Monthly Archives: January 2014

1.1 Billion

That’s the number of heartbeats in every animal’s lifetime*. Don’t believe me?

Let’s consider an extreme comparison. A mouse can live for 3 years, and has a heartbeat of about 670 beats per minute. There are 525600 minutes in a year (365 days/year * 24 hours/day * 60 minutes/hour). So, that’s 3 years/lifetime *525600 minutes per year * 670 beats/minute ≈ 1.1 billion beats/lifetime. What about an elephant? They can live up to 70 years and have a heartbeat of about 30 beats/minute. 70 years/lifetime * 525600 minutes/year * 30 beats/minute ≈ 1.1 billion beats/lifetime. Woah… what?!

Ok, ok… you probably noticed that those “equals” signs are actually squiggly “approximately” signs, and if you did the math (you should!) you would see that they are both a little off from exactly 1.1 billion. But still, they are damn close. What gives? Why would the number of heartbeats be an invariant property of the animal kingdom? Let’s dive a little deeper.

The answer lies in allometric scaling, or how different properties of life scale with the body mass of organisms. It turns out that the power (energy per time, metabolism) required to support a given unit of mass of an organism scales with the mass of that organism to the (-1/4) power- meaning that smaller organisms use energy at a faster rate per unit mass than larger organisms. Other rates, such as breathing rate and heartbeat rate, also scale with bodymass^(-1/4). Lifespan, on the other hand, has been shown to scale with bodymass^(1/4). If you want to find how the lifetime total beats scale, you can multiply those two together (beats/time * time = beats). Bodymass^(-1/4) * Bodymass^(1/4) = Bodymass^0, which is always 1, meaning that the total beats is invariant of bodymass! More on allometry and metabolism in later posts. And maybe I’ll learn how to show equations in wordpress someday.

This paper (which probably takes into account more than the 2 points I used above) cites the total number of heartbeats in an animals lifetime as 1.5 billion.

Now, given this number, can we backtrack and use the relationship to see how long humans are predicted to live? Given a certain heart-rate, how long would it take us to use up our 1.5 billion?


R code:
curve(1.5e9/(x*525600), xlim=c(40,100), lwd=5,
ylab=”Lifetime (years)”, xlab=”beats/minute”);
abline(v=60, col=”red”);abline(v=70, col=”red”)

If an animal beats its heart between 60 and 70 times a minute, it would use up its 1.5 billion beats in around 40-45 years. Is this a ballpark estimate of a human’s lifetime in the wild? (Aside: if you take the 1.1 billion heart beats derived from mice and elephants and assume a heart-rate of 70 beats per minute for humans you get 29.9 years!)

Now, don’t worry. Humans have found amazing ways to increase their lifespan, and it’s not like everyone has a set number of heart beats to get through before it’s all over. This is just an interesting result of looking at metabolism and ecology – and what’s even more interesting is looking at the animals that stray from the predictions.

*That’s about the predicted number of heartbeats in an average organism’s lifetime

Flocking Science

Check out the beautiful video below of a “murmuration” (flock) of starlings acting in hypnotic unison:

Now, if you spend all day thinking about how to model biological systems (who doesn’t?), you might see that video and wonder about the rules each bird must follow to allow such spectacular emergent dynamics. Every individual bird probably gets some simple cues (direction, speed) from its neighbors, who get some from their neighbors (and that first bird), etc etc, and when these simple cues are acted upon and combined together all the birds form a giant complex morphing swarm.

A quick search reveals that the starling dynamics, and swarming behavior in general, have been the focus of a considerable amount of research and modeling. I’ll link this PLoS ONE paper since it’s open access (meaning everyone can view it in its entirety for free) and has some really cool videos showing off the modeling endeavors of the authors. In their simulation, each individual is characterized by parameters like mass, speed, position, and orientation- and these parameters get updated based on interactions with other individuals within a certain neighborhood. Just like in real life, these simple interactions scale up to show a swarm of individuals that behave as a complex, yet unified, group. (check out the videos in the link!)

I’ll also share this PLoS Computational Biology paper (also open access) which explores why individual starlings pay attention and respond to exactly seven of their neighbors (the authors report the number is special because it optimizes the balance between group cohesiveness and individual effort).

Another side effect of thinking about biology all day is always having to ask “Why (and how) did this evolve?” That is, what benefit does this intricate dance give the birds that allowed it to selected for and maintained? Being relatively ignorant of birds and their behaviors, it seems that such a show would turn into a buffet for predators. Well, maybe not. Here is a video of a Peregrine Falcon trying to snatch a starling during the flocking behavior and continually coming up empty handed (clawed?). The Peregrine Falcon is the fastest member of the animal kingdom, reaching diving speeds of over 200mph, so maybe this dizzying behavior is a great way to confuse even the quickest of predators.

I’m sure there is more to it than just predator avoidance, so feel free to add your 2 cents below!

Cool weather

The recent cold snap across the U.S. dusted off some neurons that hadn’t been used since Earth Science- and in the process I made a pretty cool (lol) connection with some images of Saturn recently released from NASA. The Earth has a vortex of cold air spinning around its North Pole, and in early January this vortex branched out and dropped a blanket of cold air onto the Americas.

Image Image

As you can tell from the above images, our polar vortex isn’t especially consistent or symmetrical in shape. The same can not be said for Saturn’s polar vortex


Credit: NASA/JPL-Caltech/SSI/Hampton University

The beautiful series of images above was taken from the Cassini spacecraft. “The hexagon”, as it’s known, has a hurricane at its center with cloud speeds of 330 miles per hour.


Credit: NASA/JPL-Caltech/SSI

It’s awesome to see well-documented phenomena on Earth taken to their extreme on foreign planets. Hopefully we’ll see more as we continue to explore the worlds in our solar system and beyond.

Check out more stunning images of the hexagon here.