3,185 research outputs found
The Population Genetic Signature of Polygenic Local Adaptation
Adaptation in response to selection on polygenic phenotypes may occur via
subtle allele frequencies shifts at many loci. Current population genomic
techniques are not well posed to identify such signals. In the past decade,
detailed knowledge about the specific loci underlying polygenic traits has
begun to emerge from genome-wide association studies (GWAS). Here we combine
this knowledge from GWAS with robust population genetic modeling to identify
traits that may have been influenced by local adaptation. We exploit the fact
that GWAS provide an estimate of the additive effect size of many loci to
estimate the mean additive genetic value for a given phenotype across many
populations as simple weighted sums of allele frequencies. We first describe a
general model of neutral genetic value drift for an arbitrary number of
populations with an arbitrary relatedness structure. Based on this model we
develop methods for detecting unusually strong correlations between genetic
values and specific environmental variables, as well as a generalization of
comparisons to test for over-dispersion of genetic values among
populations. Finally we lay out a framework to identify the individual
populations or groups of populations that contribute to the signal of
overdispersion. These tests have considerably greater power than their single
locus equivalents due to the fact that they look for positive covariance
between like effect alleles, and also significantly outperform methods that do
not account for population structure. We apply our tests to the Human Genome
Diversity Panel (HGDP) dataset using GWAS data for height, skin pigmentation,
type 2 diabetes, body mass index, and two inflammatory bowel disease datasets.
This analysis uncovers a number of putative signals of local adaptation, and we
discuss the biological interpretation and caveats of these results.Comment: 42 pages including 8 figures and 3 tables; supplementary figures and
tables not included on this upload, but are mostly unchanged from v
A Morse index theorem for elliptic operators on bounded domains
Given a selfadjoint, elliptic operator , one would like to know how the
spectrum changes as the spatial domain is
deformed. For a family of domains we prove that the
Morse index of on differs from the Morse index of on
by the Maslov index of a path of Lagrangian subspaces on the
boundary of . This is particularly useful when is a domain
for which the Morse index is known, e.g. a region with very small volume. Then
the Maslov index computes the difference of Morse indices for the "original"
problem (on ) and the "simplified" problem (on ). This
generalizes previous multi-dimensional Morse index theorems that were only
available on star-shaped domains or for Dirichlet boundary conditions. We also
discuss how one can compute the Maslov index using crossing forms, and present
some applications to the spectral theory of Dirichlet and Neumann boundary
value problems.Comment: 21 pages; weaker regularity assumptions than in the first versio
The Generic Approximation Lemma
The approximation lemma is a simplification of the well-known take lemma, and is used to prove properties of programs that produce lists of values. We show how the approximation lemma, unlike the take lemma, can naturally be generalised from lists to a large class of datatypes, and present a generic approximation lemma that is parametric in the datatype to which it applies. As a useful by-product, we find that generalising the approximation lemma in this way also simplifies its proof
Voluntary Euthanasia and 'Assisted Dying' in Tasmania: A Response to Giddings and McKim
This paper provides a consolidated response to the Honourable Lara Giddings (MP) and the Honourable Nick McKim (MP), offering analysis and critique of their ‘Voluntary Assisted Dying - A Proposal for Tasmania' (2013) paper. Their paper puts forward a radical proposal that, if legislated, would make Tasmania one of a very small number of jurisdictions in the world to legalise voluntary euthanasia and assisted suicide. From close examination of their paper and proposed model, it is argued that while a number of their claims are evidence based, others are unsubstantiated. Their claims often represent one perspective or type of response to complex issues and questions -- the answers to which may never be agreed upon by relevant stakeholders. This paper draws on international literature as well as insights from well-credentialed Tasmanian practitioners to analyse Giddings and McKim' (2013) representation of what has (and has not) happened elsewhere and to critique their bid for euthanasia law reform in Tasmania. We conclude that the paper produced by Ms Giddings and Mr McKim does not constitute a compelling evidence-based case for changing the law. The risks of proceeding with the model that they propose are not justified
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