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It is standard practice to model site-to-site variability of substitution rates by discretizing a continuous distribution into a small number, K, of equiprobable rate categories. We demonstrate that the variance of this discretized distribution has an upper bound determined solely by the choice of K and the mean of the distribution. This bound can introduce biases into statistical inference, especially when estimating parameters governing site-to-site variability of substitution rates. Applications to two large collections of sequence al
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