https://www.youtube.com/watch?v=6_XMKmFQ_w8

On 3/27/23 22:21, Popping Mad wrote:
> https://www.youtube.com/watch?v=6_XMKmFQ_w8

https://www.youtube.com/watch?v=y1UfsYTrlXo

This video is one of the two introductory lectures (Introduction to
Discrete Mathematical Biology) given by Momoko Hayamizu as part of an
omnibus lecture series "Advanced Modern Mathematical Sciences 2" for
undergraduate mathematics majors at Waseda University. In this lecture,
she gives a detailed description of a structure theorem for rooted
binary phylogenetic networks, which is an analogue of the structure
theorem for finite Abelian groups. Hayamizu's structure theorem states
that any rooted binary phylogenetic network can be decomposed into a
unique set of maximal zig-zag trails and characterises the set of
subdivision trees of a tree-based network in terms of a direct product.
Using the result, she derives a series of linear time (and linear time
delay) algorithms for various computational problems. She also provides
a numerical example to demonstrate that those algorithms can help
biologists.

On Monday, March 27, 2023 at 10:21:56 PM UTC-4, Popping Mad wrote:
> https://www.youtube.com/watch?v=6_XMKmFQ_w8

Thanks for posting this, Ruben. It's a very clear and very basic lecture. Still, there was someone who did not understand completely, named Shelley Lauritsen, who wrote:

"Question for this cladogram - doesn't everything to the right of the organism you are comparing have the same recent ancestor and have the same number of similar traits. Wouldn't this make each of those things equally related- for instance the sea bass and the eagle or the sea bass and the antelope. Both have the same most recent ancestor and have the same number of shared traits?"

A few minutes ago, I answered this question, the first to do so in 4 years:

"The answer is Yes to "same recent ancestor"; this is exactly how cladists define "equally closely related," except they use the more precise designation Last Common Ancestor (LCA for short). The question "same number of shared traits" works for this highly simplified example with just four traits, but might fail in a tree where many more traits are included."

Peter Nyikos
Professor, Dept. of Mathematics -- standard disclaimer--
University of South Carolina
http://people.math.sc.edu/nyikos

On 3/29/23 2:11 PM, Peter Nyikos wrote:
> On Monday, March 27, 2023 at 10:21:56 PM UTC-4, Popping Mad wrote:
>> https://www.youtube.com/watch?v=6_XMKmFQ_w8
>
> Thanks for posting this, Ruben. It's a very clear and very basic lecture. Still, there was someone who did not understand completely, named Shelley Lauritsen, who wrote:
>
> "Question for this cladogram - doesn't everything to the right of the organism you are comparing have the same recent ancestor and have the same number of similar traits. Wouldn't this make each of those things equally related- for instance the sea bass and the eagle or the sea bass and the antelope. Both have the same most recent ancestor and have the same number of shared traits?"
>
> A few minutes ago, I answered this question, the first to do so in 4 years:
>
> "The answer is Yes to "same recent ancestor"; this is exactly how cladists define "equally closely related," except they use the more precise designation Last Common Ancestor (LCA for short). The question "same number of shared traits" works for this highly simplified example with just four traits, but might fail in a tree where many more traits are included."
>

The question is unclear, but your answer seems to be right as far as it
goes. Would you not agree that the eagle and the antelope (and the
crocodile, for that matter) are equally closely related to the sea bass?

Naturally, "same number of similar traits" can only be relative to the
traits being mentioned at the time, which is one per internal node and
not any sort of representative sample.

On 3/29/23 08:17, John Harshman wrote:
> Would you not agree that the eagle and the antelope (and the crocodile,
> for that matter) are equally closely related to the sea bass?

No - I don't think so, FWIW but I am not an expert.

I can say that Crocs and Eagles are more closely related to each other
than they are to Antelope and more closely related to Antelope than a
Bass. But I really can't say anything about how closely related the
entire group is compared to a bass, and I am not even sure what the
measurement is?

Is a Croc more closely realted to a Bass and an Antelope or less or
equal? I have no idea since they are not all on the same lineage.

On 3/30/23 4:50 PM, Popping Mad wrote:
> On 3/29/23 08:17, John Harshman wrote:
>> Would you not agree that the eagle and the antelope (and the crocodile,
>> for that matter) are equally closely related to the sea bass?
>
>
> No - I don't think so, FWIW but I am not an expert.
>
> I can say that Crocs and Eagles are more closely related to each other
> than they are to Antelope and more closely related to Antelope than a
> Bass. But I really can't say anything about how closely related the
> entire group is compared to a bass, and I am not even sure what the
> measurement is?

I'm not even sure what you're saying there. But the cladistic meaning of
"more closely related" is "having a more recent common ancestor". Since
the common ancestor of a bass and an eagle is the same as the common
ancestor of a bass and an antelope, we say that the bass is equally
closely related to both of them.

> Is a Croc more closely realted to a Bass and an Antelope or less or
> equal? I have no idea since they are not all on the same lineage.

That was not a grammatical sentence. You can't be more closely related
to two things. You can only be more closely related to one thing than to
another. "Than" is essential to any sentence that includes "more". I
could speculate on what you meant to say but nothing comes to mind. And
of course no two extant species are on the same lineage.

On 3/30/23 14:07, John Harshman wrote:
> "having a more recent common ancestor"

That is a definiton based on TIME and by that definition, that would be
correct. Any species that shares the common ancestor with Bass and
Tetrapods, even other fish, as all equally related by that defintion.

But that is not how we conventionally compare species in relationship to
their evolution. Evolution might speed up or slow down under different
circumstances. In computer sciences we measure and create these graphs
baces on nodes and costs between nodes. Maybe a species or a lineage
desn't evolve much over time, and the only lineage from the LCA between
Antelope and Bass DOES evolved rapidly giving rise to numerous species
over the same period of time. Now which one is more closely related to
the LCA. You are saying they have the same degree of relativity.

Look at it this way. All sharks share a LCA about 400 million tears go.

https://hoopermuseum.earthsci.carleton.ca/sharks/PMP.htm
https://hoopermuseum.earthsci.carleton.ca/sharks/P1-1B.htm

Two sharks that have a LCA 400 million years old are less closely
related than placentals like a Bat and an Elephant?

Now look at Sharks, Bass, and Bats. Now Bass and Bats likely have a
that a LCA of a fish not a decendent of sharks. Call is hypetheticalfishA.

HypertheticalfishA almost certainly shares a very ancient fish LCA with
sharks because sharks lineage are so ancient and we expect that LCA to
be before that node. It might even be a Placoderm

https://ucmp.berkeley.edu/education/events/carlson2.html

I'm willing to bet that there are a lot more synapomorphy between
placoderms and bats than between placoderns and bass, let alone a common
dogfish regardless of the fact that they all share the same LCA.

On 3/31/23 6:34 PM, Popping Mad wrote:
> On 3/30/23 14:07, John Harshman wrote:
>> "having a more recent common ancestor"
>
> That is a definiton based on TIME and by that definition, that would be
> correct. Any species that shares the common ancestor with Bass and
> Tetrapods, even other fish, as all equally related by that defintion.

Careful, "even other fish" is ambiguous. All sarcopterygians are equally
closely related to bass, but actinopterygians are closer than that, and
sharks are farther.

> But that is not how we conventionally compare species in relationship to
> their evolution.

But it is, though that may depend on who "we" are.

> Evolution might speed up or slow down under different
> circumstances.

True, but relationships are not generally judged on genetic distance.

> In computer sciences we measure and create these graphs
> baces on nodes and costs between nodes. Maybe a species or a lineage
> desn't evolve much over time, and the only lineage from the LCA between
> Antelope and Bass DOES evolved rapidly giving rise to numerous species
> over the same period of time. Now which one is more closely related to
> the LCA. You are saying they have the same degree of relativity.

Yes, this is in fact the conventional view. You may look more like your
grandparents than your first cousin does, but you are still equally
closely related to them.

> Look at it this way. All sharks share a LCA about 400 million tears go.
>
> https://hoopermuseum.earthsci.carleton.ca/sharks/PMP.htm
> https://hoopermuseum.earthsci.carleton.ca/sharks/P1-1B.htm
>
> Two sharks that have a LCA 400 million years old are less closely
> related than placentals like a Bat and an Elephant?

Yes, of course.

> Now look at Sharks, Bass, and Bats. Now Bass and Bats likely have a
> that a LCA of a fish not a decendent of sharks. Call is hypetheticalfishA.

Again, those weren't grammatical sentences. But I think I understand
what you were trying to say. The common ancestor of bass and bats is
more recent than the common ancestor of bass and shark. Therefore we say
that bass are more closely related to bats than to sharks.

> HypertheticalfishA almost certainly shares a very ancient fish LCA with
> sharks because sharks lineage are so ancient and we expect that LCA to
> be before that node. It might even be a Placoderm
>
>
> https://ucmp.berkeley.edu/education/events/carlson2.html
>
> I'm willing to bet that there are a lot more synapomorphy between
> placoderms and bats than between placoderns and bass, let alone a common
> dogfish regardless of the fact that they all share the same LCA.

Again, you aren't actually saying what you think you are saying. In this
case "synapomorphy between" actually refers to similarity, not distance.
It's probably true that by some objective measure, the morphological
distance between a bass and the common ancestor is greater than that
between bats and that ancestor. One may question whether that would hold
true for the genetic distance, especially since the bass has gone
through an additional round of whole-genome duplication relative to the
bat and that ancestor. But none of that is relevant to the standard
definition of closeness of relationship. And this is reflected in
classification: bass and bats are included in a taxon, Osteichthyes,
that excludes sharks.

On 3/31/23 09:13, John Harshman wrote:
> True, but relationships are not generally judged on genetic distance.

Hmm - well try marrying your 1st cousin in most US states...

:)

On Friday, March 31, 2023 at 8:07:03 AM UTC-7, Popping Mad wrote:
> On 3/31/23 09:13, John Harshman wrote:
> > True, but relationships are not generally judged on genetic distance.
> Hmm - well try marrying your 1st cousin in most US states...
>
> :)

Both you and John have the advantage of me with respect to knowledge of phylogenetic tree
construction and structure, but I will stick my less-informed oar in the water anyway. "X is more/less
closely related to Y than Z" lacks the precision implicit in the construction of a tree. It's just a sentence
in English, and as such "closely" and "related" inherit some wiggle. The "conventional view" may look
or sound surprising or counterintuitive, but at least it's consistent.

On 3/31/23 09:13, John Harshman wrote:
> Osteichthyes, that excludes sharks.

I could be wrong but perhaps sharks are Ostriethyes that lost the bone?
I was reading something like that.

I chose sharks because they have several long lived species, living
fossils, so it would better emphasis my point, and chose bats because
they recently radiated in the mamialian line and evolved and speciated
quickly with a lot of diversity.

On 3/31/23 11:31, erik simpson wrote:
> "X is more/less
> closely related to Y than Z" lacks the precision implicit in the construction of a tree.

I agree. That was my first statement. The question might not even make
any sense. John is saying that the question actually can be
conventionally understood by the rules of phenology and a cladgraph. I
disagree. A cladograph has a lot of information about the relationships
between species. You can say that these two species are closely related
because they share a node... a Hyrax and an Asian Elephant. It doesn't
do much to quanity how much closer or less closer either are to a NYC
subway rat.... IMO, and I don't even know what units I can hang such a
measurement on. In that context, I don't know what closely related even
means... exactly.

On 3/31/23 09:13, John Harshman wrote:
> Yes, this is in fact the conventional view. You may look more like your
> grandparents than your first cousin does, but you are still equally
> closely related to them.

That is a bad example because it doesn't resolve the issue any closer.
It doesn't address something like the radiation of bird species in the
last 20K years compared to the radiation of sharks in the great white
family.. whatever that family is called.

On 4/1/23 3:36 AM, Popping Mad wrote:
> On 3/31/23 11:31, erik simpson wrote:
>> "X is more/less
>> closely related to Y than Z" lacks the precision implicit in the construction of a tree.
>
>
> I agree. That was my first statement. The question might not even make
> any sense. John is saying that the question actually can be
> conventionally understood by the rules of phenology and a cladgraph.

I think you meant "phylogeny" and "cladogram" there. What I provided was
a definition of "related" that is easily and obviously read from a
cladogram. It can be extended to other cases that require a
time-calibrated tree, but nobody ever does that.

> I
> disagree. A cladograph has a lot of information about the relationships
> between species. You can say that these two species are closely related
> because they share a node... a Hyrax and an Asian Elephant.

"Closely related" has no objective definition. "More closely related to
A than to B" is what the definition applies to.

> It doesn't
> do much to quanity how much closer or less closer either are to a NYC
> subway rat.... IMO, and I don't even know what units I can hang such a
> measurement on. In that context, I don't know what closely related even
> means... exactly.

It means nothing, really, but that isn't what we were talking about.

On 4/1/23 3:26 AM, Popping Mad wrote:
> On 3/31/23 09:13, John Harshman wrote:
>> Osteichthyes, that excludes sharks.
>
>
> I could be wrong but perhaps sharks are Ostriethyes that lost the bone?
> I was reading something like that.

You confuse etymology with meaning. Osteichthyes is a particular clade,
not a collection of fish species with bones. It refers to the common
ancestor of Sarcopterygii and Actinopterygii and all its descendants,
and that excludes sharks.

> I chose sharks because they have several long lived species, living
> fossils, so it would better emphasis my point, and chose bats because
> they recently radiated in the mamialian line and evolved and speciated
> quickly with a lot of diversity.

None of that is relevant to cladistic relationships. You are looking for
a measure of similarity, not relationship. Those are not at all the same
thing.

On 4/1/23 3:38 AM, Popping Mad wrote:
> On 3/31/23 09:13, John Harshman wrote:
>> Yes, this is in fact the conventional view. You may look more like your
>> grandparents than your first cousin does, but you are still equally
>> closely related to them.
>
>
> That is a bad example because it doesn't resolve the issue any closer.
> It doesn't address something like the radiation of bird species in the
> last 20K years compared to the radiation of sharks in the great white
> family.. whatever that family is called.
>
>
Pretty sure there is no "radiation of bird species in the last 20K
years". But what does that have to do with relationships?

On 3/31/23 09:13, John Harshman wrote:
>"synapomorphy between" actually refers to similarity, not distance.

that is not computationally correct. synapomorphy represent nodes on a
map that are branching points based on the development of a novel
feature which is then inherited in a unidirection - evolution is a
unidirectional graph (although that might be coming into question with
some of the genetics papers I have read of late when you resolve the
graph more closely).

I might not be an expert on evolution but I am an expert in
computational math.

I would say the more Synapomorphic nodes that exists between two species
is a truer measure of the distance between species, rather than just
time on the clock.

I wouldn't consider time at all as a factor and neither does a
cladogram. Distance is the sum of the cost between all adjecent pairs
of nodes on a path, in this case between a LCA and several different
species.

C D
| | |
/-----*----*----*---A
* LCA
\-------*-------*----B
| |

If the cost of between each node is equal (and it is not but we will
make this assumption here to simplify this arguement),

Species A is computationally more closely related to the LCA than B by
on unit.

Also - C is closer to D

which C, D, A, and B are al extanct species.

With regard to the original question, two species along a path I can
compare ... say A and C. A is more closely related to the LCA than C.

It is harder to compare A and B because they don't share the same path
and costs between nodes are not shared, or well known.

On 4/1/23 10:25 AM, Popping Mad wrote:
> On 3/31/23 09:13, John Harshman wrote:
>> "synapomorphy between" actually refers to similarity, not distance.
>
>
> that is not computationally correct. synapomorphy represent nodes on a
> map that are branching points based on the development of a novel
> feature which is then inherited in a unidirection - evolution is a
> unidirectional graph (although that might be coming into question with
> some of the genetics papers I have read of late when you resolve the
> graph more closely).
>
> I might not be an expert on evolution but I am an expert in
> computational math.

The immediate subject isn't computational math; it's phylogenetic
terminology. The term "synapomorphy" was coined by Willi Hennig, and its
definition is "a shared, derived character". A synapomorphy arises on
some internal branch of a phylogenetic tree. It's a similarity between
taxa descendant from that branch, and it's a difference between those
descendant taxa and other taxa. You don't get to redefine common terms.

Your apparent definition of "node" also differs from the one in use in
phylogenetics. An internal node is the point at which three or more
branches meet (exactly three in a fully resolved tree). A terminal node
is, well, terminal. A point along a branch is not a node.

You should also know that most trees are estimated as unrooted, using a
reversible model of evolution, so the direction of time is not relevant.
(A direction of time is added later, by using some process to designate
a root to the tree.)

> I would say the more Synapomorphic nodes that exists between two species
> is a truer measure of the distance between species, rather than just
> time on the clock.

I would say that the patristic distance along the tree is a truer
measure. But I would also say that distance is not a measure of
relationship, which is the supposed subject.

> I wouldn't consider time at all as a factor and neither does a
> cladogram. Distance is the sum of the cost between all adjecent pairs
> of nodes on a path, in this case between a LCA and several different
> species.
>
> C D
> | | |
> /-----*----*----*---A
> * LCA
> \-------*-------*----B
> | |

What you have described is called "patristic distance". But we're
supposed to be talking about relationship, a different thing.

> If the cost of between each node is equal (and it is not but we will
> make this assumption here to simplify this arguement),
>
> Species A is computationally more closely related to the LCA than B by
> on unit.

That's only true if you define relationship as distance, which we don't.

> Also - C is closer to D
>
> which C, D, A, and B are al extanct species.
>
>
> With regard to the original question, two species along a path I can
> compare ... say A and C. A is more closely related to the LCA than C.
>
> It is harder to compare A and B because they don't share the same path
> and costs between nodes are not shared, or well known.

I don't understand why that should be true. Isn't the distance between A
and C merely the sum of the distances A-LCA and B-LCA, which you have
already determined?

On 3/31/23 22:03, John Harshman wrote:
> The immediate subject isn't computational math;

Actually, that is EXACTLY the subject.

On 4/1/23 7:53 AM, Popping Mad wrote:
> On 3/31/23 22:03, John Harshman wrote:
>> The immediate subject isn't computational math;
>
> Actually, that is EXACTLY the subject.

How so?

On Saturday, April 1, 2023 at 7:29:22 PM UTC-4, John Harshman wrote:
> On 4/1/23 7:53 AM, Popping Mad wrote:
> > On 3/31/23 22:03, John Harshman wrote:
> >> The immediate subject isn't computational math;
> >
> > Actually, that is EXACTLY the subject.

> How so?

You are missing Ruben's point, just as you did way back in 2016.

See my comments on a thread Ruben ("Popping Mad") began at 6:11 am EDT today:

https://groups.google.com/g/sci.bio.paleontology/c/rX_v-fcwq7s/m/3Y7nZwYrAwAJ
Re: Phylogenetic Trees: The What and The Why
[EXCERPT:]
For this first post, I am skipping over how phylogenetic diversity is calculated,
and moving to an issue that has caused untold confusion down through the decades,
both in s.b.p. and in the big outside world: how closely related are two species?

This is quantified in the article by using the best weights we can assign to each edge in the tree,
and adding together the ones on the unique path through the tree from species A to species B.
This is called "the path metric" between A and B.

The article avoids defining "related" [specifically, "more closely related"]
because of the way the systematists who dominate systematics define it.
Their method cannot be quantified because of its rudimentary nature.
And it is totally at odds with the quantification I gave above.

The dominant definition is the analogue of saying,
"Mitochondrial Eve is more closely related to everyone on earth today than she was
to anyone alive before she had children, including her parents and her siblings, if any."

On the other hand, look at the sentence "Species A is more closely related to species B
than it is to species C because the path metric from A to C is greater than the one from A to B."
This corresponds closely to the way we, including genealogists, use "more closely related" in everyday life.
[END OF EXCERPT]

Peter Nyikos
Professor, Dept. of Mathematics -- standard disclaimer--
University of South Carolina
http://people.math.sc.edu/nyikos

On Friday, March 31, 2023 at 11:31:45 AM UTC-4, erik simpson wrote:
> On Friday, March 31, 2023 at 8:07:03 AM UTC-7, Popping Mad wrote:
> > On 3/31/23 09:13, John Harshman wrote:
> > > True, but relationships are not generally judged on genetic distance.
> > Hmm - well try marrying your 1st cousin in most US states...
> >
> > :)
> Both you and John have the advantage of me with respect to knowledge of phylogenetic tree
> construction and structure, but I will stick my less-informed oar in the water anyway. "X is more/less
> closely related to Y than Z" lacks the precision implicit in the construction of a tree.

On the contrary, it has a degree of precision to which the dominant definition of "more closely
related" cannot aspire. See my reply to John about half an hour ago.

>It's just a sentence
> in English, and as such "closely" and "related" inherit some wiggle.

A lot of that wiggle can be eliminated by adopting the concept of "path metric"
and using the best available data for the estimates. This concept is rigorously defined
in the following article:

https://people.math.wisc.edu/~roch/research_files/review-steel-ams.pdf
The following sentence sets the stage:

"The edges of a phylogenetic tree T are often associated with weights {we}e∈E(T) which may represent either the time elapsed or the expected amount of evolution (e.g., in number of mutations in a segment of the genome) along that edge."

The path metric between species A and species B is obtained by using the weights we assign to each edge in the tree,
and adding together the ones on the unique path through the tree from species A to species B.

This metric is only as good as our data, but we can strive for precision by using the available data
to the best of our ability.

> The "conventional view" may look
> or sound surprising or counterintuitive, but at least it's consistent.

So is the use of the path metric, where the estimated distances are sufficiently far apart.

Peter Nyikos
Professor, Dept. of Mathematics -- standard disclaimer--
Univ. of South Carolina at Columbia
http://people.math.sc.edu/nyikos

. . . . . QUOTE OF THE DAY

A foolish consistency is the hobgoblin of little minds.
— Ralph Waldo Emerson, "Self-Reliance", Essays: First Series, 1841

On 4/3/23 2:20 PM, Peter Nyikos wrote:
> On Saturday, April 1, 2023 at 7:29:22 PM UTC-4, John Harshman wrote:
>> On 4/1/23 7:53 AM, Popping Mad wrote:
>>> On 3/31/23 22:03, John Harshman wrote:
>>>> The immediate subject isn't computational math;
>>>
>>> Actually, that is EXACTLY the subject.
>
>> How so?
>
> You are missing Ruben's point, just as you did way back in 2016.

What is Ruben's point, then?

> See my comments on a thread Ruben ("Popping Mad") began at 6:11 am EDT today:
>
> https://groups.google.com/g/sci.bio.paleontology/c/rX_v-fcwq7s/m/3Y7nZwYrAwAJ
> Re: Phylogenetic Trees: The What and The Why
>
> [EXCERPT:]
> For this first post, I am skipping over how phylogenetic diversity is calculated,
> and moving to an issue that has caused untold confusion down through the decades,
> both in s.b.p. and in the big outside world: how closely related are two species?
>
> This is quantified in the article by using the best weights we can assign to each edge in the tree,
> and adding together the ones on the unique path through the tree from species A to species B.
> This is called "the path metric" between A and B.
>
> The article avoids defining "related" [specifically, "more closely related"]
> because of the way the systematists who dominate systematics define it.
> Their method cannot be quantified because of its rudimentary nature.
> And it is totally at odds with the quantification I gave above.
>
> The dominant definition is the analogue of saying,
> "Mitochondrial Eve is more closely related to everyone on earth today than she was
> to anyone alive before she had children, including her parents and her siblings, if any."
>
> On the other hand, look at the sentence "Species A is more closely related to species B
> than it is to species C because the path metric from A to C is greater than the one from A to B."
> This corresponds closely to the way we, including genealogists, use "more closely related" in everyday life.
> [END OF EXCERPT]

What you call "path distance" is called "patristic distance" in
phylogenetics. But I wouldn't call that a measure of relatedness, and it
certainly doesn't fit the ordinary meaning, especially if evolutionary
rates differ among lineages. The cladistic definition could be
quantified on a time-calibrated tree, i.e. one on which the ages of the
ancestral nodes are estimated. But since in general this information is
unavailable (or at least unreliable), we content ourselves with only
relative ages, such that ancestral nodes are older than descendant nodes.

I reject the idea that evolutionary distances should be equated with
closeness of relationship.

On Monday, April 3, 2023 at 8:25:17 PM UTC-4, John Harshman wrote:
> On 4/3/23 2:20 PM, Peter Nyikos wrote:
> > On Saturday, April 1, 2023 at 7:29:22 PM UTC-4, John Harshman wrote:
> >> On 4/1/23 7:53 AM, Popping Mad wrote:
> >>> On 3/31/23 22:03, John Harshman wrote:
> >>>> The immediate subject isn't computational math;
> >>>
> >>> Actually, that is EXACTLY the subject.
> >
> >> How so?
> >
> > You are missing Ruben's point, just as you did way back in 2016.

> What is Ruben's point, then?

It would be best if he were to state it in his own words. However, I can say this much:
if "patristic distance" does not involve computational math, then you are wrong
about it being the same thing as "path metric."

> > See my comments on a thread Ruben ("Popping Mad") began at 6:11 am EDT today:
> >
> > https://groups.google.com/g/sci.bio.paleontology/c/rX_v-fcwq7s/m/3Y7nZwYrAwAJ
> > Re: Phylogenetic Trees: The What and The Why
> >
> > [EXCERPT:]
> > For this first post, I am skipping over how phylogenetic diversity is calculated,
> > and moving to an issue that has caused untold confusion down through the decades,
> > both in s.b.p. and in the big outside world: how closely related are two species?
> >
> > This is quantified in the article by using the best weights we can assign to each edge in the tree,
> > and adding together the ones on the unique path through the tree from species A to species B.
> > This is called "the path metric" between A and B.
> >
> > The article avoids defining "related" [specifically, "more closely related"]
> > because of the way the systematists who dominate systematics define it.
> > Their method cannot be quantified because of its rudimentary nature.
> > And it is totally at odds with the quantification I gave above.
> >
> > The dominant definition is the analogue of saying,
> > "Mitochondrial Eve is more closely related to everyone on earth today than she was
> > to anyone alive before she had children, including her parents and her siblings, if any."
> >
> > On the other hand, look at the sentence "Species A is more closely related to species B
> > than it is to species C because the path metric from A to C is greater than the one from A to B."
> > This corresponds closely to the way we, including genealogists, use "more closely related" in everyday life.
> > [END OF EXCERPT]

> What you call "path distance" is called "patristic distance" in
> phylogenetics.

Are you sure these designate the same thing? Ruben linked the following review
article, which I was using for "path metric," and it is quite computational..

https://people.math.wisc.edu/~roch/research_files/review-steel-ams.pdf

It's a review of the following book (for want of a better word):
Phylogeny—discrete and random processes in evolution1 by Mike Steel, CBMS-NSF Regional Conference Series in Applied Mathematics, 89, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2016. xvi+293 pp

By the way, the review does not use the word "patristic" anywhere:

> But I wouldn't call that a measure of relatedness,

That's because you are locked in to the definition of "relatledness" which triumphed
during the cladist wars. The famous cow - lungfish -salmon cladist victory
could have been avoided if someone who was well clued into vertebrate paleontology
and its evolutionary trees had been given a hearing during that debate.

> and it certainly doesn't fit the ordinary meaning, especially if evolutionary
> rates differ among lineages.

The ordinary meaning accommodates cases where a sequence of four successive generations
starting with one couple occurs in the same amount of time as a sequence of two generations
comes from another couple.

Perhaps you forgot, also, that one extended family could remain at the same level wrt class or income or influence
for many generations while another improves dramatically and while a third goes to pot.

Different rates of evolution, y'see.

>The cladistic definition could be
> quantified on a time-calibrated tree, i.e. one on which the ages of the
> ancestral nodes are estimated.

This would not work very well in the two kinds of everyday examples I gave.
Time calibration would not shed much light on the social dynamics involved.

>But since in general this information is
> unavailable (or at least unreliable), we content ourselves with only
> relative ages, such that ancestral nodes are older than descendant nodes.

Looks like you are using a concept that uses only extant organisms
and ignores fossils.

> I reject the idea that evolutionary distances should be equated with
> closeness of relationship.

But the one that depends only on the topology should be, in your opinion. Why,
What, besides your loyalty to the dominant group of systematics, accounts for this?

Peter Nyikos
Professor, Dept. of Mathematics -- standard disclaimer--
Univ. of South Carolina at Columbia
http://people.math.sc.edu/nyikos

QUOTE OF THE DAY

Why has not anyone seen that fossils alone gave birth to a theory about the formation of the earth, that without them, no one would have ever dreamed that there were successive epochs in the formation of the globe.
—Georges Cuvier

On 4/4/23 7:36 PM, Peter Nyikos wrote:
> On Monday, April 3, 2023 at 8:25:17 PM UTC-4, John Harshman wrote:
>> On 4/3/23 2:20 PM, Peter Nyikos wrote:
>>> On Saturday, April 1, 2023 at 7:29:22 PM UTC-4, John Harshman wrote:
>>>> On 4/1/23 7:53 AM, Popping Mad wrote:
>>>>> On 3/31/23 22:03, John Harshman wrote:
>>>>>> The immediate subject isn't computational math;
>>>>>
>>>>> Actually, that is EXACTLY the subject.
>>>
>>>> How so?
>>>
>>> You are missing Ruben's point, just as you did way back in 2016.
>
>> What is Ruben's point, then?
>
> It would be best if he were to state it in his own words. However, I can say this much:
> if "patristic distance" does not involve computational math, then you are wrong
> about it being the same thing as "path metric."
>
>>> See my comments on a thread Ruben ("Popping Mad") began at 6:11 am EDT today:
>>>
>>> https://groups.google.com/g/sci.bio.paleontology/c/rX_v-fcwq7s/m/3Y7nZwYrAwAJ
>>> Re: Phylogenetic Trees: The What and The Why
>>>
>>> [EXCERPT:]
>>> For this first post, I am skipping over how phylogenetic diversity is calculated,
>>> and moving to an issue that has caused untold confusion down through the decades,
>>> both in s.b.p. and in the big outside world: how closely related are two species?
>>>
>>> This is quantified in the article by using the best weights we can assign to each edge in the tree,
>>> and adding together the ones on the unique path through the tree from species A to species B.
>>> This is called "the path metric" between A and B.
>>>
>>> The article avoids defining "related" [specifically, "more closely related"]
>>> because of the way the systematists who dominate systematics define it.
>>> Their method cannot be quantified because of its rudimentary nature.
>>> And it is totally at odds with the quantification I gave above.
>>>
>>> The dominant definition is the analogue of saying,
>>> "Mitochondrial Eve is more closely related to everyone on earth today than she was
>>> to anyone alive before she had children, including her parents and her siblings, if any."
>>>
>>> On the other hand, look at the sentence "Species A is more closely related to species B
>>> than it is to species C because the path metric from A to C is greater than the one from A to B."
>>> This corresponds closely to the way we, including genealogists, use "more closely related" in everyday life.
>>> [END OF EXCERPT]
>
>> What you call "path distance" is called "patristic distance" in
>> phylogenetics.
>
> Are you sure these designate the same thing? Ruben linked the following review
> article, which I was using for "path metric," and it is quite computational.
>
> https://people.math.wisc.edu/~roch/research_files/review-steel-ams.pdf
>
> It's a review of the following book (for want of a better word):
> Phylogeny—discrete and random processes in evolution1 by Mike Steel, CBMS-NSF Regional Conference Series in Applied Mathematics, 89, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2016. xvi+293 pp
>
> By the way, the review does not use the word "patristic" anywhere:
>
>
>> But I wouldn't call that a measure of relatedness,
>
> That's because you are locked in to the definition of "relatledness" which triumphed
> during the cladist wars. The famous cow - lungfish -salmon cladist victory
> could have been avoided if someone who was well clued into vertebrate paleontology
> and its evolutionary trees had been given a hearing during that debate.
>
>
>> and it certainly doesn't fit the ordinary meaning, especially if evolutionary
>> rates differ among lineages.
>
> The ordinary meaning accommodates cases where a sequence of four successive generations
> starting with one couple occurs in the same amount of time as a sequence of two generations
> comes from another couple.
>
> Perhaps you forgot, also, that one extended family could remain at the same level wrt class or income or influence
> for many generations while another improves dramatically and while a third goes to pot.
>
> Different rates of evolution, y'see.
>
>
>> The cladistic definition could be
>> quantified on a time-calibrated tree, i.e. one on which the ages of the
>> ancestral nodes are estimated.
>
> This would not work very well in the two kinds of everyday examples I gave.
> Time calibration would not shed much light on the social dynamics involved.
>
>
>> But since in general this information is
>> unavailable (or at least unreliable), we content ourselves with only
>> relative ages, such that ancestral nodes are older than descendant nodes.
>
> Looks like you are using a concept that uses only extant organisms
> and ignores fossils.
>
>
>> I reject the idea that evolutionary distances should be equated with
>> closeness of relationship.
>
> But the one that depends only on the topology should be, in your opinion. Why,
> What, besides your loyalty to the dominant group of systematics, accounts for this?
>
>
> Peter Nyikos
> Professor, Dept. of Mathematics -- standard disclaimer--
> Univ. of South Carolina at Columbia
> http://people.math.sc.edu/nyikos
>
> QUOTE OF THE DAY
>
> Why has not anyone seen that fossils alone gave birth to a theory about the formation of the earth, that without them, no one would have ever dreamed that there were successive epochs in the formation of the globe.
> —Georges Cuvier
>
>
Two attempts to reply were lost in the ozone. I may try again later.
Now, I'll just say that your approach has significant problems that the
standard one does not.