@inbook{3575,
abstract = {The Jacobi set of two Morse functions defined on a common - manifold is the set of critical points of the restrictions of one func- tion to the level sets of the other function. Equivalently, it is the set of points where the gradients of the functions are parallel. For a generic pair of Morse functions, the Jacobi set is a smoothly embed- ded 1-manifold. We give a polynomial-time algorithm that com- putes the piecewise linear analog of the Jacobi set for functions specified at the vertices of a triangulation, and we generalize all results to more than two but at most Morse functions.},
author = {Herbert Edelsbrunner and Harer, John},
booktitle = {Foundations of Computational Mathematics},
pages = {37 -- 57},
publisher = {Springer},
title = {{Jacobi sets of multiple Morse functions}},
doi = {10.1017/CBO9781139106962.003},
volume = {312},
year = {2004},
}
@inbook{3587,
author = {Ulrich, Florian and Heisenberg, Carl-Philipp},
booktitle = {Fish development and genetics : the zebrafish and medaka models},
editor = {Korzh, Vladimir and Gong, Zhiyuan},
pages = {39 -- 86},
publisher = {World Scientific Publishing},
title = {{Gastrulation in zebrafish}},
volume = {2},
year = {2004},
}
@misc{3595,
abstract = {Genome sizes vary enormously. This variation in DNA content correlates with effective population size, suggesting that deleterious additions to the genome can accumulate in small populations. On this view, the increased complexity of biological functions associated with large genomes partly reflects evolutionary degeneration.},
author = {Charlesworth, Brian and Nicholas Barton},
booktitle = {Current Biology},
number = {6},
pages = {R233 -- R235},
publisher = {Cell Press},
title = {{Genome size: Does bigger mean worse?}},
doi = {10.1016/j.cub.2004.02.054},
volume = {14},
year = {2004},
}
@article{3614,
abstract = {We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(Δz̄) =inline imagewhere n is the number of loci contributing to the trait variance, VA(1)=VA is the additive genetic variance, and VA(k) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*A), is closely related to var(Δz̄); (V*A) (1 –F)inline imageThus, epistasis inflates the expected additive variance above VA(1 –F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*AA)). This is not true in general with diploidy, because dominance alone can reduce (V*A) below VA(1 –F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(Δz̄)=inline image=1 (2F) kVA(k) and (V*A) = (1 –F)inline imagek(2F)k-1VA(k) With dominance (and even without epistasis), var(Δz̄)and (V*A) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*A)(1 –F) VA+ 4FVAA+2FVD+2FCAD, where CAD is a sum of two terms describing covariances between additive effects and dominance and additive × dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase VA, we question the evolutionary importance of such increases.},
author = {Nicholas Barton and Turelli, Michael},
journal = {Evolution; International Journal of Organic Evolution},
number = {10},
pages = {2111 -- 2132},
publisher = {Wiley-Blackwell},
title = {{Effects of allele frequency changes on variance components under a general model of epistasis}},
doi = {10.1111/j.0014-3820.2004.tb01591.x},
volume = {58},
year = {2004},
}
@article{3615,
abstract = {We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., ρ2ij > 3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.},
author = {Turelli, Michael and Nicholas Barton},
journal = {Genetics},
number = {2},
pages = {1053 -- 1079},
publisher = {Genetics Society of America},
title = {{Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and GxE interactions}},
doi = {10.1534/genetics.166.2.1053},
volume = {166},
year = {2004},
}