Wednesday, June 17, 2015

Fibonacci Numbers And Odd Lungs

Biology concepts – respiratory system, bilateral asymmetry, evolution, estivation, Fibonacci scaling in nature


Worf, although raised by humans,was mostly Klingon.
He definitely adhered to their warlike nature. His
three lungs would make him a great fighter. More
oxygen exchange means more ATP production
and more energy for the muscles. 
Not that I’m a devout Star Trek fan, but did you know that Klingons are supposed to have three lungs? The third lung was supposed to give them extra endurance on the battlefield – makes sense.

Closer to home, there was a soccer player from South Korea, Park Ji-Sung, who played for Manchester United. His nickname was “Three Lungs Park” because he could run and run without tiring.  Maybe he’d still be playing if figured out where the ball was going to be and attacked there; a Klingon would have.

Continuing our stories of internal bilateral asymmetries, let’s look at the lungs. Most people have a general idea of what their lungs look like, they seem to be fairly symmetric – but they’re not, not by a long shot. Lungs are perhaps the most asymmetric of the paired organs. Knowing this, I started to wonder if there are any animals with three lungs, or maybe just one lung.

I wonder weird things, don’t I? As it turns out, we can find examples of both in the same animal group. Snakes come in several flavors with respect to lungs and breathing. Some snakes have just one lung. This is helpful for maintaining their svelte figures, losing a lung for them was strictly a space saving measure.


See in this picture how the trachea can stick out
and to the side while it swallows prey. As it
draws in the prey, the right and left sides of the
jaw will ”walk” over the body. As this happens,
the trachea will switch back and forth from side
to side to maintain an open airway.
Snakes have a trachea that is somewhat like ours. It has rings or partial rings of cartilage that carry air from the mouth to the lung(s). They mouth breathe, but occasionally their mouths are full, having unhinged to swallow something whole. So how do they breathe when they have their mouths, throats and bodies stuffed with a rat or a goat or overly curious next door neighbor?

I'd think they would have a hard time of it. Could you breathe through your mouth after stuffing it with the last four dinner rolls just so your brother wouldn't get them? I think not. But the trachea of snakes is better than ours. It isn’t anchored in the throat, so it can actually move forward like a snorkel (see the picture). The trachea will stick out the side of their mouth as they stuff it full of very surprised frog legs, allowing them to breathe and eat at the same time.

A snake’s trachea communicates with its lung or lungs, depending on how many they have. Many species have a long, skinny right lung and a very small, nonfunctional left lung. As far as I can tell, it’s always the right lung that functions. So for snakes, possibility number one is just a right lung; possibility two is having a right lung and a small, nonfunctional left lung.


Atretochoana eiselti is the only known species
of lungless caecilian, a legless type of amphibian
that looks much like a worm. You can see in the
lower image that it has sealed, nonfunctional
nostrils. It gets its oxygen through its skin in its
moist environment. A second lungless caecilian,
this one totally terrestrial, was supposedly found
 in 2009. But a later study showed that it does
have a well-developed single lung.
The exceptions are the boide snakes. These are the boas and pythons. They have a left lung that exchanges gases just fine, it just happens to be a bit smaller than the right lung. That's possibility number three.

In the cases of snakes with nonfunctional or barely functional left lungs, some can have a tracheal lung. This is a sac that sits on the dorsal (back) side of the trachea, above the level of where the trachea enters the lung(s). Even though this sac may or may not have typical gas exchange epithelial structures, it can exchange oxygen for carbon dioxide because it is highly vascularized and has a very thin barrier. That's four - four different lung anatomies and numbers, and all within the snakes.  

If a snake swallows something wider than its body, it makes it very hard to expand the lung(s) to breathe. The tracheal lung comes directly off the trachea, so if the snake can get air into its trachea, it can breathe via the tracheal lung, even if it can’t expand its large right lung.

So there we have it, evolution resulted in some snakes with one lung, some with two, and others with three (big right lung, small left lung and a tracheal lung). This begs the questions – did snakes originally have two lungs and were reduced to a single lung and perhaps a tracheal lung? Or did primitive snakes have one lung and some have developed more over evolutionary time?

A 2015 paper has compared the anatomy and development of vasculature in three lineages of snakes lung numbers that represent the versions we have talked about here. This paper concludes that there has been a step-wise reduction in the functionality and size of the left lung through evolutionary time.

Most animals with lungs have two of them (snakes not withstanding). How about animals with no lungs? There are so many that you could hardly call them exceptions. Nematodes, flatworms, placazoans, sponges, cnidarians, some arthropods (insects) and some annelids (earthworms and such) – the animals of these phyla exchange oxygen for carbon dioxide via direct diffusion through skin and outer layers.


Mudskippers are not lungfish. They have functional
gills and can trap an air bubble in their gills to
breathe while they are out of water.
Echinoderms, some arthropods (crustaceans), some annelids (polychetes), most mollusks, and most fish have gills that extract oxygen from the water. So really, it’s just a few snails and most of the tetrapods (four limbed animals) that have lung(s). Maybe we’re the exceptions.

Amphibians present some exceptions. Most have lungs, but can also absorb oxygen through their skin. Frogs have gills as tadpoles, but adults can breathe air via lungs, diffuse oxygen through their skin, and even exchange gases through the lining of their mouth. Of course, there is an exception to the exception in frogs. In 2008, scientists discovered the first lungless frog, on Borneo. This species only exchanges gases through its skin and mouth; the rest of its organs have expanded to take up the space of the lost lungs.

Did you notice above that fish were on our list of lungless animals, since they use gills to exchange gases? Well, that’s not true for all fish. The lungfish are aptly named; they have lungs and can breathe out of water.


The lungfish can hibernate (estivate) for years
until the rain brings it out of stasis. It can only
do this because it is an obligate air breather.
Many species of lungfish (the Dipnoi subclass) are obligate air breathers even though they do have gills. Most lungfish have two lungs, but the Australian lungfish only has one (yet another animal with one lung). These lungs look more like ours than like a tracheal lung air sac of snakes. They aren’t just highly vascularized bags, they are divided and have terminal gas exchanging structures like our alveoli.

The lungs of lungfish are modified swim bladders. The swim bladder is a buoyancy device; by altering the amount of gas in the bladder, the density of the fish is altered and helps it to dive, surface or maintain a certain depth. Without a swim bladder, the fish would constantly be working harder to dive, surface, or maintain its place in the water column.

The lungs of all tetrapods evolved from the swim bladder of fish when their ancestors left the water for land. However, some just modified their swim bladder and stayed in the water. It was thought for a long time that the lungs of lungfish and birchi (another type of fish that have lungs) evolved to help them survive in water that had little dissolved oxygen.


The top image shows the three lobes of the right
lung and the two lobes of the left lung. Notice the
cardiac notch in the left lung. Each lung is divided
 into lobes, segments, and lobules. The bottom
image shows the bronchial tree. This tree goes
along with the caption in the next figure. Notice
how much longer the left bronchus is than the
right. Does it look like the tree branching in the
picture below?
This is possible, since many live in freshwater that can have very low oxygen levels (like in Amazon or some African rivers), but it may also be that the lungs developed to provide more oxygen to the heart. This in turn allowed them to have more energy, grow bigger and be more active – gars and tarpon fall into this class. They have swim bladders that connect to the pharynx or esophagus, so they can gulp air for more energy.

Lungfish may have developed lungs for another reason. Many live in rivers that will dry up in the hot summer. If they relied only on gills, this would be the end of them. But by being air breathers, they can go into a state called estivation (aestas = summer, a dormancy in hot/dry period, like hibernation, see this video). They hole themselves up in the mud, excrete a layer of mucous to keep themselves moist, then breathe air in the dried up river hole until the rains come.

Regardless of their motivation, it was one of these bony fish that took to living on land and evolved some version of the various respiratory systems that today’s tetrapods can display. Most have developed the two-lunged version because symmetry of body plan makes things easier during development.

But that doesn’t mean that we two lunged animals have lungs that are perfectly symmetric – far from it. In the vast majority of cases, the right lung is bigger than the left lung, just like in the snakes. But I don’t think it’s for the same reason.

Most animals have a smaller left lung because the left lung has a cardiac notch, a space for the left ventricle of the heart. The size asymmetry is often reflected in the subdivisions of the lungs. Each lung can be divided into lobes by the fissures that are easily seen with the naked eye. The lobes are then divided into segments and lobules.


Fibonacci series and phi are found all over nature.
The bottom image shows how trees, and bronchial
trees branch in Fibonacci scaling. The top image
shows how phalanges are scaled in Fibonacci
numbers. If you divide the last Fibonacci by the
previous, the answer tends toward phi
(1:1.618033…). Divide 13/8 or 21/13 or 34/21;
see how it gets closer to phi? The distance
between branches of bronchial tree does
the same thing.
This branching system is asymmetric, complex, and varies from species to species. Because of this, many tetrapods have specific numbers of lobes for right and left lungs. The left lung almost always has fewer lobes. In humans, there are three lobes to the right lung and two in the left – some others (R/L): dog 4/2, cat 4/3, rat 4/1, cow 4/2, horse 3/2, gorilla 4/2, sheep 4-5/3, pig 4/3.

But some animals have an equal number of lobes in each lung – armadillos and harbor seals have three lobes to each lung, while wombats, whales, two-toed sloths, elephants and rhinos all have one lobe to each lung. I couldn’t find a single example of an animal that had more lobes in the left lung.

The number of lobes and lobules has to do with the branching of the bronchial tree. And this has to do with math. I'm sorry, but yes, there's math involved. The Fibonacci sequence (0,1,1,2,3,5,8,13…) is found often in nature. So is phi, a non-repeating decimal like pi. Phi is 1.618033…. and can be found as a ratio in many biologic measurements (1:1.618). The length of your forearm to arm will tend toward phi, as will the curve of a nautilus shell if you break down a phi rectangle into other phi rectangles.

The branching in a lung is also phi; the distance to one branch (1) will be shorter than the distance to the next (1.618). Also, the number of branches will be fractals (a scaling pattern, based on Fibonacci and phi). So, the lung is asymmetric but not random. There - that much math wasn’t too painful, was it?

Next week, the left/right asymmetry continues in your body. Why is the right version of so many paired organs bigger?




Wilkinson M, Kok PJ, Ahmed F, & Gower DJ (2014). Caecilita Wake & Donnelly, 2010 (Amphibia: Gymnophiona) is not lungless: implications for taxonomy and for understanding the evolution of lunglessness . Zootaxa, 3779, 383-8 PMID: 24871732

Bickford, D., Iskandar, D., & Barlian, A. (2008). A lungless frog discovered on Borneo Current Biology, 18 (9) DOI: 10.1016/j.cub.2008.03.010

van Soldt, B., Metscher, B., Poelmann, R., Vervust, B., Vonk, F., Müller, G., & Richardson, M. (2015). Heterochrony and Early Left-Right Asymmetry in the Development of the Cardiorespiratory System of Snakes PLoS ONE, 10 (1) DOI: 10.1371/journal.pone.0116416

Goldberger AL, West BJ, Dresselhaus T, & Bhargava V (1985). Bronchial asymmetry and Fibonacci scaling. Experientia, 41 (12), 1537-8 PMID: 4076397




For more information or classroom activities, see:

Lungs –

Lungfish –

Snake respiratory systems –

Fibonacci sequence and phi in nature -