Wednesday, May 27, 2015

Naudin, Wallace and Darwin — the tree idea

Charles Darwin's most poetic published words concern his image of the Tree of Life. However, he did not claim to have originated the image. For example, Alfred Russel Wallace had already used it. Recently, the Natural History Apostilles blog has mentioned another important predecessor of both Englishmen, the Frenchman Charles Naudin, who deserves wider recognition.

Darwin's well-known words from On the Origin of Species (1859) are:
The affinities of all the beings of the same class have sometimes been represented by a great tree. I believe this simile largely speaks the truth. The green and budding twigs may represent existing species; and those produced during each former year may represent the long succession of extinct species ... As buds give rise by growth to fresh buds, and these, if vigorous, branch out and overtop on all sides many a feebler branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications.
Wallace seems to have developed the Tree of Life metaphor quite independently (1855. On the law which has regulated the introduction of new species. Annals and Magazine of Natural History, 2nd series 16: 184-196):
"the analogy of a branching tree [is] the best mode of representing the natural arrangement of species ... a complicated branching of the lines of affinity, as intricate as the twigs of a gnarled oak ... we have only fragments of this vast system, the stem and main branches being represented by extinct species of which we have no knowledge, while a vast mass of limbs and boughs and minute twigs and scattered leaves is what we have to place in order, and determine the true position each originally occupied with regard to the others."
Darwin freely admitted having read Wallace's work. Moreover, he was well aware of the other of his predecessors, Charles Naudin, because on p.167 of his 'Books Read' and 'Books to be Read' notebook of 1852-1860 (see Darwin Online CUL-DAR128) he recorded:
"Revue Horticol Imp. 1852. p. 102. Naudin Consid. Phil, sur l'espèce"
Charles Naudin's words are these, roughly translated from the original French (1852. Considérations philosophiques sur l'espèce et la variété. Revue Horticole, 4th series 1: 102-109) [NB. the long convoluted sentences are in the original]:
This doctrine of inbreeding among organic beings of same family, the same class, and perhaps of the same kingdom, is not new; men of talent, both in France as well as abroad, among them our learned Lamarck, have supported it with all of the authority of their names. We do not deny that, on more than one occasion, they have reasoned upon assumptions which were not adequately supported by observation, that they did sometimes apply to the facts forced interpretations, that finally resulted in exaggerations that have mainly helped to push their ideas. But these defects in details do not diminish the greatness and perfect rationality of the whole system that, alone, reflects, by the community of origin, the great fact of the organizational community of the other living beings of the same kingdom, the primary basis of our rankings of species into genera, families, orders and phyla. In the opposing system now in vogue, in this system which involves many partial and independent creations we recognize or think we recognize as distinct species, one is forced to be logical, to admit the similarities exhibited by these species are only fortuitous coincidence, that is to say an effect without a cause, concluding that the reason is not acceptable. In our own [system], on the contrary, these similarities are both the consequence and proof of a relationship, not metaphorical, but real, that they hold a common ancestor, which they left at times more or less remote and through a series of intermediaries greater or fewer in number; so they express the true relationships between species by saying that the sum of their mutual similarities is the expression of their degree of relationship, as the sum of the differences is that of the distance they are from the common stock from which they derive their origin.
Considered from this point of view, the plant kingdom would present, not as a linear series whose terms would increase or decrease in organizational complexity, according as we consider starting with one end or the other; it would not be more of a disordered tangle of intersecting lines, like a geographical map, whose regions, different in shape and size, would touch by a greater or lesser number of points; it would be a tree the roots of which, mysteriously hidden in the depths of cosmological time, would have given birth to a limited number of successively divided and subdivided stems. These first stems would represent the primordial types of the kingdom; their last ramifications would be the current species.
It follows from there that a perfect and rigorous classification of the other organized beings of the same kingdom, of the same order, of the same family, if something other than the family tree even of the species, indicates the relative age of each, its degree of speciation and the line of ancestors from which it descended. Thereby would be represented, in a manner of some sort so palpable and material, the different degrees of relationship of the species, such as that of groups of varying degrees, dating back to the primordial kinds. Such a classification, summarized in a graphical table, would be seized with much facility by the mind through the eyes, and present the most beautiful application of this principle generally accepted by naturalists: that nature is avaricious [stingy?] of causes and prodigal of effects.
This is quite clearly a description of a modern phylogenetic tree, and the taxonomic consequences of adopting that conception.

It is, however, rather a pity that he explicitly rejects a network ("a disordered tangle of intersecting lines") as a suitable model, along with the chain ("a linear series").

Monday, May 25, 2015

Walking can be more dangerous than cycling

We are often told that flying is the safest way to travel, at least as far as the use of commercial airlines is concerned. In an early stand-up comedy routine, Shelley Berman noted: "Statistics prove that flying is the safest way to travel. I don't know how much consideration they've given to walking!" Well, actually, they have included walking.

Governments like to keep a track of these things, and the Department for Transport in Great Britain has released statistics on "Passenger casualty rates for different modes of travel" for 2003-2012. These modes include:
  • Air (passenger casualties in accidents involving UK registered airline aircraft)
  • Rail (passenger casualties involved in train accidents and accidents occurring through movement of railway vehicles)
  • Water (passenger casualties on UK registered merchant vessels)
  • Bus or coach (passenger casualties)
  • Car (driver and passenger casualties)
  • Van (driver and passenger casualties)
  • Motorcycle (driver and passenger casualties)
  • Pedal cycle
  • Pedestrian
The data are yearly averages for Great Britain from 2003-2012 inclusive, standardized as persons per billion passenger kilometres. The data are provided separately for the number of people killed, seriously injured, or slightly injured.

As usual, we can employ a phylogenetic network as a form of exploratory data analysis for these data. I first used the manhattan distance to calculate the similarity of the seven transportation modes for which there are complete data, followed by a Neighbor-net analysis to display the between-mode similarities as a phylogenetic network. So, modes that are closely connected in the network are similar to each other based on their accident figures across the ten years, and those that are further apart are progressively more different from each other.

The probability of incidents increases from right to left in the graph.

Some notable conclusions from the data are:
  • The probabilities of being killed, seriously injured or even slightly injured are all minuscule for air travel compared to anything else. This is a topic explored more thoroughly in an earlier blog post (A network analysis of airplane disasters).
  • You are much more likely to be injured in a bus than in a truck, but more likely to be killed in the truck than in the bus.
  • You are slightly more likely to be killed walking than cycling, but much more likely to be injured cycling.
  • A motorbike is the most effective way to get killed or seriously injured in Britain.

The walking versus cycling data are likely to surprise many people, but the average data across the 10 years are clear:

Pedal cycle
Seriously injured
Slightly injured

Danny Yee (Walking and cycling: relative risks) provides one explanation:
People who wouldn't even contemplate wearing special high-visability clothing or a helmet for a walk to the shops do so when cycling the same route.