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Evolution in Structured Populations

Multilevel Selection On Mating Success In Water Striders

Posted: January 31st, 2014 by Charles Goodnight

In the past several weeks I have been discussing how multilevel selection was very common in plants.  Of course, we should not be surprised that multilevel selection would be important in plants, since they are sessile, and often have limited gene flows.  Thus, they are forced to interact with a consistent set of partners, and the population viscosity will lend heritability to many contextual traits.  Animals have much fewer constraints on their interactions, thus we might expect group selection to be rarer in animals than plants.  I am not sure if I believe that or not.  All of the original theorizing around group selection was about animals, and plants because they didn’t “behave” were essentially never discussed.  Indeed, Herron and Freeman’s Evolutionary Analysis uses my thesis on Arabidopsis to point out that group selection isn’t just in animals.  So my early training tends to make me assume that group selection is more important in animals than plants.

Be that as it may, it is worth looking at a contextual analysis experiment in animals.  The study I want to talk about is Eldakar, Wilson, Dlugos, and Pepper (2010, Evolution 64, 3183).  This study is also interesting in that it uses contextual analysis in a manipulated experimental setup.  In this study Eldakar and colleagues set up a large pool (basically a child’s wading pool) with partial partitions and a current running around the outer rim of the pool.  I have looked around the web for a picture, but I couldn’t find one (Omar:  We need pictures!), so based on my reading of their paper this is what it looked like.

Eldakar pool

Schematic of experimental pools used by Eldakar et al.  The pools were 3 meters in diameter, and had six sub pools with a current flowing around the outside edge.

Water striders were added to this experimental metapopulation and allowed to interact, and mate.  This was a typical behavioral experiment in that the different water striders were individually identified, and at regular intervals their behaviors were scored.  The water striders were given 10 days to settle in, and initial observations were made, and then a further 10 days in which data were gathered.

interacting striders

A pair of individually marked water striders.  Based on my total lack of knowledge of water strider biology I will not hazard a guess as to what is going on here! (from http://scienceblogs.com/evolution/2009/11/05/new-evidence-for-group-selecti/)

It is important to spend a little time commenting on water strider behavior (of which I know very little).  In particular, as with many animals there is strong sexual selection, which means that the females are continually harassed, and males are more or less constantly trying to mate with them.   As you might expect the females don’t particularly appreciate (or need) all of this attention, so generally speaking females spend a lot of time avoiding having to copulate with males.  On the other hand males can be ranked for aggressiveness.  Eldakar and his colleagues identified a series of mating related behaviors, and using the frequency of these behaviors classified the males as to degree of aggressiveness.  As you might expect, in a confined space very aggressive males get more matings than less aggressive males, however, when females have a choice in the matter they are inclined to run away from these hyper-aggressive males.

So with that in mind the water striders were placed in the pool and allowed to move wherever they wanted.  Naturally the assorted into the six quiet sub pools, but they were able to use the current along the edge to move from sub pool to sub pool.  From this an interesting thing happened.  That is females tended to leave sub pools with a lot of aggressive males, and congregate in pools with more docile males:

Eldakar females by male aggression

“Figure 1: Individual dispersal in response to local aggression imposes sex-ratio heterogeneity among subpools. The frequency of females within subpools decreased as the average aggression score within subpools increased.” (from Eldakar, Wilson, Dlugos, and Pepper. 2010, Evolution 64, 3183).

What this means is that the very aggressive males got fewer matings, because although they were more successful at obtaining matings, because of their aggressiveness and female movement they had less access to females than did less aggressive males.  In short, the highest mating success was found in males with an intermediate level of aggression.

Eldakar mating successs by aggression

“Figure 2. Male aggression had a quadratic unimodal relationship with the number of successful matings with selection favoring intermediate levels of male aggression.” (from Eldakar, Wilson, Dlugos, and Pepper. 2010, Evolution 64, 3183)

They used contextual analysis to estimate the strengths of selection on individual aggressiveness and selection on group mean aggressiveness.  In this they found that there was strong individual selection favoring more aggressive males (slope of regression of relative fitness on individual aggressiveness score = strength and direction of individual selection = 0.752, P=0.019), and group selection favoring decreased average aggressiveness (slope of regression of relative fitness on group mean aggressiveness score = strength and direction of group selection = – 0.556, P=0.076).  The group selection regression coefficient is not significant (probably due to the lower power and smaller degrees of freedom at the group level), nevertheless, it is certainly having an effect on the outcome, so this is a place were it seems to me that special pleading is justified.

That this was indeed to female movement can be seen from two observations.  First, less aggressive males tended to be near females more often than highly aggressive males:

Eldakar neighbor distance by aggressiveness

Figure 3. Subjective frequency of females decreases as males increase in their aggressive phenotype. More aggressive males experienced fewer females in their local subpool (open circles) as well as in nearest neighbor interactions (filled circles) than lessaggressive males. Dashed and solid fit lines correspond to local subpool and nearest neighbor frequencies, respectively.  (from Eldakar, Wilson, Dlugos, and Pepper. 2010, Evolution 64, 3183).

Second, in an earlier paper (Eldakar, Dlugos, Pepper, and Wilson 2009. Science 326, 816.) they showed that limiting the dispersal of females qualitatively changed the relationship between aggression and mating success in the males, with more aggressive males always getting more matings.

Eldakar Science mating success by aggression

“Fig. 1. Differences in mating success of aggressive males between dispersal conditions. In the dispersal condition, male aggression score (A) and harassment (B) had moderate quadratic relationship with the mating success of males. When blocking dispersal, aggression (C) and harassment (D) both strongly predicted the mating success of males.” (Eldakar, Dlugos, Pepper, and Wilson 2009. Science 326, 816.)

As I advocated for last week, this study uses contextual analysis to measure the strength of selection, and to form the hypothesis that group selection against aggressiveness is acting through female dispersal.  However, it is the additional observations on the behavior of females, and manipulations of their ability to emigrate that confirm that the group selection is mediated by dispersal of females.

Another interesting point is that if we assume that aggressiveness is at its multilevel selected optimum, and make the probably silly assumption that the traits at the two levels are uncorrelated, we can actually estimate the ratio of the heritability of the group level trait to the individual level trait.  As I discussed earlier, using Goodnight (2005 Population Ecology 47, 3) and assuming that selection is in equilibrium, with no correlated responses to selection, then we can re-write Hamilton’s rule as:

Eldakar equation

In other words, accepting all of my sketchy assumptions, this suggests that the heritability of the group trait of mean aggressiveness has a heritability that is a third greater than the heritability at the individual level.  This might not be unreasonable given that interactions among individuals (males scaring off females) can contribute to the group heritability, but not the individual heritability.

In any case I have over-extended by stay on this weeks post, so suffice it to say that I suspect that sexual selection may be a ripe place to look for group selection in animals.


Selection in Impatiens: Moving beyond correlation

Posted: January 22nd, 2014 by Charles Goodnight

Last time I reviewed our study of contextual analysis in Impatiens capensis.  We came up with a standard result, and drew a radical conclusion.    The standard result is that Impatiens obeys the constant yield rule that Harper claims is nearly universal, and a result that had been seen in the past (e.g., Schmitt, Eccleston and Ehrhardt 1987 J. Ecol 651-665).  Basically, I argued that the constant yield law is a version of “soft selection”, and that our theoretical analysis showed that this was multilevel selection.  A result that indicates that multilevel selection is nearly universal in plants.

However, as has been amply pointed out in this blog and elsewhere regression is a glorified form of correlation, and as we all know correlation is not causation.  What methods such as contextual analysis do is that they show us that there is an association between phenotype (and contextual phenotype) and fitness.  What they do not show us is that that correlation is causal.  This is exactly the issue that Wade and Kalisz (1989 Evolution 44:1947-1955) addressed.  They raise the important point that if we want to get away from correlation and understand causation we need to do manipulative experiments.

In this view, regression analyses of fitness such as contextual analysis show an association between phenotype and fitness.  From this we posit that the variation in phenotype is causally affecting fitness.  Of course, the phenotype itself does not affect fitness, rather it is the interaction of the phenotype with the environment that causes variation in fitness.  This provides a mechanism for turning the correlational approach into a causal approach.  If we have correctly identified the agent of selection we should be able to modify that agent, and in the process modify the selection gradient.  For example, in Franks, Wheeler and Goodnight (2012, Evolution 66, 1398-1412) we reasoned that the plants varied in secondary compounds and insect damage was a significant selective agent on the plants.  We found that for several secondary compounds selection was significantly weaker in plants sprayed with insecticide than it was in unsprayed plants.  By calculating the selection gradient in two situations, with and without the putative selective agent, we were able to show that insect herbivory was indeed a causal selective agent.

Australian paperbark tree Melaleuca quinquenervia or punktree

Melaleuca quinquenervia, the Paperbark tree is native to Australia, but an invasive pest species in Florida.  It is the species studied by Franks, et al. (2012, Evolution 66, 1398-1412) (picture from http://majikphil2.blogspot.com/2013/02/trade-in-rare-plants.html)

Returning to multilevel selection in Impatiens, it turns out that John Kelly did manipulative study to confirm that multilevel selection (he called it kin selection) was acting in Impatiens (Kelly 1996. 147:899-918).  In his study he used the fact that you can make Impatiens short and bushy by pinching off the apical meristem.  This removes the apical dominance and allows the side branches to grow, but of course it prevents the plant from growing any more vertically (at least until a new dominant takes over).  He set up several plots at, Kellogg Biological Station again, that differed in their light environment.  In each of these plots he set up four treatments:  (1) Unmanipulated plants; (2) the focal individual was pruned, and the neighbors unmanipulated, (3) focal individual unmanipulated, the neighbors pruned, and (4) both focal individuals and neighbors pruned. Full factorial experiments are the best aren’t they!

One of the interesting things he found is that when the neighbors were pruned (and therefore stunted) the focal individuals seed production (fitness) was significantly greater than the seed production of plants surrounded by un-pruned neighbors.

Kelly results

Fitness of a focal plant as a function of whether the neighbors were un-pruned (left) pruned (right).  (from Kelly 1996. 147:899-918)

In short, the pruning of the neighbors was releasing the focal plant from the pressures of group selection, and as a consequence the fitness was entirely determined by the individual traits, rather than the combined effects of group and individual selection.  In other words, Kelly showed that the stature of the neighbors was a causal selective force on the focal individual, confirming that the regression of contextual traits on fitness that we observed was indeed causal, and that there is group selection against large size in Impatiens capensis.

However, Kelly raised an excellent additional point.  He points out that Impatiens, like most plants, are very plastic.  As a result their size is modified by density effects and crowding from other plants.  Kelly represents this as a path diagram:

kelly path diagram

The path diagram proposed by Kelly (1996. 147:899-918).

Using this path diagram Kelly pointed out that with phenotypic plasticity you would have paths f and g.  That is the neighbor’s phenotype changes the focal individuals phenotype and vice versa.  He then goes on to correctly argue that contextual analysis cannot detect these inter-individual modifications of phenotype, thus there is a component of kin selection that contextual analysis will not detect.

This is actually an interesting philosophical point.  The phenotype is the phenotype, and contextual analysis as we did it is purely a phenotypic analysis.  Based on this the path diagram should be:

My version kelly path diagram

Encompassed in the “r2” term are all of the arrows that link the two phenotypes, that is paths a, c, f, and e of Kelly’s path diagram.  The important point is that in the genic view it is important to distinguish between “genotype” and ecological interactions.  In the phenotypic view such distinctions are nice to know but not necessary.  Both are part of the transition equation that gave rise to the focal plant’s phenotype.

It also shows a different and important point.  We can redraw the left half of Kelly’s path diagram as follows:

left half of kelly path diagram

I moved the focal plant phenotype to the right and dropped the g arrow to make my point clearer, but otherwise it is identical to the right part of Kelly’s diagram.  He measured the focal plants phenotype, so it IS that individuals phenotype, further, if selection is acting solely on the individuals phenotype we have to call it “individual selection”.  However, (and this is a big however) just because it is a trait measured on the individual, does not mean it is a trait solely of the individual.  In this case the plants phenotype is determined by a number of factors only some of which are intrinsic to the focal individual, driving home the point that we need to distinguish between selection and inheritance.  From a phenotypic perspective contextual analysis is not a problem.  Rather it is kin selection, with its conceit that our genes are some how qualitatively different than other forces affecting our phenotype, that is the problem.

Multilevel Selection In Impatiens

Posted: January 15th, 2014 by Charles Goodnight

Last week’s post was bit of a set up.  To reiterate I made the point that lab selection experiments really tell us about the ability of population to respond to imposed group selection, and the one early study on group selection in nature did not provide a convenient protocol that could be easily extended to other systems.  This brings us to contextual analysis.  It is a statistical method, and as such it is not particularly beholden to any single system.  This can be applied to virtually any natural system in the same manner that an Arnold and Wade (1984 Evolution 38, 720-34; Evolution 38, 720-34) selection analysis can be applied.  As an example, I want to talk about Stevens, Goodnight and Kalisz (1995. Am. Nat. 145, 513-26).

First, as an anecdote to show that motivations are perhaps not as honorable as they should be, the reason we undertook this study is that after we published Goodnight, Schwartz, and Stevens (1992 Am. Nat.140:743-761), Lori Stevens and I were sitting around the lab talking and decided that SOMEBODY was going to use this in a field study.  We decided the first to publish such a study would have to be cited by everybody doing field work on multilevel seleciton, and I didn’t care what we studied, but that somebody was going to be us.  So, we recruited a fine plant biologist, Susan Kalisz, and set off to study multilevel selection in a plant that very obviously had group selection acting.  Sadly, at least in retrospect, we thought that there was some sort of hurry to do this study before we were scooped.  Another funny story worth mentioning is that the work involved spending long periods lying prone on a scaffold hanging over the plants censusing them.  Sadly, both Lori and Susan were quite pregnant, and somehow they thought this was an excuse for not having to do the censuses.  Bottom line:  I spent a lot of that summer being bit by mosquitoes while draped over a board measuring plants with the blood rushing to my head.

We did this study at Kellogg Bird Sanctuary (I was working at the biological station that summer), which was a great place to work.  It had large continuous stands of impatiens in areas that were restricted so there was no danger of having your work disturbed (although one of our sites was destroyed when a duck made her nest in the middle of it).

KBird Sanctuary

Kellogg Biological Station and Bird Sanctuary:  A great place to do research. (Photo from http://activerain.com/states/MI/cities/Augusta/communities/The%20Kellogg%20Bird%20Sanctuary)

In the first year of the study we determined the appropriate neighborhood size, which we decided was basically only the nearest neighbors, those in a ½ meter circle around the focal plants.  We then measured a bunch of traits associated with growth and size, and three “fitness” traits, number of cleistogamous (self pollinated) flowers, number of chasmogamous (open pollinated) flowers, and survival.

Impatiens flowers

Impatiens capensis cleistogamous and chasmogamous flowers. (http://homebuggarden.blogspot.com/2012/02/self-pollinator-of-week-cave-hortulanus.html)

 The problem with the large number of traits we measured is the typical problem with regression analysis:  you run out of degrees of freedom.  Fortunately path analysis provides a way out.  In particular, we did a factor analysis to reduce the large number of traits down to a few manageable factors.  We ended up with three factors.  Second, used the neighborhood means for the factors as the contextual traits.  Finally, we did separate analyses for each of the three measures of fitness.  As a result we had a manageable data set for contextual analysis that conceptually looked like this:

analysis schematic

Analysis schematic.  We censused a large number of traits, then used factor analysis to reduce that number to a manageable number of (three) factors.  The neighborhood mean of those factors was then used as the contextual traits. 

As is virtually always the case with factor analyses the first factor could be roughly called “size”, and that is the one I will focus on.  What we found was that the results of the contextual analysis depended on the measure of fitness we were using.  For open pollinated chasmogamous flowers there was strong individual selection for larger plants, but essentially no group selection.  For survival we used a logistic regression (either a plant was alive or dead), and found that although group and individual selection were in apparent opposition, only the individual selection component of the multiple regression was significant.  Finally, and very interestingly, for the self pollinated cleistogamous flowers we found that group and individual selection were both significant, and of equal magnitude but acting in opposite directions.

impatiens CA results

The strength of selection on Impatiens capensis.  The bar graph is the distribution of factor 1, (which is a measure of size).  For open pollinated (chasmogamous) flowers there is strong individual selection, but no neighborhood selection for large size.  For survival group and individual selection are in opposite directions, but group selection is not significant.  For closed pollinated (cleistogamous) flowers group and individual selection are of equal magnitude, but in opposite directions.

Focusing on the cleistogamous flowers, this is something we have seen before.  In fact, this IS soft selection, which occurs when every group (or neighborhood) produces the same number of progeny, but there is selection acting with groups.  In an earlier post I showed that this was a mix of group and individual selection in which selection at the two levels was of equal magnitude but opposite sign.

Of course there is nothing new under the sun, and our results were consistent with old published results, indeed, they are so consistent that they have been called the “law of final constant yield (Kira, Ogawa Shinozaki 1953 J. Inst. Polytech. Osaka Cy. Univ. D. 4, 1-16, cited in Harper 1977) .  In fact, people have observed constant yields in crop plants over several orders of magnitude of planting densities.  According to Harper the constant yield law is extremely common, if not nearly universal in plants.  What we found in Impatiens is that the constant yield law is soft selection, and what we found in the theoretical work (and the Impatiens) is that soft selection is multilevel selection.

What this is saying is that, at least for yield, multilevel selection is nearly universal in plants.  So, it appears that to answer to the question of how common is group selection in nature:  In plants it is nearly universal.




Lab and Field Experiments of Group Selection

Posted: January 10th, 2014 by Charles Goodnight

Late as usual.  I think I will not be able to keep up the weekly posting.  This week I want to talk a little about what why we do group selection experiments, and what they tell us about group selection in nature.

In a standard laboratory group selection experiment several sets of metapopulations are set up.  The different metapopulations are subjected to group selection for a particular trait.  For example, an easy to describe early, actually the first, group selection experiment is that of Wade (1977. Evolution 31: 134-153.).  In this experiment he set up four treatments, although I will only discuss three of them, a group selection for high population size, a group selection for low population size, and a no group selection treatment (the fourth treatment is a random group selection treatment).  Each treatment was a metapopulation of 48 populations of 16 beetles each.  These populations were raised for 37 days (one generation), and then censused for population size.  In each metapopulation the populations were ranked by their population size.  In the group selection for high population size treatment the largest population was taken, and as many populations as possible were set up from that population.  When that population was exhausted the next largest was taken until the metapopulation of 48 populations was obtained.  For the group selection for low population size treatment the smallest population was used to establish as many populations as possible, then the second smallest etc. until the necessary 48 populations were obtained.  Finally in the no group selection treatment each population established exactly one population in the next generation.

wade experimental design

The Wade 1977 experiment.  Shown here are three treatments, group selection for large population size, group selection for low population size, and no group selection.  Redrawn from Wade (1977. Evolution 31: 134-153.)

Wade got what we now know to be a typical result:  There was a significant response to selection both for increased and decreased population size.

Wade response to selection

The response to selection in the Wade 1977 experiment, reported as a deviation from controls. Redrawn from Wade (1977. Evolution 31: 134-153.)

This was the first group selection experiment ever, so perhaps you can find some flaws in the design (they are there), but his general result of a solid response to group selection has been replicated many times at this point.  Below is a list of group (or community) selection studies I compiled some time ago that all show a significant response to group selection.  There would be more if I brought it up to date.

Other studies of group selection

So what these experiments tell us is that group selection can bring about a response to selection.  They actually don’t tell us whether or not there is group selection, rather, what they tell us is whether group selection can bring about a response to selection.  In other words, what they tell us is that there is heritability at the group level.  They don’t tell us whether group selection is acting in nature, rather they tell us that if there is group selection in nature we can expect that that selection will cause adaptive evolution to occur.

Historically this was a bit of a conundrum in the early days of group selection experiments.  The earliest criticisms of group selection, such as Maynard Smith’s famous “hay stack model” (J. Maynard Smith 1964. Nature 201:1145) posited on theoretical grounds that group selection should not work.  Experiments such as Wades quickly demonstrated that group selection does work, and that it works far better than anybody could have expected.  This simply shifted the debate.  Now that we knew it could cause evolutionary change, the argument against group selection simply became that it didn’t occur in nature.

Unfortunately, no amount of laboratory studies will ever show whether or not group selection is an important force in nature.  I am not sure who said it, but I once heard it said that theory was the realm of all conceivable worlds, the lab is the realm of all possible worlds, and nature is the realm of the real world.  Yes, group selection experiments work, but it would never be convincing as long as the selective force was the investigator.

To study the importance of group selection in nature, it is important to actually go into nature and measure the effects of selection on natural populations.  When doing this we typically do not know the heritability of the traits on which we are measuring selection.  The reason for this is two-fold.   First, we know the genetic basis for traits in model organisms, but our model organisms are not typically what we study in the field.  Second, in natural populations we tend to be interested in complex behavioral traits that are often poor candidates for genetic studies.  In any case, this is why the distinction made in quantitative genetics between selection and the response to selection is so important.  It is indeed legitimate to study selection even if we do not have a way to find out what the evolutionary consequences of that selection are.  As a general rule, we study genetics and heritability in the lab, and selection in nature.

The first study to actually demonstrate group selection actually occurring in nature was done by Breden and Wade (1989. Am. Nat. 134:35-50).  They did a series of experiments on cannibalism in the imported willow leaf beetle, Plagiodera versicolor.  With out going into detail, what they found was that there was a general advantage at the individual level to being a cannibal: cannibals grew faster, and generally survived better.  However, they found a positive relationship between group size and survival.  Fairly obviously, eating your brethren negatively impacts your group size.

B n W grp size by survival

Copied from (Breden and Wade 1989. Am. Nat. 134:35-50)

This relationship between group size and survival is not surprising.  Leaf beetle larvae are group foragers, and collectively defend against predators.  Larger groups are more efficient foragers (perhaps because they can better break the leaf cuticle, and more resistant to predation (they exude noxious chemicals, and large groups are more toxic than small groups).  On the other hand cannibals benefit from the very high nutrient and energy content of their victims.


Imported willow leaf beetles are group foragers.  Larger groups survive better than small groups.  Photo by J. Hahn, University of Minnesota http://www.extension.umn.edu/garden/diagnose/plant/deciduous/willow/leavesholes.html

As I said, this was the first study of group selection in natural populations, and it successfully found group selection.  On the one hand this is heartening:  You look for group selection and there it is.  On the other hand, there is no question that Breden and Wade went out and looked for a good candidate species to find group selection.  Thus, this is perhaps a biased sample.  The real problem with this study, however, is that the methods that they used were very species specific, and they do not provide a protocol that is easily generalized to the study of group selection on any trait in any species.

Regardless, this emphasizes my point nicely:  Lab studies of group selection successfully answered the question of whether group selection works.  It does.  This field study, and others I will discuss show that there is group selection in nature.  Collectively these experiments suggest that the role of group selection in evolution is something that should not be ignored.

Contextual analysis and Hamilton’s rule

Posted: January 3rd, 2014 by Charles Goodnight

After another brief hiatus to talk about religion, lets return to contextual analysis.  As I have pointed out several times contextual analysis uses the same equation as the direct fitness approach of kin selection.  This implies that we can re-capture Hamilton’s rule using contextual analysis.

Hamilton’s rule is the center of kin selection.  In one of its standard forms it is argued that an altruistic trait will evolve whenever:

Ham rule equation 1

Hamilton’s rule applies specifically to the evolution of altruism, which is a special case of multilevel selection in which group selection and individual selection are acting in opposition.  In fact, that is my definition of altruism:  An altruistic trait is a trait that is favored by group selection, but opposed by individual selection.  Thus, we can say that altruism will increase (within a generation, more on that later) whenever the strength of group selection is greater than the strength of individual selection.  Thus we need to satisfy the condition:

The strength of group selection > The strength of individual selection


Ham rule equation 2

Where the vertical lines mean absolute value.  In words the absolute value of the partial covariance between relative fitness and the contextual trait must be greater than the partial covariance between relative fitness and the individual trait.

If you square both sides and do a bunch of algebra you eventually get:

Ham rule equation 3


Ham rule equation 4

Where  Ham rule equation 5etc. is the correlation between relative fitness and the contextual or individual trait,  Ham rule equation 6etc. represent the partial correlations, and Ham rule equation Ais the correlation between the individual trait and the group mean of the trait.  When these correlations are squared they are equal to the fraction of the variance in the first variable that is “explained” by the second.  Thus:

Ham rule equation 7= the fraction of the variance in relative fitness that is attributable to variation in the contextual trait holding the individual trait constant = the strength of group selection
Ham rule equation 8 = the fraction of the variance in relative fitness that is attributable to variation in the individual trait holding group mean constant = the strength of individual selection

and perhaps surprisingly

Ham rule equation 9= the fraction of the variance that is among groups.

Thus, this gives us a very nice equation:

Strength of Individual Selection   < the fraction of variance among groups
Strength of Group selection

Now, in Hamilton’s hyper-additive gene centric world it turns out that the fraction of variance among groups is exactly equal to the relatedness within groups. Thus in Hamilton’s world Ham rule equation 9 = “r”, or relatedness.

Similarly, we can equate the strength of individual selection with Hamilton’s “cost”, and the strength of group selection with Hamilton’s “benefit”.  Thus in additivity land we have exactly recaptured Hamilton’s rule.

Howeverrrrrrrrr, it is not exactly Hamilton’s rule.  Hamilton was working strictly from optimality theory, and with the genic view.  Turning first to the optimality issue, the problem is that an optimality approach finds the place where the forces are exactly in balance.  But notice it is the FORCES.  This makes an implicit assumption about the underlying genetic nature of the traits, and the population structure.  In particular, it assumes that even though kin interact, when it comes to mating they nevertheless mate at random.  Consider what would happen if kin interacted because the population was structured, and they therefore also had to mate with each other.   What happens is that the variance within kin groups goes down, and the variance among kin groups goes up.  In the extreme you would end up with two kinds of groups (remember, kin selection typically assumes a “gene” for altruism).  Some groups would be homozygous for the altruistic gene, some would be homozygous for the cheater gene.  Guess what:  The altruistic gene would win every time.  In other words, balancing the forces is not the whole story.  The partitioning of heritable variance to the variation within and among groups also matters.

In contrast the contextual analysis version of Hamilton’s rule is actually a competing rates solution.  That is the forces balance out where the intensity of selection and heritabilities at the two levels balance out.  This brings us to our second difference, the idea that Hamilton’s original perspective used a “genes eye” view, and assumed that the group mean altruism was a simple function of the average frequency of an altruism gene.  On the other hand contextual analysis treats the individual trait and the group trait as separate traits that may have different heritabilities.  This gives rise to a very interesting point.  If we are interested not just in the within generation balance of forces, but also the response to selection then we need to add in the heritabilities.  In a paper (Goodnight 2005, Popul Ecol 47:3) I derive the following equation:

Ham rule equation 11
where h2grp and h2ind are the heritabilities at the group and individual levels, VA(*) is the additive genetic variance for the trait, and rA is the additive genetic correlation between the two traits.

Man that is ugly.  Its ugly because it includes heritability, plus the effects of both direct and indirect selection.  If we ignore indirect selection for the moment (I am not trying to pull a fast one, just trying to make the equation pretty) and do some rearranging we get:

Ham rule equation 12(plus correlated responses to selection)


Ham rule equation 13

This is actually pretty profound.  What it is saying is that Hamilton’s “r” is really the ratio of the heritabilities of the group trait to the individual trait.  The heritability is affected both by the genetic structure AND the breeding structure.  Consider, for example, our bodies.  In this case because the cells in our bodies are the product of mitosis, and genetically nearly identical h2ind will be very nearly zero.  This same process that makes the cells within an individual more similar makes different individuals more different.  As a result in this case the ratio of group heritability to individual heritability will be very nearly infinity.  Compare this to Hamilton’s rule where r maxes out at 1 (which I emphasize is somewhat smaller than infinity).  Yes, when you take heritability and breeding structure into account under many circumstances the evolution of “altruism” becomes hardly surprising at all.


Hmmm, relatedness close to infinity.  Inconceivable! (image taken from http://software-carpentry.org/blog/2013/10/you-keep-using-that-word.html)

Group Selection and Religion

Posted: December 26th, 2013 by Charles Goodnight

Figuring this is the week between Christmas and New Years I can write about just about anything I want, and nobody will read it.  My original thought was to talk about cultural transmission and what happens when Christmas gets transmitted to a non-Christian society, such as Japan, but well one picture really says all that needs to be said:


from (http://geeknation.com/huge-smoke-breathing-godzilla-christmas-tree-in-japan/ )

Instead, I figured that since one of the most common periods for religious celebration is around the winter solstice I might talk about religion.  In particular, I wanted to talk about some of my thoughts that arose from reading one of my favorite books on the subject, D. S. Wilson’s “Darwin’s Cathedral”.  I recognize that David is a bit of a controversial figure, and not everybody sees eye to eye with him, but I must say that with Darwin’s Cathedral he really did hit a home run.  Wilson has some interesting ideas, and his online magazine, This View of Life, is well worth looking at once in a while.

Before starting, there is one important point to make.  Science is one of many ways of knowing.  Scientists, as scientists, can only address issues that are in some sense observable, and which can be described using naturalistic explanations.  A naturalistic explanation is an explanation that relies on the known physical properties of the universe.  Gods and deities are supernatural beings – That is they reside outside of the world of known physical mechanisms.  Religion relies on faith and supernatural explanations to explain the existence of deities, and many of the trappings of religion.   As such science has nothing to say about whether religions explain some fundamental truth or whether there is a God of gods.  Importantly, I consider myself to be a scientist, and I have opinions about God — I am an atheist, and I do not believe there is a god; however, that is my opinion as a person.  As a scientist I do not and cannot have an opinion about the existence of God.  While science has nothing to say about the validity of religion, it can have something to say about the human practice of religion, and that is what I want to talk about.

The first observation to make is that in humans religion is virtually universal.  As far as I know secularism is a relatively modern concept, and that primitive societies all have some form of belief in the supernatural or some form of deity.  The reason that this is important is that when we see a structure or behavior in animals that is wide spread among a large number of species we tend to reason that it is an adaptation.  Thus, we find that most four legged mammals have tails and reason that it is an adaptation.  When functional analysis shows that, for example, cats use their tails for balance, and that they can turn on their tails and land on their feet we are hardly surprised.


(from http://survivalistics.com/cat-stat-felines-survive-falls-except-floors-7-to-10/)

By the same reasoning, because it is nearly universal, it makes sense to speculate that religion is an adaptation for humans.  The question is what is that adaptation.

A hint to the answer to this question can be found in the ten commandments.  Without repeating them here, suffice it to say that they can be divided into three distinct groups.  Commandments 1 through 4 all are say that there is only a single deity that should be worshipped in a particular fashion.  Commandment 5 (honor they mother and father) basically tell us to act in a fashion that promotes the family.  Finally, commandments 6 through 10 tell us to act in a fashion that promotes the good of the group.   Thus, to be totally crass the ten commandments basically say that there is one police officer (God), that you need to obey that officer, and that the laws are that you should sacrifice your own fitness for the good of the group.  It is worth pointing out that God is the perfect police officer.  God is always watching, and metes out justice after you die, so you never can report on it.

This, then, suggests that religion is an adaptation to promote group cohesiveness and group functionality.  As far as adaptive story telling goes, one can imagine that human groups that had some sort of religion or other organizing social structure would be more cohesive and survive better than groups that lacked religion.

Indeed, this is D. S. Wilson’s thesis: religion is an adaptation that promotes and enforces group level cooperation.  Unlike me, however, he is able to back up his ideas with a high-quality qualitative and quantitative analysis.   Sadly, I loaned out my copy of the book, and the library is closed on Christmas day, so you will have to live with my remembering.  Suffice it to say that in his survey of numerous religions, all of them had some form of edict or statement about how people should behave, and in all cases the statement was that individuals should sacrifice their individual fitness for the good group.

This idea is not new.  There are a number of “social solidarity” theories for religion (Sosis, R.; Alcorta, C. 2003. Evol. Anth. 12: 264–274), which are essentially what I am suggesting here.    However, among “evolutionary biologists” religion is generally considered an “exaptation” Gould, S. J. 1991. J. Social Issues 47: 43–65, or some form of cultural virus, or an evolutionary by product or mistake (Dawkins).  What I am suggesting here is standard adaptive story telling; however with the twist that I am allowing the possibility that group selection is important in human evolution.  If we allow this possibility many new and potentially important adaptive stories become reasonable.



A theoretical test of contextual analysis

Posted: December 18th, 2013 by Charles Goodnight

After two weeks off – week one was the fun review of Allen et al. week two was grading – it is time back to my main agenda of wandering through the things the ideas that have made me question the genic approach.

When I was first introduced to contextual analysis I was convinced that it didn’t work.  As an aside, this was distressing because it was introduced to biology by two of my former room mates in graduate school, and I really didn’t like being at odds with them!  So, we set out to prove them wrong.  We failed.  BUT we did get a paper out of it for our efforts (Goodnight, Schwartz and Stevens 1992 Am. Nat. 140:743-761)!

What we did was imagined we had a metapopulation that consisted of a large number of subpopulations, and then imagined that there was a trait, Z, and for each subpopulation a group mean trait Z̄  .

Metapopulation structure

We then assigned fitnesses based on three classic models of selection: group selection, hard selection, and soft selection.

Models of Selection

Group selection:  The fitness of an individual is determined entirely by the group mean phenotype and the individual phenotype has no effect on fitness.  Hard Selection:  The fitness of an individual is determined entirely by its individual phenotype, and the group mean phenotype has no effect on fitness.  Soft selection:  The fitness of an individual is a function of its phenotype relative to the group mean phenotype.  Top:  Degree of shading indicates fitness.  Bottom:  Red lines shows the relationship between individual fitness and individual phenotype, blue line shows the relationship between group mean phenotype and fitness.

Intuitively we would like contextual analysis to detect the “group selection” model as group selection, the “hard selection” model as individual selection, and the “soft selection” model as, well um, not really sure.  The Soft selection model is a classic frequency dependent selection model.  Consider an individual of intermediate phenotype.  This individual will have a high fitness in groups that have on average low phenotypes, and a low fitness in groups that have on average high phenotypes.  Thus, it clearly has a component of individual selection, but the fitness of an individual is, at least in part, a function of the characteristics the group they belong to.  This sounds a lot like group selection.

What we need to have to analyze these are the simple regressions of fitness on Z and Z̄:

relative fitness = intercept + slope * Z  (or Z̄ )

and what we are really interested in are the slopes.  The other thing we need are the slopes of the partial regressions of relative fitness on Z holding Z̄ constant, , and the partial regression of relative fitness on Z̄ holding Z constant.

In the rarified world of theory regressions are best expressed as covariances.  To scare off the mathematically uninitiated I will spell the first equation out as summations, but because that ends up cluttering up the work space, I will skip the summations in the later equations.  In any case our four regressions are:

Covariance Equations

Key to terms:  Cov(X,Y) = covariance between X and Y, Var(X) = variance of X, Corr(X,Y) = the correlation between X and Y. Cov(X,Y.Z) etc. is the partial covariance between X and Y holding Z constant etc.

The point of that ugly math is that regressions and partial regressions are different things.  If you believe me, feel free to ignore the math!

So now that we have these we can actually work out our different models of fitness.  Turning first to group selection, in contextual analysis we use partial regressions.  Without going into the rather gruesome math (and ignoring some very cute tricks) it turns out that:

partial corr equal 0

and thus,

bwzzbar equal zero

On the other hand,

bwzzbar equal b

In words, when we analyze a model of group selection, we discover that contextual analysis can be used to identify that group selection, but not individual selection is acting.

This seems like a trivial point:  If we apply group selection we detect group selection, but it is an important step in confirming that this is a valid approach.  Does the model provide the correct answer in a simple well understood system.

In contrast to the group selection model, the hard selection model intuitively should be individual selection with no group selection.  After all, the fitness of an individual is determined entirely by its own phenotype, with no influence from the group mean phenotype.  Again using the same reasoning as before, and a couple of clever tricks – We wrote this paper a long time ago and every time I go back to it, it throws me for a loop because of all of the clever tricks in it.  In the hard selection case the clever trick was figuring out that the simple regressions of fitness on phenotype and fitness on group mean phenotype were parallel. In any case, it is possible to show that there is individual selection:

Hard Sel ind component

but no group selection:

Hard sel group component

As an aside, this is in contrast with the Price equation, which would “detect” group selection, but that is for a future post!

Finally, if we apply contextual analysis to the soft selection model you find that there is individual selection acting, but the slope is not quite what you would expect:

Soft Sel ind component

and it becomes clear that individual selection is not the whole story.  Turning to the partial regression of fitness on group phenotype, it can be seen that there is group selection that is equal and opposite in strength to the individual selection:

Soft Sel group component

This result has generated a lot of confusion and senseless hot air.  This is because in a pure soft selection model there is no among group variance in fitness, and thus it seems reasonable that there should be no group selection.  However, the truth is that in the pure individual selection (hard selection) situation there IS variance among groups, due to indirect selection.  In the soft selection case group selection is PREVENTING there from being any variance among groups. This is seen in the simple regressions of relative fitness on group phenotype:

Hard Soft simple regs

In other words, there must be group selection acting if you are going to have individual selection with no variation in fitness among groups.  This should come as no surprise, since this result is completely non-controversial when talking about selection on correlated traits at the individual level, as I discussed in my blog on selection on multiple traits .

As a result of doing these analyses I was convinced that contextual analysis was in fact the correct way to analyze multilevel selection.  Several years after the original (to biology) publication of the contextual analysis approach (Heisler and Damuth 1987 Am. Nat. 130: 582-602) the kin selection folks re-discovered it and called it the direct fitness approach (Taylor  and Frank 1996 J. Theor. Biol. 180: 27-37).  It was satisfying to see the efficacy of this approach independently confirmed.  Sadly, it also confirmed that many “kin selectionists” were bound and determined to pointedly ignore the multilevel selection people.  A point that was driven home several years later when Taylor, Wild and Gardner (2007 J. Evol. Biol. 20: 301-309) confirmed the efficacy of the “direct fitness approach”, and then West, Griffin and Gardner (2008 J. Evol. Biol. 21:374-385, Gardner, A. and A. Grafen 2009 J. Evol. Biol. 22: 659-671) subsequently dismissed contextual analysis as being incorrect.

Ignorance is Bliss 1 quarter

(http://www.gocomics.com/calvinandhobbes/2012/05/20#.UrHXro2kBVs).  I thought the whole comic was a bit more catty than I wanted to be.

No post this week

Posted: December 12th, 2013 by Charles Goodnight

I am afraid I just got too busy grading this week.  I will be back next week.


from PHD Comics.

Now I know I am “El Lobo Solitario”: I don’t even agree with Allen, Nowak, and Wilson

Posted: December 4th, 2013 by Charles Goodnight

And now for something completely different.

something different

Up until this point I have been writing my own thoughts about my own little world.  Given that Allen, Nowak and Wilson recently published a sure to be controversial paper on inclusive fitness (Allen, Nowak and Wilson 2013 Limitations of inclusive fitness.  PNAS early edition), and given the role I played in their thinking (i.e., none at all), I figured I should weigh in on their paper.  So, on with the show.

The main point of the paper is that fitness components are not additive.  That is, that you cannot make a clean partitioning between the effects of a behavior on the actors direct effects on themselves, and their indirect effects on others.  They quote Hamilton’s original definition in support of this.  They are of course correct; however, here they might have done well to read Williams:

“No matter how functionally dependent a gene may be, and no matter how complicated its interactions with other genes and environmental factors, it must always be true that a given gene substitution will have an arithmetic mean effect on fitness in any population.” (G.C.Williams, Adaptation and Natural Selection).

The point is that at any given moment it must be true that you can divide anything, including fitness, into components by whatever criteria you choose.  The other point is that I have used that quote for years as a straw man, and I simply cannot believe that I just used it in a positive setting!  What they are really complaining about is whether or not that partitioning is meaningful.  Their point is thus incorrect in that yes, you can partition fitness into direct and inclusive components, but it is correct that in a non-additive system that partitioning will be good for the moment, and will qualitatively change every time the conditions change.

Their second point is that this applies both to Hamilton’s original formulation of inclusive fitness and to the neighbor modulated, or direct, fitness approach.  They make the point that the direct fitness approach is a regression method, and regression is not a causal analysis, that in fact, it is little more than a glorified correlation:

regression equation

As we all know correlation is not causation.  The way regression is supposed to be used is to find the best prediction of Y given a known X.  This is the classic problem that I discussed as recently as last week.  Yes, we should all be using path analysis, yes it is a lot of work and, as often as not, we don’t use path analysis.  Nevertheless, there has been a lot of darn good work on selection has used a regression approach, so I, at least, hesitate to dismiss correlational approaches out right.

There is another important point here that strikes close to home.  That is, contextual analysis not only is a regression approach, but as I have shown elsewhere (Goodnight, 2013. Evolution 67: 1539-1548) contextual analysis uses the SAME regression equation used in the direct fitness approach.  So, why do I like contextual analysis and not like the direct fitness approach?  It turns out that there is a difference between the two approaches, and the difference is exactly the problem that Allen et al. are complaining about.  When using contextual analysis a tangent is calculated for the fitness surface at the point that the population currently occupies.  This tangent is used to calculate the strength of selection acting on the population at the current moment.  This calculation is frequently used to project the future potential response to selection, but the this is an extension, not a basic part of the model.  In contrast, the direct fitness approach establishes the equation at the current state of the population, and then the equation is solved for the conditions under which the slope (dW/dX) equals zero.  This, then is the problem that Allen et al. identified.  Using the kin selection approach we extrapolate from the current conditions to identify the optimal conditions that the population is presumably moving towards.  This extrapolation works fine in a linear system, but such extrapolations are notoriously problematical in complex non-linear systems.

CA VS kin sel

So, as far as this point goes, Allen et al. and I are on the same page.  Kin selection has a serious problem because it is an optimality approach that uses extrapolation of the current conditions in a non-linear complex system to predict the outcome of evolution.  We actually saw the same thing happen with optimal foraging theory.  Twenty years ago it was a hot topic.  Now days it basically doesn’t exist.  When I ask people about it the general answer seems to be that it only works in overly simplistic situations, and at most can provide a qualitative guide to the real world, which is acknowledged to be a complex system.

There is actually a fairly confusing ambiguity in the paper over this topic.  The real problem with kin selection stems from it being based in optimality theory, and thus requires simplistic assumptions so that it is possible to extrapolate from current to future conditions.  In my mind this would bring all optimality approaches into question.  Nevertheless in the discussion they bring in game theory, which is a variant on optimality theory, as one of the saviors of sociobiology.  It seems to me that if kin selection is suspect, then game theory ought to be just as suspect.  Perhaps I am wrong, and perhaps one of my readers can explain it to me.

It is the last part where Allen et al and I part ways.  In their last section (common-sense approaches to evolutionary theory) they state: “The target of selection is not the individual, but the allele or the genomic ensemble that affects behavior.”  This just floored me.  They have just explained to us that biological systems are complex, and yet somehow they fail to understand that genetic systems are complex?  Kin selection can be useful for developing an intuitive or qualitative grasp of social evolution, but for many reasons, including those given by Allen et al. it fails when it is applied to the real world.  Similarly, purely genetic models can be useful for developing intuitive and qualitative understandings of evolution, but for many of the same reasons they fail when applied to the real world.  Selection acts on the phenotype, not genes, and that is a fact.  Even in rare situations where we see selection acting on the sequence of a gene, it is in fact acting on the genes phenotype, not on the gene as a purveyor of information.

fallen runner

Like New Zealand runner Nikki Hamblin, Allen, Nowak and Wilson ran a good race, but ultimately fell short. (http://www.stuff.co.nz/sport/other-sports/5522807/Hamblin-protest-fails-after-world-champs-fall)

Introduction to Contextual Analysis

Posted: November 26th, 2013 by Charles Goodnight

First off, I have been told that you can’t talk about social evolution without mentioning kin selection:  “kin selection”.  With that done, lets now talk about contextual analysis.  (Ok, lets be honest, in future posts I will more fully diss kin selection.  Suffice it to say, as presently constructed it simply makes no sense from a phenotypic, or for that matter, a reality based perspective.)

The basic idea with contextual analysis is that we do a standard Arnold/Wade selection analysis almost exactly like I described it last week, thus the first thing of which to remind you is that we are talking about phenotypic selection and, at least as originally formulated and as typically used in experimental situations, we are talking about the selection vector, S, and the selection gradient b = P-1S.

R = G P-1S = Gβ

The difference is that the S vector will include traits measured on more than one level of organization.  For example, in a standard group selection setting, both traits measured on the organism and on the group would be included in the selection analysis.  These group level traits could potentially be summary traits for organismal level traits, or they could be traits that only can be measured on the group. As an example, an individual trait might be the leaf area of a plant, then a group summary could be the group mean leaf area, and group size might be a contextual trait.

CA S vector

In this S vector the  ΔZ1 through ΔZN are observed changes in N organismal level traits, the  ΔZ1 through ΔZN are observed changes in the group mean of the N organismal level traits, and the green ΔC1 through ΔCK are observed changes in the group mean of K “contextual” traits that can only be measured on the group.

As with any selection analysis selection of the traits is critical.  From a practical perspective the total number of traits needs to be kept small.  As anybody who has worked with real data knows multivariate methods eat degrees of freedom for lunch.


In addition, it is important to thoughtfully select the traits based on the biology of the organism.  One major issue with selection analyses in general is that the outcome of the analysis may qualitatively change depending on the selection of the traits.  For this reason people are beginning to advocate for using path analysis as in preference to a standard multivariate regression (e.g., Scheiner, Mitchell & Callahan J. Evol. Biol. 13:423-433.  I believe that Michael Morrissey is working on a paper on the topic, but I can’t find it right now)

The problem of thoughtfully choosing the correct trait becomes a bit more complicated when you move to contextual or group summary traits.  Consider that in the above I defined the summary trait as the group mean of the organismal traits.  In fact, you can immediately ask the question whether it should be the group mean, or some jackknifed version of the group mean that leaves out the focal individual.  Also, there may be times when the group mean isn’t important, rather it is some trait of the most extreme individual.  For example, in lions usurping males often kill the cubs, and for cubs the probability of survival is influenced by the ability of the dominant male to fend off other males.  In this case, the group mean could be very misleading.

lions fighting - carole white_medium

The survival of the cubs may depend on the outcome of this fight. (http://www.governorscamp.com/blog/migration-wildlife-update-masai-mara)

In any case, once the traits are identified it is then possible to do a regression of fitness on phenotype, giving the multilevel selection gradient.   This raises the interesting point that there is only a single dependent variable (relative fitness), thus, fitness can only be assigned at one level.  Thus, in our classic group selection example, we assign fitness at the level of the organism, and measure traits on the organism and on the group to which they belong.  In essence, using a perhaps bizarre perspective, we are treating the group level traits as if they were individual traits, thus we are treating, say, population size as the population size that an individual experiences.

This, then, gives us a very nice definition of group selection:  Group selection is occurring when there is significant selection on a contextual trait.  Or in more general terms, group selection is occurring when the fitness of an individual is a function of the characteristics of the group to which they belong.

I will not lie:  When I started out I did not believe that contextual analysis would work.  It was a HUGE paradigm shift for me (Kuhn, forgive me! I really try to avoid that term! ).  First, as a graduate student I had always used individual fitness and group mean fitness, and group selection to me was the differential survival and reproduction of groups.  Contextual analysis does neither of these things.  Nevertheless, it does work – Next week I will talk about how I tried, and failed, to prove that contextual analysis would not work – and for the moment I will ask you to believe it works.

In any case this change in perspective significantly broadens the concept of group selection.  When Maynard-Smith (1964. Nature 201: 1145-1147) first imposed himself on the group selection debate he basically defined a group as something with clear boundaries; metaphorically speaking, something you can walk around.  Contextual analysis makes it clear that the phenomenon of what Maynard-Smith called group selection is part of a much larger phenomenon.  Contextual analysis works equally well with “continuous” groups.  In a continuous plant population a contextual trait might be the mean leaf area of all plants within a 30 cm radius of the focal plant.  Notice that in this case every individual is at the center of their own “group”, so unlike classic group selection every individual will have a unique value for their contextual traits.  Another point is that the groups need not be physical at all.  For species with kin recognition selection on kin groups makes perfect sense.  Finally, it quickly becomes clear that many forms of frequency dependent and density dependent selection are indeed forms of multilevel selection.

Basically, what contextual analysis shows is that classic group selection is part of some sort of multivariate continuum that at one end has Maynard-Smith’s clearly delineated groups and at the other end(s) has frequency dependent selection, continuous groups and “virtual” groups.  If you want to say that there are some things that are group selection and others that are frequency dependent selection you can do that, but since they are on a continuum, there can be no objective criterion for drawing that line and where you draw it will inevitably be arbitrary.



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