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DATE 2017-03-05
FROM Ruben Safir
SUBJECT Subject: [Learn] cost in evolution
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https://astrocladistics.org/2012/01/31/evolutionary-cost/



Evolutionary cost

Cladistics looks for the relationships between taxa in terms of an
evolutionary cost. By minimizing this cost, it is expected to find an
evolutionary scenario that closely matches the hierarchical
diversification process through transmission with modification. In
other words, inheritance of innovations from common ancestors is the
simplest way to explain diversity.

To understand why this can only be achieved by using character (or
parameter) matrix instead of distances that measures global
similarities, consider the case of a journey between two cities.

Looking at a map, you can easily measure the distance between the two
cities with a rule. This might be ok if you fly, but this is not very
useful if you travel by car because then you have to take into account
the landscape and the existing roads among other things.

First you have to look at a precise roadmap, and compute for each road
and considering all possible bifurcations, the true number of kilometers
you will have to travel. Note that there is no trick to avoid looking at
all possible paths. Then you can decide to choose the shortest way
according to the parsimony criterion.

But cost might not be measured by kilometers only. You may consider the
time it takes. Highways are certainly faster, but you should consider
the probability of traffic jams or that of slow trucks or animals on
smaller roads. It is common wisdom that the quickest ways are not
necessarily the shortest or the most direct ones.

You can also think about money with the fuel you will burn. Depending on
your car, depending on the slopes for the different roads, the cost can
be quite different in every case.

Lastly, you can consider the pleasure or the comfort of the journey.
This is certainly less quantitative and objective, but still important.

We have here a typical multivariate problem, and defining an
evolutionary cost is not always straightforward. As the above should
illustrate, character-based methods like cladistics explore an unknown
landscape with a metrics which is defined by the choice of the
multivariate cost. Indeed, for living organisms or for galaxies, there
is no roadmap…

Distance-based approaches assume a metrics and do not care very much on
the cost (and even on the landscape). To understand further the
difference, let us be more precise and consider the following parameter
or character matrix:


p1 p2 p3 p4
O 0 0 0 0
A 1 0 0 0
B 0 1 1 0
C 0 1 1 1

If you have learned to build a tree
, you are
able to find that the most parsimonious tree rooted with O is:

Now,
from the parameters, you can compute a distance, the most common being
the euclidian distance. The corresponding distance matrix (showing here
the square of the euclidian distance) is:


O A B C
O 0 1 2 3
A 1 0 3 4
B 2 3 0 1
C 3 4 1 0

One could also compute the “edit” or Levenshtein distance, which
measures the number of substitution (here 0-1) occuring in the full set
of parameters between two objects. The matrix distance in the present
case is identical to the one above. Note that even though it might look
like cladistics because it compares the changes in parameter values, it
is a distance and thus measures these changes globally.

From any character matrix you can compute a distance matrix, but the
reverse is most generally untrue. Hence, somehow, when we use distances,
we loose some information.

From a distance matrix, we can build a hierarchical tree representing
the relative distances between the objects. Using hclust in R, this gives:

From
this tree, one concludes that there are two groups: (O,A) and (B,C). The
distance within the two members of each group is 1 while the minimum
distance between the groups is 2. So the two methods agree that B and C
are very close to each other and could form a group, but cladistics do
not see any reason to put O and A in a same group. Indeed the cladogram
is easier to interpret because it must be read in terms of the
evolutionary cost.

In general, it appears that character-based and distance-based analysis
in phylogeny give very close results. I think this is because if only
synapomorphies are used, which ideally should be the case for
cladistics, then the landscape is not too much tortuous so that the
metrics assumed by distance-based approaches is more or less adequate.

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bifurcations , global
similarities ,
parsimony

This entry was posted on January 31, 2012, 13:28 and is filed under
Classification .
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* Comments (1)


1.

#1

by *dranorter* on July 3, 2013 - 07:10

You say there is no trick to avoid looking at all possible paths.
However, I think you are thinking of the Traveling Salesman Problem,
where we must visit every node in an efficient manner. When
traveling from point A to point B there certainly are useful tricks
and shortcuts. Dijkstra’s Algorithm is a common approach, and is
much faster than looking at all possibilities.

Of course, the ‘multivariate’ case gets more complicated. I’m only
disagreeing with that one sentence.


--------------080201020508090007040306
Content-Type: multipart/related;
boundary="------------050900050102060903090100"


--------------050900050102060903090100
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: 8bit







https://astrocladistics.org/2012/01/31/evolutionary-cost/








Evolutionary cost




Cladistics looks for the relationships between taxa in
terms of an evolutionary cost. By minimizing this cost, it
is expected to find an evolutionary scenario that closely
matches the hierarchical diversification process  through
transmission with modification. In other words, inheritance
of innovations from common ancestors is the simplest way to
explain diversity.


To understand why this can only be achieved by using
character (or parameter) matrix instead of distances that
measures global similarities, consider the case of a journey
between two cities.


Looking at a map, you can easily measure the distance
between the two cities with a rule. This might be ok if you
fly, but this is not very useful if you travel by car
because then you have to take into account the landscape and
the existing roads among other things.


First you have to look at a precise roadmap, and compute
for each road and considering all possible bifurcations, the
true number of kilometers you will have to travel. Note that
there is no trick to avoid looking at all possible paths.
Then you can decide to choose the shortest way according to
the parsimony criterion.


But cost might not be measured by kilometers only. You may
consider the time it takes. Highways are certainly faster,
but you should consider the probability of traffic jams or
that of slow trucks or animals on smaller roads. It is
common wisdom that the quickest ways are not necessarily the
shortest or the most direct ones.


You can also think about money with the fuel you will burn.
Depending on your car, depending on the slopes for the
different roads, the cost can be quite different in every
case.


Lastly, you can consider the pleasure or the comfort of the
journey. This is certainly less quantitative and objective,
but still important.


We have here a typical multivariate problem, and defining
an evolutionary cost is not always straightforward. As the
above should illustrate, character-based methods like
cladistics explore an unknown landscape with a metrics which
is defined by the choice of the multivariate cost. Indeed,
for living organisms or for galaxies, there is no roadmap…


Distance-based approaches assume a metrics and do not care
very much on the cost (and even on the landscape). To
understand further the difference, let us be more precise
and consider the following parameter or character matrix:










































p1 p2 p3 p4
O 0 0 0 0
A 1 0 0 0
B 0 1 1 0
C 0 1 1 1

If you have href="https://astrocladistics.org/cladistics/constructing-a-tree/">learned
to build a tree
, you are able to find that the most
parsimonious tree rooted with O is:


href="https://astrocladistics.files.wordpress.com/2012/01/treeclad1rooted.png"> data-attachment-id="228"
data-permalink="https://astrocladistics.org/2012/01/31/evolutionary-cost/treeclad1rooted/"
data-orig-file="https://astrocladistics.files.wordpress.com/2012/01/treeclad1rooted.png?w=620"
data-orig-size="144,135" data-comments-opened="1"
data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":""}"
data-image-title="treeclad1rooted"
data-image-description=""
data-medium-file="https://astrocladistics.files.wordpress.com/2012/01/treeclad1rooted.png?w=620?w=144"
data-large-file="https://astrocladistics.files.wordpress.com/2012/01/treeclad1rooted.png?w=620?w=144"
class="aligncenter size-full wp-image-228"
title="treeclad1rooted"
src="cid:part2.03080401.01040408-at-panix.com" alt="">Now,

from the parameters, you can compute a distance, the most
common being the euclidian distance. The corresponding
distance matrix (showing here the square of the euclidian
distance) is:










































O A B C
O 0 1 2 3
A 1 0 3 4
B 2 3 0 1
C 3 4 1 0

One could also compute the “edit” or Levenshtein distance,
which measures the number of substitution (here 0-1)
occuring in the full set of parameters between two objects.
The matrix distance in the present case is identical to the
one above. Note that even though it  might look like
cladistics because it compares the changes in parameter
values, it is a distance and thus measures these changes
globally.


From any character matrix you can compute a distance
matrix, but the reverse is most generally untrue. Hence,
somehow, when we use distances, we loose some information.


From a distance matrix, we can build a hierarchical tree
representing the relative distances between the objects.
Using hclust in R, this gives:


href="https://astrocladistics.files.wordpress.com/2012/01/hclust_tree_12.png"> data-attachment-id="234"
data-permalink="https://astrocladistics.org/2012/01/31/evolutionary-cost/hclust_tree_1-3/"
data-orig-file="https://astrocladistics.files.wordpress.com/2012/01/hclust_tree_12.png?w=620"
data-orig-size="288,288" data-comments-opened="1"
data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":""}"
data-image-title="hclust_tree_1"
data-image-description=""
data-medium-file="https://astrocladistics.files.wordpress.com/2012/01/hclust_tree_12.png?w=620?w=288"
data-large-file="https://astrocladistics.files.wordpress.com/2012/01/hclust_tree_12.png?w=620?w=288"
class="aligncenter size-full wp-image-234"
title="hclust_tree_1"
src="cid:part4.02090701.00040708-at-panix.com" alt=""
srcset="https://astrocladistics.files.wordpress.com/2012/01/hclust_tree_12.png
288w,
https://astrocladistics.files.wordpress.com/2012/01/hclust_tree_12.png?w=150
150w" sizes="(max-width: 288px) 100vw, 288px">From
this tree, one concludes that there are two groups: (O,A)
and (B,C). The distance within the two members of each group
is 1 while the minimum distance between the groups is 2. So
the two methods agree that B and C are very close to each
other and could form a group, but cladistics do not see any
reason to put O and A in a same group. Indeed the cladogram
is easier to interpret because it must be read in terms of
the evolutionary cost.


In general, it appears that character-based and
distance-based analysis in phylogeny give very close
results. I think this is because if only synapomorphies are
used, which ideally should be the case for cladistics, then
the landscape is not too much tortuous so that the metrics
assumed by distance-based approaches is more or less
adequate.



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href="https://astrocladistics.org/tag/bifurcations/"
rel="tag">bifurcations, href="https://astrocladistics.org/tag/global-similarities/"
rel="tag">global similarities, href="https://astrocladistics.org/tag/parsimony/" rel="tag">parsimony







  • href="https://astrocladistics.org/2012/01/31/evolutionary-cost/#comments">Comments
    (1)







  1. href="https://astrocladistics.org/2012/01/31/evolutionary-cost/#comment-1090">#1
    by dranorter on July
    3, 2013 - 07:10




    You say there is no trick to avoid looking at all
    possible paths. However, I think you are thinking
    of the Traveling Salesman Problem, where we must
    visit every node in an efficient manner. When
    traveling from point A to point B there certainly
    are useful tricks and shortcuts. Dijkstra’s
    Algorithm is a common approach, and is much faster
    than looking at all possibilities.


    Of course, the ‘multivariate’ case gets more
    complicated. I’m only disagreeing with that one
    sentence.













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  1. 2017-03-02 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] neutal networks and pacman
  2. 2017-03-02 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Ultrametric networks: a new tool for phylogenetic analysis
  3. 2017-03-05 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] cost in evolution
  4. 2017-03-09 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] CatScan fossil files
  5. 2017-03-10 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] neural Networks and Quantum Mechanics
  6. 2017-03-12 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] I just found a GREAT video on partial derivatives
  7. 2017-03-13 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] Contact DOJ and thell them to blow it out their ass
  8. 2017-03-14 Ruben Safir <ruben-at-mrbrklyn.com> Re: [Learn] CatScan fossil files
  9. 2017-03-14 Ramon Nagesan <ramon.nagesan-at-gmail.com> Re: [Learn] CatScan fossil files
  10. 2017-03-16 Ruben Safir <ruben-at-mrbrklyn.com> Re: [Learn] is this up
  11. 2017-03-16 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] hang out is down
  12. 2017-03-16 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] is this working
  13. 2017-03-16 Charlie Gonzalez <itcharlie-at-gmail.com> Subject: [Learn] Registration for The Perl Conference 2017 is now open!!
  14. 2017-03-16 From: "soledad.esteban" <soledad.esteban-at-icp.cat> Subject: [Learn] [dinosaur] Advanced course Geometric Morphometrics in R,
  15. 2017-03-17 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Fwd: [dinosaur] Advanced course Geometric Morphometrics in
  16. 2017-03-17 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] good news !
  17. 2017-03-18 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] circles
  18. 2017-03-20 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Alice
  19. 2017-03-20 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] hough transform - Lecture 9
  20. 2017-03-21 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Anyone understand this well
  21. 2017-03-21 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Fwd: [dinosaur] Digital mapping of dinosaurian tracksites
  22. 2017-03-22 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] ODBASE 2017 - The 16th International Conference on
  23. 2017-03-24 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Decision Tree
  24. 2017-03-24 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Genetic Modification with decent
  25. 2017-03-27 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] Fwd: Re: hough transform - Lecture 9
  26. 2017-03-27 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] MOOCS
  27. 2017-03-27 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Peter Novig learning and on line teaching
  28. 2017-03-28 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] computations
  29. 2017-03-29 Christopher League <league-at-contrapunctus.net> Re: [Learn] This is hard to understand what the logic is here
  30. 2017-03-29 Ruben Safir <ruben-at-mrbrklyn.com> Re: [Learn] This is hard to understand what the logic is here
  31. 2017-03-29 Christopher League <league-at-contrapunctus.net> Re: [Learn] This is hard to understand what the logic is here
  32. 2017-03-29 Ruben Safir <mrbrklyn-at-panix.com> Re: [Learn] This is hard to understand what the logic is here
  33. 2017-03-29 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] perseptors
  34. 2017-03-29 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] This is hard to understand what the logic is here
  35. 2017-03-29 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] This is hard to understand what the logic is here
  36. 2017-03-30 Ruben Safir <mrbrklyn-at-panix.com> Re: [Learn] c arrays
  37. 2017-03-30 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] c arrays
  38. 2017-03-30 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] random weights
  39. 2017-03-30 Ruben Safir <mrbrklyn-at-panix.com> Subject: [Learn] randomize with commentary
  40. 2017-03-31 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Computational Paleo

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