![]() Thus the chosen model should have enough parameters to adequately explain the data-but no more. In addition, the biological meaning of each parameter becomes harder to decipher so the explanatory power of the model decreases ( Figure 1). The degree to which a model fits the data at hand (accuracy) is always improved by adding more parameters (complexity), but since the amount of data remains constant the statistical uncertainty about each parameter increases. The task of deciding amongst these competing models is known as statistical model selection and can be thought of as a trade-off between model accuracy and model complexity. More complex models loosen these assumptions, allowing heterogeneity in the process of sequence change, but they can be reliably applied to larger datasets only. The simplest models assume that all types of mutation are equivalent and that all sites in a sequence change at the same rate. There is a bewildering hierarchy of substitution models available, each making a different and specific set of assumptions about the evolutionary process of sequence change. Statistical tools, called nucleotide or amino acid substitution models, are therefore used to estimate genetic distances between sequences. Unfortunately, this approach underestimates the amount of evolutionary change because it does not account for the fact that each site may change more than once during evolutionary history. Genetic distances can be calculated for a pair of sequences by simply counting the number of nucleotides or amino acids that differ between them. The simplest weapon in the armoury of evolutionary genetics is genetic distance, a measure of the number of evolutionary changes between sequences from different organisms. Fisher, published only fifty years after Darwin's death, is full of equations. The Genetical Theory of Natural Selection by R. ![]() Consequently, the mathematical foundations of evolutionary genetics have, somewhat unusually for biology, tended to precede the data to which they are applied. Of course, the discrete, ordered nature of genetic information and the stochastic character of Mendelian inheritance have naturally lent themselves to numerical analysis. Much of it concerns the development of an expanding arsenal of mathematical and statistical techniques, necessary to do battle with the relentless onslaught of gene and genome sequences. Modern research in evolutionary biology can make for less easy reading. ![]() A good thing too, you might think, and it is undoubtedly true that Darwin's clear and flowing narrative style helped ensure the popularity of his writings.
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