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Evolution in Structured Populations

A conversation with a physicist: Some thoughts on fitness

Posted: October 29th, 2014 by Charles Goodnight

This past week I went over to the university at a nearby city, and talked to some physicists interested in complex systems, and among other things, biology. As seems to be the nature of physicists turned biologists, I was impressed with some of their ideas, but also impressed with their lack of knowledge of biology, and, to be blunt, their view that biologists were basically inept when it came to theoretical issues. Perhaps the most impressive simple example was one (note no names, but an American, not a Brazilian) wanted to publish a paper showing that the Fisher’s fundamental theorem was not universal. Now that is a paper that would be met with a large yawn. Aside: I find FFT to be a fun mathematical truism, given a set of assumptions, but I seriously doubt anybody has taken its universality seriously in a very long time.

FFT equation 7

Fisher’s fundamental theorem is a mathematical truism, but only if the underlying assumptions are met. It is well known that these assumptions will only rarely be exactly met in real systems, and that this theorem should be used to guide intuition, rather than to make quantitative predictions.

However, there were two issues that came up that I want to cover more seriously. Today I will talk about fitness, and next week I will talk about variance in evolution.

I was telling this physicist about some of my ideas, and in the process talking about “fitness”. In the course of this discussion I was repeatedly told that unless we really understood terms we couldn’t proceed. So as a result I kept being more and more specific, sadly, about everything but fitness. It was only later that it dawned on me that he didn’t think I knew what I meant by fitness. I actually think that this is one of the problems that physicists have with biologists. They tend to come up with wacky examples of where a naïve concept they attribute to biologists doesn’t apply, and then say that because this definition does not apply in this case we have no idea what we are talking about. This is, of course, a bit disturbing for somebody who has published models in which naïve definitions of fitness don’t apply (e.g., Goodnight et al. 2008. Complexity 13(5): 23-44). In short, I think I have a pretty danged good idea of what I mean by fitness.


I might just know something about fitness!      bankai.    (from http://pt.wikipedia.org/wiki/Ichigo_Kurosaki)

What this physicist was missing is that when I talk about “fitness” it is in fact shorthand for “temporal component of fitness”. Please bear with me on this, since I have never attempted to define fitness in a way that I would apply to all situations. But if I were to attempt to define fitness it would define it to be something along the lines of:

Fitness is the probability that an organism will start a lineage that will persist for an arbitrary period into the future.

I think a good boundary would be speciation, thus, I might narrow the definition of fitness to be:

Fitness is the probability that an organism will start a lineage that will eventually participate in the founding of a new species.

Obviously, this is an unworkable definition, but still, there are reasons why a truly general definition would need to be something along these lines. For example in the paper cited above (Goodnight et al. 2008. Complexity 13(5): 23-44) we examined the dynamics of a predator that was subject to mutations with how aggressive it was. What we found was that the optimal aggressiveness was a balance between growing quickly, but not so quickly that a lineage exhausted its prey and went extinct. The interesting thing was that in the short term these “optimal” lineages were always invasible by a more aggressive mutation, but in the long term these more aggressive lineages always went extinct. The point is that very aggressive lineages had an apparent high fitness over the course of a few generations, but a low fitness over a longer term. A true definition of fitness would have to incorporate this.


long term pred prey study

τ is a measure of aggressiveness, or how quickly the predator consumes the prey. Note that in this example a highly aggressive (cyan and dark blue) predator appears, but eventually burns out and goes extinct. (Figure from Goodnight et al. 2008. Complexity 13(5): 23-44.)

So, how do we deal with this obviously unworkable definition of fitness? The answer that my colleague did not understand is that we work with components of fitness. As Arnold and Wade (1984. Evolution 38: 709-718)pointed out so long ago, as long as episodes of selection are described in a multiplicative manner (that is conditional probabilities) it is valid to study a component of selection. In the predator prey example, it is perfectly valid to define a component of fitness that is lifetime reproductive success. If you did this you would discover that for this fitness component, the “fitness” of an aggressive mutant was very high. A biologist who chose their words very carefully would acknowledge that there may well be other later selective events that would counter the effects of this fitness component, but that would not invalidate conclusions about differences within lifetime fitnesses.

Since we are being careful, there are caveats even here. That is, technically the selection events have to be independent, and that will often not be the case. I think that this is another issue between biologists and physicists, however. That is, that in theoretical physics there is this concept of an exact solution. I seriously doubt that any theoretical biologist believes that we could develop a model that gave an exact solution in a living system. It is simply too complicated. Thus, as long as different episodes of selection, and thus temporal components of fitness, are not too highly correlated the assumption of independence will not hurt the ears of biologists too badly.


Unless you are really sensitive, a small amount of non-independence among selection episodes should not hurt your ears. (http://factsaboutbirds.blogspot.com.br/2010/08/desert-animals-list.html)

So, in sum, is life time reproductive success “fitness”? The answer is clearly no, since multigenerational processes can also enter into the equation. Instead, we need to think of it as a temporal fitness component. Am I apologetic about frequently referring to life time reproductive success as fitness, even though I know it is technically incorrect? No, I am not. Referring to it as something else is cumbersome, and honestly, in nearly every experimental system I am aware of, it is the major component of true fitness. It is basically a convenient shorthand and something that is usually pretty close to the truth.


In “truth” as in horseshoes sometimes close is good enough.  (http://lrossentertainment.wordpress.com/tag/outdoor-games-wedding-ideas/ photo credit, Sam Beebe, Ecotrust)

Spider Group Selection

Posted: October 22nd, 2014 by Charles Goodnight

I could keep going on what an individual is, but at least at this point I have put out the main points I have been thinking about. It may be a subject we will return to in the future. What I really should talk about a bit is our recent paper, “Site-specific group selection drives locally adapted group compositions” (Pruitt and Goodnight, Nature 514:359–362).

I am actually a bit surprised that it has gotten so much positive press with so little backlash. But with a very few exceptions we are not being dismissed. I guess times have changed. I am actually not so much going to describe the study so much as talk about what we demonstrated and why it is in actuality a fairly small step.

First a disclaimer: This is John Pruitt’s project. I was honored when he asked me to participate in the analysis of the data, and sometimes I am not sure I did a lot more than provide cover so that he could talk about multilevel selection.

As with all science, this study is but a small step in a long line of studies.


Two very apt adages “the cutting edge of science is dull” and more positively “if I can see so far it is because I stand on the shoulders of giants.” I have also heard this second being “if I can see so far it is because I stand on a mound of midgets”. It seems to me that all three are apt. The first because science proceeds in small steps. The giant and midget analogies are correct because there are giants (Darwin, Fisher Wright and the like) but advancing science also depends on midgets like you and I. (left: http://www.telegraph.co.uk/travel/travelnews/10088510/Bland-reaches-out-to-Dull-and-Boring.html, right: http://www.stellabooks.com/articles/dr_seuss.php )

The reason for that long-winded preamble is that in reality we did a relatively small thing. First some history. It has long been demonstrated that there were serious flaws in the reasoning of theoreticians dismissing group selection (Wade 1978, Quart. Rev. Biol. 53:101-114 – this paper is remarkable in how prescient it is given that it was published nearly 40 years ago). At the same time Wade was also doing the first studies showing that group selection worked in the lab (Wade 1977 Evolution 31:134-153). Later studies would demonstrate that indeed Wade had been correct in his quarterly review article: group selection could act on interactions among individuals in a way that simply was not available to individual selection (see Goodnight and Stevens 1997 Amer. Natur. 150:S59-S79), and a series of selection experiments led to the wide-spread adoption of group selection as a means of live stock improvement (e.g., Muir 1996 75:447-458). Thus, by this time we really have answered the early questions: In the lab group selection works, and it works so well because it can act on interactions among individuals. The next question was whether group selection IS acting in nature. The methodology for this was brilliantly provided by Heisler and Damuth (1987 Amer. Natur. 130:582-602), and promptly ignored. Fortunately, in recent years this method has been rehabilitated, and shown to work both in theory and in action. The results of these efforts is that, although not enough cases have been examined, it is pretty clear that group selection is at least not uncommon. To give you some idea about how common it might be, (1) recognize that theoretically we can show that soft selection is a mixture of group and individual selection (Goodnight, Schwartz and Stevens 1992, Amer. Natur. 140:743-761), (2) the constant yield law (Weiner and Freckleton 2010 Ann. Rev. Ecol. Evol., & Syst. 41:173-192) is almost universal in plants and (3) the constant yield law is a form of soft selection. Thus, group selection may indeed be extremely common in nature.

So, in some sense the main questions are answered: The models were wrong, group selection works, and it may be very common in nature. What was missing is that up to this point we did not actually have an example of an adaptation that was unequivocally a result of group selection. That is what Pruitt and Goodnight provided. This is no small feat. Consider how many solid examples we have of adaptation due to individual selection. There are a lot of traits that almost certainly are, but have never been demonstrated to be individual level adaptations. Examples of these are things like our hearts. Clearly an adaptation, but has it ever REALLY been demonstrated to be so? The examples we do have are few and far between, and all represent a huge amount of work on somebodies part. I am thinking of examples like the evolution of lead tolerance in grasses (Antonovics and Bradshaw 1970 Heredity 25:349-362) peppered moths (Kettlewell and later Majerus), and beak size in Galapagos finches (Peter and Rosemary Grant).


Social spiders have a group level adaptation that is the proportion of the colony that is aggressive vs. the proportion that is more docile. Populations have evolved to display a mix of these two proportions that is apparently optimal for their local environment. When the distribution is experimentally adjusted it always returns to the evolved ratio regardless of the environment in which they are raised. By the way, this strikes me as grasshopper hell. (From http://www.readcube.com/articles/10.1038/nature13755 — this is a nice writeup by Tim Linksvayer. I recommend it if you have not already seen it.)

Notice that in the cases where we have good evidence of evolution by natural selection there is environmental variation. In the case of lead tolerance there are mine tailings such that soils with high lead content are adjacent to pristine land lacking the metal. In the case of the moths and birds there is sufficient data over a long enough period of time that we can see adaptation occurring as the environment changes. Pruitt’s spiders were closer to the mine tailings scenario. That is there were different local environments that had different optimal mixtures of spider behaviors, and we were able to show that the spiders are locally adapted, and regardless of the environment we placed them in, they always adjusted their colony to reflect the adaptive mixture of behaviors in the environment they evolved in. Thus, Antonovics and Bradshaw were able to show that “normal” plants were unable to grow well in lead poisoned soil, we showed that spiders are unable to adjust their mix of behaviors when placed in the “wrong” local environment.

In reality, then, that is all we really did. We showed that these spiders have a group level adaptation to local conditions. Since it is a property of the group that cannot be meaningfully measured on individuals, it really is a group level adaptation, and since it is non-plastic it is a heritable change. This is the last of the qualitative issues to be addressed about group selection. Group selection works in theory, group selection works in the lab and in agriculture, we see group selection in nature, and now we know that group selection leads to adaptive change in nature. What is left is to work out the quantitative questions, such as how common is group selection relative to lower levels of selection, under what circumstances is it sufficiently powerful (and traits sufficiently heritable) that it leads to adaptations that can be attributed to evolution by group selection.

Individuals as Multispecies Entities

Posted: October 15th, 2014 by Charles Goodnight

I am feeling a bit schizophrenic these days, splitting my time between developing models of species differentiation, experimental design to measure the genetics of species differentiation – yes, it can be done, and blogging. The last is a bit confusing because it starts me wondering, when did I become a philosopher.   And lets just say, there is a reason that they give PhDs for philosophy, and a reason I don’t have one.

Any way on the philosophy issue, today I want to clean up and finish up my discussion of individuality. Hopefully this will be short and sweet.

Here is the issue: I have defined individuality in terms of selection and evolution. I stand by those definitions, but it occurs to me that this does not fit well with our concept of organism. Consider the point I raised before which is that if we choose selection as defining the individual, in many, if not most cases, we will logically assign fitness at what we commonly call the organism. However, what we colloquially call organisms, it is now becoming apparent, are not a single species.



Revisiting an issue raised a few weeks ago, when studying selection on running speed in cheetahs it makes sense to assign fitness at the level of the organism. In this case the “organism” is a multispecies assembly. (http://theruniverse.com/2012/07/running-tips-from-cheetahs/)

It may be that there are a bunch of commensals and parasites inside that organism, but it is still the cheetah that eats or doesn’t eat, and reproduces or doesn’t reproduce. For the rest of this post I will use commensals to mean all of the species associated with a metazoan, including parasites and symbionts.  Remember, selection is blind as to the causes of the phenotype.   If our cheetah cannot run fast because it has a bad mix of gut bacteria (and a belly ache?) it still doesn’t get to eat, and it still starves. Thus, our selection definition of fitness is in this case identifying the assembly of species that is a cheetah as the “individual”.

Fine, you may argue, but it is the cheetah that survives and reproduces, and as such we ignore the rest as environment. The philosophical problem with this is that it is exactly the same issue with the gene-centered view. The gut bacteria may be along for the ride, but they are there. To ignore them is the same as in the gene-centered view ignoring other loci even though they are interacting with the locus you are focusing on. We know that doesn’t work. I would argue that the reason we know the reductionism to only the colony of “cheetah” cells doesn’t work is because nobody has ever bothered to ask the question.

There is, however, another issue. I would also argue that many of these commensals ARE heritable. Remember using the phenotypic view I consider “heritability” referring only to genes to be far too narrow. Basically many of the commensals ARE heritable. At one extreme, we can consider mitochondria to be “commensals”. The only reason that we normally don’t is that they are strictly vertically transmitted, and they have coevolved with their host cells to the point that neither can survive without the other (except, the case of chloroplasts and nudibranchs )


The emerald green sea slug, Elysia chlorotica, isolates cholorplasts from algae and incorporates them into their own cells, using them for photosynthesis. (from http://scienceblogs.com/notrocketscience/2008/12/28/solarpowered-green-sea-slug-steals-ability-to-photosynthesis/)

The case of mitochondria is not really so different from that of Wolbachia, except that insects cured of Wolbachia typically survive, whereas “curing” animals of mitochondria is probably not a good idea! (OK, our cheetah neither uses chloroplasts, nor has a wolbachia infection, hopefully you get the point).

Other commensals have a looser association, nevertheless, in the context of the phenotypic approach they have to be considered heritable. For example, an old study (Bettelheim, Breadon, Fairs, O’Farell and Shooter 1974, J. Hyg. Camb 72:67) found that in most cases mothers and their babies had the same serotypes of E. coli. One can imagine similar “inheritance” of even ectoparasites such as fleas (mother cheetahs infecting their offspring). Thus, yes, many of these commensals WILL be part of the patterning node. Others will be more opportunistic infections and thus nonheritable, but that does not negate the fact that many are indeed heritable.

So, that leaves us with the reality that in many cases “individuals” will be multispecies entities. You are not just you, you are you and your pets. Lest this bother you, please remember that commensals CAN affect your behavior. I have a friend that swears that an amoeba infection he got caused him to become depressed, and toxoplasmosis can apparently make people more reckless (and make the cat litter box less offensive). So, yes, parasites do affect the way you think, and no, even your behavior is not just your own.

So, here is my proposal. I think we do need a name for a colony of cells of the same species. I suggest we define “organism” as a colony of cells derived from a single cell and physically connected to each other.   In this view the cheetah “organism” would be the set of cells derived from the fertilized egg from the mother cheetah. On the other hand, the cheetah “individual” would be the actual creature that includes the organism and its commensals. I am not sure that this will ultimately end up being a good idea, but hopefully it is a good place to get the discussion started.


No, not that cheetah, I am talking about the one that can run fast. (from http://www.lavantis.com/2011/12/cheetah-chimp-of-tarzan-dies-at-80/)

Heritability and the individual

Posted: October 9th, 2014 by Charles Goodnight

First off, an ad from a former graduate student I used to work with. Josh Payne, who was an author on the speciation in continuous populations paper I discussed some time ago , is looking for students and a postdoc to study evolution and robustness. Check out his ad if you are interested.

To summarize to this point, I first defined an individual as that which you define to be an individual, or more specifically, the level at which you assign fitness. This definition makes sense since there may be constraints on what can be measured. There are a trillion some odd cells in our bodies. Assigning fitness at the level of the cell would be a huge chore unless there was some compelling reason to do otherwise. On the other end, a paleontologist may have access to presence or absence data for species in a fossil assemblage, but no way of assigning fitness to individual organisms, or even knowing how many individuals there are in the population. Thus, they may forced to assign fitness at the level of the species. This first definition is entirely consistent with the pragmatic needs of research.

At this point an admonition to paleontologists: Do not apologize for studying “species selection”. In your world species ARE individuals. From this perspective, the waxing and waning of the range of a species, or anagenesis of the species is simply “species development”. It may well be that if we had a time machine, and ear tagged all of the mastodons, and measured traits and their reproductive success we would discover that the change in their distribution was due to selection at the level of the organism, but we can’t and because we can’t we cannot study it as evolution, and we need to let go of that and be happy with the evolution we can study. By the way, this also means that two investigators could choose to assign fitness at different levels, and as a result come to very different conclusions about how evolution works. It being the nature of biologists, they will almost certainly argue about which one is “right” when in fact, since they are using different definitions of what the individual is, they can both be correct.

My second definition is that the individual is the level at which selection is acting. I like this definition a lot since it is logically appealing that selection should define the individual. It also suggests that metazoans are metazoans because groups of cells have higher fitness than individual cells. Following this through, it logically also suggests that under some circumstances groups of organisms have higher fitness than individual organisms. We actually see that eusocial organisms often exploit environments and resources that solitary organisms can’t. Thus, naked mole rats can live in an environment that is too harsh for other rodents.   Social wasps can have open nests even though their larvae are extremely attractive food sources.   And ants have virtually taken over the world. It also suggests that there are times when social living may not improve an organism’s fitness. Just as there are environments where naked mole rats out compete all other rodents, there are many other environments where naked mole rats cannot compete. Presumably, in these richer environments the strength of group selection is lower and individual selection higher and as a result the naked mole rat cannot compete with its solitary brethren.

naked mole rats

Naked mole rats live in a harsh environment where other rodents cannot survive, but have not spread into more benign environments. Presumably this is because the balance of selection tips towards group selection in harsh environments. (http://adarwinstudygroup.org/illustrations/#img-01-2402 )

There is one last concept of individuality that needs to be discussed. This is the classic one that is the subject of books such as Maynard-Smith’s book supporting group selection (he said laughing in his hat five ways*), “The Major Transitions in Evolution“. That is the observation that selection at the group level can overwhelm individual selection, and effectively suppress evolution at the lower level.

The interesting thing about metazoans is that they rather famously start from a single fertilized egg, and eventually divide into trillions of cells. Importantly, the cell division is via mitosis, which has almost unbelievable fidelity. Thus, all of the cells are genetically virtually identical. From the perspective of individuality, what this does is that it lowers the heritability at the cellular level to nearly zero. To remind you, the breeder’s equation is:

R = h2S

Which basically means that if we are going to get evolution by natural selection we need both selection and heritability. In my second definition I identified the individual as the level at which selection is acting. Lowering the heritability has exactly the same effect. Thus a reasonable definition of individuality is the lowest level at which there is heritable variation for a trait under selection acting at that level.

It is important to recognize that mitosis is but one way that heritability can be minimized. In social insects you get the same minimization of heritability through “policing” behaviors. For example, in worker bees there is variation in their propensity to lay eggs (all haploid male eggs, of course); however, because workers eat eggs laid by other workers, this variation does not translate into reproductive success, and there is no variation among workers in offspring produced. Other mechanisms for reducing variation that have evolved are things such as having a single reproductive in a colony. Such reproductive behaviors increase relatedness within groups, having the effect of reducing heritability, and decreasing the response to selection.


A bee killing a worker laid egg. This policing effectively eliminates the heritability of fertility among worker bees. (from http://www.nature.com/news/2002/020425/full/news020422-16.html)

An interesting anecdote on this is that as good as mitosis is at making exact copies, there are mistakes. As a consequence there IS heritable variation among cells in metazoans. This would suggest that there should be strong selection, but low heritability, for cells becoming reproductive cells. So, why hasn’t your liver evolved to become a gonad? Obviously, part of this is the fidelity of mitosis, but another part is that the reproductive cells are isolated very early in development, and actually while development is still under maternal control. What I mean by that is that early cell division in vertebrates occurs far faster than is apparently possible based on normal rates of protein synthesis. The way this can occur is that the mother “packs” the cells with RNA and proteins before fertilization. Thus, the early cell division is under maternal control but after a few divisions the zygote derived gene products take over control of cell division. It turns out that in Drosophila for at least one important gene product, notch, isolation of the germ line occurs immediately before the shift from maternally derived notch to zygotically derived notch occurs. Of course I have no real idea, but as an adaptive story it is tempting to suggest that the maternal control of germ line segregation is similar to policing in social insects. (don’t ask me for references on this. Years ago I wrote a grant for this with somebody. We got the grant, but my collaborator left and I never saw the money or did the research. Also, this idea can be traced to Leo Buss [http://www.amazon.com/The-Evolution-Individuality-Leo-Buss/dp/0691084696], so I take no credit.)

Thus, the three definitions of individuality, and particularly, the second and third are really cut from the same cloth. An individual is an evolving unit. At the simplest, it is that which we recognize as an individual. Given that humans are good at recognizing patterns, it is hardly unreasonable that we intuitively identify “individuals” more or less correctly. The second and third are more formal definitions in the sense that we are saying that individuals are units of adaptation. They can be units of adaptation either because of the patterns of selection, or because of the patterns of heritability, or both.

* 10 points if you can identify that reference! The actual quote is “One little sniffer with his eyes half shut and a mitten on his nose, laughed in his hat five ways and said, ‘They are going to the moon and when they get there they will find everything is the same as it always was.’ ” And by the grace of the cosmos Disney never laid waste to those stories.

Selection and Individuality

Posted: October 1st, 2014 by Charles Goodnight

Apparently I have shifted to an every other week post. It is not that I am lazy, just that my life is a bit chaotic. A week ago Saturday my daughter got married, and this week I am flying back to Brazil. Somewhere in the haze last weeks post simply didn’t happen.


blame the lack of post last week on the haze of getting out of town for a year. Besides, how else am I going to work Jimi Hendrix into a post? (from http://markmywordssite.com/2011/05/05/purple-haze-all-in-my-brain/)

In any case, I felt that I left you last time with a rather unsatisfying answer: An individual is that which you define to be an individual. This week I want to argue that some designations of “individual” are better than others. To see this we need to continue to work with contextual analysis.

To start, lets imagine we assign fitness at the lowest possible level, that is the cell. Ten points if you can tell me why it is NOT the gene! Twenty points if you can tell me why the lowest level might be the organism! – hint: What is an orgamism?. In that case we are calling the cell the “individual”.


Selection at the level of the Gene (Simmons) makes no sense. (from http://musicrowgirl.com/tag/gene-simmons/)

First lets look at cancer. If we imagine that fitness is just the rate at which cells divide (and ignoring organismal mortality for the moment) then cancer cells have a higher fitness than “normal” cells because they divide more rapidly. Thus in contextual analysis we can imagine a case of pure cellular (individual) selection then:

sel and ind eq 1

Here is the kicker: If we assume that there is ONLY cellular selection and we do a bit of math I prefer not to show you then we quickly discover that:

sel and ind eq 2


sel and ind eq 3

what this tells us is that, because we assumed it to be that way, there is selection at the level of the Individual cell, but no selection at the level of the organism. Thus, in this simple case the qualitative result is that selection is acting at the cell level.

If we assign fitness at the level of the organism then we are de facto defining the organism to be an individual. Here we get a very different answer. In particular, since there is no assignment of fitness at the cell levelsel and ind eq 4 and sel and ind eq 5are undefined. Similarly we cannot do the partial regression sel and ind eq 6, and can only do the simple regression, sel and ind eq 7, which emphatically does not equal zero, and in fact had we measured it, sel and ind eq 8.

Whether we assign fitness at the level of the cell or the level of the organism, we still measure evolution by natural selection; however, what happens is that our interpretation of how selection is acting qualitatively changes as we move between levels.

Now, lets consider selection on a second trait. In this case it is something that only acts at the organismal level, nevertheless we will assign fitness at the level of the cell. Because, by assumption, selection is only acting at the whole organismal level

sel and ind eq 9

On the other hand

sel and ind eq 10

Again, because we considered only a situation with selection at the organismal level, contextual analysis says there is group (organismal) selection, but no individual (cellular) selection.

Now, if we were to assign fitness a the level of the organism instead of the cell we would discover that sel and ind eq 7 had not changed, and that we still detected exactly the same strength of selection at the organismal level as we did when we assigned fitness at the level of the cell. In other words, in this second case when we changed levels at which we assigned fitness we got no qualitative change in our interpretation of how selection was acting.

So, what does this have to do with individuality? I would defend the statement I made in the last post that the individual is at some level arbitrary, and it is the level at which you assign fitness, however I would argue that some choices are better than others. In particular, if we imagine that we assign fitness at the lowest conceivable level, for selection on most traits we would find some higher level at which “contextual” selection is acting. If we assign fitness at the level of the cell we would find that for a large number of traits there is a strong contextual component of fitness that is at the level of the organism. I would argue that for selection on any given trait the logical level at which to assign individuality is the level at which there is a strong contextual component to fitness.

Logically, how do we find this “natural” level of individuality? The easy way is simply to do the contextual analysis and find the level at which contextual selection is acting. A corollary to this is that when you move through that level at which contextual analysis is acting you will see a qualitative change in your interpretation of how selection is acting. In the example above when selection was acting at the cell level, assigning selection at a higher level qualitatively changed our interpretation. That is when we assigned fitness a the level of the organism what had formerly been interpreted as cellular level selection becomes organismal level selection. Importantly, when we had a situation in which selection was acting at the organismal level then moving up the level of individuality from the cell to the organism does not qualitatively alter our interpretation of how selection is acting, and we see that in this later case the cell is not the natural individual, whereas the organism is.

This actually has some important philosophical implications. First, it appears that selection in some sense defines individuality. Since selection acts on traits that means that these selection defined individuals will be trait dependent. Thus, the selection defined individual for cancer or differential cell proliferation will in most cases be the cell, whereas selection on running speed will most likely end with defining the individual as an organism. Now we ask the musical question of whether a bee colony is an individual. From a selection standpoint the answer is it depends. For the probability of a worker producing an egg we might decide the bee (the organism) is the individual, whereas for a trait such as the probability of the colony surviving the winter we may well decide that the colony is the individual.


Japanese honey bees mob and “cook” an Asian hornet. The Asian hornet hunts honey bees, however if the colony detects one they will mob it, surrounding the hornet and raising its body temperature until it dies. European honey bees do not have this behavior. For this trait the hive is the individual. (http://www.nbcnews.com/id/20823983/ns/technology_and_science-science/t/surprise-strategy-bees-smother-enemies/#.VCw2n-dfnzg)

The final question is why is multilevel selection a better term than say, “group selection”. The answer, of course, is that selection is acting at only one level then that level is the selection defined individual. In the simplistic world of selection acting at only one level there is only individual selection, but sometimes the “individual” will be a group. The only time it makes sense to talk about group selection in this view is when selection is acting at more than one level. In this case the lowest level at which selection is acting would be “individual selection”, and selection on contexts larger than the individual would be “group selection”.


What is an individual (Part 2): An arbitrary definition

Posted: September 17th, 2014 by Charles Goodnight

Last week I discussed why defining the individual is so difficult. Having put you in an existential crisis over whether or not you are an individual, it is time to pick up the pieces and see if we can come up with a useful phenotypically based definition of an individual. At the very least perhaps I can help you decide whether or not you need to buy an extra bus ticket, one for you one for your symbionts, or whether one bus ticket is enough.

jadzia of deep space 9

Does Jadzia Dax of Deep Space 9 need one ticket or two when she takes the megabus to Leran Manev (the capital city of Trill)? (https://mycrazylosttheory.wordpress.com/tag/trills/)

So, what is an individual? It turns out that a big hint comes from contextual analysis. Who would have thought that a statistical technique that is frankly just multiple regression could provide answers to philosophical questions! To remind you, contextual analysis is a method of analyzing multilevel selection. Using this method the fitness of an individual is measured, as well as a set of traits measured on the individual and on the group (or neighborhood, or kin group etc) that they belong to. A multiple regression is then done, and if there is a significant partial regression of individual fitness on a group level trait we say that group selection is acting. This makes sense because a significant regression implies (taking all of the appropriate caveats into account) that the fitness of an individual is a function of the group to which they belong.

Here is point number 1: in contextual analysis fitness can only be assigned at one level. It is measured by the investigator, and the level at which they measure fitness is a function of what is possible, and on the investigator’s understanding of biology. Thus, if you want to see if there is selection for running speed in cheetahs it makes sense to measure and assign fitness at the level of the whole organism. You could assign it at the level of the cell, but it would be a waste of time (who wants to measure the fitness of a trillion cells?). On the other hand, you could measure it at the level of the population of cheetahs, but from our understanding of biology, we would be inclined to decide that this would not be terribly helpful. Thus, logically, it makes sense to assign fitness at the level of the organism. I will make the interesting point that in this case the “organism” is actually a multi-species assemblage that collectively hurtles through space trying to catch gazelles.


When studying selection on running speed in cheetahs it makes sense to assign fitness at the level of the organism. Interestingly, in this case the “organism” is a multispecies assembly. As an aside, this stretched out all legs off the ground position is the one part of the cheetah gate that is found in very few if any other animals. (http://theruniverse.com/2012/07/running-tips-from-cheetahs/)

Point number 2: Nature changes as nature changes. That is, change in groups occurs at all levels at all times. Cells in our bodies are produced by mitosis, and lost through cell death, organisms live and die, populations are founded and go extinct, as do communities, species, ecosystems, and presumably planets. Every one of these may cause a change in the distribution of their appropriate population. That is, if you drink a lot of alcohol perhaps some liver cells die. This is a change in the distribution of cell types in your body. If some cheetahs run to slow perhaps they starve, this can result in a change in the distribution of running speed in the cheetah population. In the first situation case we are inclined to call the decrease in the proportion of liver cells as development (or perhaps stupidity), in the second situation we would be inclined to call the change in running speed evolution. I would argue that both cases are qualitatively similar, however the difference is that we intuitively assign fitness at the level of the organism. Because we assign fitness at that level there can be variation among organisms in fitness, and since there is variation in fitness among organisms and we can speak of changes in running speed in terms of evolution. In contrast, in the case of the case of the liver cells, since we intuitively assign fitness at the level of the organism speaking of the fitness of cells within that organism makes no sense. Thus, we have to call differential death and proliferation of cells by another name, such a “development”.

The point is that there is no qualitative difference from nature’s perspective between these two scenarios, but there IS a qualitative difference in our interpretation of these two scenarios. The difference is that in the case of the liver cells we are speaking of a process taking place at a level below that which we assign fitness, and thus call it development, whereas in the second it is above the level at which we assign fitness, and thus we an call it evolution.

So, this gives us a very simple and unsatisfying definition of what an individual is: An individual is the level at which we assign fitness.

So, to consider the examples I talked about last week. For an aspen stand, is the individual the clone or the tree? For identical twins are they one or two individuals? Based on my argument, the answer is you decide.

There are a couple of interesting points about this idea. The first is that this explains why we have so much trouble defining the individual. The definition I gave suggests that from a very fundamental perspective what an individual is is an arbitrary construct of how we view nature. It is not a natural unit any more than any other part of nature is (remember Mayr arguing that the species is the only natural unit in phylogenetics?). The more interesting point is that in almost every case, probably every case for metazoans, what we call an “individual” is typically a multi-species assemblage. In other words, not only is the individual an arbitrary construct, it is not even a single organism, if you define “organism” as a colony of cells derived from a single fertilized egg.

Next week I will expand on this definition of the individual, and hopefully make it a little less arbitrary. Nevertheless, I do stand by this as a perfectly valid definition of the individual, oh and Jadzia Dax should be fine buying only one bus ticket.

What is an individual (Part 1)

Posted: September 10th, 2014 by Charles Goodnight

It seems to me that the bad-boy question of evolution that sneaks around the edges, and nobody seems to notice is what is an individual? Think about it: My definition of evolution is change in the distribution of a population due to the gain or loss of individuals. I use “individuals” as if that were a known and obvious entity. I am not alone in that. Futuyma defines evolution in terms of “individual organisms”. Other writers are less explicit, but the implication is that evolution is defined in terms of individuals, which are assumed to be organisms.

Normally, our concept of what an individual is makes sense. That is, we see a human: that is an individual. We see an oak tree: that is an individual. As usual in biology, most of the time our intuition isn’t bad. Where it falls apart is when we get to the fuzzy edges. When we see two identical twins, are they one or two individuals? What about a stand of aspen trees (which clonally reproduce), or even worse, a huge fungus that covers 2,384 acres (http://www.scientificamerican.com/article/strange-but-true-largest-organism-is-fungus/)?


The worlds largest organism is a fungus, but is it an individual? (From http://www.scientificamerican.com/article/strange-but-true-largest-organism-is-fungus/ )

So, at the macro level, we have the question of whether genetic identity is enough to make two things (twins, a cutting off of a plant) the same individual, or do they need to be physically connected. Either answer raises a bunch of issues. For example, if we only require genetic identity, then I can take a cutting of your Christmas cactus, and take it with me to the other side of the world, and they are still the same individual, even though they have absolutely no contact with each other. Similarly two identical twins would probably be at least slightly offended to learn that they were the same individual.

Lindsey Lohan twins

Are they one individual or two. In this case, we can definitively answer the question, it is one individual, Lindsey Lohan, playing identical twins, but in cases of real identical twins the answer may not be as obvious. (from http://une10.blogspot.com/2011/08/visboo_29.html)

The other possibility is also difficult. With aspen clones some ramets (individual trees) are connected, others may not be. Thus, we really cannot know how many individuals are present without excavating them.

Aspen Clones[6]

How many individual aspens are in this picture? Is it three or is it hundreds, or somewhere in between? (http://watchingtheworldwakeup.blogspot.com/2008_09_01_archive.html)

It becomes even more difficult if we consider the other side of the equation. That is, it is tempting to define an individual as perhaps a set of genetically identical cells of the same species, perhaps requiring them to be physically in contact, and physically separated from other sets of cells. This is a made up on the spot definition probably won’t satisfy anybody, but it is close to the intuitive notion. However, this definition has a host of problems. Starting at an issue that nobody will lose sleep over: are mitochondria part of the individual? Mitochondria are a symbiosis between two cells, presumably an Archea like host cell and a Bacteria like symbiont, that has coevolved to the point that we no longer consider them separate entities. Instead the coevolution is so complete that we consider them to be their own (synthetic?) kingdom Eukarya.

eucaryote origins

The well established endosymbiotic theory of the origin Eukarya. (from http://www.nature.com/scitable/topicpage/eukaryotic-cells-14023963).

That is something of a straw man argument, but consider that in our bodies well over half of the cells are not human cells. Included in that are some symbionts that are passed from parent to offspring at or before birth, some that are acquired through social interactions with family and other important people in our lives, and finally some are acquired from the environment (I mean “symbiont” in the classic sense that includes both mutualists and parasites). Importantly, some are life-time residents, such as much of our gut fauna, and intra-cellular parasites, and others, such as pathogens, are temporary visitors using our bodies as environments in which to breed.


“Wolbachia bacteria, green, infect the ovaries of the malaria-transmitting mosquito Anopheles stephensi.” Wolbachia are maternally transmitted, and thus effectively evolutionarily similar to mitochondria. Should they be considered part of the individual? (http://www.npr.org/blogs/health/2013/05/08/182339563/using-bacteria-to-swat-malaria-inside-mosquitoes)

In short, it seems that the boundaries of what is an individual, or even an organism start to become fuzzy when we start poking at the edges. We should hardly be surprised by this. After all, one of the hot topics in biology has been the issue of “major transitions”, which, for example, Maynard-Smith felt was sufficiently important that it deserved to be the subject of one of his last books, and (shameless self plug here) there has been a recent a volume on evolution and emerging individuality edited by Bouchard and Huneman. If individual cells evolved for group living, then eventually became an “individual” then we should expect our concept of individuality and organismality to be difficult, this is simply the nature of biology.

A final issue that we have to consider is that if that transition from groups to individuals is actually took place in the past, we should be seeing that occurring in the present as well. This goes both directions. Going downward, when should we consider a cell in a metazoan to be an individual? And going upward, when should we think of colonies of insects as individuals? Should we ever consider herds of mammals, or communities of humans as individuals?

lazy or sick

We absolve the man on the left for staying in bed calling him “sick”, whereas we blame the man on the right for being “lazy”. In both cases the result is the same: they are lying in bed, only in the second we assign causality to the person. ( left: http://donlonpharmacy.com/flu-season-is-not-over/ right: http://www.cc-chapman.com/2011/social-media-has-made-you-lazy/ )

There are a lot of questions surrounding what we mean by an “individual”, however, interestingly, we have a good intuitive notion about what an individual is. Consider the example I use in my chapter in the Bouchard and Huneman book in which I imagine two people, one who is in bed because they have the flu, and one who is in bed because they don’t feel like getting up. The first person we might excuse because they are sick with the flu, and we do not assign blame to them, since they are “sick”. We might label the second as being “lazy”, and blame them for their failure to get up, or in other words, we assign the choice not to get out of bed to them as an individual. In thefirst case we assign blame to the disease, and absolve the individual, in the second we assign blame directly to the individual. In both cases the outcome is the same: The person stayed in bed. The question becomes why is laziness a property of the individual in the second case, but not the first? I think that the phenotypic perspective, and multilevel selection have a lot to say about this question, and it is something I will be exploring in the next week or two.

Speciation in continuous populations

Posted: August 28th, 2014 by Charles Goodnight

I am in Brazil this week to give a talk about speciation in continuous populations, so I figure I will save a little effort by summarizing some of the stuff that is in that talk. By the way, Sao Carlos is a wonderful town, and if you can come up with an excuse to come to Brazil I strongly recommend it. Of course, if you are a vegetarian, while it SHOULD be a good place for you, man do these folks like their meat!

So, on to speciation. This is a project I did with Maggie Eppstein, currently chair of the University of Vermont Computer Science department, and Josh Payne, then a computer science graduate student and now a postdoc at the University of Zurich. In other words, it was big on computer science, and maybe a bit less big on biology, but the implications for biology are important. (Payne, J.L., Eppstein, M.J., and Goodnight, C.J. “Sensitivity of Self-Organized Speciation to Long Distance Dispersal”, Proceedings of the 2007 IEEE Symposium on Artificial Life (Alife’07), pp. 1-7, 2007.  Eppstein, M.J., Payne, J. L., and Goodnight, C.J., “Underdominance, Multiscale Interactions, and Self-Organizing Barriers to Gene Flow”, J. Artificial Evolution and Applications (special issue on Biological Applications), Volume 2009, Article ID 725049, 13 pages, 2009

This project stemmed out of a discussion I had with several people at NECSI (http://necsi.edu/). So, in talking to them I came to realize that when you had two types that were incompatible, they were distributed randomly on a plain, interactions were local, and the types spread contagiously that there would be this interesting process of coarsening. That is if you started out with the types randomly distributed the locally common type would have an advantage and increase, whereas the locally rare type would have a disadvantage and decrease. The net result would be your random distribution would devolve into regions that were primarily one type, and other regions that were the opposite type. I also found out that the boundary between these regions would wander about randomly across the plain, but it would get trapped by any sort of boundary

Sayama coarsening

Coarsening. In this example the fitness of an individual is proportional to the number of neighbors of the same color. This results in a process of coarsening in which the once uniform distribution becomes clumped with low fitness boundaries between the different color regions.

In any case the question becomes whether speciation this process of coarsening in populations with local interaction lead to speciation. We decided to look at the very simplest case, that of simple underdominance. That is, can we take a population with within locus underdominance, and have it self organize into two species.

By the way, as with any good theoretician, I will use Mayr’s biological species concept as my definition of a species. I know that this is really not a great definition, but heck, I got to meet Professor Mayr on several occasions and he said nice things about my research, so I stand by my decision. . .

First off, the trivial case is where the underdominance is so extreme that the heterozygote is lethal:

Genotype       A1A1             A1A2           A2A2

Fitness               1                   0                   1

Obviously, such a population will immediately split into two reproductively isolated “species”. Yes, this works, but it is biologically totally unconvincing.

I won’t go into the details, however, what we can show is that it is quite easy to introduce mild underdominance into a viscous population. Thus, we would be hardly surprised to see underdominance such as:

Genotype       A1A1             A1A2           A2A2

Fitness               1                   0.9                   1

The problem is that this is not an effective barrier to gene flow. Indeed we were able to show that it takes a complete reproductive isolation to prevent the movement of a neutral gene across the boundary.

gene penetration

Gene flow of a neutral gene across a underdominant boundary. Note that there is a linear relationship between the degree of underdominance and neutral gene penetration, and importantly, a discontinuity when gene flow is zero.

Thus, we are only going to allow mild underdominance, yet we want the population to divide into two completely reproductively isolated populations. It turns out that it is not that hard if we allow multiple loci with mild underdominance. To illustrate this consider two loci with underdominance of 50%, so that the double heterozygote is lethal.

two loci no epistasis

Two underdominant loci. Double homozygotes have the highest fitness, single heterozygotes (yellow) have lower fitness, double heterozygote (white) is lethal.

If we set up this system on a 100 by 100 field with nearest neighbor mating and dispersal we see “coarsening”, but because the coarsening is not focused there is no speciation: coarsening

Local mating leads to “coarsening”, patches of one double homozygous genotype (A1A1B1B1 etc) separated by hybrid zones.

In other words, simply by having localized mating and underdominance we are half way there. We get the coarsening, and regions of the two species, but in all cases there is a pathway through a viable hybrid zone between any two regions.

This is where we had to introduce some epistasis. In our next iteration we added a bit of epistasis so that the two opposite corner genotypes were favored:

Two loci, epistasis = 0.1

Two underdominant loci. Double homozygotes of the same numerical value have the highest fitness, single heterozygotes (yellow) have lower fitness, double heterozygote (white) is lethal.

This now results in coarsening and eventually speciation:


Local mating leads to coarsening, and domination of the two most fit genotypes (A1A1B1B1 and A2A2B2B2). In this case all of the hybrids are lethal, and the two populations are reproductively isolated.

This is actually very interesting, because you will note that in the early stages all four homozygous forms are formed, but the single locus heterozygous boundaries wander around randomly. When two such come into contact they coalesce into a single stronger boundary, eventually leading to speciation. Importantly, this is not limited to only two loci. It turns out that this coarsening and coalescence of leaky boundaries will continue regardless of how many loci are involved. Thus, even extremely mild underdominance at a large number of loci will eventually lead to speciation in this model:

speciation with multiple loci

The effect of number of loci on speciation. In a panmictic population (black line) the population always fixes on one of the two best genotypes, although the time to fixation changes as the number of loci increases. In spatically structured populations speciation always occurs, with the time to speciation being a function of the number of loci required and the amount of epistasis.

This is a very simple simulation, yet it makes the important point that when there are genetic incompatibilities speciation can easily occur. Indeed, this implies that the speciation may be the expected outcome for a widespread species with limited gene flow.

Wright’s Shifting Balance Process revisited one last time

Posted: August 13th, 2014 by Charles Goodnight

It is shaping up to a busy summer, mostly because I am packing up my house so I can go to Brazil for a year. And that is my rather lame excuse for neglecting my blog.

In any case, what I did so many weeks ago was go through the three phases of Wright’s shifting balance process one at a time. Perhaps it is time to do a summary post.

To review, the three phases are (1) the phase of random drift, (2) the phase of mass selection, and (3) the phase of interdeme selection. As I pointed out before Wright’s initial model is undoubtedly naïve, nevertheless, it forms a good basis for thinking about evolution. Importantly, Wright thought all three of the phases were acting simultaneously, so in a sense the phases might be thought of as a human construct based on our need to categorize things. The question becomes how can all of these phases be acting simultaneously when they apparently have very different requirements, what with drift working best with small population size, and selection working best with large population size, and needing isolated demes for phase one, and differential migration for phase three, etc. Any way, if other people can tell just so stories so can I. The scenario I am going to paint may work, then again, it may not. I am not going to defend it either way.

I am inclined to suspect that the answer may lie in how additive genetic variances change over the adaptive topography. In particular consider the adaptive topography. If we choose an adaptive topography in which the axes are phenotypic then at any point we can take the tangent to the multidimensional surface, and I would argue that the slope of that tangent is the phenotypic variance for fitness. If we then projected that on to axes of the heritable components of the phenotype and again made an adaptive topography then the tangent would be the (effective) additive genetic variance for fitness.


The reason that this is important for the shifting balance process is that this is the element that has been missing from discussions of the shifting balance process. The point being that what is important is not population size or strength of selection per se, but rather the ratio of selection to drift. When NeS <<1 a gene is effectively neutral. In words if the effective population size (Ne) times the strength of selection (S) is much less than one the gene can be considered effectively neutral. There is an interesting subtext here, in that Ohta was thinking about selection acting directly on genes (yea, we phenotypic selectionists don’t believe in such nonsense), so in effect the heritability in this case is one. In the case of traits should neutrality be related to Ne(h2S)? I am at my in-laws, so I don’t have time or facilities to work that out.

The important point is that Ne(h2S) can become small either by Ne becoming small (what is typically being considered), or by h2S becoming small. Thus, in the region of selective peaks and valleys Neh2S will be small. At peaks although the population size is large, the tangent is very small, and fitness is nearly neutral. In valleys both Ne and Ne(h2S) will be small, and again the trait will be nearly neutral. It is mainly on the slopes of the peaks that the effective additive genetic variance will be large enough that selection, and thus phase 2 will be important. This makes the point that phase one and phase two can coexist, with phase one being dominant at peaks and valleys, and phase two being dominant on slopes.

This still leaves the problem of escaping from a local adaptive peak, but I suspect there may be some ways around that as well. To me the big problem is getting a metapopulation in which there are populations on more than one peak. My first thought is that this may be in some sense fractal. That is, populations differing on different tiny peaks within a major overall local adaptive peak may be common, but populations differing in major adaptive peaks may be quite rare. Thus, the probability of metapopulations with subpopulations on different peaks probably depends on how different the peaks are. That said, there are a number of ways that such metapopulations might arise. The easiest to imagine is a changing environment in which a former adaptive peak suddenly becomes much lower. Such changes need not be permanent. For example, an unusual weather year might effectively change selection enough that a peak temporarily disappears leaving the populations free to drift. Alternatively, even if an environmental change didn’t change the height of a peak it could lower population sizes enough to decrease NeS sufficiently that phase one becomes important. Finally, it is quite possible that environmental variation could increase dramatically for what ever reason. This would have the effect of increasing the phenotypic variance, and lowering the heritability. This could lower Ne(h2S), and allow genetic drift to become the dominant force.

Once we get a metapopulation with subpopulations spread over several adaptive peaks then phase three can start participating. As pointed out in my previous post, this requires differential migration, which can be a force that overwhelms selection. That is, populations that export migrants will have a powerful influence on populations that import migrants. Also as I pointed out last week, whether a migrant can enter a population will depend on the fitness of the individual (not their offspring). Thus, a net exporter of migrants can be that simply because they have a larger population size and export more migrants, or because their migrants have a higher fitness, and are always able to invade the other population. Once the migrants invade they will mate and produce offspring. If the subpopulations are truly on different adaptive peaks than their offspring will be of low fitness, and there will be a general increase in non-additive variance (due to decreased inbreeding, and the introduction of new alleles). The net result is that the migrants will pull the subpopulation down the slope, decrease the heritability, and generally set up the population to be more susceptible to genetic drift. As a result this interpopulation migration may in fact support phase one due to its effect on population size and variance components. Remember, one migrant every four generations is optimal for speciation to occur!

I have run out of space, so I will sum this up by pointing out that the argument that the three phases or Wright’s shifting balance process have difficulty coexisting may have more to do with our emphasis on additive models and our lack of understanding of the effects of non-additivity and less to do with real problems with how this process actually works in the real world.

Wright’s Shifting Balance Process: Phase 3 part 2

Posted: July 25th, 2014 by Charles Goodnight

Last week I tried to establish that group selection by differential migration can work.   On both experimental and theoretical grounds we find it does work, and in fact will frequently be stronger than individual selection. The question comes where does it fit into Wright’s shifting balance process.

The first problem we need to confront is that Wright apparently thought that the group level trait would be concordant with the individual level trait. That is, he thought that with greater absolute fitness would come the production of more individuals, and with that a greater emigration rate. There really is no reason for this to be true. For one thing, the important factor is relative fitness, not absolute fitness. The problem is that as overall fitness increases in population so does the resulting competition. Thus, a population may experience a steady increase in some measure of absolute fitness, but no overall change in population size. This is actually the basis for the Alice in Wonderland (AKA the red queen) hypothesis. That is, Fisher’s idea that the environment is always deteriorating is largely due to the fact that other individuals are always evolving. Thus, the improvement in absolute fitness (survivorship, number of offspring produced) is completely offset by the similar improvement in other individuals with no resulting increase in apparent fitness or population size.


who , Me?

So, how to resolve this? I think the answer may lie in the Wright’s words. (I am away from my books at the moment, so this is a paraphrase). When Wright was investigating the effects of migration on population differentiation he stated something to the effect that it would appear that one migrant every other generation would be sufficient to destroy population differentiation. After uttering this now famous platitude he went on to say: However, given that immigrants will have a much lower survival and mating success than residents there could be many thousands of migrants and yet there will be population differentiation. OK, I have no idea what he really said, but this is how I remember it.

What this has to do with phase three is that even if migrants are moving randomly among subpopulations, they have to survive and reproduce once they get there.   Thus, if one group has a lower absolute fitness than another group migrants from the low fitness group will have a low relative fitness in the group they move into, and as a result may not survive and reproduce. On the other hand, migrants from the high absolute fitness group will have a high relative fitness in the low fitness group, and they will have a better than average chance of surviving and reproducing. Thus, even random migration can potentially lead to differential migration once within group individual selection is added in.

The second issue is rather interesting. When talking about phase three it is convenient to say something to the effect that migrants from high fitness populations send out migrants that lead or convert the low fitness population over to the new higher peak. This sounds something like the five rusty rats leading the founding of the village of cream puffs.

rusty rats

“And so, while the wind and the snow blew and the blizzard beat its icicles in their faces, they held on to the long curved tails of the rusty rats till they came to the place where the Village of Cream Puffs now stands.” If you don’t know the rutabaga stories by Carl Sandberg you should. (http://www.josephperry.net/rootabaga/01-03rustyrats.html)

The reality is that the offspring of these migrant individuals will be hybrids between the two peaks, which ought to put them smack dab in the middle of an adaptive valley. In other words, these migrants are more like genetic terrorists than saviors. What they do is trash the adaptive gene complex by adding genes that are generally bad for the current population.

chu red

I was looking for a non-controversial revolutionary. I came up with Pika Ché (http://www.redbubble.com/people/meganegi/works/8351063-chu?p=t-shirt)

So, my thought on phase three is that at the “end” of phase 2 you have a set of populations distributed about two or more peaks (I put end in quotes, because the phases all go on simultaneously). At this point they are all sending out and receiving migrants, but the ones on the higher peaks are net senders, and immigrants tend not to survive and reproduce. Those on lower peaks are net recipients of migrants since immigrants tend to have higher fitness than the locals. That said, the offspring of these migrants is low, and has the effect of dragging the low fitness population off of its local peak, and basically allowing drift to have its effect. However, in a sense it might be called directed drift, since there will be a continued input of new migrants from the higher peaks. These migrants will “encourage” drift in the direction of the new peak, but by no means guarantee it. In other words rather than the lower peak being led to the new higher peak, I see it getting dragged kicking and screaming through the adaptive valley.

jones dragged

Indiana Jones being dragged kicking and screaming to the lost ark (http://www.propstore.com/cms/the-prop-store-collection/indiana-jones-and-the-raiders-of-the-lost-ark/harrison-fords-whip/)

So, then we can start to see what phase three is really doing. When a metapopulation is spread across multiple adaptive peaks migration will have the effect of moving populations off of those peaks. Because the fitness of the incoming migrants will reflect their population of origin, by in large low fitness populations will have more effective migrants (migrants that enter and survive and reproduce) than high fitness populations. Thus, the low fitness populations will be more likely to be driven away from their peak, and on average, they will tend to be dragged towards the new higher peak. Will they make it to the new peak? That is hard to say in a complex stochastic world. Some will at least temporarily climb back to their old peak, others may climb the new peak, and still others, having been dragged off of their local peak may drift around and discover yet a new and even higher peak.

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