Fast-food maps — a network analysis

Season's greetings!

For Christmas last year in this blog we had a Network analysis of McDonald's fast-food, in which I examined the food nutrient content of a well-known fast-food vendor. This year I continue the same theme, but expand it to cover an analysis of the geographical locations of various fast-food chains within the USA.

The US restaurant industry included about 550,000 restaurants in 2012 (SDBCNet). Technically, this food industry distinguishes different types of restaurant. The ones we are interested in here are called "quick service restaurants" (QSR), which includes what are known as fast-food and fast-casual restaurants. These are sometimes also called "limited service restaurants".

There are quite a few QSR companies in the USA, and each of them has quite a few locations. In 2012, there were apparently 313,000 fast-food and fast-casual restaurants (Yahoo Finance blog The Exchange), which is more than 50% of the total restaurants. In 2005, more than two-thirds of the largest 243 cities in the US had more fast-food chains than all other restaurant types combined (Zachary Neal).

The QSRs serve an estimated 50 million Americans daily (The Statistic Brain). Indeed, in a 2011 poll of people in 87 U.S. cities, there were several places where >30% of the people had visited QSRs 20+ times in the previous month (nearly once per day), while in all cities >80% of the people had visited at least once (Sandelman & Associates).

The QSR group reports that the national top 20 fast-food chains for 2012 were as shown in the first graph. This includes both company-owned units as well as franchised locations. Note that McDonald's had 34,480 restaurants in its worldwide system, with 14,157 of those being in the USA (The Exchange).

It is of interest to look at how this pattern has changed through time, and so I have taken the data from the QSR group's reports for 2003 to 2012, inclusive (these are the only ones available online). These data are for the number of locations of each of the top 50 chains each year in terms of dollar income. There are 61 chains that appear in the list for at least one of the years, but only 46 of these appeared often enough in the top 50 to be worth including in the analysis.

For this analysis, we can use a phylogenetic network. As usual, I have used the manhattan distance (on range-standardized data) and a neighbor-net network. The result is shown in the next figure. Fast-food chains that are closely connected in the network are similar to each other based on their restaurant numbers over the past decade, and those that are further apart are progressively more different from each other.

The network forms a simple chain from Subway (the biggest) through to the group of very similar-sized chains at the bottom-left. This indicates that most of the restaurant chains have been fairly consistent in their relative sizes throughout the past decade (ie. the big stayed big and the small stayed small), although some chains have changed size. For example, KFC and Taco Bell have each shrunk by 15% since 2007, while Jack in the Box has expanded by 10%.

However, there is a large reticulation in the network involving Starbucks. This is caused by the fact that Starbucks started the decade as a much smaller chain than both Burger King and Pizza Hut, but it is now much larger than either of them. Similarly, there is another reticulation involving Cold Stone Creamery, which expanded rapidly in 2005 (increasing their number of locations by 50%).

The number of locations does not relate directly to dollar turnover, of course, as Subway has much smaller restaurants than do most of the other chains. In this respect, McDonald's leads the way by a considerable margin, with $35,600,000,000 in system-wide sales in the USA during 2012, versus $12,100,000,000 for Subway. This works out at $2,600,000 and $481,000 per restaurant per year, respectively. Starbucks comes in third, with $10,600,000,000 in 2012 ($1,223,000 per unit).

However, let's stick to the number of units, rather than the dollars, and consider their geographical locations. There are several datasets available on the internet that provide this information for different chains (which you actually could get yourself by visiting the homepage of each chain and asking for the location of each restaurant, one at a time!). If you are prepared to pay some money, then you can have the latest list from AggData; but I am not in that league.

However, apparently the man at the Data Pointed blog is in that league, or was in 2010. His mapped version of the data for McDonald's (only) looks like this next figure (each dot represents one restaurant).

This has led him to contemplate the McFarthest Point, which is the point in the contiguous US states that is furthest from a McDonald's restaurant. He reckons that its map co-ordinates are: +41.94389, –119.54010. He has made an excursion to this spot (along with some fast-food), which you can read about in A Visit To The McFarthest Spot.

In turn, this caused the man at the Consumerist blog to contemplate the equivalent spot for Subway. This is currently estimated to be +42.397327, –117.956840 (Is This the Farthest Away You Can Get From a Subway in the Continental U.S.?).

Returning now to the data sources, you could also look at the data from the Food Environment Atlas (by Vince Breneman and Jessica Todd, of the USDA Economic Research Service). At the time of writing, this contains a Map with Fast-food restaurants / 1000 population for 2009, showing each individual county. This refers to the total number of units, summed across all fast food chains. A similar map is available at Business Insider, aggregated by state (but based on the 2008 data).

However, I cannot pay for the data, and I want the data separately for the different fast-food chains. That leads me to the Fast Food Maps by Ian Spiro. In 2007, he scraped the data from the web pages of various chains (as I noted above), and has made it available as a web page and an associated datafile.

He has included data for 10 of the fast-food chains, based on those present in the state of California. So, he covers only 8 out of the top 20 national chains: McDonald's, Burger King, Pizza Hut, Wendy's, Taco Bell, KFC, Jack in the Box, and Hardee's. To these, he adds Carl's Jr (mainly on the West Coast of the USA) and In-N-Out Burger (mainly in the South-West), which I did not include in my analysis.

To analyze these data, I took the information for each chain in each state and divided this by the number of people in that state (to yield the number of restaurants per 100,000 people per chain per state). I then produced a phylogenetic network, as described above, and as shown in the next graph. States that are closely connected in the network are similar to each other based on the density of restaurants of each chain, and those that are further apart are progressively more different from each other. I have color-coded the states to highlight the similarities.

In the network, the states turn out to be arranged roughly geographically, with a few exceptions. In other words, neighboring states have similar densities of restaurants from certain fast-food chains.

For example, the red-colored states are from the West (including in the Pacific!), and they don't have Hardee's, but do have most of the Jack in the Box restaurants. The brown-colored states are from the North Centre, and these have the highest density of Burger King and Pizza Hut. Montana is separate from this grouping because it has a lower density of both Burger King and KFC.

The orange-colored states are from the Mid West and the South, and these have the highest density of Hardee's. Georgia is separate from this grouping because it has a lower density of Hardee's; and Florida is separate because it has a lower density of most chains. The blue-colored states are also from the Mid West, and these have the highest density of McDonald's and Wendy's. Illinois is separate because of a lower density of most chains (particularly KFC) except for McDonald's.

The dark-green-colored states are from the North East, and these don't have Hardee's, and they have the lowest density of Pizza Hut. The light-green-colored states are also from the North East, and these form a separate grouping because they have a higher density of most chains except McDonald's. Maryland is separate because it has an even higher density of most chains (particularly Hardee's); and Delaware has a higher density of Hardee's and Taco Bell.

Finally, Oklahoma and New Mexico have the highest density of KFC.

NB. For an interactive map showing the locations of the 507 Dunkin' Donuts, 269 Starbucks and 235 McDonald's in New York City (in October 2013), check out Mapping the Big Apple's Big Macs, Coffee, and Donuts. The concentration of Starbucks in downtown and midtown Manhattan is truly impressive. Indeed, 43% of the city's cafés are either Dunkin' Donuts or Starbucks (Coffee and Tea in New York City).

Conclusion

So, there you have it — fast-food is not randomly distributed in the USA. Where you live determines how much you have available of the different types. Indeed, as Pam Allison's Blog notes: "Although restaurants like McDonalds are very popular nationwide, they aren’t necessarily the most popular on a local level. In fact, there are only a handful of zip codes in the United States where McDonald's is the most popular. Rather, many local or regional chains are the more likely choice with consumers."

There are many other aspects to the geography of food, especially fast-food; but these can wait until a later blog post.

Is rate variation among lineages actually due to reticulation?

Non-congruence among characters has traditionally been attributed solely to so-called vertical evolutionary processes (parent to offspring), which can be represented in a phylogenetic tree. For example, phenotypic incongruence was originally attributed solely to homoplasy (convergence, parallelism, reversal). For molecular data this could be modeled with DNA substitutions and indels, along with allowance for variable rates in different genic regions (e.g. invariant sites, or the well-known gamma model of rate variation).

This approach was not all that successful, and so the substitution models were made more complex, by allowing different evolutionary rates in different branches of the tree (e.g. substitutions are more or less common in some parts of the tree compared to others). For many researchers this is still as sophisticated as their phylogenetic models get (Schwartz & Mueller 2010), allowing for a relaxed molecular clock in their model rather than imposing a strict clock.

There is, however, a fundamental limitation to trying to make any one model more sophisticated: the more complex model will probably fit the data better but it might be fitting details rather than the main picture. Consider the illustration below. There is a lot of variation among these six animals and yet they are all basically the same. If I wish to devise a model to describe them, do I need a sophisticated model that describes all the nuances of their shape variation, or do I need a simple model that recognizes that they are all five-pointed stars? The answer depends on my purpose — if I wish to identify them to class then it is the latter, if I wish to identify them to species then it might be the former.

Vertical process models

This is relevant to phylogenetics. For example, if I wish to estimate a species tree from a set of gene trees, do I need a complex model that deals with all of the evolutionary nuances of the individual gene trees, or a simpler model that ignores the details and instead estimates what the trees have in common? It has been argued that the latter will be more useful under these circumstances. On the other hand, if I am studying gene evolution itself, I may be better off with the former.

So, adding things like rate variation among lineages (and also rate variation along genes) will usually produce "better fitting" models. However, this is fit to the data, and the fit between data and model is not the important issue, because this increases precision but does not necessarily increase accuracy.

Therefore, modern interest is in changing the fundamentals of the model, rather than changing its details. There are many possible causes of gene-tree incongruence, and maybe these should be in the model in order to increase accuracy.

For example, there has been interest in adding other vertical processes to the tree-building model, most notably incomplete lineage sorting (ILS) and gene duplication-loss (DL). ILS means that gene trees are not expected to exactly match the species tree, but will vary stochastically around that tree, with probabilities that can be calculated using the coalescent. DL means that gene copies appear and disappear during evolution, so that gene sequence variation is due to hidden paralogy as well as to orthology.

ILS has been modeled by being integrated into a more sophisticated DNA substitution model (see the papers in Knowles & Kubatko 2010). Originally, DL was dealt with at the whole-gene level (Slowinski and Page 1999; Ma et al. 2000), but there have been recent attempts to integrate this into the DNA substitution models, as well (Åkerborg et al. 2009; Rasmussen & Kellis 2012). These models are not yet widely used, and so most published empirical species trees still rely on modeling incongruence using rate variation among branches.

Horizontal process models

However, this whole approach restricts the phylogenetic model to vertical processes alone. It is entirely possible that the sequence variation that is being attributed to rate variation among branches is actually being caused by horizontal evolutionary processes, such as recombination, hybridization, introgression or horizontal gene transfer (HGT). For example, an influx of genetic material from outside a lineage could be mis-interpreted as an increase in the rate of substitutions and indels within that lineage. That is, long branches might represent introgression (or HGT) rather than in situ rate variation. If this is true then we would be modeling the wrong thing.

There has been little explicit discussion of this point in the literature. Syvanen (1987) seems to have been among the first. However, his premise was that the molecular clock is ultimately correct (and that "the basic observation has been that different macromolecules yield roughly the same phylogenetic picture"), and he was arguing that HGT does not necessarily violate the clock. Our modern perspective is, of course, that a strict clock is unlikely unless it has been demonstrated, and that genes are incongruent as often as they are congruent.

Recent models for ILS and DL have started to broach this issue, by adding reticulation to their underlying models. Rather oddly, this has usually been described as:

• ILS + hybridization (Meng & Kubatko 2009; Kubatko 2009; Joly et al. 2009; Bloomquist & Suchard 2010; Yu et al. 2011; Marcussen et al. 2012; Jones et al. 2013; Yu et al. 2013); and
• DL + HGT (Mirkin et al. 2003; Górecki 2004; Hallett et al. 2004; Csürös & Miklós 2006; Doyon et al. 2010; Tofigh et al. 2011; Bansal et al. 2012; Sjöstrand et al. 2012).

This pairwise association seems to reflect historical accident, rather than any actual mathematical difference in procedure — the gene-tree incongruence patterns are essentially the same for hybridization, introgression and HGT, as well as recombination. In the mathematical models, all we can really talk about is "reticulation" — it is up to the biologist to determine the nature of the horizontal process in each case.

Conclusion

The point here is essentially the same one that I made in a previous post (Resistance to network thinking). Currently, phylogenetics is approached in a very conservative manner. The "old way" is the best way, and things change very slowly. The currently popular phylogenetic models are simply variants of the same models that have been used for 30 years. Temporal rate variation (among lineages) and spatial rate variation (along genes) have been added to the original model from the 1970s, but not yet more complex vertical processes (ILS or DL), and not yet horizontal processes. For these, specialist programs need to be used.

Essentially, all variation in branch length is still attributed to homoplasy and rate variation, rather than considering the myriad of other biological processes that will produce the same apparent phenomen. With this attitude we might be getting more precise models but not necessarily more accurate one.

References

Åkerborg Ö, Sennblad B, Arvestad L, Lagergren J (2009) Simultaneous bayesian gene tree reconstruction and reconciliation analysis. Proceedings of the National Academy of Sciences of the USA 106: 5714-5719.

Bansal MS, Alm EJ, Kellis M (2012) Efficient algorithms for the reconciliation problem with gene duplication, horizontal transfer and loss. Bioinformatics 28: i283-i291.

Bloomquist EW, Suchard MA (2012) Unifying vertical and nonvertical evolution: a stochastic ARG-based framework. Systematic Biology 59: 27-41.

Csürös M, Miklós I (2006) A probabilistic model for gene content evolution with duplication, loss, and horizontal transfer. Lecture Notes in Computer Science 3909: 206-220.

Doyon J-P, Scornavacca C, Gorbunov KY, Szöllösi GJ, Ranwez V, Berry V (2019) An efficient algorithm for gene/species trees parsimonious reconciliation with losses, duplications and transfers. Lecture Notes in Computer Science 6398: 93-108.

Górecki P (2004) Reconciliation problems for duplication, loss and horizontal gene transfer. In: Bourne PE, Gusfield D (editors). Proceedings of the 8th Annual International Conference on Research in Computational Molecular Biology, pp. 316-325. ACM Press, New York.

Hallett M, Lagergren J, Tofigh A (2004) Simultaneous identification of duplications and lateral transfers. In: Bourne PE, Gusfield D (editors). Proceedings of the 8th Annual International Conference on Research in Computational Molecular Biology, pp. 347-356. ACM Press, New York.

Joly S, McLenachan PA, Lockhart PJ (2009) A statistical approach for distinguishing hybridization and incomplete lineage sorting. American Naturalist 174: E54-E70.

Jones G, Sagitov S, Oxelman B (2013) Statistical inference of allopolyploid species networks in the presence of incomplete lineage sorting. Systematic Biology 62: 467-478.

Knowles LL, Kubatko LS (editors) (2010) Estimating Species Trees: Practical and Theoretical Aspects. Wiley-Blackwell, Hoboken NJ.

Kubatko L (2009) Identifying hybridization events in the presence of coalescence via model selection. Systematic Biology 58: 478-488.

Ma B, Li M, Zhang L (2000) From gene trees to species trees. SIAM Journal on Computing 30:
729-752.

Marcussen T, Jakobsen KS, Danihelka J, Ballard HE, Blaxland K, Brysting AK, Oxelman B (2012) Inferring species networks from gene trees in high-polyploid North American and Hawaiian violets (Viola, Violaceae). Systematic Biology 61: 107-126.

Meng C, Kubatko LS (2009) Detecting hybrid speciation in the presence of incomplete lineage sorting using gene tree incongruence: a model. Theoretical Population Biology 75: 35-45.

Mirkin BG, Fenner TI, Galperin MY, Koonin EV (2003) Algorithms for computing parsimonious evolutionary scenarios for genome evolution, the last universal common ancestor and dominance of horizontal gene transfer in the evolution of prokaryotes. BMC Evolutionary Biology 3: 2.

Rasmussen MD, Kellis M (2012) Unified modeling of gene duplication, loss, and coalescence using a locus tree. Genome Research 22: 755-765.

Schwartz RS, Mueller RL (2010) Variation in DNA substitution rates among lineages erroneously inferred from simulated clock-like data. PLoS One 5: e9649.

Sjöstrand J, Sennblad B, Arvestad L, Lagergren J (2012) DLRS: gene tree evolution in light of a species tree. Bioinformatics 28: 2994-2995.

Slowinski J, Page RDM (1999) How should species phylogenies be inferred from sequence
data? Systematic Biology 48: 814-825.

Syvanen M (1987) Molecular clocks and evolutionary relationships: possible distortions due to horizontal gene flow. Journal of Molecular Evolution 26: 16-23.

Tofigh A, Hallett M, Lagergren J (2011) Simultaneous identification of duplications and lateral gene transfers. IEEE/ACM Transactions on Computational Biology and Bioinformatics 8: 517-535.

Yu Y, Barnett RM, Nakhleh L (2013) Parsimonious inference of hybridization in the presence of incomplete lineage sorting. Systematic Biology 62: 738-751.

Yu Y, Than C, Degnan JH, Nakhleh L (2011) Coalescent histories on phylogenetic networks and detection of hybridization despite incomplete lineage sorting. Systematic Biology 60: 138-149.

Phylogenetics, ecologist style

Many of us are familiar with how a phylogeneticist, systematist or evolutionary biologist constructs a phylogenetic tree. However, ecologists apparently do it differently. Scott Chamberlain explains this procedure in one of his blog posts (Networks phylogeny):

There were about 500 species to make a phylogeny for, including birds and insects, and many species that were bound to end up as large polytomies. I couldn't in reasonable time make a molecular phylogeny for this group of species, so I made one ecologist style.

That is, I:

• Created a topology using Mesquite software from published phylogenies, then
• Got node age estimates from timetree.org (p.s. Wish I could use the new datelife.org, but there isn't much there quite yet), then
• Used the bladj function in Phylocom to stretch out the branch lengths based on the node estimates.

Unfortunately, this process can't all be collected in an R script.

He then describes this process in more detail, which he hopes "makes it more reproducible". Here is his final tree (produced by FigTree).

This is an interesting bioinformatic solution to a biological problem, when empirical data collection has failed. I am not sure that I can recommend its widespread use, though.

Textbooks and phylogenetic networks

The question has been asked as to which of the current general books about phylogenetics actually cover phylogenetic networks. There are collections of essays where networks are covered, and there are specialist books, of course, but the question here is about general introductory books. While a number of books mention tree incongruence, and that this phenomenon could be represented using a reticulating graph, there appear to be only two books that specifically cover the topic of phylogenetic networks.

(1)
Barry G. Hall (2011) Phylogenetic Trees Made Easy: A How-To Manual, Fourth Edition. Sinauer Associates, Sunderland MA.

The first three editions (2001, 2004, 2008) discussed trees only, but the fourth edition has added a chapter on networks. Chapter 15 (pp. 219-248) explicitly notes that "The material presented here is drawn almost entirely from the new book Phylogenetic Networks: Concepts Algorithms and Applications", which is also noted was "made available to me in manuscript prior to its publication."

There are four sections in the chapter:
  Why Trees Are Not Always Sufficient
  Unrooted and Rooted Phylogenetic Networks
  Learn More about Phylogenetic Networks
  Using SplitsTree to Estimate Unrooted Phylogenetic Networks
  Using Dendroscope to Estimate Rooted Networks from Rooted Tree

The first three sections are theoretical introductions to the topic, and the final two sections proceed through a worked example (a different one each).

The book provides a basic introduction to phylogenetics, which is its intent. So, the network topics are presented in a straightforward manner, which makes them easy to grasp. The worked examples are cookbook style, intended solely to get you started using the two chosen computer programs.

The author is to be congratulated for producing not only the first, but so far the only, general book that covers evolutionary networks.

(2)
Philippe Lemey, Marco Salemi, Anne-Mieke Vandamme (editors) (2009) The Phylogenetic Handbook: A Practical Approach to Phylogenetic Analysis and Hypothesis Testing, Second Edition. Cambridge Uni Press, Cambridge.

The first edition (2003) had a chapter on SplitsTree by Vincent Moulton, and this was revised in the current edition to Split Networks: a Tool for Exploring Complex Evolutionary Relationships in Molecular Data, Chapter 21 (pp. 631-653), by Vincent Moulton and Katharina Huber.

The chapter provides a general introduction to the theory of splits graphs and their uses; and the practical exercises use SplitsTree. This was the first general book on phylogenetics to include networks, although evolutionary networks are not covered.

Conclusion

The coverage of networks is the final topic in the book in both cases, so it can hardly be claimed to have an important place. Nevertheless, these books are at least one step ahead of their competitors.

All of these books are examples of the contemporary focus on congruent tree patterns in evolution, with reticulate relationships being almost an afterthought. There is nothing in the word "phylogeny" that specifies a shape for evolutionary history — it comes from the Greek phylon "race" + geneia "origin". Evolutionary groups may arise by either vertical or horizontal processes, and so evolution may be tree-like or it may not. The current focus almost exclusively on trees is therefore somewhat misplaced.

Results of some bioinformatics polls

In 2008, Michael Barton conducted a Bioinformatics Career Survey. Since then, various groups have updated some of that information by conducting polls of their own. Below, I have included some of the more recent results, for your edification.

This first one comes from the Bioinformatics Organization, in response to the question: What is your undergraduate degree in? It is interesting to note that more bioinformaticians are biologists by training, rather than computational people.

The next one is actually an ongoing poll at BioCode's Notes, in response to the question: Which are the best programming languages for a bioinformatician? R is an interesting choice as the most useful language, given the more "traditional" use of Perl and Python.

That leads logically to another of the Bioinformatics Organization's questions: Which computer language are you most interested in learning (next) for bioinformatics R&D? I guess that if you already know R, then either Python or Perl is a useful thing to learn next.

Furthermore, the Bioinformatics Organization also asked: Which math / statistics language / application do you most frequently use? The choice of R here is more obvious, given that it is free, which most of the others are not. I wonder what the answer "none of the above" refers to.

The phylogenetics of Little Red Riding Hood

A couple of weeks ago we received an unexpected influx of visitors to this blog, being directed here by at article at the NBC News site. This article cited one of our blog posts (Network analysis of Genesis 1:3) as an example of the use of phylogenetic analysis in stemmatology (the discipline that attempts to reconstruct the transmission history of a written text). The NBC article itself is about a recently published paper that applies these same techniques to an oral tradition instead — the tale of Little Red Riding Hood. This paper has generated much interest on the internet, being reported in many blog posts, on many news sites, and in many twitter tweets. After all, the young lady in red has been known for centuries throughout the Old World.

Needless to say, I had a look at this paper (Jamshid J. Tehrani. 2013. The phylogeny of Little Red Riding Hood. PLoS One 8: e78871). The author collated data on various characteristics of 58 versions of several folk tales, such as plot elements and physical features of the participants. These tales included Little Red Riding Hood (known as Aarne-Uther-Thompson tale ATU 333), which has long been recorded in European oral traditions, along with variants from other regions, including Africa and East Asia (where it is known as The Tiger Grandmother), as well as another widespread international folk tale The Wolf and the Kids (ATU 123), which has been popular throughout Europe and the Middle East. As the author notes: "since folk tales are mainly transmitted via oral rather than written means, reconstructing their history and development across cultures has proven to be a complex challenge."

He produced phylogenetic trees from both parsimony and bayesian analyses, along with a neighbor-net network. He concluded: "The results demonstrate that ... it is possible to identify ATU 333 and ATU 123 as distinct international types. They further suggest that most of the African tales can be classified as variants of ATU 123, while the East Asian tales probably evolved by blending together elements of both ATU 333 and ATU 123." His network is reproduced here.

There is one major problem with this analysis: all three graphs are unrooted, and you can't determine a history from an unrooted graph. A phylogeny needs a root, in order to determine the time direction of history. Without time, you can't distinguish an ancestor from a descendant — the one becomes the other if the time direction is reversed. Unfortunately, the author makes no reference to a root, at all.

So, his recognition of three main "clusters" in his graphs is unproblematic (ATU 333; East Asian; and ATU 123 + African) although the relationship of these clusters to the "India" sample is not clear (as shown in the network). On the other hand, his conclusions about the relationships among these three groups is not actually justified in the paper itself.

Rooting the trees

So, the thing to do is put a root on each of the graphs. We cannot do this for the network, but we can root the two trees, and we can take the nearest tree to the network and root that, instead.

There are several recognized ways to root a tree in phylogenetics (Huelsenbeck et al. 2002; Boykin et al. 2010):

1. a character transformation series (i.e. non-reversible substitution models)
2. an outgroup
3. mid-point rooting
4. assume clock-like character replacement (e.g. the molecular clock).

The first one implies that we know the order in which at least some of the characters changed through time, which is not true for these folk tales. The second one requires us to know the next most closely related folk tale, which we cannot decide in this case. The third one is always possible, for any tree; and the fourth one is possible if a likelihood model has been used to model character changes. So, in this case, we can apply both of options 3 and 4.

I therefore did the following:

• For the parsimony analysis, I imported the author's consensus tree into PAUP* (the program he used to produce it), calculated the branch lengths with ACCTRAN optimization, and found the midpoint root.
• For the bayesian analysis, I re-ran the MrBayes analysis exactly as described by the author, except that I added a relaxed clock (with independent gamma rates model for the variation of the clock rate across lineages).
• For the phylogenetic network, the neighbor-net is basically the network equivalent of a neighbor-joining tree, and so I calculated this in SplitsTree (the program the author used), and found the midpoint root.
• Also, the strict clock version of a neighbor-joining tree is a UPGMA tree, which I calculated using SplitsTree.

The complete trees can be seen elsewhere (ParsimonyMidpoint; BayesRelaxed; NJmidpoint; UPGMA), but the figure below shows the relevant parts of the four rooted trees. As you can see, the first three analyses agree on the root location (shown at the left of each graph), with only the UPGMA tree suggesting an alternative.

Having the East Asian samples as the sister to the other tales does not match what would be expected for the historical scenario suggested by the original author from his unrooted graphs — that the East Asian tales "evolved by blending together elements of both ATU 333 and ATU 123".

Instead, this placement exactly matches an alternative theory that the author explicitly rejects: "One intriguing possibility raised in the literature on this topic ... is that the East Asian tales represent a sister lineage that diverged from ATU 333 and ATU 123 before they evolved into two distinct groups. Thus, ... the East Asian tradition represents a crucial 'missing link' between ATU 333 and ATU 123 that has retained features from their original archetype ... Although it is tempting to interpret the results of the analyses in this light, there are several problems with this theory."

The UPGMA root, on the other hand, would be consistent with the blending theory for the origin of the East Asian tales. However, this tree actually presents the African tales as distinct from ATU 123, rather than being a subset of it.

Anyway, the bottom line is that you shouldn't present scenarios without a time direction. History goes from the past towards the present, and you therefore need to know which part of your graph is the oldest part. A family tree isn't a tree unless it has a root.

References

Boykin LM, Kubatko LS, Lowrey TK (2010) Comparison of methods for rooting phylogenetic trees: a case study using Orcuttieae (Poaceae: Chloridoideae). Molecular Phylogenetics & Evolution 54: 687-700.

Huelsenbeck J, Bollback J, Levine A (2002) Inferring the root of a phylogenetic tree. Systematic Biology 51: 32-43.

The bioRxiv — not just a preprint server for biology

The physical sciences have long had preprint archives, notably the arXiv (founded in 1991), which is managed by Cornell University Library. Bioinformaticians have been active users of these archives, at least partly because getting mathematical papers published can take up to 2 years (see Backlog of mathematics research journals). Bioinformatics moves faster than that. There have been more general preprint services, as well, such as Nature Precedings, which operated from 2007 to 2012.

There have recently been moves afoot to provide similar services specifically for biologists; and the beta version of the bioRxiv has now come online:

bioRxiv (pronounced "bio-archive") is a free online archive and distribution service for unpublished preprints in the life sciences. It is operated by Cold Spring Harbor Laboratory, a not-for-profit research and educational institution. By posting preprints on bioRxiv, authors are able to make their findings immediately available to the scientific community and receive feedback on draft manuscripts before they are submitted to journals.

Many research journals, including all Cold Spring Harbor Laboratory Press titles, EMBO Journal, Nature journals, Science, eLife, and all PLOS journals allow posting on preprint servers such as bioRxiv prior to publication. A few journals will not consider articles that have been posted to preprint servers.

Preprint policies are summarized here: List of academic journals by preprint policy.

Many people seem to see archives such as this as having their principal role in bridging the publication delay caused by the peer-review process (see The case for open preprints in biology for a summary of the argument). Indeed, much of the online discussion of preprints in biology seems to be about why biologists have not taken to preprints like ducks to water, asking the rhetorical question: "What are biologists afraid of?" This question pre-supposes that everyone should use preprints unless there is a good reason not to, rather than the more obvious assumption that no-one will use them unless there is a good reason to do so. On the whole, shortening the peer-review process by a few months (as is typical in biology) hardly seems like a sufficient incentive for mass usage of preprints.

However, there does seem to be a possible incentive beyond break-neck speed. An equally important point is that archives act as a powerful means of making unpublished work available online. Even if a particular manuscript is ultimately never published in a journal or book, it will still be available in the archive in its final draft form, since the archives are intended to be permanent repositories. That is, the archives are not only for pre-prints.

There are many reasons why some work never gets formally published, including incompleteness of the data, negative results, lack of perceived profundity, and being out of synch with current trends. If there is nothing inherently faulty about a manuscript, then there is no reason for it to remain unavailable to interested readers. We are no longer beholden to the publishers (or to the referees) for disseminating our data and/or ideas, although we may still prefer formal publication as the primary conduit.

For example, I started using the arXiv after it added a section on "Quantitative Biology" in 2003. I have several manuscripts in the ArXiv that, for one reason or another, have not (yet) made it into print:

• Morrison DA (2005) Counting chickens before they hatch: reciprocal consistency of calibration points for estimating divergence dates. arXiv
• Morrison DA (2005) Bayesian posterior probabilities: revisited. arXiv
• Jenkins M, Morrison DA, Auld TD (2005) Estimating seed bank accumulation and patterns in three obligate-seeder Proteaceae species. arXiv
• Morrison DA (2009) How and where to look for tRNAs in Metazoan mitochondrial genomes, and what you might find when you get there. arXiv
• Kelk S, Linz S, Morrison DA (2013) Fighting network space: it is time for an SQL-type language to filter phylogenetic networks. arXiv

I do not see these manuscripts as in any way inferior to my published papers.

They have all been indexed by search engines such as Google, and they are thus available via Google Scholar (which also keeps track of citations of preprint papers), as well as via professional sites such as ResearchGate. In this sense, the data and ideas are just as "available" as they would be in any peer-reviewed publication, and potential "scholarly impact" is not compromised. Indeed, Twitter mentions of arXiv papers are recognized as being a powerful means of disseminating their content, irrespective of later publication (see How the scientific community reacts to newly submitted preprints: article downloads, twitter mentions, and citations). I even know of bioinformatics papers that were still being cited via the online pre-print (labeled as a "Technical Report") long after they finally made it into print.

So, preprint archives are a valuable tool for academics, especially when those pesky referees are not being co-operative.

PS. This is post number 200 for this blog.