally derived, and genes that are expressed when paternally derived.

(Kinda makes you wonder why the Designer did it that way, doesn’t it?)

Can readers think of other counterintuitive evolutionary truths?

Addendum

4. Mutant organism loses its innate capacity to reproduce and becomes a great evolutionary success. Can anyone guess which organism(s) I’m thinking of?

836 thoughts on “Counterintuitive evolutionary truths

  1. Joe Felsenstein: People like phoodoo and WJM seem to be calling for completely realistic simulations of reality.

    I suspect that WJM is not actually making a point about what we think he’s making a point about. Rather it’ll be some abuse point about the specific terminology used and how he’s not actually arguing that models of evolution don’t work or don’t model evolution but that we should have a different name for an incomplete simulation. Or something like that.

    William J. Murray: Asserting it isn’t demonstrating it.

    You make assertions all the time and never demonstrate them (the dead can be talked to, mystery knowledge you had no access to appears in your head). And in any case, what level of evidence is required for any demonstration for you? An impossible level, as nobody can ever prove that the demonstration was not being controlled by an Intelligent Designer who can control what we perceive to be random events.

    Convenient that.

  2. New page, so I’ll ask once again for the record.

    William, is there such a thing as a fair die?

  3. Joe Felsenstein said:

    People like phoodoo and WJM seem to be calling for completely realistic simulations of reality.

    No. Nice straw man, though. Since the rest of your post addresses this straw man and not what has actually been argued, there’s no reason to further address it.

  4. William J. Murray:
    Joe Felsenstein said:

    No. Nice straw man, though.Since the rest of your post addresses this straw man and not what has actually been argued, there’s no reason to further address it.

    Nope. The whole middle part of my comment was about how, and whether, we see whether alleles that decrease your fitness and increase your relative’s fitness can be increased in frequency by natural selection. And how we can do mathematics and simulation on that issue.

    You must have missed that part of my comment. Do read it again.

  5. William J. Murray: No. Nice straw man, though. Since the rest of your post addresses this straw man and not what has actually been argued, there’s no reason to further address it.

    What, you mean like how you argued that the variation in nature is not random as Asserting it isn’t demonstrating it.?

    Tell me William, is there such a thing as a fair die?

    And anyway, what do you know so that you can claim so confidently that the idea that the variation in nature is not guided is merely an assertion? What’s your actual evidence for that claim?

    Oh, that’s right, you are not making a claim, you are asking others to demonstrate that their claims are supported.

    Is there such a thing as a fair die William?

  6. Joe Felsenstein: You must have missed that part of my comment. Do read it again.

    I’d like to see William address some of the comments aimed at him line by line then we can see for ourselves what his thoughts are instead of a blanket dismissal. I see this

    William J Murray
    Since the rest of your post addresses this straw man and not what has actually been argued, there’s no reason to further address it.

    as “I have no response so I’ll make up a spurious reason to not address the content”. Your protestations of straw-man would carry more weight if you were to demonstrate how the straw-man was constructed rather then just claiming it exists.

    I don’t see a straw-man, enlighten me!

  7. William J. Murray: No. Nice straw man, though. Since the rest of your post addresses this straw man and not what has actually been argued, there’s no reason to further address it.

    Shit, if I was having this conversation/argument with someone who actually knew what they were talking about, I’d take the damm time to address the straw-man as you might actually learn something or find out you still have things to learn about what you are critiquing or, crazily, find out that you are wrong about some things!

    But damn, your attitude amazes me. You literally know better then everyone don’t you? You can’t learn a damm thing from nobody. When did you come into your knowledge about evolution? Did it arrive fully-fledged or over time?

    So yeah, when someone responds to you at some length and you reply “strawman” you’d better put something behind those words.

    William J. Murray: Asserting it isn’t demonstrating it.

    Exactly so. You’ve asserted “straw-man”. So demonstrate it.

  8. OMagain: Indeed. If only there was a way to programatically measure FSCO/I (or whatever) then we could feed the output of various existing simulations into it and see if FSCO/I (or whatever) is actually being generated or not.

    If it is, well, no designer required to generate all that FSCO/I nonsense the IDers observe (but can’t quantify for some odd reason) in biology. If not, well, score one for the ID crowd. I’d be happy to give it to them too, they would have dun a science at that point!

    I’ve pointed out Thomas Schneider’s ev to intelligent design creationists as an example of calculating the information change due to known evolutionary mechanisms. For some reason, they immediately decide that Shannon information isn’t what they meant.

  9. Patrick: For some reason, they immediately decide that Shannon information isn’t what they meant.

    Hence the proliferation of less specific, more malleable alternatives: FSCI, dFSCI, FSCO/I, dFSCO/I.

  10. OMagain: Hence the proliferation of less specific, more malleable alternatives:FSCI, dFSCI, FSCO/I, dFSCO/I.

    The only thing that has evolved without passing a fitness hurdle..

  11. olegt:

    phoodoo: I know why, because it would fail every time.

    Where have we heard this before? Oh, I remember!

    phoodoo on January 7, 2014 at 4:29 pm said:

    Start with one, see where it goes. It will die every time. I can tell you that even without a little computer program.

    🙂

    Some people never learn.

    phoodoo,

    How is your incompetence evidence against evolutionary models?

  12. Joe Felsenstein: Nope.The whole middle part of my comment was about how, and whether, we see whether alleles that decrease your fitness and increase your relative’s fitness can be increased in frequency by natural selection.And how we can do mathematics and simulation on that issue.

    You must have missed that part of my comment.Do read it again.

    So have you located the gene that makes people want to want soap operas yet Joe? How about the gene that turns on the chemical signals that turn on the genes that make people want to watch soap operas? Have you figured out how the chemical signals that tells genes when to turn on and turn off know how do to do? Have you figured out how this chemical signals are passed from one generation to the next, without modification?

    Since you haven’t and you never will, your premise that you are even close to modeling evolution is pointless. Altruism as a computer model? You are robbing our children of a proper education.

  13. phoodoo,

    phoodoo is admitting that calling my comment a straw man argument was way off.

    We model specific, limited phenomena, and that way, building up our understanding, we make progress. Wild straw man arguments such as phoodoos are just plain silly. Does phoodoo understand Hamilton’s definition of “inclusive fitness”? The distinction between group and kin selection? The relationship between them?

    Nope.

  14. Allan Miller:

    Genomes in Conflict by Burt and Trivers. Very comprehensive.

    Thanks, Allan! I ordered a copy.

  15. phoodoo:

    Altruism as a computer model? You are robbing our children of a proper education.

    Joe:

    Wild straw man arguments such as phoodoos are just plain silly. Does phoodoo understand Hamilton’s definition of “inclusive fitness”? The distinction between group and kin selection? The relationship between them?

    Nope.

    He was robbed of a proper education.

  16. walto, to Joe:

    There’s an additional point to be taken from phoodoo’s diatribe. If the term “genetic explanation” is made too broad or is not properly defined at all, the bar will be either raised too high for scientists or a contradictory story will be required of them. Obviously, that situation can only help the anti-science crowd.

    What’s wrong with the straightforward meaning? A genetic explanation is one that is expressed mainly in terms of genetic concepts, just as a chemical explanation is one that uses mainly concepts from chemistry.

  17. William J. Murray,

    Allan Miller said:

    The variation in nature is random,

    WJM Asserting it isn’t demonstrating it.

    You’ve been listening to that Joe Gallien again. By the definition I chose – stochastic – it is, and is demonstrably so. Which definition of ‘random’ are you using?

    Allan: and so is that in most computer simulations.

    WJM: Within parameters specifically attuned to the target condition.

    Have you ever even written one? You don’t appear to have the first idea how they are constructed. The variation takes no account of the ‘target condition’. Absolutely none. It is random, by whichever definition you prefer.

    Allan: EAs are deliberately made as ‘evolution-like’ as possible.

    WJM: No, they are made as “evolution-like” as is possible within the framework of acquiring specified target conditions, something that is precisely not “evolution-like”, at least not by the standard meaning of the term.

    Is there a standard definition of ‘evolution-like’? 🙂 They use random variation and differential survival in a pool of replicated strings. That’s evolution, pretty much.

    Allan That’s the whole point of the method: it has been found to be a powerful approach to certain problems.

    WJM The problem is that in order for the method to be of any value whatsoever, the pool from which random variants are drawn and employed must be tuned to the target conditions, and the selection process must also be tuned to the target conditions. You don’t get squat in the lab or in the computer sim without the tuning the system to explore towards the specified target conditions. Like altruistic behavior. Or winged flight.

    The method is used to solve specific problems, not to make a parasite or a beating heart. It has been discovered that just allowing the nuts and bolts of evolution, incorporated as faithfully as is practical, to proceed in such an algorithm, problems can be solved. Practical problems. It has real applications. That is a heck of a thing for a method that in nature is asserted (by ID-ers) to be incapable of anything out there in the ‘real’ world from whence it came.

  18. Kin selection has an ‘all else being equal’ flavour. If there is a straight choice between assisting a gene copy and promoting one’s own copy, then the relatedness and cost/benefit relationship will help determine whether a costly act can spread and be maintained through copy benefit.

    This is not the choice in a social insect colony, because there are differentiation and dispersal to consider. If we ignore the complication of haplodiploidy (not a necessary condition for eusociality), and consider the early evolution of social behaviour from a solitary species, it still appears that relatedness is a significant condition. Queen monogamy appears to be a precursor state in all the separate instances where eusociality has evolved. This ensures sibling relatedness in her offspring – all of them.

    An early state may be the non-dispersal of progeny. Clearly, this is not sustainable indefinitely, since several generations of this would strip local resources. Nonetheless, any ‘assisting’ behaviour that arises during this would be less susceptible to cheating than in a more genetically heterogeneous population. Everyone’s kin. If a ‘helper’ gene H+ is present in a queen, half her progeny will possess it. They will incidentally help their H- siblings that lack it – the ‘cheats’, in the game-theoretic parlance that became popular in the 1970’s.

    The spread of this behaviour is then conditioned upon how these colonies disperse. Some or all of the progeny may found new colonies. Those from the H+ group may have helped H- siblings, but the offspring of those gain no help in the next generation (unless mated with a H+ drone). H+, meanwhile, pass the behaviour on. The spread is thus governed by the relative success of H+ and H- colonies – which is to say, the lines between kin selection and group selection become somewhat blurred due to details of life history.

    If the colony becomes differentiated, opportunities for ‘cheats’ become still fewer – if you lack the capacity to disperse or breed, because this is a specialism within the hive, then I think this is too asymmetric a situation to be considered as simple kin selection. If you can breed but cannot found a colony, you can’t propagate the successful strategy, just yourself.

  19. Joe Felsenstein:
    phoodoo,

    phoodoo is admitting that calling my comment a straw man argument was way off.

    We model specific, limited phenomena, and that way, building up our understanding, we make progress.Wild straw man arguments such as phoodoos are just plain silly.Does phoodoo understand Hamilton’s definition of “inclusive fitness”?The distinction between group and kin selection?The relationship between them?

    Nope.

    So you haven’t yet identified the gene for soap operas yet, correct?

    Maybe you can find the one for altruism soon after that.

  20. Allan Miller,

    Allan,

    To suggest that GA’s solve problems through “random” variation is such a misleading description of what these programs can do.

    You build into the program what you want to define, what you accept as good and what you accept as bad, you disallow conditions that would throw the program into a collapse, you tell it what a good solution would be like, and then you brag that it magically came up with a solution.

    Anyone who could take such a simplistic set of circumstances and then suggest that this is exactly what evolution does, and thus I am convinced, really is wearing blinders about all of the obstacles that evolution has to overcome in reality.

    Again, why do you feel it would be so impractical to just let a computer generate copies of something, with an occasional unplanned copying error, and see what it produces that is useful. Because that is the entire claim that evolution makes-something (you have no idea what) just started copying itself, but because it was so bad at copying itself, it created all of life on earth-every precisely tuned life systems and functions-just because the copying was bad.

    If that is all evolution needed, why is it so hard to make THAT computer simulation?

  21. phoodoo:

    Again, why do you feel it would be so impractical to just let a computer generate copies of something, with an occasional unplanned copying error, and see what it produces that is useful.Because that is the entire claim that evolution makes-something (you have no idea what) just started copying itself, but because it was so bad at copying itself, it created all of life on earth-every precisely tuned life systems and functions-just because the copying was bad.

    If that is all evolution needed, why is it so hard to make THAT computer simulation?

    It seems your knowledge of computer programming is at a similar level to your knowledge of evolution.

  22. phoodoo,

    To suggest that GA’s solve problems through “random” variation is such a misleading description of what these programs can do.

    Misleading, yet strangely accurate! They generate random strings. Using ‘random’ number generators. They mutate them or generate crossovers. Randomly.

    You build into the program what you want to define, what you accept as good and what you accept as bad, you disallow conditions that would throw the program into a collapse, you tell it what a good solution would be like, and then you brag that it magically came up with a solution.

    No you don’t. You take a runtime parameter that determines, for that run, what string characteristics are favoured. This is little different from a bunch of lions ‘determining’ what gazelle characteristics are favoured. It’s just that, on this occasion, the ‘lions’ favour less optimal solutions to the problem for their lunch, leaving the remainder to breed.

    Just write one. You never bothered last time, on the selection-free baseline version (where there is NO TARGET WHATSOEVER), so I hold out no hope you will this. But you might gain some understanding, instead of pontificating about something you have never tried, and only grasp dimly. You didn’t bother last time because you KNEW what would happen. Many people had a go and it didn’t happen the way you expected at all, for any of them. So you could be wrong. Only one way to find out. How do you get to know so much from doing so little?

  23. Allan Miller:
    phoodoo,

    No you don’t. You take a runtime parameter that determines, for that run, what string characteristics are favoured. This is little different from a bunch of lions ‘determining’ what gazelle characteristics are favoured.

    That in a nutshell sums up the insanity of your belief!

    And the characteristic that lions prefer most from gazelles are gazelles that happen to be near them when they are hungry. Unfortunately there isn’t a gene for this.

  24. phoodoo: That in a nutshell sums up the insanity of your belief!

    And the characteristic that lions prefer most from gazelles are gazelles that happen to be near them when they are hungry.Unfortunately there isn’t a gene for this.

    Why do you suppose gazelles have that particular color coding?

  25. phoodoo,

    Of course. There is nothing whatever in gazelle variation that might make it more or less likely to be prey, simply proximity. Biology, computer science – there is no beginning to your talents!

  26. phoodoo, you know you could simulate the ‘proximity effect’ in this GA you can’t be bothered to write, don’t you? Make the selection process position-dependent. A static ‘lion’ that always and only assesses the fitness of the ‘gazelle’ that is in position 1123 of your string array. Then allow the ‘gazelles’ to mill about a bit … the lion will always indeed have a go at the closest gazelle – Gazelle 1123. But a different gazelle occupies that slot at different times, because they move. Some will be a bit better at escaping than others.

  27. olegt: phoodoo can tell you it will fail “even without a little computer program.”

    Four does not equal one. I don’t know if they taught you that in physics school.

  28. phoodoo:

    And the characteristic that lions prefer most from gazelles are gazelles that happen to be near them when they are hungry. Unfortunately there isn’t a gene for this.

    phoodoo,

    Individuals that like being near lions and seek out their company are rather quickly eliminated from the gazelle population.

    Those that avoid being near lions and are good at vamoosing do better.

    I can tell you that even without a little computer program.

    Allan, to phoodoo:

    Biology, computer science – there is no beginning to your talents!

    🙂

  29. phoodoo: Four does not equal one. I don’t know if they taught you that in physics school.

    It’s amazing that you still can’t understand this simple thing about units, phoodoo. Take a freshman physics course. That might cure it.

    12 inches = 1 foot, right? It doesn’t mean that 12 = 1.

  30. Allan Miller,

    Allan,

    Perhaps I didn’t explain it to you clearly enough. Taking a runtime parameter and pre-determining which string characteristics you favor is ABSOLUTELY nothing like life. I thought that was clear that this was my meaning, but I guess not to some people (ahem).

    In no way shape or form is it like life, unless choosing what strings you favor meant a thousand things other than meaning what it actually does.

    Those thousand things include things every hour and every minute that could be a threat to how one survives, along with a thousand other factors that determine what makes someone comfortable. Life can’t choose which characteristic can be preserved to keep one from being eaten by a lion, if at the same time it has to chose what type of skin will keep you from getting too sunburned, and what type of skin will keep you from breaking out in hives from willow trees, and what type of kidney can process the water you drink, and what type of jaw structure lets you chew your food, and what kind of air sacks will develop into what kind of lungs.

    This is one small problem, along with the fact that there is no one single gene which determines your jaw structure, and no one single gene which makes your skin, and no gene at all which determines what turns on and off the chemicals which tell your body to make a jaw.

    Since you think its such a bad idea to write a computer that actually does what you claim evolution does, then you could at least just let the computer write its own software, just like you claim life does with DNA. Just turn the computer on, start short circuiting it occasionally and see what kind of damage you can do to the cpu to get it to start writing program.

  31. olegt: It’s amazing that you still can’t understand this simple thing about units, phoodoo. Take a freshman physics course. That might cure it.

    12 inches = 1 foot, right? It doesn’t mean that 12 = 1.

    I guess that is true, unless you just get to make up whatever meaning you want for an inch to suit your plea.

    Since that is apparently what they teach in physics school, instead of teaching that numbers are supposed to represent a physical reality, I think I will pass on your generous advice.

  32. keiths,

    That’s great Keith, oh except how do we pass on the gene that keeps gazelles from being near lions, when THERE IS NO GENE WHICH keep gazelles from being the closest to a lion. Dam!

    If we can’t get past that fact, we are going to have a heck of a lot of trouble writing a computer program which passes on characteristics which don’t even exist and thus can’t be inherited!

  33. phoodoo,

    So, you agree that 12 in = 1 ft is a correct statement. Saying that it boils down to the patently absurd 12 = 1 is silly. The use of physical units is what makes a difference.

    That’s what you were doing with 4 = 1. That’s a logically incorrect expression. But it was wholly your own invention. I never said that 4 = 1. My statement was that N deaths = 1 generation. With N = 4 organisms, 4 deaths = 1 generation. Again, we have units here.

    Write that down.

  34. phoodoo, to Allan:

    Since you think its such a bad idea to write a computer that actually does what you claim evolution does, then you could at least just let the computer write its own software, just like you claim life does with DNA. Just turn the computer on, start short circuiting it occasionally and see what kind of damage you can do to the cpu to get it to start writing program.

    phoodoo,

    Have you heard the name “Gil Dodgen”? He is famous for being unable to distinguish the model from the thing being modeled — just like you.

    ETA:

    See these UD threads:

    A Realistic Computational Simulation of Random Mutation Filtered by Natural Selection in Biology

    Gil Has Never Grasped the Nature of a Simulation Model

  35. keiths,

    “He is famous for being unable to distinguish the model from the thing being modeled ”

    Were you talking to Olegt?

  36. GilDodgen:

    All computational evolutionary algorithms artificially isolate the effects of random mutation on the underlying machinery: the CPU instruction set, operating system, and algorithmic processes responsible for the replication process.

    If the blind-watchmaker thesis is correct for biological evolution, all of these artificial constraints must be eliminated. Every aspect of the simulation, both hardware and software, must be subject to random errors.

    phoodoo:

    Since you think its such a bad idea to write a computer that actually does what you claim evolution does, then you could at least just let the computer write its own software, just like you claim life does with DNA. Just turn the computer on, start short circuiting it occasionally and see what kind of damage you can do to the cpu to get it to start writing program.

  37. keiths,

    Obviously, a computer can’t simulate guided-airdrop technology unless it is thrown out of an airplane.

    And a program can’t simulate formation of a galaxy unless it is run in the cosmic void.

  38. olegt,

    Obviously, a computer can’t simulate guided-airdrop technology unless it is thrown out of an airplane.

    And it can’t simulate a flu epidemic unless it’s sick.

  39. keiths,

    Gil Dodgen explained to your perfectly how you would have to model a process which you all claim is based on a completely random bunch of replicators which just happen to be very sloppy in their replicating. Make everything random, just like you claim life is.

    So no one is claiming you can’t make a computer model of things, we are simply saying make the model have to use the same parameters as what it is representing.

    Maybe its the whole “physics school” problem Olegt has, in that he doesn’t understand that when you use the numbers they represent “things.”

    Four only equals one when you change the meaning of four and of one.

  40. phoodoo: Maybe its the whole “physics school” problem Olegt has, in that he doesn’t understand that when you use the numbers they represent “things.”

    LOL.

    That’s what theoretical physicists do for a living, phoodoo. We use numbers* to represent things.

    *and other, more advanced mathematical concepts like matrices, vectors, operators, groups, spaces, and on and on.

  41. olegt:
    keiths,

    Obviously, a computer can’t simulate guided-airdrop technology unless it is thrown out of an airplane.

    And a program can’t simulate formation of a galaxy unless it is run in the cosmic void.

    Gil Dodgen,

    One other obvious point: A simulation must accurately depict the system being modeled. The computational machinery and information content of biological systems is inherent in, and quintessentially critical to, the function of the system being modeled, and therefore cannot be excluded from the effects of mutations, without the simulation being rendered completely meaningless.

    There is nothing analogous in guided-airdrop simulations. My sims have been proven to work in the real world. Bio-sims have not.”

    Your can’t understand the problem until you understand the paragraph Olegt. Physics school can’t teach you that I am afraid.

    You could try the English or Philosophy departments though perhaps.

  42. phoodoo,

    A simulated thunderstorm will involve simulated air, simulated moisture, simulated heat, and so on. The computer itself does not need to get wet.

    See if you can apply this concept to evolutionary simulations.

  43. olegt:
    phoodoo,

    What’s your level of education, phoodoo? Have you finished high school?

    Olegt,

    You asked that stupid question once already. I told you, I am a dumb rice farmer, that can’t read. I just learned that there is way to tie shoes to keep them from falling off the other day.

    But EVEN I know that four doesn’t equal one, and I also know that telling a computer what you want it to create is no where near the same as telling a computer to create unguided chaos and seeing what it comes up with that is useful.

    So it seems you might being getting ripped off by your great education there Olegt. You can’t even remember your own questions. Maybe you could try rice farming and actually make something.

  44. phoodoo: But EVEN I know that four doesn’t equal one,

    That’s quite an achievement, phoodoo! But that’s a purely mathematical statement. Knowing some basic math does not entitle you to pontificate about science.

    What you also need to understand is that 4 quarts can equal 1 gallon. This is not saying that 4 equals 1. It is still a correct statement. Like 12 inches = 1 foot.

    When you understand that, you can try to figure out how 4 deaths of M&Ms can equal 1 generation.

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