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Let $\alpha \colon X \to Y$ be a general degree $r$ primitive map of nonsingular, irreducible, projective curves over an algebraically closed field of characteristic zero or larger than $r$. We prove that the Tschirnhausen bundle of $\alpha $ is semistable if $g(Y) \geq 1$ and stable if $g(Y) \geq 2$.

Abstract

Data accompanying the paper Szydlowski et al. "Macrophyte and snail community responses to 30 years of population declines of invasive rusty crayfish (Faxonius rusticus)." Macrophytes and snails were sampled in ten lakes in Vilas County, Wisconsin, USA during summer sampling events in 1987, 2002, 2011, and 2020. Lakes had varying levels of invasion by F. rusticus, which affected measures of macrophytes and snails. Macrophytes were sampled using a point-intercept transect method and snails were sampled using different sampler types which were dependent on substrate. Macrophytes were sampled at 6-14 sites per lake and snails were sampled at 16-31 sites per lake. Crayfish were regularly sampled at either 24 or 36 sites per lake between 1987 and 2020. Overall, this dataset provides abundance and richness data for over 25 species of snails and over 40 species of macrophytes in 10 north temperate lakes.

Synopsis Mechanistically connecting genotypes to phenotypes is a longstanding and central mission of biology. Deciphering these connections will unite questions and datasets across all scales from molecules to ecosystems. Although high-throughput sequencing has provided a rich platform on which to launch this effort, tools for deciphering mechanisms further along the genome to phenome pipeline remain limited. Machine learning approaches and other emerging computational tools hold the promise of augmenting human efforts to overcome these obstacles. This vision paper is the result of a Reintegrating Biology Workshop, bringing together the perspectives of integrative and comparative biologists to survey challenges and opportunities in cracking the genotype to phenotype code and thereby generating predictive frameworks across biological scales. Key recommendations include promoting the development of minimum “best practices” for the experimental design and collection of data; fostering sustained and long-term data repositories; promoting programs that recruit, train, and retain a diversity of talent; and providing funding to effectively support these highly cross-disciplinary efforts. We follow this discussion by highlighting a few specific transformative research opportunities that will be advanced by these efforts.