Discussion of Shaw et al.

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The paper

Shaw, F. H., Promislow D. E. L., Tatar, M., Hughes, K. A., and Geyer, C. J. (1999).
Toward Reconciling Inferences Concerning Genetic Variation in Senescence in Drosophila melanogaster.
Genetics, 152, 553-566.

was discussed in the Statistical Genetics Seminar of the statistical genetics group in the departments of biostatistics and statistics at the University of Washington.

Discussion with Frank Shaw

One of the authors was present at the seminar and relayed some questions to the first author. The following is a somewhat edited e-mail exchange.

CJG: So some questions that arose in the discussion of your reanalysis of the Promislow-Tater and Hughes-Charlesworth data.

FHS: HC were in vials; PT were in big jars where there was real competition. I think this was discussed in the paper at some length.

CJG:

FHS: Not really. The real reason for the comparison was to see if the HC [Hughes and Charlesworth] ad hoc analysis gave the correct answers.

CJG:

FHS: I think that's the case. Of course, I never was satisfied with the confidence intervals that came out of that analysis, as I've never been easy with any confidence interval generated since then by MCMCML [Markov Chain Monte Carlo Maximum Likelihood] as I've over all the MA [Mutation Accumulation] work I'm currently doing.

CJG:

FHS: I thought the model was rather good, that different lines had different mortality trajectories, and that these were in part genetically determined. We started there, perhaps because that was the HC [Hughes and Charlesworth] idea. It was you, of course, who developed the statistical model that we used. It's hard to imagine what the missing data would be if variance parameters, making variance as a function of time were being estimated. The dimension of the problem grows a lot, it seems to me.

One of the frustrating aspects of that TRT [The Right Thing] paper was that pretty much everyone in the scenescence community had lost interest in these experiments by the time the paper was done. The Nature splash was over, and PT [Promislow and Tatar] had already published the data in two papers using the ad hoc analysis that HC employed. Ultimately, the experiments don't answer an interesting question, since, it was latterly concluded, MA [Mutation Accumulation] and AP [Antagonistic Pleiotropy] were expected to show the same thing.

CJG:

FHS: I think that the different mutation effects models (Keightley, Lynch, Geyer-Shaw), and their statistical properties are very interesting, but maybe you have already been over that [this refers to Shaw, Geyer, and Shaw (2002)].

CJG: In regard to your saying

Ultimately, the experiments don't answer an interesting question, since, it was latterly concluded, MA and AP were expected to show the same thing.

But was this clear before the TRT paper?

FHS:

I think that the idea that MA and AP weren't distinguishable was recognized as early as the publication of the earlier P-T papers. It was simply that they couldn't bring themselves to say so, since it would then mean that they were wasting their time. Same with our paper, though at least we were bringing in a new analysis technique.

CJG: In regard to your saying

It was you, of course, who developed the statistical model that we used. It's hard to imagine what the missing data would be if variance parameters, making variance as a function of time were being estimated. The dimension of the problem grows a lot, it seems to me.

I did contribute the basic idea of using MCMCML and what is now called generalized linear mixed model (GLMM) modeling, but the Gompertz curve and Logistic (Vaupel) curve, etc. you put in. And yes, the dimension of the problem would grow making estimation intractable if we hadn't used some low-dimensional model.

I was just wondering if everyone else got the point.

Addendum Requested by Bill Stewart

Curves

What does a Gompertz curve or that logistic curve look like?

Numbers for the parameters came from Table 3 in the paper (just the top row).

Variance as a Function of Time

So what about the additive genetic variance of log mortality rate as a function of time? Here we simulate (B, A, λ) triples from the estimated multivariate normal distribution variance-covariance matrix VA, again using the the parameters from Table 3 in the paper.

In the figure the variance of the green smear (Gompertz) or red smear (Logistic) at a particular time point is the V(t) in equation (4) of the paper or the analog for the Logistic curve.

Gompertz

Logistic