Circular 87

High rates of female breeding success and offspring survival are the two major factors in productivity of any commercial livestock industry. To im prove breeding success and offspring survival, the herd m anager will establish selection criteria and choose which males and females will breed. The genetics or characteristics of future animals will reflect their parentage. Selection pressure is evident in both wild and captive populations of herbivores. Predators, environment, and human harvest strategies are a few forces which influence the characteristics of freeranging populations of reindeer, caribou, moose, wapiti, etc. In livestock production systems, herd managers often breed for specific characteristics such as larger body size, high birth and growth rates, leanness, etc. A single color or combination of colors has been another characteristic often selected by purebred cattle producers as well as reindeer herders

Relative Entropy in Biological Systems

In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy - that is, the Kullback--Leibler divergence, or various generalizations of this - provides a quantitative measure of how far from equilibrium the system is. We explain various theorems that give conditions under which relative entropy is nonincreasing. In biochemical applications these results can be seen as versions of the Second Law of Thermodynamics, stating that free energy can never increase with the passage of time. In ecological applications, they make precise the notion that a population gains information from its environment as it approaches equilibrium.Comment: 20 page

Network Models

Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of networks. We show that each network model gives rise to an operad, whose operations are ways of assembling a network of the given kind from smaller parts. Such operads, and their algebras, can serve as tools for designing networks. Technically, a network model is a lax symmetric monoidal functor from the free symmetric monoidal category on some set to $\mathbf{Cat}$, and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction.Comment: 46 page