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The residuals were analysed to understand the fit of the negative binomial model to the data.

Initially, we analysed pairs of exomes and fitted a binomial model to the genome-wide distribution of read depth data for the reference and the test sample (see Section 3).

Goodness-of-fit of the final models were evaluated visually by comparing the estimated cumulative probability distributions from the negative binomial model to the observed cumulative probability distribution and comparing the value of the deviance factor statistic and the Pearson's chi-squared statistic to 1.

We also performed an independent test using DESeq (Anders and Huber, 2010), which fits a negative binomial model to the read count data, and observed considerable overlap of differentially expressed genes predicted by these two independent statistical methods (supplementary material Fig. S4C,D and Table S4).

The algorithm of edgeR fits a negative binomial model to the count data, estimates dispersion, and measures differences using the generalized linear model likelihood ratio test which is recommended for experiments with multiple factors, such as the simultaneous analysis of age and diet in our study.

The algorithm of edgeR fits a negative binomial model to the count data, estimates dispersion, and measures differences using the generalized linear model likelihood ratio test which is recommended for experiments with multiple factors, such as the simultaneous analysis of the effects of age and diet in our study.

We used ExomeDepth (Plagnol et al., 2012, available at http://cran.r-project.org/) to fit a robust beta-binomial model to the read count data.

The ability of the binomial model to predict the outcome was estimated using as cut-off point the mean of the fitted probabilities predicted by the model in order to transform them into a binary outcome [ 34].

Yuen et al. [2] introduced the bivariate compound binomial model to approximate the finite-time survival probability of the bivariate compound Poisson model with common shock.

We consider the Poisson, negative binomial, and sCMP(m) models where m=1,2,3,4 to describe the data distribution; Bailey (1990) previously considered a binomial model to describe the data.

In such scenarios, one can use zero-inflated Poisson or zero-inflated negative binomial model to fit the data [19].