A power law for cells

Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.

An economic analysis of unilateral refusals to license intellectual property

The intellectual property laws in the United States provide the owners of intellectual property with discretion to license the right to use that property or to make or sell products that embody the intellectual property. However, the antitrust laws constrain the use of property, including intellectual property, by a firm with market power and may place limitations on the licensing of intellectual property. This paper focuses on one aspect of antitrust law, the so-called “essential facilities doctrine,” which may impose a duty upon firms controlling an “essential facility” to make that facility available to their rivals. In the intellectual property context, an obligation to make property available is equivalent to a requirement for compulsory licensing. Compulsory licensing may embrace the requirement that the owner of software permit access to the underlying code so that others can develop compatible application programs. Compulsory licensing may undermine incentives for research and development by reducing the value of an innovation to the inventor. This paper shows that compulsory licensing also may reduce economic efficiency in the short run by facilitating the entry of inefficient producers and by promoting licensing arrangements that result in higher prices.