Is there any relationship between heartbeat rate and life span of an animal?

Question

Is there any relationship between heartbeat rate and life span of an animal?

Do they belong to a cause-and-effect relationship or are they both caused by some phenomenons or a common cause?

Answer 1

Interestingly there is a inverse negative correlation between heart rate and life span, meaning the faster your heart rate is, the shorter is your lifespan. See this figure (from the paper 2 cited below):

When the authors plotted the approximately total heartbeats vs. the lifespan, the amount of total heartbeats was in a pretty narrow corridor:

So it seems that at least the hearts in mammals have a maximum number of strokes they could do. The obvious question what causes this phenomenon is not really answered. Since the metabolism of small animals is (compared to their weight) higher and also their oxygen consumption is higher because of that, it is hypothesized that this causes more reactive oxygen species and related damage which subsequently leads to an earlier death.

See the references for more details:

• Rest heart rate and life expectancy.
• Heart rate, lifespan, and mortality risk
• Oxidative damage to DNA: relation to species metabolic rate and life span

Answer 2

There is a relationship: they are negatively correlated. Shorter-lived animals tend to have faster heartbeats, and longer-lived animals tend to have slower heartbeats. It gets more striking than that, however: they aren't just negatively correlated, they're approximately inversely proportional. A mouse, and an elephant, will both have around 1.5 billion heart beats before they die.

Poetic as this is, the relationship probably isn't causal. It's not that you have a given number of heartbeats, and when you use up your last one your heart dies of exhaustion. That would be silly.

It is illuminating to view the invariance as emerging from how both heart rate and lifespan scale allometrically with body size ($mass=W$).$^1$ Larger animals tend to have slower heart rates, and also tend to live longer; both relationships are in the form of power functions, whose exponents are multiples of $1/4$.

• Heart rate ($R$) scales with a negative quarter power exponent: $R \propto W^{-1/4}$
• Lifespan ($E$) scales with a positive quarter power exponent: $E \propto W^{1/4}$

"Total number of heartbeats in a lifetime" is just the product of heart rate and lifespan. As such, it should scale as

$R \cdot E \propto W^{-1/4} \cdot W^{1/4}$

$R \cdot E \propto W^{-1/4+1/4}$

$R \cdot E \propto W^0$

$R \cdot E \propto 1$

That is: if $R$ and $E$ scale in these ways - which they do, approximately, within many taxa - then their product $R \cdot E$, the total number of heartbeats in a lifetime, will be approximately invariant.

The question is why they scale in this way; and, beyond that, why the exponents in rate and time allometries are so ubiquitously multiples of $1/4$.

• Does lifespan scale with $M^{1/4}$ because (for whatever reason) heart rate scales with $M^{-1/4}$; and your heart dies of exhaustion after a billion beats? (Call this the Heartbeat hypothesis.)
• Does heart rate scale with $M^{-1/4}$ because (for whatever reason) lifespan scales with $M^{1/4}$; and, at the pearly gates, if the ledger says your heart beat 1.5 billion times before dying, you get a free t-shirt; and the heart likes t-shirts, but is also economical, beating as fast as necessary but no faster? (Call this the T-Shirt hypothesis; in my opinion it's barely sillier than the Heartbeat hypothesis.)
• Does lifespan scale with $M^{1/4}$ because (for whatever reason) something else, like mass-specific metabolic rate, also scales with $M^{-1/4}$; and that something has damaging and life-shortening effects? (This was the once-popular Rate of Living theory.$^2$)
• Does lifespan scale with $M^{1/4}$ because longer life causes selection for larger body size, in such a way that gets you the appropriate scaling? (Long-lived animals can afford to sexually mature later; maturing later means they have more time to grow, and will be bigger when they finally do mature. Apparently this can get you $M^{1/4}$ lifespan allometry if you combine it with certain assumptions about growth and fecundity, you model selection as happening in a stationary population, etc. This is sometimes called the Charnov model.$^3$)
• Does heart rate scale with $M^{-1/4}$ because mass-specific metabolic rate does? Does mass-specific metabolic rate scale with $M^{-1/4}$ because heart rate does? (I dunno, these sound plausible? A cell's metabolism is fueled by stuff delivered to it by the blood stream, so it'd make sense for them to be proportional, right?)
• Does mass-specific metabolic rate scale with $M^{-1/4}$ because that's how the optimum scales for efficient resource delivery through fractally branching networks like the bloodstream? (The proof is too math-y for me. This idea is the current mainstream explanation for why biological times and rates ubiquitously scale with exponents that are multiples of $1/4$, instead of eg. $1/3$ as you might expect if it were just to do with surface area / volume ratios. This is called the West, Brown & Enquist model.$^{1,4,5}$)

tl;dr: There is a striking negative correlation - specifically, an inverse proportionality - between heart rate and lifespan. But there's no particular reason to think it's causal, and both also correlate strikingly with a million other things. A lot of this has to do with how things scale with body size. Such scaling is called allometry; allometries are often power functions; for biological rates and times, the exponents of these power functions are often multiples of $1/4$ (as opposed to eg. $1/3$ or $1$). This quarter-power ubiquity in biology used to be mysterious, but now has been given an explanation (at least for the scaling of metabolic rate, which intuitively could do part of the explaining for other rates) by the West, Brown & Enquist model as being the result of optimally efficient resource delivery in fractally branching transportation networks.$^1$

The Heartbeat hypothesis is silly; presumably the approximate invariance of "1.5 billion heartbeats in a lifetime" comes from the $M^{-1/4}$ and $M^{1/4}$ scaling of heart rate and lifespan, themselves occurring for some other reason. I don't know but I assume the fractally-branching bloodstream explains the heart rate allometry. The lifespan allometry is more mysterious. It was once commonly thought to follow directly from the mass-specific metabolic rate allometry (Rate of Living theory), but that theory has fallen on hard times.$^2$ It has been given other potential explanations, notably the Charnov model which suggests that low mortality rates result in selection for a later age of maturity, giving animals more time to grow large.$^3$

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1. West, G. B. "The Origin of Universal Scaling Laws in Biology". Physica A, 1999.
2. Austad, S. N. "Cats, 'Rats,' and Bats: The Comparative Biology of Aging in the 21st Century". Integrative and Comparative Biology, 2010.
3. Charnov, E. L. "Evolution of Life History Variation Among Female Mammals". Proceedings of the National Academy of Sciences, 1991.
4. West, G. B., Brown, J. H. and Enquist, B. J. "A General Model for the Origin of Allometric Scaling Laws in Biology". Science, 1997.
5. Dawkins, R. and Wong, Y. "The Cauliflower's Tale" in The Ancestor's Tale, 2004.