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Faculty of Mathematics, Bielefeld University CAS-MPG Partner Institute for Computational Biology,

Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences

and Max Plank Institute for Mathematics in the Sciences,

Leipzig, Germany

Humboldt Kolleg on Selforganized Criticality: Dynamics of Complex Systems The Indian Institute of Astrophysics Bangalore, India

Phylogenetic Trees and Networks Tools for Coping with Evolution and BiodiversityA report on joint work with Stefan Gruenewald, Katharina

Huber, Daniel Huson, Vincent Moulton, and Andreas Spillner

Feb. 3, 2011

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The Classifying Obsession

Already in prehistoric times - for sure, humans recognized that living organisms can - based on their structural and behavioural resemblance - be grouped in a natural hierarchical fashion into classes whose members exhibit (a) almost identical, (b) similar, or (c) at least somehow related shape and behaviour

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Accordingly, also the `heroes of taxonomy´classified things

according to the observed ‘degree of resemblance’ from early on: Aristoteles, Plinius the elder,

LI Shizhen (from the Chinese Renaissance in the late Ming

dyasty),and other authors of herbal books in ancient Egypt, India, China, and 16th century Europe (just

having invented its own version of book printing) - all trying to list all that is in a systematic

fashion.

The classifying obsession

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The classifying obsession

And the same principles were used later on in the work of Carolus Linnaeus (1707-1778) and his predecessors John Ray (1628-1705), August Quirinus Rivinus (1652-1723), Joseph Pitton deTournefort (1656-1708), and others. They recognised an amazing universality of certain basic laws of life (e.g. that plants also have gender)and established in particular the invariance of species as the fundamental basis of the life sciences.In the context of John Ray's THEOLOGIA NATURALIS, these early taxonomists understood the task of taxonomy as the search for - and elucidation of- a static SYSTEMA NATURAE that reflects the Divine Order of Creation.

Kingdom - Phylum - Class - Order - Family - Group - Speciesing Philipp Came Over For Green Soup

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Yet, it were the ideas of the great naturlists - including perhaps also Humboldt, but definitely Lamarque and Goethe - in the 19th century culminating in Darwin's work that allowed scientists to reinterpret Linnaeus' classes in a dynamic way as `clades´, i.e., as subsets - within a larger set of species - comprising exactly all those species in that larger set that evolved from one common ancestor.

Using this idea, the static hierarchical King -Philipp-Came- Over-For-Green-Soup-system could immediately be transformed into the - mathematically equivalent, yet a dynamic interpretation suggesting - form of an evolutionary `tree of live´.

In this interpretation, similarity reflects common descent, and higher or smaller degrees of similarity reflect later or earlier dates of descent from the last common ancestor.

The Darwian Revolution

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Haeckel´s phylogenetic trees

So, to design his celebrated phylogenetic trees, Ernst Haeckel only needed to view Carolus Linnaeus´ static Systema Naturae from Darwin´s dynamic point of view.While such dynamic interpretations of hierarchical set systems are now common place, standard descriptive bookkeeping procedures for clustering objects according to observed (dis-)similarities can, f course, be applied independently from this point of view.Indeed, ordering data hierarchically according to observed similarities was tried by Linnaeus also to classify minerals, though not with a lasting effect.

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Haeckel´s phylogenetic trees from 1866

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Excerpts from Darwin‘s book „The Descent of Man“ regarding phylogenetic reconstruction

We can understand why a classification founded on any single character or organ- even an organ so wonderfully complex and important as the brain- or on the high development of the mental faculties, is almost sure to prove unsatisfactory.

This principle has indeed been tried with hymenopterous insects; but when thus classed by their habits or instincts, the arrangement proved thoroughly artificial..

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Excerpts from Darwin‘s book „The Descent of Man“ regarding phylogenetic reconstruction

Classifications may, of course, be based on any character whatever, as on size, colour, or the element inhabited; but naturalists have long felt a profound conviction that there is a natural system.

This system, it is now generally admitted, must be, as far as possible, genealogical in arrangement,- that is, the co-descendants of the same form must be kept together in one group, apart from the co-descendants of any other form; but if the parent-forms are related, so will be their descendants, and the two groups together will form a larger group. 

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Excerpts from Darwin‘s book „The Descent of Man“ regarding phylogenetic reconstruction

The amount of difference between the several groups- that is the amount of modification which each has undergone- is expressed by such terms as genera, families, orders, and classes. 

As we have no record of the lines of descent, the pedigree can be discovered only by observing the degrees of resemblance between the beings which are to be classed. 

For this object, numerous points of resemblance are of much more importance than the amount of similarity or dissimilarity in a few points.

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Excerpts from Darwin‘s book „The Descent of Man“ regarding phylogenetic reconstruction

  If two languages were found to resemble each other in a multitude of words and points of construction, they would be universally recognised as having sprung from a common source, notwithstanding that they differed greatly in some few words or points of construction.

 But with organic beings, the points of resemblance must not consist of adaptations to similar habits of life: two animals may, for instance, have had their whole frames modified for living in the water, and yet they will not be brought any nearer to each other in the natural system.

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Excerpts from Darwin‘s book „The Descent of Man“ regarding phylogenetic reconstruction

Hence we can see how it is that resemblances in several unimportant structures, in useless and rudimentary organs, or not now functionally active, or in an embryological condition, are by far the most serviceable for classification;

for they can hardly be due to adaptations within a late period; and thus they reveal the old lines of descent or of true affinity..

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In current studies phylogenetic-tree reconstruction, the following observation has been crucial: They are characterized completely by the system of weighted splits their various branches (or “edges“) induce on the set X of species under consideration.

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However, all we may know are the observed - and carefully weighted - “degrees of resemblance” encoded in form of, say, a distance table D:=(d(x,y))x,y in X.So, how can we derive - from that table D - the corresponding system of weighted splits they induce on the set X of species under consideration?

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This is one of the most basic problems in phylogenetic

combinatorics.To solve it, one has to try to find a system S

of weighted splits (A,B|r) of X such that

(i) any two splits in S are compatible,

(ii) the distance d(x,y) between any two species x and y coincides - at least more or less - with the sum of the weights r of those splits (A,B|r) of X in S that separate x and y.

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X ={a,b}:

X ={a,b,c}:

X ={a,b,c,d}:

X ={a,b,c,d,e}:

Look at what happens if X is small:

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Apparently, we cannot always

(i) any two splits in S are compatible,

(ii) the distance d(x,y) between any two species x and y coincides - at least more or less - with the sum of the weights r of those splits (A,B|r) of X in S that separate x and y.

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So, we have to make compromises.

Many distinct proposals for doing so.

Here are some figures that we have obtained using Daniel Huson’s SplitsTree software:

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The “phylogeny”of colours I

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The “phylogeny”of colours III

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A road map from Germany

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The wife of Bath‘s Prologue (58 manuscripts)

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rRNArRNA

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HIVHIV

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HIV IIHIV II

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The network of Human mtDNA

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Linguistic Typology

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Linguistic Typology 2Linguistic Typology 2

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A Network of Fungi

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Branching Statistics of the ToL?

Some question regarding the ToL:

1)What is the distribution of its branch lengths, that is, how long does a newly formed species remain a single species before it bifurcates into two (or more) new species?

1)Are there clearly distinguishable radiation events that could be signatures of "punctuated equilibrium"

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Branching Statistics of the ToL?

3) How many distinct species have evolved over time during the last N million years (N=1,10,100,150, ...) from one single species that existed N million years ago?

4) And what is the distribution - and not just the average - of these numbers?

5) Is it normally distributed - exhibiting a bell-shaped curve - around its average and, if not, does it differ from this in a significant (e.g. perhaps "scalefree") way?