The Genealogical World of Phylogenetic Networks: Network analysis of McDonald's fast-food

Season's greetings: or as we say here in Sweden: God jul och gott nytt år! In many cultures, over-dosing on food is traditional at this time of year, so it is appropriate to have a food-related blog post this week. [Note there is a follow-up blog post called: Is there good and bad fast-food?]

In 1954 a multi-mixer salesman decided to check out the fast-food operation of a couple of brothers in California, named McDonald, and then offered to form a partnership with them. Nearly 60 years later, there are approximately 34,000 fast-food stores with this name worldwide, although there are very few in Africa, and I don't think they have any in Antarctica. This virus-like growth has been accompanied by negative comments on the nutritional quality of the food. Indeed, the international Slow Food organization, which cares very much about the traditional quality of food, was first formed to contest the opening of a McDonald's store near the historic Spanish Steps in Rome.

In a blog post amusingly entitled Infinite Mixture Models with Nonparametric Bayes and the Dirichlet Process, Edwin Chen looked at the nutritional content of the food provided by this culinary mega-chain. Another way to look these data is to use a phylogenetic network as a means of exploratory data analysis, which is what I provide here.

The data

The data are taken from the official document McDonald's USA Nutrition Facts for Popular Menu Items, dated 7 August 2012. The stated purpose of the document is this: "We provide a nutrition analysis of our menu items to help you balance your McDonald's meal with other foods you eat. Our goal is to provide you with the information you need to make sensible decisions about balance, variety and moderation in your diet." I presume that the data are accurate, at least on average for each menu item.

The data consist of measurements of 12 dietary characteristics for 82 of the menu food items available in the USA (excluding the drinks), not all of which are necessarily available in other countries. The data for each characteristic are listed as "% Daily Value" based on a 2,000 calorie diet, which thus standardizes the data to the same scale across all of the variables, thereby making them directly comparable. The characteristics are:

Calories
Total Fat
Saturated Fat
Carbohydrates
Cholesterol
Dietary Fiber
Protein
Sodium
Vitamin A
Vitamin C
Calcium
Iron

Sugar values are also listed in the original document, but there is no FDA recommended daily allowance available for sugar, and so these cannot be included in my analysis. The FDA argument is that we get enough calories out of the fat and protein that we eat, and so we don't actually need any extra sugar in our diet.

The analysis

I have analyzed these data using the manhattan distance and a neighbor-net network. The result is shown in the figure. Menu items that are closely connected in the network are similar to each other based on their dietary characteristics, and those that are further apart are progressively more different from each other.

Click to enlarge.

The network is basically a blob, with three side branches. The blob (with menu items labelled in black) represents what we could call "typical" McDonald's products, while the side-branches (with the labels in various colours) represent more extreme products, with either more or less of some of the measured characteristics. Basically, the menu items are increasingly "bad for you" at right and better for you at the very bottom.

I have numbered parts of the side-branches as 1–7 in the figure, and coloured the food names, to indicate various groups that are worth discussing. These groups can be described as follows:

The dark red menu items to the right of (1) include the two Big Breakfast with Hotcakes, each of which provides 55% of your daily calorie needs (while most of the menu items to the left provide <40% each), and 40% of your iron requirements.
The menu items to the right of (2) (in red or dark red) include all four of the Big Breakfasts, which each provide nearly 200% of the recommended daily intake of cholesterol (most of the other items provide < 90%), >60% of the total fat requirement, and >65% of your sodium needs (ie. salt).
The items to the right of (3) (in orange, red or dark red) each provide >35% of your calorie needs and >60% of the total fat requirement, while those to the left provide less.
The purple items below (4) include all of the menu items with added egg, and so these have the next highest cholesterol levels after the four Big Breakfasts, at 80-95% of your daily requirements (the other menu items have <50%).
The four menu items to the left of (5) (in light green) are unique in containing >130% of your vitamin C needs, while the other items each provide <35%.
The items to the left of (6) (in blue or light green) include all of the fruit-based items and potato-based items (fries, hash browns) plus the chicken nuggets and bites. These are distinguished by having relatively low values of several characteristics, including those that are bad for you (total fat, saturated fat, cholesterol, and sodium) and those that are good for you (protein and calcium).
The green items below (7) include all nine of the Premium Salads (but not the Side Salad!). They each provide 160% of your vitamin A requirements (the other items each contain <20%), 25-35% of the vitamin C (most of the others contain <15%), and >15% of your dietary fiber.

The conclusions

This means that, for a healthy diet, you should steer well clear of the four "Big Breakfast" menu items, as they are very extreme even by McDonald's standards — you will need to take part in a great deal of strenuous exercise, to burn off their calories, cholesterol, fat and salt. The "Premium Salads", on the other hand, are extreme by having much less of these "bad for you" characteristics than is usual for McDonald's.

Unfortunately, while the the fruit concoctions (in light green and light blue) look good in the network, they also have more sugar (20-30 g each) than any of the other menu items (except the Cinnamon Melts), and therefore not everyone is a fan of them (eg. Mark Bittman; see also the MNN blog). Incidentally, it is also worth pointing out that fast-food in the USA is often much saltier than it is elsewhere in the world (see the article in Health magazine).

Finally, you might also like to compare the network locations of the menu items to William Harris' 10 Most Popular McDonald's Menu Items of All Time (not all of which have been included in my analysis):