Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalising rate heterogeneity across sites in statistical
  phylogenetics   Phylogenetics uses alignments of molecular sequence data to learn about
evolutionary trees relating species. Along branches, sequence evolution is
modelled using a continuous-time Markov process characterised by an
instantaneous rate matrix. Early models assumed the same rate matrix governed
substitutions at all sites of the alignment, ignoring variation in evolutionary
pressures. Substantial improvements in phylogenetic inference and model fit
were achieved by augmenting these models with multiplicative random effects
that describe the result of variation in selective constraints and allow sites
to evolve at different rates which linearly scale a baseline rate matrix.
Motivated by this pioneering work, we consider an extension using a quadratic,
rather than linear, transformation. The resulting models allow for variation in
the selective coefficients of different types of point mutation at a site in
addition to variation in selective constraints.
  We derive properties of the extended models. For certain non-stationary
processes, the extension gives a model that allows variation in sequence
composition both across sites and taxa. We adopt a Bayesian approach, describe
an MCMC algorithm for posterior inference and provide software. Our quadratic
models are applied to alignments spanning the tree of life and compared with
site-homogeneous and linear models.

2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: nlin
18
The categories of this paper are: econ