Measuring the heritability of contextual traits.

First a plug for an upcoming conference.  If you are interested in artificial life there is a conference, Alife 14, being run by, among others, a friend of mine, Hiroki Sayama.  There is one week left submit abstract, and a good time should be had by all.  .  This meeting will take place in New York at the end of July, beginning of August.

I have been looking for a data set that could be used to illustrate calculating the heritability of contextual traits.  Happily one came along at the last minute, although I had to do some hard thinking to figure out how to interpret it as a contextual trait. . .

The paper I am talking about is a new one in Evolution,  Edward, Poissant, Wilson and Chapman 2014, Sexual conflict and interacting phenotypes:  A quantitative genetic analysis of fecundity and copula duration in Drosophila melanogaster. Evolution doi:10.1111/evo.12376  (http://onlinelibrary.wiley.com/doi/10.1111/evo.12376/abstract).  This is a well-done and analyzed article that is well worth reading.  However, as is my wont, I will misuse their data for my own purposes.  Thus, the caveat of the day is that I am in no way complaining about what they published, just trying to use their data to illustrate a point.

drosophila-mating

In the interests of having a picture of real organisms, I am including a pair of mating Drosophila.   The Edward et al (2014 Evolution) study is about the genetics of mating in Drosophila.  (Picture taken from http://www.wired.com/wiredscience/2011/06/flies-alter-their-ejaculate-to-get-the-best-bang-for-the-buck/)

What they did in this study was to use a half sib design, crossing each of 16 sires to 3 dams.  They then took the offspring from these crosses and put them in something that I once called an “intermixing ability” type design (sad story why I didn’t call it “ecological combining ability”) (Goodnight 1991 Am. Nat. 138, 342-54).  That is daughters and sons from each cross were crossed in all possible manners in a manner similar to a combining ability study, except that the progeny were not collected and raised, rather the mating behavior of the pair was studied.

This design is an important conceptual shift.  In effect they are treating the mating pair as a group, and the productivity of that group is a function of both the male and female phenotype, and the interaction between them.  My one complaint about their design, which I am sure is a not so much an oversight on their part, but a consequence of the already large size of the experiment, is that they only had one replicate for each full sib family pair, thus it isn’t possible to fully analyze the interaction between cross types.  Given that doing this would have at least doubling the size of the experiment, the decision not to have replicates within cells is hardly surprising.

They then measured three traits.  First, for each female they measured the egg laying rate of the females while they were still virgin, and before being placed with the male, the duration of mating, and the egg laying rate after mating.   Here is where I am going to do a little bit of perhaps inappropriate slight of hand.  First, I am going to call the virgin egg laying rate an “individual trait” of the female since it is done when there is no possible interaction, then second I am going to call the mating duration a “contextual trait” since it is a function of the interaction between the male and female, and third, I will call the post fertilization egg laying rate the “fitness trait”.

Doing this we can then do a regression of post-mating oviposition rate (fitness) on pre-mating oviposition rate (individual trait) and mating duration (contextual trait):

CA of Dros. mating

Click on the table for a clearer view.

It would have been great if the duration (Dur) and the interaction had been significant, but that’s what you get for using data designed for another purpose.  What this is basically telling us is that to the extent that selection is acting on egg laying rate, there is strong selection on female fertility (as measured by premating egg number) but no detectable selection on the copulation duration.

Even though there is no selection on the contextual trait of duration, we can nevertheless measure the heritability of this trait (remember selection and heritability are different things!).  What we need to do is simply do a nested ANOVA of duration, and since we are focusing on the females we will only include the sire and dam of the female.  We shouldn’t expect much since males are assigned to females in all possible combination there can be no population structure, and thus no shifting of the male genetics over to heritability measured using only females.  In any case the analysis looks like this:

dur heritability random assoc.

Click on the table for a clearer view.

The sire variance component is 0.56, so the additive genetic variance for mating duration is VA =  4*0.56  =  2.24.  Since the dam variance component is negative, we can say that VD = 0.  The total variance is 16.28, which implies that the heritability = h2 = 0.14.

At this point we can artificially impose population structure.  A convenient one would be to allow only brother sister mating.  The problem is that, with the data structured the way it is, it is not possible to include dams within sires in this analysis of a subset of the data, still we can get the effective additive genetic variance.  Note that this mating structure enforces a covariance between two partners in the mating group, and should affect the heritability.

variance estimates brother sister mating

Click on the table for a clearer view.

 

Indeed it does.  In this case the variance among sires goes up to 3.87, thus the effective additive genetic variance goes up to eVA = 15.48, and the heritability goes way up to eh2 =0.77.

This is the point I am trying to make about measuring the heritability of contextual traits.  Using the same data set, if we design our experiment using random mixing of interacting partners then the heritability will miss a lot of the variance that can contribute to a response to selection. In this case nearly all of it.  In contrast if we use a breeding design that preserves those interactions we can pull in the association that the interaction structure generates.  Designing such experiments will be like standard quantitative genetics, only hard, and the resulting experiments will be like standard breeding designs only big.  (For the uninitiated that is a joke.  Breeding designs are notoriously difficult to design, and result in notoriously huge experiments.)

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