We present a genomewide cross-species analysis of regulation for broad-acting transcription factors in yeast. Our model for binding site evolution is founded on biophysics: the binding energy between transcription factor and site is a quantitative phenotype of regulatory function, and selection is given by a fitness landscape that depends on this phenotype. The model quantifies conservation, as well as loss and gain, of functional binding sites in a coherent way. Its predictions are supported by direct cross-species comparison between four yeast species. We find ubiquitous compensatory mutations within functional sites, such that the energy phenotype and the function of a site evolve in a significantly more constrained way than does its sequence. We also find evidence for substantial evolution of regulatory function involving point mutations as well as sequence insertions and deletions within binding sites. Genes lose their regulatory link to a given transcription factor at a rate similar to the neutral point mutation rate, from which we infer a moderate average fitness advantage of functional over nonfunctional sites. In a wider context, this study provides an example of inference of selection acting on a quantitative molecular trait.binding energy ͉ transcriptional regulation ͉ quantitative molecular trait R egulatory elements can often be distinguished from background sequence by their evolutionary conservation. At the same time, it has become clear that many regulatory functions are not widely conserved, but are specific to certain species or clades (1). Thus, it seems likely that the evolution of regulatory function and, in particular, of cis-regulatory elements is a key component in evolutionary innovation and the differentiation between species (2-7). However, functional changes in regulation are difficult to gauge from sequence divergence alone. For example, many different sequence states of a promoter may lead to similar binding of transcription factors and thus have similar effects on the transcription of a regulated gene. Thus, discerning function from sequence requires a phenotype for regulatory elements and an evolutionary model to quantify natural selection acting on this phenotype.In this article we address regulatory evolution from a biophysical perspective. We show that the binding energy of a transcription factor (TF) provides a quantitative phenotype for its target sites, and we develop a predictive model for binding site evolution based on this phenotype. A key ingredient of this model is the mapping from genotype to phenotype, that is, the sequence dependence of the binding energy for a given TF. Direct energy measurements are available for a few (mostly prokaryotic) transcription factors (8, 9), but low-throughput experiments generally do not provide enough data to fully constrain the energy function. By contrast, high-throughput binding assays (10, 11) provide copious, if indirect, data on TF binding to promoter regions, and we use recently developed methods to infer binding energies from ...