A week late and a dollar short, but lets continue comparing matrices. Continuing on with my blatant endorsement of statistical methods attached to my name. . . Last time I talked about the “Rank”/“Signed Bartlett”/”Modified Mantel” tests for comparing the dimension size and shape of a pair of matrices. This is only one of several […]

### Statistical tests for comparing matrices

I have been remiss. Quite a few years ago I found myself in the position of wanting to compare two genetic covariance matrices. At the time it was before the Flury hierarchy had been suggested by Pat Phillips (Phillips & Arnold 1999. Evolution 53: 1506-1515), so I found myself in a position of needing to […]

### Individuality, Microbiomes, and organisms

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), […]

### What is “additive variance” in genetically uniform populations?

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 […]

### More on fitness assignments and individuality

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 […]

### Gardner’s theory of multilevel selection 3: the discussion

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 […]

### Gardner’s theory of multilevel selection: Parsing the Model

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 […]

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

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 […]

### A one line proof of Fishers fundamental theorem

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 […]

### Genes, society, sexism and racism

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” […]

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