Showing posts with label Christmas. Show all posts
Showing posts with label Christmas. Show all posts
Monday, December 23, 2019
Evolutionary processes hidden in Christmas clip arts
As a blogger, one is free to indulge in complexity in all data, although this is not necessarily a good idea in professional publications. We can thus think about the art of networks — that is, inferring networks with an artistic touch (eg. this post on artistic network depictions; and trees can be art, too). For this Christmas post, we will just take the shape of famous Christmas-themed clip art to muse about the evolutionary process that could produce a similar structure.
The snowflake
Despite climate warming, snowflakes are still the basic component of most Christmas-themed art. Phylogentically, they are just unrooted trees, no matter how complex they look, with the difference that the radiation events are trichotomous, not dichotomous, and hence represent rapid radiations (leading to soft polytomies in the inferred tree).
The Christmas tree
In Germany, a proper Christmas tree has to be a Nordmanntanne — Nord = north, Mann = man, Tanne = fir; Abies nordmanniana (since we planted all our Christmas trees in the garden, we rarely had one). This, in contrast with what you may be thinking, does not come from the north but from the south (and named after a noble Swedo-Finnish zoologist: Alexander von Nordmann), specifically, the mountains along the southern Black Sea coast. Firs are perfect trees for Christmas because they have broad bases and taper towards the tips (try to decorate a Tränenkiefer, Pinus wallichiana, which we once had as an alternative Christmas tree).
Phylogenetically, they are quite specific metaphors, as explained in the diagram.
With only one survivor, we won't have any molecular data reconstructing a fir-like phylogeny. However, we can observe appropriate phenomena in the fossil record: when lineages emerge they usually are not represented by a single form but in several, then there are phases of stasis, then their diversity explodes in a very short time, with subsequent loss until the next radiation event, although the lineage itself is on decline.
We can also turn the Christmas tree upside down, and fill it with two sister lineages, as shown here.
We then end up with a scenario not unlikely in nature. Note that due to the last extinction event the survivors cuddle in the original niche, and only genetics may give us a clue that the similar morphology is not reflecting a recent common origin or the actual phylogenetic relationships.
A last image
Despite being a geologist-palaeontologist, I early got into contact with (and was intrigued by) population genetics, due to various circumstances (mainly because I'd make a very poor taxonomist). Hence, I love cactus-like evolutionary metaphors (see here for a real-world example). In the next diagram there is one showing several common evolutionary processes, with the colors representing haplotypic or genotypic variation within the species/species complex represented by the bubbles.
This includes everything I fancy about working at the coalface of evolution: a lot of stochasticity, a bit of reticulation, spiced with potentially misleading signals in the molecular data. A truly angelic evolutionary scenario.
Frohe Weihnachten, Glad jul, Bonne noël, and a Merry Christmas to everyone (or whatever you celebrate and enjoy at the end of the year).
And in case you are looking for a New Year's resolution: next time you write a phylogeny paper, sneak in a phylogenetic (or data-display) network in addition to the always simplifying, and per se trivial, tree.
More on Christmas (and networks)
Monday, December 24, 2018
A jolly, holly network ... of Christmas carols
Today is Christmas Eve. What could be more befitting for our merry blog than to show a network of Christmas carols?
The perfect result would, of course, be a snowflake-like network. Ideally, approaching what is called a "stellar dendrite snowflake".
The data
I browsed the internet for lyrics of Christmas carols, and then scored their content in the form of a binary matrix.
The "taxon set" includes 45 traditional and (more) modern carols, some of them listed here, along with some others I remembered and sought out (eg. here). A comprehensive list of traditional carols can be found here, but using this would have made the matrix much too large for a post on Christmas Eve. (If you are reading this before Christmas, you might be spending too much time on science.) A rule of thumb is that a matrix should always have at least as many (completely defined) characters as taxa.
The 45 (hohoho!) "characters" include:
The network
The result is not a perfect stellar dendrite, but it is close enough.
It has quite a nice circular sorting of the carols, each related in some way to the ones next to it. The only oddly placed one is "Twelve Days of Christmas", which is a very peculiar one (and my English, favorite), along with the rather content-free "We wish You a Merry Christmas".
Finally, as a Christmas treat, the "great voices of the British public" singing (and reflecting on) my favorite carol: a Creature Comforts Christmas special.
A merry Christmas to everyone!
And please try out some networks during the coming year.
The perfect result would, of course, be a snowflake-like network. Ideally, approaching what is called a "stellar dendrite snowflake".
![]() |
| Stellar dendrites. (Images from a post introducing a snowflake book: The Snowflake.) |
The data
I browsed the internet for lyrics of Christmas carols, and then scored their content in the form of a binary matrix.
The "taxon set" includes 45 traditional and (more) modern carols, some of them listed here, along with some others I remembered and sought out (eg. here). A comprehensive list of traditional carols can be found here, but using this would have made the matrix much too large for a post on Christmas Eve. (If you are reading this before Christmas, you might be spending too much time on science.) A rule of thumb is that a matrix should always have at least as many (completely defined) characters as taxa.
The 45 (hohoho!) "characters" include:
- length (short = 0, long = 1), and tone (merry = 0, darkish = 1)
- topics it is about / relates to / mentions — e.g. the birth scene, love, and yuletide (the latter included because as a naturalized Swede, I love the jultiden, fancy julkaffe, and much enjoyed most of my julbord);
- major Christmas figures — Jesus, angels, drummers, elves, Jack Frost, the Grinch, milking maids, monsters, Santa Claus, shepherds, snowmen, the Wise Men from the Orient;
- mentioned animals, such as reindeer, and plants, including the Christmas tree (traditionally a Tannenbaum – fir tree), and (very important for Anglosaxons who don't kiss each other whenever they meet, like we do in France) the mistletoe
- last but not least, Christmas related objects — non-living things such as bells, Christmas food, harps, sleighs, snow, stars, and presents.
The network
The result is not a perfect stellar dendrite, but it is close enough.
![]() |
| A Neighbor-net of Christmas carols. Stippled terminal edges are reduced by factor 2. |
It has quite a nice circular sorting of the carols, each related in some way to the ones next to it. The only oddly placed one is "Twelve Days of Christmas", which is a very peculiar one (and my English, favorite), along with the rather content-free "We wish You a Merry Christmas".
Finally, as a Christmas treat, the "great voices of the British public" singing (and reflecting on) my favorite carol: a Creature Comforts Christmas special.
A merry Christmas to everyone!
And please try out some networks during the coming year.
Monday, December 25, 2017
Christmas tree networks
Greetings for the season.
Mathematicians live in a world of their own — individually, as well as collectively. Therefore, it is inevitable that among all of the graphs with names like pancake graphs, butterfly networks, star graphs, spider web networks, and brother trees, there should be a thing called a Christmas tree.
It was introduced by Chun-Nan Hung, Lih-Hsing Hsu and Ting-Yi Sung (1999) Christmas tree: a versatile 1-fault-tolerant design for token rings. Information Processing Letters 72: 55-63.
As you can see, it is a network, as well as a tree. The authors describe it as "a 3-regular, planar, [optimal] 1-Hamiltonian, and Hamiltonian-connected graph." The Hamiltonian characteristic refers to the existence of a path through the network that connects all of the nodes and ends up back at the start node (ie. a cycle). The Christmas tree is created by joining two Slim trees together, believe it or not. (The Fat tree is a Slim tree with an extra edge connecting the left and right nodes.)
The authors' particular interest was in communications networks (eg. computer networks); but to me it looks like a (historical) phylogenetic tree at the top with an extra network added at the bottom showing (contemporary) ecological connections. It could thus summarize all of the biology in one diagram!
You can read about all of the above-mentioned graph types in the book by Lih-Hsing Hsu and Cheng-Kuan Lin (2009) Graph Theory and Interconnection Networks; CRC Press. You need to be a mathematician to make sense of it, though.
Thanks to Bradly Alicea for alerting me to this graph type.
PS. The above diagram is actually take from: Jeng-Jung Wang, Chun-Nan Hung, Jimmy JM Tan, Lih-Hsing Hsu, Ting-Yi Sung (2000) Construction schemes for fault-tolerant Hamiltonian graphs. Networks 35: 233-245.
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