Sharks versus bees

A few weeks ago I recorded a slot fot the Radio 4 programme “More or Less“, volunteering to answer any question. A day before the broadcast, they sent me this, from a listener:

 I’m terrified of sharks. People tell me that I’m more likely to be killed by bees, than I am to be eaten by a shark. I’m not convinced. My thinking is that considerably more people come into contact with bees, than they do with sharks. Of these, the bee encounter must be less likely to end in death. Please help…I haven’t entered the sea for about 5 years.

So here’s what I managed to dig up. Let’s start with the bare figures. The great thing about the internet is who easy it is to get your hands on datasets. So e.g. the “International Shark Attack File“(!) attempts to collate deaths from unprovoked shark attack from 1580 onwards! I’ll start by focussing on the UK, since that’s where I assume the listener is based. They have UK data from 1847 to the present, which claims there have only been 2 unprovoked attacks, neither fatal – over that time periodaAnother effort to collect shark attacks is the “Global Shark Attack File” (which is the information source for a summary web article). They provide similar figures for unprovoked attacks, but also list a number of “provoked attacks” where e.g. fishermen have been bitten while messing with sharks in various ways – as well as some drownings where boats have been upset by sharks.. Given the media excitement associated with shark attacks, these figures won’t be much of an underestimate.

In contrast to zero fatalities from sharks in 165 years, each year in the UK, there are approximately 5 reported deaths from anaphylactic shock following a bee or wasp sting [zotpressInText item=”ASWDNI8A”][zotpressInText item=”M76Z3BMK”], of which only about a tenth are bee-induced [zotpressInText item=”JFEITQEV”]. As well as anaphylactic shock, there are presumably occasional bee-related deaths from driving while trying to get a bee out of the car, falling off a ladders when stung, etc. Although I haven’t found any reliable estimate for these, it does illustrate that – in contrast to shark deaths – 0.5 or so deaths per year from bees is likely to be a reasonable underestimate. That’s something also acknowledged when looking at the anaphylactic shock figures [zotpressInText item=”HHWM384N”]. So 1 or 2 deaths a year from bees in the UK is probably a reasonable figure to work from.

But as the listener points out, there are very few people actually swimming in the sea in the UK. So in some sense it’s unfair to compare zero shark deaths in 165 years to one bee death per year. Calculating the relative danger of sharks and bees depends how you frame the question. For example, assessing the danger per attack, I’d certainly go head-to-head with a bee rather than a great white. The relevant question here is presumably something along the lines of “if I’m at the seaside, am I more likely to die by going into the water and being attacked by a shark, or staying out and being attacked by a bee?”. The somewhat ironic possibility of someone overcoming their fear of sharks and entering the water, only to be stung to death by the bee they were hoping to avoid, is presumably rather improbable.

In other words, it’s the risk of death per hour of exposure that’s the telling figure. In fact, a recent increase in the global number of shark attacks has been put down simply to more person-hours spent in the water [zotpressInText item=”TMWBWCJN” year=2012].  So how can we estimate the fatality rate from sharks per hour of swimming versus bee fatalities per hour spent, say, on the beach? Well, there are a couple of major problems:

  1. It’s notoriously tricky to estimate the probability of rare events – in the case of shark fatalities in the UK, an event so rare that it’s never been recorded. It’s an area of statistics that’s important, for example, in aerospace, counter-terrorism, and the nuclear industrybThere’s a nice non-technical summary at http://gunston.gmu.edu/healthscience/riskanalysis/ProbabilityRareEvent.asp. There are various ways to get some sort of estimate, but I’ve taken the simplest (or perhaps most simplistic) one. Taking the 2 non-fatal attacks in 165 years, we could apply the approximate ratio of 1 fatal attack to 50 non-fatal attackscThat’s from the last 12 years in the US, where non-fatal attacks are probably more reliably reported. Recent global figures are more like 1:10, but may have a bias against reporting of non-fatal cases.. It’s perhaps reasonable to apply a low figure like this to the UK, as virtually all shark deaths are thought to be a case of mistaken identity. That gives 2/50 deaths per 165 years, or 2/50/165 ≈ 1/5000 chance of a UK shark death per year. However, there is massive uncertainty in this figure. We still have the problem that two non-fatal attacks is still a tiny number – an extra incident here or there will change our calculation rather drastically. Moreover, each incident has a worryingly large influence on our calculation. For example, if either are unrepresentative of a “normal” shark attackde.g., if they were accidental brushes with a injured shark, or a shark attack on a boat, or have been wrongly reported, then our figure will not be telling us the right story. And finally, it’s problematic to interpolate from 2 attacks in 160 years to an attack probability of 2/160 in 2012. Many relevant factors, not least the population of the UK, will have changed over that time. Nevertheless, with a gargantuan pinch of salt, I reckon that within a few orders of magnitude, bee-induced deaths are expected to be many thousands of times, perhaps tens of thousands of times, more frequent than shark-induced deaths in the UK.
  2. There are no reputable figures for numbers of person-hours spent in the sea around the UK. So let’s make some utterly unsubstantiated back-of-the-envelope calculations. Say, on average a person swims in the sea for a total of an hour a lifetime, but are exposed to bee threat for maybe an hour a day. That means people are potentially exposed to bees for 75*365 = a couple of tens of thousand more hours than they are potentially exposed to sharks. Sounds reasonable to me…

So using these (admittedly very shaky) figures, the relative amount of exposure to each threat approximately cancels out the expected death rates. When worrying about death from bees or sharks, I reckon it’s very roughlyeI.e. within a few orders of magnitude :) as dangerous to have a hour’s picnic in the UK as to go for an hour’s swim in the sea. If you’re worried about wasps rather than bees, perhaps a picnic is more dangerous, but the risks are so low that these guesses are insanely unreliable.

What it you’re on holiday in somewhere thought of as shark-infested: say Florida? Well, because there are more shark attacks, the estimates are more trustworthy.

In 25 years, from 1985-2009 there were 485 unprovoked shark attacks and 5 deaths in Florida. In 10 years, from 1996-2005, Florida reported 2 bee deaths, 2 wasp deaths, 4 fire-ant deaths, and 1 unspecified insect death [zotpressInText item=”NPARZNZM”]. Rather neatly, that’s exactly 1 death per 5 years from both bees & sharks. Again, the bee deaths are thought to be underreported – in fact, based on whole US figures, and a Florida population of 20 million, we’d expect almost 4 times more bee deaths in that time [zotpressInText item=”HHWM384N”]. So the bee figure should be higher, and it’s possible that, for our question, the shark figure should be lower, since most shark attacks are on surfers, not swimmers fAlthough perhaps that just reflects the relative person-hours spent in the water surfing versus swimming.

So as a generous estimate, in Florida we expect overall deaths from bees to be perhaps 10 times more frequent than deaths from sharks. And even in Florida, I think that an average person won’t spend as much as a tenth of their outdoor time in the sea, so sharks account for a disproportionate number of those deaths. In other words, I think the listener might have a fair point: the probability of death by shark if entering “sharky waters” such as in Florida, is greater than the probability of death by bee if you refuse to swim.

Either way, the figures are minuscule. Certainly for the UK, the shark statistics are so low that they can’t even be  for certain shark territory. Really – I wouldn’t let your activities be restricted by worrying about death by shark or death by insect sting. To cheer you up, you’re so much more likely to drown while swimming in the sea that adding sharks into the mix makes essentially no difference to the risk.

And look on the bright side. If you do die of a shark attack in the UK, you’ll be famous for centuries.

References

Notes   [ + ]

a. Another effort to collect shark attacks is the “Global Shark Attack File” (which is the information source for a summary web article). They provide similar figures for unprovoked attacks, but also list a number of “provoked attacks” where e.g. fishermen have been bitten while messing with sharks in various ways – as well as some drownings where boats have been upset by sharks.
b. There’s a nice non-technical summary at http://gunston.gmu.edu/healthscience/riskanalysis/ProbabilityRareEvent.asp
c. That’s from the last 12 years in the US, where non-fatal attacks are probably more reliably reported. Recent global figures are more like 1:10, but may have a bias against reporting of non-fatal cases.
d. e.g., if they were accidental brushes with a injured shark, or a shark attack on a boat
e. I.e. within a few orders of magnitude :)
f. Although perhaps that just reflects the relative person-hours spent in the water surfing versus swimming

4 thoughts on “Sharks versus bees

  1. Pingback: Severe morning sickness and twins | A Scientific View

  2. Shame. What started as a very good and we’ll thought out piece totally lost the rails in the final conclusion. You gave up on the stats for the conclusion, why? The percentage of human hours spent in the sea compared to spent near bees, even in Florida, is so small, that this would surely make the chance of a fatality by shark hugely, and don’t underestimate the hugeness, greater than being killed by a bee. The two are surely not similar. You have been persuaded by the sharks are not killers campaign.

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