Wednesday, January 21, 2015

Darwin, hybridization and networks

Charles Darwin's metaphor of the Tree of Life was not a tree, even in The Origin of Species. As noted by Franz Hilgendorf (see The dilemma of evolutionary networks and Darwinian trees) "the branches of a tree do not fuse again", and yet in his book Darwin discusses at least one circumstance when they do precisely that — hybridization.

Darwin's discussion of hybridization occupies all of chapter 8 of the Origin. His stated motivation is to address what many people might see as a fatal objection to his theory of species origins by means of natural selection. One of Darwin's main arguments in the book is that "descent with modification" is continuous, and therefore the distinction between species and varieties (and subspecies, etc) is an arbitrary cut in a continuum of biodiversity. However, it was conventionally accepted that varieties within the same species could cross-breed freely, but any attempt to hybridize distinct species would always fail. Darwin opposes this view by citing extensive evidence showing that varying degrees of sterility are encountered in efforts to cross-breed different species of plants (and a few birds) — if the species are closely related then often there will be a small degree of fertility in the hybrid offspring. So, as two related forms diverge from one another in the course of evolution, their ability to inter-breed gradually diminishes and eventually falls to zero (absolute sterility).

It is important to note that his motivation for writing about hybridization was independent of his ideas about phylogeny. So, he seems not to have noticed the consequence of hybridization for phylogenetic patterns.

This is similar to the situation regarding his so-called "tree diagram", in chapter 4. His motivation for the diagram (the only figure in his book) was a discussion of descent with modification, and particularly the continuity of evolutionary processes. He was expressing his idea about uninterrupted historical connections. In particular, this was part of his concern that there is no fundamental distinction between varieties and species, because evolutionary divergence is continuous — it is all a matter of degree, without sharp boundaries. His Tree of Life image expressed the continuity of evolutionary connections, not phylogenetic patterns. This is clear from his poetic invocation of the biblical Tree of Life, which is about the inter-connectedness of all living things along tree branches, not about patterns of biodiversity.

Implicit in this world view is the idea that the Tree of Life is still a tree in spite of hybridization. That is, Darwin failed to see that his "tree simile" (chapter 4) had to ignore hybridization (chapter 8) in order to work. His figure does not show any evidence of hybridization, only divergence. It was not intended to be what we would now call a phylogeny, but merely an idealized view of divergence and continuity of descent. When introducing the Tree of Life, he was using religious imagery to stimulate the imagination of his readers, and in so doing presented a contradictory argument — there is continuity along the branches as well as continuity of inter-connections.

The alternative conception is that Darwin's Tree of Life was never a tree — it was a network. From this world view, Hilgendorf's dilemma was actually irrelevant. He commented:
An observation which, as far as I know, contradicts these previously discussed views, [would be], that formerly separate species approach each other and finally merge with each other. This would not fit the beautiful image that Darwin presented about the connection of species in a branch-rich tree; the branches of a tree do not fuse again.
Well, they do, even in a Darwinian tree.

Monday, January 19, 2015

The kabbalistic Tree of Life is a network

The Tree of Life and the Tree of Knowledge are images that have appeared in many cultures throughout the world. They are often combined as a cosmic or world tree, with the tree of knowledge supporting the heavens and earth and the tree of life connecting all living beings. However, the word "tree" is obviously rather nebulous in these images, and it can take many forms.

In the christian Bible these trees appear in the garden of Eden in a more restricted form as the Tree of Eternal Life and the Tree of Knowledge of Good and Evil. Even here, though, it is not clear whether they are one and the same tree. For example, only one tree is mentioned in the book of Revelation, when promising a new Eden.

The Tree of Knowledge was co-opted in Medieval times as a symbol of learning, and a metaphor for arranging all human knowledge, the Arbor Scientiae (see Relationship trees drawn like real trees). This idea was adopted by biology in the 1700s, where trees were used as metaphors for the relationships among biological species. In modern parlance, these depicted affinity or phenetic relationships, and so they represented knowledge (not life). In the mid 1800s Charles Darwin (in the Origin of Species) took this pre-existing tree idea and instead made it represent evolutionary relationships among species. In the process he re-named it the Tree of Life, thus once again uniting the Tree of LIfe and the Tree of Knowledge. We have been stuck with the ToL name ever since.

At about the same time as the rise of the Arbor Scientiae, a combined Tree of Life and Tree of Knowledge also appeared as the central mystical symbol of the Kabbalah of esoteric Judaism, consisting of the 10 Sephirot (enumerations). It is shown above in its full modern form. This is a reinterpretation of the Hebrew Bible, conceptually representing a list the attributes of God (how God emanates).

In the Kabbalist view, both of the trees in the biblical garden of Eden were alternative perspectives of the Sephirot. The 10 Sephirot are arranged into three columns, with 22 Paths of Connection. As a tree, it has roots above and branches below. To quote Wikipedia:
Its diagrammatic representation, arranged in 3 columns/pillars, derives from Christian and esoteric sources and is not known to the earlier Jewish tradition. The tree, visually or conceptually, represents as a series of divine emanations God's creation itself ex nihilo, the nature of revealed divinity, the human soul, and the spiritual path of ascent by man. In this way, Kabbalists developed the symbol into a full model of reality, using the tree to depict a map of Creation.
My main point here is that by combining two conceptual trees this icon is clearly a network, unlike most other conceptual trees such as the dichotomous Tree of Knowledge.

The Kabbalah started without an image, being described solely in words. The diagram of the Tree used by modern Jewish Kabbalists is usually based on the diagram published in the print edition of Rabbi Moses Cordovero's Pardes Rimonim from 1591 [composed 1548], and sometimes called the "Safed Tree". It is shown in the next figure.

One of the earliest illustrations comes from the 1516 Portae Lucis of Paolo Riccio, a Latin translation of Joseph ben Abraham Gikatilla's most influential kabbalistic work, Sha'are Orah (Gates of Light) from the 1300s. It is shown in the next figure.

There are actually two modern version of the Kabbalah. The one shown here in the first illustration has the crossing diagonals lower down than does the one shown in the second illustration. The one with two diagonals at the bottom is an earlier version that is still favoured by Hermetic Kabbalists. Both made their first public appearance in the Pardes Rimonim.