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Evolution in Structured Populations

Individuality, Microbiomes, and organisms

Posted: March 26th, 2015 by Charles Goodnight

So many things to write about, and so much writing to do. Sorry about missing last week. Somehow writing this week has been more of a chore than a joy. One of the things it has been suggested I write about is the continuing brouhaha over Nowak’s paper (Nowak, et al. 2010. Nature 466: 1057), the latest response by Liao, Rong and Queller (2015. PLoS Biol 13: e1002098.), and who was right and who was wrong. To all that all I can say is “frankly, my dear, I don’t give a damn”. If you must know, the basic model, although not as bad, has the same fundamental flaw seen in Gardner’s model: It does not include indirect genetic effects. I have discussed this before, and I will probably discuss it again. But for the moment it needs a rest, you can watch Gone With The Wind to see what happens when you beat a horse too much.

rhett butler


(from http://kittenofcupcakes.tumblr.com/post/49802470800)


Instead, what I want to do is go deeper down the rabbit hole of what an individual is. In a previous blog post I argue that the individual should be the level at which we assign fitness. This is fine as far as it goes, but consider the situation in which we assign the fitness at the level of the organism. Well, organisms are not really one species. In fact, in humans, non-human cells are thought to outnumber human cells ten to one, although they are probably less than 3% of our body mass (http://www.nih.gov/news/health/jun2012/nhgri-13.htm). We also know that the microbiome has significant effects on health, ranging from effects on the ability of organisms to digest food to affecting the nervous system.



Down the rabbit hole of individuality (http://mag.splashnology.com/article/alice-in-wonderland-showcase-of-impressive-cosplay-photography/7324/)


This has a couple of interesting consequences. First off, when we assign fitness at the level of the organism, we are in fact assigning fitness to a community, which includes the host metazoan, and their microbiome. The first rather fun implication is that, except in the enlightened sense of the relativistic concept of individuality I discussed two weeks ago, there is no such thing as individual selection. “Individual selection” in the classic sense is in fact community selection.


This is not a problem for selection per se. We can assign fitness at what ever level we want. If we want to assign it at the level of the community formerly known as an organism, then that is just fine. Selection is an ecological process. Which means that for simply analyzing selection, we don’t actually need to know anything about the heritability. Of course, that is a bit unsatisfying, since we would like to know the response to selection, and for that we need to know the heritability. The problem is that with over 90% of the cells in a human being non-human, the vast majority (some estimates as high as 99%) (https://www.microbemagazine.org/index.php?option=com_content&view=article&id=3452:major-host-health-effects-ascribed-to-gut-microbiome&catid=750&Itemid=969) of the active genes in our bodies are also non-human. So, again we are confronted with a potentially serious problem with the concept of heritability. This actually poses two problems. First we need an expanded view of realized heritability that recognizes that organisms are communities. This is not really a problem for the phenotypic perspective, which defines heritability in terms of the phenotypic resemblance between parents and offspring. But it does raise the interesting possibility that many of the genes that contribute to heritability may in fact be bacterial genes. This further raises the interesting point that the heritability of an organism will now be a function of the ecology of the microbiome. If you get the microbiome from your parents, undoubtedly true for a portion of the microbiome, then it is potentially heritable. The particular case in point here would be bacteria such as Wolbachia, which is an intracellular symbiont of arthropods that is maternally inherited. Among host variation in this bacteria would show up as heritable variance in the population.


On the other hand, if the microbiome is picked up randomly from the environment then it may not be heritable. Even here there is a problem since it may be predictably acquired from the larger population, and thus heritable at a higher level. Consider termites. When a young termite first ecloses to become an adult it lacks its gut fauna, which it obtains by trophallaxis from another colony member. Basically, an older individual regurgitates and the newly emerged adult eats the symbiont containing regurgitate. What this means is that members of the same colony will all get similar gut symbionts. What this means is that in termites the gut fauna may not be heritable in the classic sense, it may nevertheless be heritable at the colony level.



Trophallaxis in termites transfers gut bacteria among colony levels, possibly making the gut fauna derived traits heritable at the colony level. (http://carronleesgspestmanagement.blogspot.com.br/2011/04/how-does-baiting-system-work-on-ants.html)


The bottom line for all of this is that yes, in my discussion I suggested that in many situations the organism would be a reasonable unit to call the individual. This week I am saying that the organism is not a single species entity, but must be considered a community. I am also arguing that if we use the phenotypic perspective the resemblance between parents and offspring then potentially the concept of inheritance can become quite complex, with some of the gut fauna being considered “environment” because it is randomly acquired throughout the life of the organism, but others need to be considered heritable variation. Even here we need to distinguish between parts of the microbiome that are inherited due to close association of the parents, and parts of the microbiome that are inherited at a higher level due to within group sharing of food, or other processes.


It is interesting to compare this to my earlier post on heritability in the absence of genetic variation . What this suggests is that we are naïve to think that heritability can be consistently and logically reduced to nuclear Mendelian genes in the host species in the community that we call an organism.

What is “additive variance” in genetically uniform populations?

Posted: March 11th, 2015 by Charles Goodnight

I recently got a comment from Michael Bentley at Oxford pointing out that he had a different interpretation of heritability among cells within higher organisms. His comment was:

“Please could I just clarify something you say in this piece, as it relates to something I’m working on at the moment. You say:

‘From the perspective of individuality, what this does is that it lowers the heritability at the cellular level to nearly zero.’

This confused me, since the heritability at the cell level via mitosis is nearly one, not nearly zero, isn’t it? If we take h^2 = Cov(zi,zi’)\Var(zi), where zi is parent cell phenotype, and zi’ is offspring cell phenotype (we have regressed parent phenotype against offspring phenotype and taken the gradient of the regression line to be the heritability). Assuming high fidelity, we have Cov(zi,zi’) approx = Cov(zi,zi) = Var(zi). Putting this back in we get h^2 = Var(zi)/Var(zi) = 1, and thus h = 1.”

The relevant post is here. Mr. Bentley raises a very good point. In this post I argue that because within an organism cells divide by mitosis, that there is essentially no genetic variation, and as a result, baring somatic mutations, the heritability within organisms is very near to zero. Michael argues that in fact the somatic cells have very high phenotypic fidelity when they divide. Thus, liver cells divide to make to liver cells, and skin cells divide to make to skin cells. By his reckoning the heritability should be very close to one.

So, how should this be handled. First off, I would argue that Michael is right, and I am wrong. Michael used an appropriate definition of “realized” heritability based on a phenotypic perspective, whereas, old fogey that I am, I somehow was stuck in trying to force Fisher’s model where it didn’t belong. Nevertheless, I do stand by my point that mitosis serves as a mechanism that minimizes the response to selection within organisms, I just should have been careful when I called it “heritability”

What this says is that we need to more carefully define heritability, and the additive variance. Fisher first defined additive genetic variance, and to paraphrase something that Walt Ewens, Fisher defined it, and thus we need to accept that his definition is correct. Fishers definition of the additive genetic variance is the sum of the covariances between average effects and average excesses, however, as Falconer has pointed out this definition is useless in the real world (Falconer 1985 Genet. Res. Camb. 46:337). Thus, we are stuck with making up a useful definition. Falconer provides an alternate definition of additive genetic variance statistically, for example as the variance due to regression of offspring on mid parents (I don’t have his book with me in Brazil, so I am not sure of his exact definition). However I would call this the “effective” additive genetic variance, since in real populations it will not exactly equal Fisher’s definition.  It is also relevant to mention that Falconer (in Introduction to Quantitative Genetics 1989) nicely demonstrates that the additive genetic variance is the genetic covariance between parents and offspring.

The way I have been thinking about phenotypic evolution is as a super-set of quantitative genetics. Fundamentally quantitative genetics is a phenotypic approach. The breeders equation demonstrates this:

R = h2S

Or in words, the response to selection is equal to the heritability times the selection differential. It is a phenotypic model because basically the heritability serves as the transition equation that converts the fitness weighted distribution of phenotypes in the parental generation (S) into the distribution of phenotypes in the next generation (R). What the phenotypic perspective does is to argue that this is a fundamentally correct perspective for thinking about evolution, but that a transition equation that is a single constant and (at least theoretically) includes only genetic effects is overly simplistic. Relevant to my discussion with Michael, quantitative genetics is also overly simplistic because it only applies to sexually reproducing organisms. Aside: It is hard to fault Fisher for this. His primary goals were to describe the genetics for humans and mammalian livestock, and to provide tools for animal breeders. His efforts were spectacularly successful to the point of saying that Fisher was the central figure in the new synthesis, and one could argue that he basically single handedly built the foundation for the new synthesis.

So, the bottom line is that we should stick with something similar to Falconer’s practical definition: The additive variance is the covariance between parents and offspring. Note that I did not say the “additive genetic variance”, and this is an important distinction. I suggest we should define the additive variance as the covariance between parents and offspring without regard to the cause of that covariance.

Of course in many situations that is not satisfying. In the discussion between Michael and I both of our perspectives were important. He was exactly right that there is a very high covariance between parent and offspring cells in metazoans, but I was also correct that there is essentially no genetic differences among cells in metazoans. So, what is causing the high covariance that Michael identified? I don’t know, but it is not genetic. More likely it is due to two causes. First there are epigenetic changes – silencing of some genes, and over expression of others – that give a particular cell type its phenotype, and importantly, these epigenetic changes are preserved during mitosis. Second there is a lot of cell-cell interaction that causes offspring cells to resemble parental cells due to the “developmental ecological” or “positional” situation a cell finds itself in. In development there are numerous examples of this sort of induction. It may well be that one reason the daughter cells of liver cells are also liver cells is because they are in the liver, and induced to be liver cells because of that.

I suggest the correct thing to do is to accept the general definition of additive variance, but then allow this to be broken up into components. That is the additive variance could be broken up into Additive “genetic” variance, Additive “epigenetic” variance, Additive “positional”, and so on. Thus, we should accept the single obvious definition of additive variance of the covariance between parents and offspring, but then use some form of least squares partitioning to divide it into sub components.

Of course there is a problem here. That is how do we do that division? Again, I suggest that we follow Fisher’s lead here. What is needed is an appropriate modification of parent-offspring regression and half sib design breeding experiments. For example, we might examine the additive variance in the natural setting to get the total additive variance. Second, we might look at the variance among cell lineages to get the additive genetic variance, and the variance within cell lineages to get the additive non-genetic variance. By transplanting cells to other locations we could get the additive physiological-ecological variance, and by using molecular methods to remove the epigenetic modifications get an estimate of the additive epigenetic variance.

What ever the actual experimental protocol that ends up being appropriate, what we want is:

Cov(Parent,Offspring) = Covgenetic(Parent offspring) + Covepigenetic(Parent offspring) + Covpositional(Parent offspring) + . . .

There are, of course, two major problems with this. The first is practical. If you decide to do that experiment, well good luck. At least at first blush it looks like it would be a horrific amount of work that would simply not be worth the information obtained. The second is statistical in nature. I am arguing for using a Fisherian least squares partitioning into the subcomponents of the additive variance. The good news is that, if done properly, such partitionings are orthogonal, so that the components would add up the total additive variance. The bad news is that such partitionings are context dependent, thus, the partitioning into sub components of the additive variance would change as conditions change. Nevertheless, it seems to me that this is a good way to think about simple linear transition equations from the phenotypic perspective. It is also a way to keep the excellent framework that Fisher provided, while allowing it to be conceptually expanded to other systems of reproduction, and non-genetic forms of inheritance.

More on fitness assignments and individuality

Posted: March 3rd, 2015 by Charles Goodnight

In my last post I briefly mentioned that the level at which fitness is assigned is an interesting problem, but not a conundrum, or a serious conceptual issue. I think it would actually be quite useful to expand on this. The basic ideas came out of discussions I had 20 some odd years ago separately with Lorraine Heisler and John Damuth over a series of years. Heisler and Damuth took this one direction (Group Selection 1 and Group Selection 2), and I went in another direction, which involved not publishing anything until my Chapter on “defining the individual” (Goodnight 2013, Chap. 2 in “Defining the individual” Bouchard & Hueneman eds).


working hard in the forest

In case you were wondering where I was, I was working hard in the Amazonian flooded forest. (I was at the Uakari lodge. I recommend it if you are ever in the Manaus area. http://www.pousadamulticultura.com/mamiraua-reserve )

So here is the basic issue: Biological things tend to be organized hierarchically. This need not be the case, but it often is. Thus, we have cells, which group together, possibly with other species, to become organisms – yes, it is probably incorrect to think of “humans” as a single species – which group together to become populations or groups, which finally group together to become communities.

Using the most basic definition of evolution: the change in the distribution of a set due to the gain or loss of members of that set, it should be clear that it is possible for evolution can take place at any of these levels. By the way, I use this very clutzy definition of evolution here to avoid using terms like “individual” and “population”. Normally this is not a problem, but in this particular circumstance we need to be very careful. The point is that change occurs, and it can be potentially defined as evolution. However, at least for selection, it can only be defined as evolution by natural selection if there is variation in fitness. Here is the problem. Contextual analysis, and I would argue human understanding, really only allows fitness to be defined at a single level.

Herein lies the issue. We can choose to define fitness at any level. Different levels may be better choices than others, but ultimately, the level at which we assign fitness is an arbitrary construct of the investigator. I would argue that once we have assigned fitness at any particular level, that becomes the “member” of the set in our definition of evolution.   In other words, when we define fitness as occurring at a particular level, we are in fact defining the individual in the less clutzy definition of evolution: Change in the distribution of a population due to the gain or loss of individuals.   Even though we really only need to define fitness with regard to selection, and adaptation, it makes no sense to have concepts of individuality for mutation, migration and drift that are different than our concept for selection. Thus, the I would argue that logically the level at which we define fitness defines individuality for all evolutionary forces acting on that trait.

Of course, the level at which we define fitness does not alter the changes that occur in the organism. The changes that occur are independent of human observation. What DOES change, however, is our interpretation of those changes. Only changes at or above the level of individuality—the level at which we assign fitness – can be interpreted in an evolutionary framework. Certainly for adaptation, we can only interpret changes as being due to natural selection if there is variation in fitness, and there is no variation in fitness below the level at which we assign fitness. So, what we do is we call those changes that occur below the level of individuality as something else. For example, we typically we assign fitness at the level of the organism, and changes within the organism are called “development”. However, were we to choose to assign fitness at the level of the cell we could reasonably call these changes evolution, and view differential cell division and mortality as selection.

This idea of the relativity of individuality, and the role of the observer in interpreting the nature of changes is at the heart of the problem that people have with Group Selection 1 and Group Selection 2.   This is also why I am not a big fan of the GS1/GS2 terminology. Basically, I think we would be better served by stating the level at which we define fitness. Thus, we might say “In this study we define the organism to be the individual”, or “we assigned fitness at the level of the colony in this study”. I think this is clearer and removes a lot of ambiguity. For example, consider a hypothetical study of Tasmanian Devil Face Cancer. This potentially has three or more levels at which we could assign fitness, including the cell, the organism, the population, and potentially the species. Defining the level of the individual has the flexibility to handle this GS1 and GS2, just gets difficult (if we assign fitness at the level of the species is that GS4?)

The problem, of course, is the idea that there is this desire to have the “individual” be a natural unit, and to have “development” qualitatively different than “evolution”. The idea that the individual is a construct of the observer is really not compatible with these thoughts. That said, I am quite comfortable with the arbitrariness of the level at which we assign fitness. I see no other way that we can have transitions of levels: There really is no qualitative difference between the most organized colonies and the least organized organisms (compare Volvox to Trichoplax). It is also the only way we can study cancer as evolution, and not have to assign fitness at the level of the cell when we are studying, say, foraging behavior. Nevertheless, I understand that many will find this deeply disturbing, and many will reject this relativity of individuality as a viable world view. That said, I think if you can get your head around it, it will help you in understanding multilevel selection.

Volvox-aureus-DF trichoplax

Volvox (left) is considered to be a colonial protist, whereas Trichoplax is considered to be a single organism and an animal. There are differences in their structure, but the differences are not great considering that one is a colony of cells and the other is multicellular organism. (Volvox: http://www.dr-ralf-wagner.de/Bilder/Volvox-aureus-DF.jpg, Tricoplax: http://www.marinespecies.org/placozoa/ )

I am out of space, but as I mentioned above, although the level at which we assign fitness is, in my view, arbitrary, there are nevertheless better and worse levels that we can choose. For example, often there is a reasonable a-priori choice. Higher organisms are made up of trillions of cells. It would be a ridiculous, and probably impossible, task to assign fitness at the level of the cell if we are studying morphology or behavior at the whole organismic level. Other times, contextual analysis can be used to identify the lowest level at which selection on a particular trait is acting, and that level becomes a reasonable one for assigning fitness. Still other times there may be adaptations (policing, mitosis) that minimizes adaptation by natural selection at lower levels. In this case it makes sense to assign fitness at the level at the lowest level that a response to selection is likely to occur. Finally, at the beginning, I mentioned that MLS works fine if groups are not nested. However, any study with non-nesting groups will only work if fitness is assigned at a level that is fully encompassed within all higher groups. For example in a continuous population of plants every organism (ramet?) can be considered to be at the center of its own neighborhood. Obviously these neighborhoods overlap. Nevertheless MLS analysis will work as long as fitness is assigned at the level of the organism instead of the neighborhood.

Gardner’s theory of multilevel selection 3: the discussion

Posted: February 11th, 2015 by Charles Goodnight

This week I will finish up with Gardner’s paper (2015 Jour. Ev. Biol doi:10:1111/jeb. 12566) which I have been discussing for the past two weeks. Given the problems with the literature review and the model, it is hardly surprising that this has led to issues with the discussion. I have problems with virtually the entire discussion; however, I will focus on the ones that I find most concerning.

First, Gardner talks of collective fitness 1 vs collective fitness 2 In doing this he continues and deepens the confusion he started when he developed the model. As I make clear in my chapter on defining the individual (Goodnight 2013, Chap. 2 in “Defining the individual” Bouchard & Hueneman eds), whether you are talking about group selection 1 or groups selection 2, or for that matter group selection 10 (there is no such thing), depends entirely on the level at which you, the investigator, assign fitness. In the example Gardner gives, Group A has 12 daughters in 4 groups of 3, whereas Group B has 12 daughters in 3 groups of 4. In this example, If you assign fitness at the level of the individual organism, and presuming no other variation, the individuals in groups A and B have equal fitness. If you assign fitness at the level of the group Group A has higher fitness than Group B. The difference, of course, is that in the second instance you have a within group “developmental” process that results in different group sizes, however since fitness is assigned at the level of the group you cannot call it selection or even evolution. The problem is that with fitness assigned at the level of the group there can be no variation in fitness within groups, and thus no evolution. This leaves the question of whether it is better to assign fitness at the level of the group or the level of the organism. This is an issue that that I address in my chapter. For fairly deep philosophical reasons it basically cannot be resolved, but as long as we are clear on where we assign fitness it is not a problem. Gardner is right that this was an important issue, but it is not a conundrum. It is one that has been resolved, and no longer presents a serious conceptual issue.

However, what I find most disturbing in this section is so jaw-droppingly silly it causes me to question whether the paper is supposed to be satire. To quote Gardner:

“Cancer is often conceptualized as involving a tension between different levels of selection, with cancerous tissues achieving higher reproductive success at a within-organism level and cancerous individuals suffering lower reproductive success at a between-organism level. However, somatic tissues – including cancerous ones – do not generally contribute genes to distant future generations, on account of the demise of their lineages upon the death of the organism. Consequently, cancerous tissues do not have reproductive value, and so their proliferation within the organism cannot correspond to selection in the strict sense of the genetical theory.” (page 6, citations removed)


Seriously? You actually believe that? ( from http://www.calgaryunitedway.org/socialvoice/wp-content/uploads/2012/10/jaw-drop.jpg )

This is basic introductory evolution material. Here is the Intro Bio version: Lewontin in his article in Annual reviews (1970, Vol 1 page 1) tells us that three things are necessary and sufficient for evolution by natural selection to occur. These are:

  • There must be phenotypic variation.
  • There must be differential fitness of different phenotypes
  • The phenotypes must be heritable.

To remind you, necessary and sufficient means that you need all three, and if you have all three evolution by natural selection will occur. So, lets think about cancer. (1) is there phenotypic variation? Yes, Cancer cells are different than normal cells in many respects ranging from physical appearance to changes in the regulation of the cell cycle. (2) Are these phenotypic differences associated with fitness? Yes. For example disregulation of the cell cycle causes cancer cells to divide more rapidly than normal cells. Cell division is reproduction. Reproduction is fitness. Yes, there is variation in fitness associated with phenotype. (3) Are these variations in fitness heritable? Yes. Most, if not all, cancers are due to at least one, and usually five or more mutations. These are genetic mutations that are passed on to daughter cells during cell division. Thus, we see that in a organism with cancer we have phenotypic variation, variation associated with fitness, and the fitness is heritable. Either Lewontin is right and Gardner is wrong, or vice versa. I am going with Lewontin being right. Yes, cancer’s “. . . proliferation within the organism cannot DOES correspond to selection”

To see how silly Gardner’s stance is, consider the Wake Island rail, a cute flightless bird that did very well until World War II. On December 23rd, 1941 the Japanese occupied Wake Island, and by the time they were expelled on September 4th 1945 the Wake Island rail was extinct. Apparently the Japanese ate them when they were placed under siege by the American military. Now the question: At some point it was safe to say that the rails did “not generally contribute genes to distant future generations” and thus “. . . their proliferation . . . cannot correspond to selection . . .”. My question is when should we consider differential survival and reproduction of Wake Island rails to no longer be selection? Was it selection in 1939 before the war? How about 1941 when the Japanese invaded? Or how about the January of the likely year of their extinction, 1943? The ridiculousness of making this judgment should be obvious. Selection doesn’t see the future and neither should we when we are identifying something as selection.

wake Island Rail

At what point did differential survival and reproduction stop being selection for the Wake island rail? ( From http://www.extinct-website.com/extinct-website/product_info.php?products_id=409 )

My goal in this is to make the important point that very smart people have thought very hard about evolution. It behooves us to know what the masters said. This does not mean reading every single paper that Lewontin ever published, but it does mean not making obvious errors in logic that have been resolved by people smarter than you and I.  It also does not mean you can’t disagree with the masters.  Science advances when old paradigms are overturned.  But it does mean if you are going to disagree with the canon you should know why you disagree, and be able to defend your position.  Again, ignorance of the literature is no excuse.

With that lapse of good sense out of the way, and ignoring MLS 1 VS MLS 2 – Been there, done that, got the tee shirt – lets move on to the units of selection. Basically the first half of this section is un-interpretable gobble-de-gook that comes from trying to force Gardner’s class structure model on to the Price equation. As I said earlier, his approach is rather clutzy, but it will work as long as there is no group selection. To add group selection you MUST turn to a multivariate approach, or make the assumption that everything is additive always, and there are no interactions of any kind. In short, it simply does not work for multilevel selection in the real world. What caught my eye, however, was his example were a wasp lays two eggs a male and a female, and males and females are reasonably being treated as different classes. He is stumped by how to use a multilevel selection approach to study this. It is actually dead easy. Each individual has a male trait or a female trait (depending on their sex) and one or more contextual traits. The contextual trait is some measure of the characteristics of the group. Note that there would be a separate phenotypic covariance matrix for males and females, but a single genetic covariance matrix for the population (Lande 1980 evolution 34:292; Goodnight et al 1992 Am. Nat. 140:743). That is, with contextual analysis, there is no problem.

So here is my opinion on this and I want to emphasize it is only my opinion. I think that Gardner has an agenda. I think that agenda is that he does not want multilevel selection to be seen as a valid research program. To this end he is willing to ignore an entire literature, to be apparently willfully ignorant of quantitative genetics, to ignore the writings of such luminaries as Richard Lewontin, and to choose not to see obvious solutions. The problem is that his agenda has clouded his vision, allowed him to use sloppy thinking and logic, and to write things that are regrettable, and frankly wrong. This does not advance science. It creates noise that interferes with people who are actually trying to understand nature. I hope I am wrong. Gardner is a good theoretician, and the world needs people like him. Hopefully this paper is simply the unfortunate type of mistake we all make, and he is really working to advance our understanding of science rather than undermine a field that he doesn’t understand.

Gardner’s theory of multilevel selection: Parsing the Model

Posted: February 2nd, 2015 by Charles Goodnight

Continuing our discussion of Gardners paper on “the genetical theory of natural selection” (Gardner 2015 Jour. Evol. Biol. doi: 10.1111/jeb.12566) I want to turn from complaining about his failure to read the literature, and this week start talking about the model itself.

He starts the model with a discussion of Fishers fundamental theorem, which I have already shown is not particularly complex. Then he goes on to expand this using Robertson’s (1968. In: Population Biology and Evolution, R.C. Lewontin, ed.) result that the change in a trait is equal to the covariance between a trait and relative fitness.

Gardner 2 eq 1

It is worth mentioning that although it is usually presented the other way around, in fact, Fisher’s fundamental theorem is actually a special case of the response to selection on any trait. To see this just replace the trait, z, with relative fitness.

Next he goes on to express concern about selection in a class structured population. His approach actually works, as long as there is no multilevel selection. As I said last week, I think his approach is rather clumsy, and there is a much better way using standard quantitative genetic methods. So, my overall comment on that part of the paper is “meh”.


Gardner’s approach to evolution in stage structured populations? “Meh” (From http://rubbercat.net/simpsons/news/2013/09/ )

Now we get to the meat of the issue. He then goes on to develop his genetical theory of multilevel selection. First off, he develops his theory in terms of breeding values. This, has a number of possible definitions. His definition is “. . . a weighted sum of the frequencies of the alleles that the individual carries, the weights being decided by linear regression analysis. This is strangely worded, but basically correct. It hides a HUGE problem that he is ignoring. To see this consider a more standard definition of breeding value: The sum of the average effects of the alleles that make up an individual. The average effect of an allele is basically the effect of that allele averaged across all possible genotypes. This works fine in Fisher’s imaginary world of infinite population size and random interactions. It does not work well when populations are structured, and interactions are not random. If you have multilevel selection then you have population structure.   If you have population structure average effects, and thus breeding values are not constant.

This is why this is so insidious: The assumption of constant breeding value appears reasonable, and it is consistent with all of the classic models. It is the central feature of his model, that there is population structure, that invalidates the assumption of constant breeding values.  It is so obvious that Gardner did not consider the possibility that breeding values might not stay constant, although quite entertainingly he did very clearly, if unknowingly, explain why they wouldn’t. On page 3 he writes:

“Fitness may be decomposed into its genetical and environmental components, that is vi = gi + ei, where ei captures nonadditive genotypic effects (such as dominance, epistasis, synergy and frequency dependence) as well as other more obviously environmental effects.”

Well, no, that is not true. That partitioning is done by least squares, and epistasis and dominance will shift between components as we move from group to group. However note that even here he is completely unaware that when genes interact it might have evolutionary implications. And that is where Gardner falls short: his model requires that breeding values stay constant. They do not. The correct subscripting should be gij, that is, the breeding value of the ith individual in the jth deme. Experimental (De Brito, et al. 2005. Evolution 59: 2333) and theoretical work shows that gij will vary in a way that is not predictable either from the individual nor the group measured in isolation. However, I am a generous man, so lets assume they are constants for the moment, and just keep in the back of our head that this is a fatal flaw in the underlying assumptions of his model.

He then goes on to use the two level Price equation to develop his “genetical model of multilevel selection”:

Gardner 2 eq 2

OK, I hate his notation. Here it is a form that doesn’t hurt my head:

Gardner 2 eq 3


Gardner 2 eq 4is the change in the mean breeding value due to selection

Gardner 2 eq 5is the between populations correlation between relative fitness and breeding value (and yes, I refuse to use v for relative fitness)

Gardner 2 eq 6is the average covariance between relative fitness and breeding value within populations

So what is wrong with this?

Well for starters its been published before. Wade, in his paper “Hard Selection, Soft Selection, Kin Selection, and Group Selection” (1985. Am Nat 125: 61) develops a model which has the following equation:

Gardner 2 eq 7

I won’t burden with telling you all of the details of what all the symbols mean, except to say the first term on the right hand side is the mean within population covariance, and the second term is the among populations covariance. I should also say that if you sum over the K loci, the result is the breeding value. In other words, with slightly different notation it is exactly the same equation that Gardner uses. One would think a proper citation would be in order.

The nice thing about Wade’s Price partitioning being published 30 years ago is that it has been around long enough, and we have known that it doesn’t work for 20 years, and we know why. As long ago as the 1990’s I was talking to Steve Frank about this (I am sure he doesn’t remember, so Steve, if you are reading this tell me if I am wrong) and he told me that he was well aware of the partitioning, but he never called the among group covariance group selection. I also know that Mike Wade, who originally published the Price covariance model 30 years ago, has come to realize that the Price equation is inadequate.

What is wrong with the Price equation is actually quite simple, and is really the same as William’s (1966, “Adaptation and Natural Selection”) famous distinction between a “fleet herd of deer” and a “herd of fleet deer”. The problem is that if there is only selection at the individual level, say the slowest deer get eaten, then there will be some herds that by chance have a large proportion of fast deer. The Price partitioning will identify this variation in group composition as a positive covariance between group mean fitness and group mean phenotype; however, it will be entirely due to individual selection and the fact that there is variation among groups in the proportion of fleet deer. In mathematical terms, we can divide the Price covariance at the group level into a partial covariance between group mean fitness and group mean phenotype independent of individual level effects, plus a residual covariance between group mean fitness and group mean phenotype that is caused by individual fitnesses and phenotypes.  Only the partial covariance holding individual effects constant should be considered “group selection”  the other portion is changes due to selection at the individual level:

Gardner 2 eq 8

The Price equation cannot make this separation.  It should come as no surprise that this partitioning is best done using contextual analysis. You can work out the math yourself if you want. The equations you need are in Goodnight et al. (1992 Am. Nat. 140:743).

However, there is a much more serious issue than something so minor as the model being fundamentally flawed at this high level. This is the problem I mentioned before, and that is that he is partitioning breeding values. In an additive world this should work, however, if there is one lesson that comes out of the experimental group selection literature it is that it does not work in the real world (Goodnight and Stevens 1997. Am. Nat. 150:S59). This is an important point I have made in the past, when theory and experiment disagree the theory is wrong.

Indeed, there is no theoretical justification in Fisher’s additive world for me saying it is wrong. The reason I know that you can’t do that partitioning is because I have done and read the experiments (e.g., Goodnight 1990 Evolution 44:1614 & 44:1625). The problem is that when individuals interact their interactions affect the phenotype. While it may not change breeding values at the individual level, it does change them at the group level. And this is exactly what we have found. Group selection experiments work way too well. When we have done experiments where the causes can be teased apart we know that the reason that group selection works so well is because it can act on the interactions among individuals. In other words interactions among individuals become part of the breeding value at the group level. The Price partitioning assumes you are partitioning a constant, however experiments show us that the breeding value at the group and individual levels are not the same thing.

In short, the only way to develop a “genetical theory of natural selection” is to go Full Monty multivariate quantitative genetics, and treat the group and individual traits as separate, but correlated traits. Contextual analysis does half of this, what remains to be done is to work out why the G matrix is the way it is. Fortunately, Bijma and friends have gone a long way in this direction (e.g., Bijma et al. 2007. Genetics 175: 277, Bijma 2014 Heredity 112:61).


You have to go Full Monty multivariate quantitative genetics if you want to have a chance at developing a genetical theory of multilevel selection. (hope the beefcake doesn’t offend.) (http://www.theage.com.au/articles/2004/05/10/1084041332216.html?from=storyrhs)

So, thus we find that the basic model is flawed in several fundamental ways. First, it is a re-derivation that is, except for details of notation, identical to a model by Wade published in 1985 (it is clear he was unaware of Wade’s work so there is no possibility of plagiary here). Second, Wade’s model, and thus Gardner’s model, was shown to incorrectly partition group and individual selection, and third, based on experimental and theoretical work, it is clear that the basic underlying assumption of constancy of breeding values is fundamentally flawed. Efforts to partition breeding values into within and among group components using the Price equation are doomed to failure due to interactions among genes and individuals. Ignoring these issues, however, well, I guess the model is fine.

Next week will be the last on this paper.  Basically last week we covered the introduction, this week was the model.  Next week will be the discussion.  If I can’t cover it in three weeks it ain’t getting covered.

Added in postscript:  Andy:  I feel badly about so thoroughly trashing this paper.  If you would like to respond I will post your response with no edits other than a short paragraph at the beginning giving attribution.  (you might want to wait until next week after I discuss the implications of your model).


Gardner’s theory of multilevel selection: Where he goes wrong and why

Posted: January 28th, 2015 by Charles Goodnight

Two things have happened recently. First, Jonathan Pruitt and I (Pruitt and Goodnight 2014 Nature 514:359) have been asked to reply to a goodly number of letters to the editor concerning our paper on multilevel selection in Nature. These letters have made it clear to me that many people have a very basic misunderstanding of multilevel selection. Second, I was made aware of a recent paper by Andy Gardner (2015 Jour. Evol. Biol. doi: 10.1111/jeb.12566), which is impressive in the depths of  misunderstanding of multilevel selection that is in the paper. I have never met Andy, but I do know he is well established, and he can stand a little criticism from me. Thus, I thought his paper would be perfect for highlighting some of the very more serious misunderstandings people have about multilevel selection. There are so many problems with the Gardner paper that it will take me several weeks to work through them, so on that note, lets take his paper and start turning it into confetti. You have actually seen the opening salvo in my post last week about Fisher’s fundamental theorem. What brought that up was Gardner suggesting that the fundamental theorem was somehow special, or that it applied only to a specific subset of biological entities.

What I want to talk about this week is an idea that Gardner puts out nicely in the first sentence of the abstract: “The theory of multilevel selection (MLS) is beset with conceptual difficulties.” The truth is that MLS is in fact a mature theory. One that, at this point, has very few conceptual difficulties. We know group selection works, we know why it is so effective, we know how to extend quantitative genetics along several different pathways to incorporate the interesting results of group selection experiments, and we know how to measure MLS in the field. Finally, MLS methods are widely used in agriculture – your breakfast this morning may well have been dependent on MLS theory. Eggs, bacon (hogs) and toast (wheat) are commonly or exclusively selected using MLS methods. It is a mature settled theory, sure there is much to be done, but isn’t that true of all science?

So, why is Gardner so wrong? Well that can be seen in the first sentence of his introduction (Do you start to see why this might take a few weeks!): “Recent years have seen a resurgence of interest in the theory of multilevel selection (MLS: Price, 1972a; Hamilton, 1975; Sober & Wilson, 1998; Keller, 1999; Okasha, 2006; Wilson & Wilson, 2007; West et al., 2008; Gardner & Grafen, 2009; Leigh, 2010; Nowak et al., 2010; Lion et al., 2011; Marshall, 2011; Frank, 2012a, 2013).” What you should notice is that there are no serious multilevel selection experimentalists on this list, nor is there anybody on that list who I would call a true MLS theorist. I will not go through the list of why these people are inappropriate, other than to say that some are very old, many are philosophers, and many are advocates of kin selection, or for other reasons really should not be considered authorities on multilevel selection. One has to question where are (to list only modern authors) Wade (1977 Evolution 31:134, Wade et al 2010 Nature 463:E8), Bijma (Bijma et al 2007 Genetics 175:277), Muir (1996 Poultry Science 75:447), Eldakar (Eldakar et al 2010 Evolution 64:3183) Simon (Simon et al 2013 Evolution 67:1561), Ratcliff (2012 PNAS 109:5), Travisano (2004 Trends Microbiol. 12:72), Driscoll (Driscoll and Pepper 2010 Evolution 64:2682) or dare I suggest myself? These are people who understand multilevel selection. I should point out that it is not just this sentence where he fails to cite the relevant literature. With the exception of one vacuous (it will come up later) reference to a paper of mine, none of these authors appear in the literature cited.

This is a fundamental problem that I am seeing. Gardner, not to mention the authors of the letters to nature that we have been fielding, appear to be completely ignoring the MLS literature. I will admit my own failings in this matter. It is not infrequent that I will glance over an abstract and decide it is not important to what I am writing about. However, when writing outside my field (and yes, Gardner is working outside his field) I really do try to ask colleagues if they know of anything I have missed. In this case there is plenty that Gardner missed. As an example, the model he develops in his paper is totally incompatible with the results of Goodnight and Stevens (1997 Am Nat 150:S59). Nobody but Andy knows the real reason ignored the body of MLS literature. Hopefully it won’t happen in the future.

With these weak foundations, Gardener then goes on to list a series of things that he believes to be difficulties. These include:

  • the “precise meaning of group trait” – A group trait is either a trait measured on the group itself, or a composite of measures taken on the group members. Both can be appropriate. Like all studies of selection an understanding of the underlying biology is needed to identify relevant traits. Bottom line: experimentalists need to actually measure these “group” (really contextual) traits. As you might expect, those who measure them know what they are.
  • The “precise meaning of group fitness” – I have to give you that. However, the reason for this is that it is not relevant to the study of MLS. The relevant issue here is measuring selection in the field, and for this the appropriate approach is contextual analysis, which does not use “group fitness” (see Taylor, Wild and Gardner 2007 J. Evol Biol 20:301 for a demonstration that direct fitness, which is the same thing as contextual analysis, is an appropriate metric, Snideness aside, also look at Goodnight 2013 Evolution 67:1539).
  • There is “ambiguity as the focal level in a MLS analysis”. Here he is complaining about the distinction between multlevel selection 1 and 2. I do not like this language, and I am not the best to comment on it. The term was coined over 25 years ago, can we give it a rest? The basic problem is the level at which you assign fitness. Sadly he again shows his ignorance because the actually most relevant paper that gives a relatively simple explanation for this non-controversy is the one paper of mine he cites: Goodnight 2013 (pp 37-53 in: From Groups to Individuals). Sadly, while he did cite this chapter, it was not in the context of this problem, and when he did cite it, it is to make an invalid point.
  • Finally, he makes a big deal about MLS theory does not adequately able to handle class structured populations. First, off, there actually is a nice old paper on multilevel selection in age-structured populations (Mertz et al 1984 Evolution 38:560), although it really isn’t very useful in this context. More relevant, the reason that nobody has developed a method to study MLS in a class-structured population is that nobody has bothered – Most ant people these days are kin selectionists. The basic approach is actually conceptually quite simple:   I would follow Lande’s lead on analyzing sexual dimorphism (Lande 1980 Evolution 34:292) and phenotypic plasticity (Via and Lande 1985 Evolution 39:305). I would describe a separate trait for each cast, plus one or several contextual traits to describe the overall composition of the colony. Each individual would express only one of the individual traits, but of course, all would experience the contextual traits. Then it would be a small matter to modify the methods of Lande and Via and Lande to use them in this system. It actually isn’t that different from the approach Gardner advocates, but it is far more elegant, and it is far more consistent with the existing methodologies for related problems.

So basically what we see in Gardner’s paper (and by extension many of the letters to Nature) is a failure to be aware of and to understand the relevant literature. The problem is not failure to cite the relevant papers per say, rather the problem is that by they do not know the literature and understand the field. As a result the authors end up looking foolish for raising issues that do not exist, and suggesting methodologies that in this case are clumsy, but as we shall see in the next week or two, also methodologies that simply give the wrong answer. I am aware that it is often easy to miss important papers, but to paraphrase the old saying about the law: Ignorance of the literature is no excuse.


We all are guilty of not adequately reading the literature. Nevertheless, it is something to be avoided.  (From http://imgur.com/gallery/1DEYI)



A one line proof of Fishers fundamental theorem

Posted: January 21st, 2015 by Charles Goodnight

Lots of people get bent out of shape about Fisher’s Fundamental theorem, and spend lots of pages talking about it. The problem is that people tend to see the FFT as being magical. Theoreticians promote this because, well, the basic proof is so simple that you need to add some sort of complication to justify your existence (Ok, some of the complications are interesting). So without further adieu, here is my one line proof of Fishers Fundamental Theorem

Added in edit:  I completely forgot to tell you what Fisher’s Fundamental Theorem was!

Fisher (1930) stated that “The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.”.  I would strike the word “genetic” from that sentence.

First, define terms:

The relative fitness of the ith individual =Relative fitness

The frequency of the ith individual = pi (usually that will be 1/N, but the truth is general, all we need is a frequency, and in reality it should be particle, not individual in the definition)

The frequency of the ith individual after selection, or put another way, the fitness weighted frequency of the ith individual =freq after selection

The mean relative fitness isMean relative fitness

I use the symbol mean fitness after selectionto denote the mean fitness after selection


Some math you need to know:

12=1 (not sure what to call this other than a truism)

(A*B)*C = A*(B*C) (the associative property of multiplication)


SO the one line proof:

FFT proof



In a recent article, Andy Gardner (1015, J. of Evol. Biol, DOI:10.1111/jeb.12566)says:


“Today, disagreement still persists as to the correct interpretation of the fundamental theorem. For example, whereas Okasha and Ewens both regard the theorem as concerning the selection of genes, I regard it as concerning the selection of individuals.”


Are you serious? I don’t think it applies to Koalas. Of course FFT applies to genes, and to phenotypes, and yes, even to Koalas. Heck it applies to anything to which relative fitness can be applied. OK, maybe I will give this to Andy: there is really no meaningful way to assign fitnesses to genes, so maybe the fundamental theorem isn’t so useful in that situation.


This actually raises an important point. Yes, the FFT is a truism, but that doesn’t mean it is meaningful in all circumstances. When people refer to it as the “not so fundamental theorem” they are not complaining about the theorem itself, but about the application of that theorem to a particular biological situation.


Koalas don’t know or care about Fisher’s Fundamental Theorem. However, just because you don’t know or care about something doesn’t mean it doesn’t apply to you. (http://en.wikipedia.org/wiki/Koala)

Genes, society, sexism and racism

Posted: January 7th, 2015 by Charles Goodnight

James Watson has been in the news for more than just his efforts to sell some bullion. He has also been in the news for his completely outrageous racist and sexist comments. Two of the more famous ones are the time he told a reporter that he is “inherently gloomy about the prospect of Africa” because “all our social policies are based on the fact that their intelligence is the same as ours whereas all the testing says not really”; and, with regard increasing the number of women scientists, the time he wrote “I think having all these women around makes it more fun for the men but they’re probably less effective.”. It is tempting to dismiss this as Watson being a jerk, until we get Lawrence Summers more eloquently saying pretty much exactly the same thing. One suspects that these characters are simply the tip of an iceberg dominated by people who are better able to hold their tongue, but are nevertheless to some degree racist and sexist. The bottom line is that racism and sexism are everywhere. Indeed I would be lying if I claimed not to be racist, and I suspect most of my readers would be as well. The point of this is that if you consider yourself to be part of a particular group, be it a racial group, a sex, a sexual orientation, or a social or religious group, if there is a stereotype associated with that group, you will be reminded of it on a daily basis.

imposter syndrome

Stereotype threat: living up or down to the stereotype of the group you self associate with. http://web.stanford.edu/dept/CTL/cgi-bin/academicskillscoaching/its-not-you-its-stereotype-threat/

Here is where it gets interesting. It turns out that these stereotypes do affect your performance in many aspects of life. There is a group of psychology and education researchers who have been studying what is now called “stereotype threat”.   It turns out that if, before giving them a test, you remind students of a standard stereotype, it will affect their performance. This is very nicely described in a review article by Schmader and Croft (2011, How Stereotypes Stifle Performance Potential. Social and Personality Psychology Compass: 792–806):

In 1995, Stanford researchers Claude Steele and Joshua Aronson published a series of highly influential experiments. They reasoned that for those who are the targets of negative stereotypes of intellectual inferiority, even subtle reminders of these stereotypes can cue a concern with confirming them. . . . To demonstrate this phenomenon, they asked White and Black undergraduates to complete a set of verbal problems. For half of the sample, they described this task as a diagnostic measure of verbal intelligence. For the other half of the sample, it was merely described as a problem solving exercise. When students believed that their intelligence was being assessed, Black students performed more poorly than their White peers, replicating the typical racial gap in standardized test scores that is so often found. Remarkably, when the same task was described in a more neutral way – as a laboratory exercise – Black students performed significantly better and their performance was equivalent to that of their White peers after controlling for individual differences in past test performance.



When students were given a test in which they were made aware that it was an important test, (and one that blacks might stereotypically be thought to do poorly in) blacks, but not whites, were negatively influenced by that information. http://menghublog.wordpress.com/2012/12/06/race-and-iq-stereotype-threat-r-i-p/

Apparently you can do this with almost any group for which there is a stereotype. Tell the women in a class that this is a subject women are not good at and they will perform poorly, or convince any group that they are inferior, and they will perform poorly. Importantly, however, the students must believe the stereotype at some level. In the Steele and Aronson study Blacks, but not Whites, were affected by the doubt raised by the investigators. I could not find a study addressing it, but I would tend to doubt that stereotype threat would work for made-up stereotypes that were not part of our underlying cultural assumptions.

So, what does this have to do with evolutionary biology? WELLLLLL, once long ago I was asked if I thought there were racially associated genes for intelligence. I answered Yes, I thought there were, and that they were exactly the same genes that cause the features we use to identify race. The next thing that happened is that I realized keeping my mouth shut was a good idea.

This is where the phenotypic view comes in. My argument is that because genes (broadly defined, since X chromosome number enters into this too), in addition to what we traditionally might assign to a gene, also have effects associated with them due to the social milieu in which they are found.   I seriously doubt that the loci that effect skin melanization also have a physiological effect on intelligence. But there is no doubt that an individual with sufficiently dark skin to be considered to be an African-American is treated differently from a White-American (great example of micro-aggression: What do you call a Caucasoid-American?). This differential treatment is part of their phenotype that, within the context of our society, is every bit as much a property of the loci in question as their effect on skin color.

This is an important aspect of the phenotypic approach. The phenotype is a construct of the patterning elements, including the non-heritable elements. Context means everything. Normally we think of this in terms of epistasis and the idea that gene expression depends on its interacting partners. However, it is more than that. The effect of a gene on the phenotype must take into account all of the forces affecting the formation of the phenotype. This is not to say that in many circumstances these can be ignored, but this racial bias is very emphatically a situation in which non-genetic cultural factors ARE influencing the expression and even the very function of a gene, and cannot be ignored.

So the bad news is yes, there are racially associated genes for intelligence; they are the ones that influence the phenotypes we associate with race. The good news is that we, as a society, made them intelligence genes, and we can unmake them. There are good solid strategies for minimizing stereotype threat. The best one is to get rid of the stereotype. That may be impossible, but as teachers we can also be aware of this and help our students. We can make them aware of stereotype threat. Just being aware that it exists will help a student recognize it and perhaps reduce their response to it. We can also work to encourage students to think of themselves as individuals and work to turn the negative stereotypes into personally positive messages. Finally, interestingly, stereotype threat apparently isn’t as powerful when a test is perceived as being not very important. Perhaps having more evaluations that are individually worth relatively less might help vulnerable students.

Genetic distance and FST

Posted: December 17th, 2014 by Charles Goodnight

First off, I did a search for papers that used contextual analysis in some form or another to analyze experimental data. This is the list I came up with. It seems pretty pitiful for a statistical method that (1) works and (2) with the exception of Heisler and Damuth using a very small data set to demonstrate the technique, has been wildly successful at detecting multilevel selection. I am hoping that I missed some important references. If you know of any that I missed, please let me know! If I didn’t miss anything, well, it looks like it is time for us to get to work!

Aspi, J., A. Jåkålåniemi, J. Tuomi and P. Siikamåki (2003). “Multilevel phenotypic selection on morphological characters in a metapopulation of Silene tatarica.” Evolution 57: 509-517.

Donohue, K. (2003). “The Influence of Neighbor Relatedness on Multilevel Selection in the Great Lakes Sea Rocket.” American Naturalist 162(1): 77-92.

Donohue, K. (2004). “Density-dependent multilevel selection in the great lakes sea rocket.” Ecology 85: 180-191.

Eldakar, O. T., D. S. Wilson, M. J. Dlugos and J. W. Pepper (2010). “The role of multilevel seleciton in the evolution of sexual conflict in the water strider Aquarius remigis.” Evolution 64(11): 3183-3189.

Heisler, L. and J. D. Damuth (1987). “A method for analyzing selection in hierarchically structured populations.” American Naturalist 130: 582-602.

Herbers, J. M. and V. S. Banschbach (1999). “Plasticity of social organization in a forest ant species.” Behavioral Ecology and Sociobiology 45: 451-465.

Laiolo, P. and J. R. Obeso (2012). “Multilevel Selection and Neighbourhood Effects from Individual to Metapopulation in a Wild Passerine.” PLoS ONE 7(6): e38526.

Moorad, J. A. (2013). “Multi-level sexual selection.” Individual and Family-level selection for mating success in a historical human population 67(6): 1635-1648.

Pruitt, J. N. and C. J. Goodnight (2014). “Site-specific group selection drives locally adapted group compositions.” Nature 514: 359-362.

Stevens, L., C. J. Goodnight and S. Kalisz (1995). “Multi–Level Selection in Natural Populations of Impatiens capensis.” American Naturalist 145: 513-526.

Tsuji, K. (1995). “Reproductive conflicts and levels of seleciton in the ant pristomyrmex pungens: contextual analysis and partitioning of covariance.” American Naturalist 146: 587-607.

Weinig, C., J. Johnston, C. G. Willis and J. N. Maloof (2007). “Antagonistic multilevel selection on size and architecture in variable density settings.” Evolution 61: 58-67.

The second thing I wanted to talk about was that I was asked about the relationship between inbreeding coefficients and genetic distance. I thought I would share my answer, in part to be told where I was wrong. My disclaimer is that all I know about genetic distance, is that it is something I rarely care about. . .

Consider a metapopulation with M alleles, with the mth allele having a frequency of pm in the overall metapopulation. We would like to calculate d, which from I got a formula cited by Smouse and Peakall (1999, Heredity 561-573) to be:

Screen Shot 2014-12-17 at 11.43.46 AM

Here the summation is over the M possible alleles, and yijm is the number of alleles of type m in individual i in the jth deme. This takes on a value of 0, 1, or 2.

If we are interested in the average genetic distance between deme j and deme l then we would calculate this as:

Screen Shot 2014-12-17 at 11.44.02 AM

We can now define dmax to be the maximum value that can take on. This will occur when the FST = 1. In an infinite metapopulation this means that every population will be fixed for an allele, and pm of the populations will be fixed for the mth allele.

If demes j and l are fixed for the same allele the genetic distance is 0. For allele m this occurs with probability (pm)2. If deme j and l are fixed for different alleles the genetic distance is:

Screen Shot 2014-12-17 at 11.44.11 AM

For alleles m and n this occurs with probability pmpn, thus:

Screen Shot 2014-12-17 at 11.44.20 AM

We want a measure that is a function of FIT and FST (I just figured out that I have never talked about FIS,  FST and FITTry this) that goes from zero to 1. When FST = 0, dij,kl = 0, and when FST = 1 dij,kl =1.

Working this out (the excel worksheet is available here: genetic distance work sheet)

Screen Shot 2014-12-17 at 11.44.34 AM

If we assume random mating within demes then FIT = FIS.

Screen Shot 2014-12-17 at 11.44.44 AM


Note that when FST=0, d = 0, and when FST=1, d = 4. The problem, of course is that we want to multiply this by dmax. For this to work we need the equation to go from 0 to 1. Thus, we divide by 4:

Screen Shot 2014-12-17 at 11.44.54 AM


Screen Shot 2014-12-17 at 11.45.03 AM

OK, A lot of algebraic noise. What this is telling us is that using Smouse and Peakall’s formula, there is a fairly direct relationship between FST and Screen Shot 2014-12-17 at 11.45.14 AM. Basically the difference is that genetic distance is based on identity by state, whereas F is based on identity by descent. If, at the start, every allele is unique then Screen Shot 2014-12-17 at 11.45.23 AM. If not, then dmax will be some number smaller than 4, and Screen Shot 2014-12-17 at 11.45.32 AM. If you care here is a graph of my equation:

Screen Shot 2014-12-17 at 11.47.04 AM

Genetic distance standardized to a maximum value of one as a function of FST.  If mating is non-random then  FIT will not equal FST and the results will be somewhat different.

Finally, I was asked about our fly collecting trip. Well do to a whole bunch of odd events we are understaffed to take care of a new batch of flies, so the trip has been postponed until January. The other question was about how I was going about bringing flies back to the US. The answer is I am not. I strongly recommend doing research in Brazil, but if you do get a Brazilian collaborator, and do your experimental work in Brazil, and leave your samples there. The reason is simple. We, as in the US and other first world countries, have been pillaging countries like Brazil for too long, and they are, unsurprisingly, sensitive about this. Doing research in Brazil is dead easy IF you have a Brazilian collaborator and you do the work in Brazil.

OH, and yes, I am slowing down my posts for a while, but I will still be occasionally posting as the occasion arises.

Hiatus announcement and group selection 1 and 2.

Posted: December 4th, 2014 by Charles Goodnight

The main piece of sad news this week is that I am just simply overwhelmed, and I am going to have to take a hiatus from writing. I will try to post occasionally, but look for once or twice a month rather than weekly. The reason is that I signed a book contract. I need to get writing on that, but before I do I have a chapter to complete, and I need to keep my research going – we are off to collect Flies in Southern Brazil next week. In some sense, it is good that I am slowing down. The logical progression of the blog would start to lead me into unpublished territory. The phenotypic approach has a lot to say about the evolution of sex, and the origin of life, for example. I think it makes sense to keep these a bit under my hat until they can get out in a citable peer reviewed format. The reason it is perhaps not so good is that there are a lot of ideas tearing at me that really do belong in the blog. Some subjects I should write about: It dawned on me that there is a difference between the contextual traits of contextual analysis on the one hand and indirect genetic effects on the other; I am once again confronted with philosophers of science talking about “group selection 1” and “group selection 2”, which are terms that I think confuse the issue and interfere with a nuanced understanding of multilevel selection. These are just issues that came up in the last week. Thus, I am not ready to abandon the blog yet, but I do think I need to slow down.

The book contract mentioned above is to write a book on exactly the topic of the blog, and as a result hopefully put it in a more permanent and citable form. The target date for a draft is a year from January, so it will be occupying a lot of my time for the next year.

So to rather randomly choose one of these topics. Lets talk about group selection 1 and group selection 2. This concept was introduced by Heisler and Damuth (1987, Am Nat 130:582), and recently popularized by Okasha (2006) (http://www.amazon.com/Evolution-Levels-Selection-Samir-Okasha/dp/0199556717/). The basic idea is that when you have individuals, or particles, you can do a multilevel analysis of selection on particles and selection on the collective, or you can just do an analysis of collective. Group selection 1 is an analysis in which fitness is measured at the particle level, and contextual effects of higher levels of organization are included. In other words, group selection 1 is what we think of when we think of group and individual selection acting simultaneously. In contrast, in group selection 2 we ignore the particles and focus on the collective. Thus, we might look at the fitness of bacterial colonies even though we know full well that these colonies are made up of individual cells.

This concept has gotten good traction in the philosophy world, and I will agree that it raises an important point. That is, it makes clear that results change depending on your point of reference. In the past there has been a lot of useless ink wasted when people were arguing about things like whether species selection was just the summed effects of individual selection, when in fact, they might be the same thing. That is, from a group selection 1 perspective in which the individual organisms are included in the analysis, it could indeed be that species selection is just the cumulative effects of selection on individuals. Even if this is true, however, if we take a group selection 2 perspective then indeed it is species selection, since we are only looking at the collective, or species.

So, this all sounds very positive, so what’s the problem? The problem is that every system is always group selection 1 and group selection 2 at the same time. Cells are made up of subcellular components, organisms are made of cells, groups are made of organisms. The levels need not be strictly hierarchical. For example, I “belong” to a number of different groups: My family, my department, the Evolution society, the blogosphere. These groups are in no sense hierarchical, and yet the do overlap to some extent. The group selection 1/2 perspective implies that there are really only two such levels, and basically enforces a false dichotomy. Question: are you working on particles or collectives? Answer: Yes.

So, rather than be destructionist I would like to offer a much better alternative. Let us clearly identify the level at which we assign fitness. This is Okasha’s particle, and my individual. Let me repeat that: The level at which we assign fitness is the individual. Then, rather than having the ambiguities of what exactly the levels are when we talk about group selection 1 and 2, we can instead clearly say that in this study the individual is the cell, whereas in that study the individual is the organism. The conclusions will, of course be different, but we don’t have to argue about them. We will know why they are different. They are different because they have different perspectives, they assign fitness at different levels.

Again, I apologize for taking a hiatus on my blogging. Hopefully I will be able to put up posts at a lower rate, and still keep this blog alive. One reason I will not be blogging next week is that we are going fly collecting. This will be an adventure, so don’t feel sorry for me!

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We will be driving south into wine country to sample Tephritid flies.  There are a number of interesting species complexes here.  Hopefully we will be able collect some of interesting species.


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