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.

On Thu, 15 Jun 2023 06:49:11 -0700, John Harshman
<john.harshman@gmail.com> wrote:

>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.

It appears to be a chapter from,
https://link.springer.com/book/10.1007/978-0-387-70984-0

a rather general introductory text on mathematical methods in biology.
At the end they do suggest Felsenstein's 2004 book "Inferring
Phylogenies", which of course has all the primary references to JC69,
K80 (K2P), etc.