Discontinuity in codimension-k manifold decompositions

AbstractMuch has come in the study of the decompositions of manifolds having manifold fibers from the examination of the discontinuity set of the decomposition map. The main result of this paper gives a limitation to the extent of the discontinuity set. Let π:M → B be a codimension-k manifold decomposition of M, an (n + k)-manifold, into sets having the shape of closed oriented n-manifolds. Suppose that the dimension of B is finite. Then D, the discontinuity set of π, does not locally separate B. The result is proved using the Leray-Grothendieck spectral sequence for the map π along with careful manipulation of subsets of the target space B. Crucial to the proof is the manipulation of the coefficient modules used in the cohomology of both M and B. Under the assumption that the dimension of B is finite, we go on to prove that if the point preimages of the map π have trivial first homology, the dimension of D is less than or equal to k − 2 for k ⩾ 2. The same conclusion is reached if the point preimages have the shape of S1

Variance component analysis of skin and weight data for sheep subjected to rapid inbreeding

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Rapid Independent Trait Evolution despite a Strong Pleiotropic Genetic Correlation

This is the publisher's version. It can also be found here:http://dx.doi.org/10.1086/661907Genetic correlations are the most commonly studied of all potential constraints on adaptive evolution. We present a comprehensive test of constraints caused by genetic correlation, comparing empirical results to predictions from theory. The additive genetic correlation between the filament and the corolla tube in wild radish flowers is very high in magnitude, is estimated with good precision, and is caused by pleiotropy. Thus, evolutionary changes in the relative lengths of these two traits should be constrained. Still, artificial selection produced rapid evolution of these traits in opposite directions, so that in one replicate relative to controls, the difference between them increased by six standard deviations in only nine generations. This would result in a 54% increase in relative fitness on the basis of a previous estimate of natural selection in this population, and it would produce the phenotypes found in the most extreme species in the family Brassicaceae in less than 100 generations. These responses were within theoretical expectations and were much slower than if the genetic correlation was zero; thus, there was evidence for constraint. These results, coupled with comparable results from other species, show that evolution can be rapid despite the constraints caused by genetic correlations

Strong ecological but weak evolutionary effects of elevated CO2 on a recombinant inbred population of Arabidopsis thaliana

Summary • Increases in atmospheric CO 2 concentration have an impact on plant communities by influencing plant growth and morphology, species interactions, and ecosystem processes. These ecological effects may be accompanied by evolutionary change if elevated CO 2 (eCO 2 ) alters patterns of natural selection or expression of genetic variation. • Here, a statistically powerful quantitative genetic experiment and manipulations of CO 2 concentrations in a field setting were used to investigate how eCO 2 impacts patterns of selection on ecologically important traits in Arabidopsis thaliana ; heritabilities, which influence the rate of response to selection; and genetic covariances between traits, which may constrain responses to selection. • CO 2 had strong phenotypic effects; plants grown in eCO 2 were taller and produced more biomass and fruits. Also, significant directional selection was observed on many traits and significant genetic variation was observed for all traits. However, no evolutionary effect of eCO 2 was detected; patterns of selection, heritabilities and genetic correlations corresponded closely in ambient and elevated CO 2 environments. • The data suggest that patterns of natural selection and the quantitative genetic parameters of this A. thaliana population are robust to increases in CO 2 concentration and that responses to eCO 2 will be primarily ecological