http://mitran-lab.amath.unc.edu/courses/MATH564/textbook/15.pdf
don't bet on this lasting forver so download it.
Introduction
One of the purposes of this chapter is to introduce the reader to the
new mathematical
field of algebraic statistics; cf. [5]. Among the many topics in biology
in which
algebraic statistics is making an impact, we have chosen phylogenetics
as the vehicle
for showcasing this new discipline. Our reasons are that
• phylogeny and cladistics are important semiclassical fields in biology (with beginnings in the mid-1950s) quite different from anything we have studied up to now;
• postgenomics phylogeny makes extensive use of algebraic statistics and demonstrates more of its techniques than other branches of biology;
• phylogeny draws heavily on genomic searches, which we studied in the
last chapter,
and hence reinforces what we investigated there; and
• phylogeny is related to several of the new fields of biology that have arisen with
genomics that we outlined in the first section of the genomics chapter, Section 14.1.
Algebraic statistics, as mentioned above, is a new branch of mathematics arising
out of the many needs and uses of mathematics in genomics. Not
surprisingly, the
basic mathematics of algebraic statistics originates in the fields of
algebra and statistics, but already new mathematics, inspired by the
biology, has been created in the
discipline.
This chapter will take us to a higher level of mathematical abstraction, skill, and
reasoning than in the other chapters of the book and is likewise more demanding.
As in the earlier parts of the book, we make every effort to explain the mathematics
we need from first principles, principles that one would encounter in
two years of
a college mathematics curriculum, one that includes linear algebra.
Still, very little
abstract algebra makes its way to this level, and so we pay extra
attention to illustrate
the ideas and terms with examples.
Phylogenetic trees contain a great deal of biological and evolutionary information. Taxa closer together on the tree signify a greater degree
of shared evolutionary
novelties. The tree shows ancestral relationships among taxa and
indicates the geological time the process of evolution has taken step by step.
On 6/15/23 3:25 AM, Popping Mad wrote:
http://mitran-lab.amath.unc.edu/courses/MATH564/textbook/15.pdf
don't bet on this lasting forver so download it.
Introduction
One of the purposes of this chapter is to introduce the reader to the
new mathematical
field of algebraic statistics; cf. [5]. Among the many topics in biology
in which
algebraic statistics is making an impact, we have chosen phylogenetics
as the vehicle
for showcasing this new discipline. Our reasons are that
• phylogeny and cladistics are important semiclassical fields in biology
(with beginnings in the mid-1950s) quite different from anything we have
studied up to now;
• postgenomics phylogeny makes extensive use of algebraic statistics and
demonstrates more of its techniques than other branches of biology;
• phylogeny draws heavily on genomic searches, which we studied in the
last chapter,
and hence reinforces what we investigated there; and
• phylogeny is related to several of the new fields of biology that have
arisen with
genomics that we outlined in the first section of the genomics chapter,
Section 14.1.
Algebraic statistics, as mentioned above, is a new branch of mathematics
arising
out of the many needs and uses of mathematics in genomics. Not
surprisingly, the
basic mathematics of algebraic statistics originates in the fields of
algebra and statistics, but already new mathematics, inspired by the
biology, has been created in the
discipline.
This chapter will take us to a higher level of mathematical abstraction,
skill, and
reasoning than in the other chapters of the book and is likewise more
demanding.
As in the earlier parts of the book, we make every effort to explain the
mathematics
we need from first principles, principles that one would encounter in
two years of
a college mathematics curriculum, one that includes linear algebra.
Still, very little
abstract algebra makes its way to this level, and so we pay extra
attention to illustrate
the ideas and terms with examples.
Phylogenetic trees contain a great deal of biological and evolutionary
information. Taxa closer together on the tree signify a greater degree
of shared evolutionary
novelties. The tree shows ancestral relationships among taxa and
indicates the geological time the process of evolution has taken step by
step.
Looks fine up to a point, but it goes off the rails when it starts
talking about "phylogenetic trees", meaning those in which internal
nodes are identified as known species. That's not what the term means in >systematics, at least these days, and it's hardly ever possible to do.
And I see that they abandon this definition immediately, calling their
trees for which real taxa occupy only terminal nodes ("leaves")
"phylogenetic trees".
Minor point, but it annoys me: they consistently misspell "Kimura".
Finally, there seems a real paucity of references. Shouldn't there be a >reference for "Jukes-Cantor" and "Kimora-80"? It also seems as if the >discussion of maximum likelihood should reference Felsenstein. Etc.
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