@article{4231, abstract = {The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nμ > 1). We show how the method can be modified for small mutation rates (4Nμ → 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.}, author = {Barton, Nicholas H and De Vladar, Harold}, journal = {Genetics}, number = {3}, pages = {997 -- 1011}, publisher = {Genetics Society of America}, title = {{Statistical mechanics and the evolution of polygenic quantitative traits}}, doi = {10.1534/genetics.108.099309}, volume = {181}, year = {2009}, } @article{4242, abstract = {Felsenstein distinguished two ways by which selection can directly strengthen isolation. First, a modifier that strengthens prezygotic isolation can be favored everywhere. This fits with the traditional view of reinforcement as an adaptation to reduce deleterious hybridization by strengthening assortative mating. Second, selection can favor association between different incompatibilities, despite recombination. We generalize this “two allele” model to follow associations among any number of incompatibilities, which may include both assortment and hybrid inviability. Our key argument is that this process, of coupling between incompatibilities, may be quite different from the usual view of reinforcement: strong isolation can evolve through the coupling of any kind of incompatibility, whether prezygotic or postzygotic. Single locus incompatibilities become coupled because associations between them increase the variance in compatibility, which in turn increases mean fitness if there is positive epistasis. Multiple incompatibilities, each maintained by epistasis, can become coupled in the same way. In contrast, a single-locus incompatibility can become coupled with loci that reduce the viability of haploid hybrids because this reduces harmful recombination. We obtain simple approximations for the limits of tight linkage, and strong assortment, and show how assortment alleles can invade through associations with other components of reproductive isolation.}, author = {Barton, Nicholas H and De Cara, Maria}, journal = {Evolution; International Journal of Organic Evolution}, number = {5}, pages = {1171 -- 1190}, publisher = {Wiley}, title = {{The evolution of strong reproductive isolation}}, doi = {10.1111/j.1558-5646.2009.00622.x}, volume = {63}, year = {2009}, } @article{3870, abstract = {Games on graphs with omega-regular objectives provide a model for the control and synthesis of reactive systems. Every omega-regular objective can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (Buchi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. We show that finitary parity games can be solved in polynomial time, which is not known for infinitary parity games. For finitary Streett games, we give an EXPTIME algorithm and show that the problem is NP-hard. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian}, journal = {ACM Transactions on Computational Logic}, number = {1}, publisher = {ACM}, title = {{Finitary winning in omega-regular games}}, doi = {10.1145/1614431.1614432}, volume = {11}, year = {2009}, } @article{517, author = {Barton, Nicholas H}, journal = {Genetics Research}, number = {5-6}, pages = {475 -- 477}, publisher = {Cambridge University Press}, title = {{Identity and coalescence in structured populations: A commentary on 'Inbreeding coefficients and coalescence times' by Montgomery Slatkin}}, doi = {10.1017/S0016672308009683}, volume = {89}, year = {2008}, }