Roadkill Arithmetic

by zebra on 22 December 2011 · 26 comments

Returning for another guest post, James Glover is once again drawn to a beer coaster for some quick, if somewhat morbid, calculations. For those taking to the road over the Christmas period, this post should also serve as a reminder to drive carefully!

Why did the chicken cross the road? To get to The Other Side. This twist on the ending to the iconic joke was based on the observation of a single dead chicken on the road while I was returning by car from Sydney to Melbourne at the end of my recent touring holiday. The holiday in fact started two weeks earlier when I was driving around Tasmania. While there were no chickens, there was a dead sperm whale on the road.

In Tasmania I noted that in addition to its abundance of quality food, beer and wines, it has a remarkable supply of one other thing compared to the mainland: native fauna road kill. If you think that the occasional dead kangaroo (or more likely fox) you see driving in the country is plenty, then you haven’t been to Tassie. We are talking a dead possum or wallaby every kilometre or so, which means if you are driving at 100km/hr means you see one every 36 seconds. While it is unfortunate, particularly for the animals involved, to see so many native animals dead (but no foxes because they have been eradicated from the island), it is actually cause for joy because it indicates a very healthy population of native wildlife.

This got me thinking. Could you actually use the number of road kill to estimate the density of animals living in the bush? The answer is yes, and without any derivation or proof I present it here:

density = road kill ratio/kill zone area


road kill ratio = av. distance between cars/
                   av. distance between road kill
kill zone area = 2 x car velocity x time x car width

It’s a surprisingly simple formula, and can also be handy for keeping children occupied on long car trips (at least in Tasmania). The model it is derived from is admittedly fairly simplistic – let’s just call it the “Frogger model of vehicle/animal interaction”. Here the time is important because clearly if we had an infinite amount of time and no method of disposal of road kill then the number would build up without limit. In practice the attendant carrion birds on each road kill and its, shall we say, “freshness” (blood, guts, brains you get the picture) suggests that they were all products of the previous nocturnal period’s collisions. In fact there are road signs indicating to drivers to be particularly careful between dusk and dawn to avoid animals so I take “time” to be 10 hours and assumed all carrion are fresh. Taking the average distance between road kill to be 1km and cars to be 10km gives a road kill ratio of 10. The average car speed was 100 km/hr and my car is about 2.5m wide so putting this all together gives an estimated bush density of 20 animals per square km. That’s about one per 5 hectares. That seems a little on the low side for a densely populated area but as “beer coaster” estimates go, it’s probably not a bad start.

This reasoning got me thinking that there probably true that there are no Tasmanian tigers left, because one would have shown up as road kill by now. Tasmanian rangers patrol the roads every morning looking for Tassie devils to monitor the spread of that awful face tumour disease they get. In fact, I saw two Tassie devils on the road and they were both alive and moving. I also saw three live echidnas: three more than I have seen in my life up to now. As mentioned I also saw a dead sperm whale on the road. Not some replica or whale skeleton either: it had died the day before. It was on the beach near Strahan which I was driving on at the time. So, yes, it was on my road and hence I feel justified classifying it as road kill. And no, I don’t know why the whale crossed the road. Perhaps it mis-heard someone say that in Tasmania there was an abundance of “road krill”.

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{ 26 comments… read them below or add one }

1 Magpie December 23, 2011 at 10:04 am

Hey Zebra!

I’ll guess you didn’t go to the West Coast…

Next time you’ve got to do some hiking around the Pieman River and talk to the locals. I hear they are fond of hunting, so they could tell you about the local fauna. Maybe, you know, you could find a Tassie Tiger.

2 Zebra December 23, 2011 at 10:58 am

Mule, at this time of year you also have to beware of bad puns.

3 Magpie December 23, 2011 at 4:53 pm

Bad puns? Bad puns! Humph!

But, considering the time of the year, I won’t hold grudge. Instead, for your listening pleasure, I’ll link to this song:

A Tale They Won’t Believe (by Weddings Parties Anything):

I take it you haven’t heard of good ole Alexander Pearce… MWAHAHAA!

4 Zebra December 23, 2011 at 5:03 pm

Dear Magpie – I’m sure you know the Magpie poem – “one is for sorrow, two is for joy…”

always good to hear from you…have a happy xmas mate.

5 Zebra December 23, 2011 at 8:09 pm

I sent this separately to the Mule in case he wanted to put it up which is a derivation of the above formula. In case you are interested here it is:

I assume the animals are evenly spread out with density r. A car travels along a (wlog straight) path for time T so road length L=vT where v is is the velocity. It sweeps out an area of w*v*t where w is the width of the car. The number of cars of the road is 2*L/dc (2 because there are 2 lanes) where dc is the average distance between cars so the the total number of dead animals after time T is N=r*(2*w*L)*(L/dc). If db is the average distance between dead animals then N=L/db so substituting this in and rearranging gives: r=(dc/db)/(2*w*v*T) = road kill ratio/kill zone area.

One aspect of this formula is that it implicitly assumes the animals aren’t moving. Does this matter? Well it is based on an “expected number” formula so in a sense the animal density is smeared (pardon the pun) over all possible states so no it doesn’t. There are a number of possible reasons why it might not be accurate the most obvious one is that animals may avoid the road or be attracted to it. I was told that Tammar Wallabies are “particularly stupid” and they certainly seem to be well represented amongst the road kill. If one had an alternative estimate for bush density of a particular species then you could use it to work out to what extent a particular species was likely to end up road kill given their population, and attraction or repulsion to roads. I guess that would be an interesting statistic in itself.

6 Emmjay December 24, 2011 at 7:00 pm

Thank Christ you don’t work for the climate change denialists (do you ?) or the poker machine lobby.

With maths like this, I reckon poker machine odds look pretty reasonable. And Alan Moran over at the ABC’s Drum is starting to make sense… Whoa !!!!

Have a great Christmas, sport. Drop into the Pig’s Arms some time.

7 PFH007 December 25, 2011 at 8:42 am

Very good!

Yes those wallabies are particularly committed to crossing to the other side (in both senses) at the most inopportune times.

But the possums are not far behind.

A few years ago we were driving at night (at about 15kph) and spotted a Brushtail possum walking down the dividing line away from us. As we approached to within about 20 metres , he glanced overs his haunches but then kept on walking. We literally drove up beside him, waved, and then continued on.

I suppose he may have been reasonably safe provided he stayed right on the dividing line but I wouldn’t recommend it as a means of extending one’s membership of the gene pool.

8 Zebra December 27, 2011 at 11:29 am

@PFH007 – in Tassie I had to stop to let an echidna cross the highway in front of me, which entailed traffic backing up behind me. This made me feel inordinately good all day for some reason. I recently read that echidnas split, in evolutionary terms, about 25m years ago from platypus. Given that monotremes have been around for 200m years it goes to show how resilient this last remnant of that unorthodox mammal group are. It is therefore even more surprising that we haven’t wiped them out in the last 200 years.

9 Occassional traveller December 31, 2011 at 3:16 pm

On my travels a few years ago I too noted the large amount of road kill vis the mainland – in particular in the south east.

As for the formula – I suspect that the mainland marsupials have pre-empted it and have found a way to avoid not only the night traffic but also your formula ….


Have a great 2011

10 dan January 9, 2012 at 10:37 am

i think this may bugger up your data.

just back from a glorious week up the coast from Sydney, and noticed – for the first time – “aerial fauna rope bridge crossings” spanning the Pacific Highway at many points.

you can see one being installed here:

god help them if they start installing these things in the NT:

11 Zebra January 9, 2012 at 6:28 pm

that’s awesome @dan but are you sure you’re not pulling my leg?

12 Dan January 9, 2012 at 8:45 pm

No leg pulling. Google “aerial fauna bridge NSW” and you’ll find them in approvals and env impact assessments up and down the highway. And the Hume too.

I’d love to know if the animals actually use them? Gotta be someone somewhere monitoring them. Assuming they weren’t just a sop to local greens.

13 Pfh007 January 9, 2012 at 8:54 pm

They probably will use them judging from the possum highway in our street – the power lines are their preferred cat avoidance technique.

14 dan January 10, 2012 at 10:50 am

our possums seem to prefer avoiding cats by hiding in our roof

15 Stubborn Mule January 10, 2012 at 3:11 pm

@dan that is very cool.

16 dan January 10, 2012 at 3:22 pm

@Pfh007 – you could always get these guys to install one in your street:

17 zebra January 10, 2012 at 5:57 pm

I love this but when they say on their website they are used by “possums, gliders and other animals” I wonder what “other animals”? Tree snakes?

18 dan January 11, 2012 at 1:40 pm

dropbears i think

19 Pfh007 January 11, 2012 at 3:37 pm

Thanks Dan, but the possum survival rate seems pretty good near me. They seem to have already mastered abseiling, pole vaulting, trapeze work and from the sounds i hear , cage fighting.

20 zebra January 11, 2012 at 7:11 pm

@dan – so it’s not enough dropbears can attack innocent bushwalkers but now with these devices they can drop in on cyclists and cars as well.

21 Pfh007 January 12, 2012 at 1:58 am

@zebra – wise advice re drop bears! Apparently you are safe in a Prius – it seems they acknowledge good intentions and move on to more deserving prey – hummer drivers perhaps.

22 Zebra January 12, 2012 at 9:20 am

@Dan – I ‘ve heard in the lower north shore of Sydney that dropbears target open topped Porsche convertibles. They’re attracted to the authentic plush leather interiors apparently.

23 Plunko January 13, 2012 at 11:42 pm

Errrr – Stubby, the only reason a whale would cross the road would be if he/she was getting fat from bad puns (this would be over-krill) and was looking for a whale weigh station….sorry, couldn’t help myself!!!

24 dan January 30, 2012 at 2:56 pm

Sorry to come back to this. (We’ve all moved on to the JJJ Top 100) but, just back from 4 glorious days in Tasmania – including driving much of the east coast from Hobart to Launceston the long way round. You simply could not imagine the amount of road kill. Wallabies, Possums, Devils, Foxes, Cats, Birds, no doubt the odd Wombat – it was hard to tell (still no whales). So I have to concur with original post.

According to this Catalyst report: “The density of roadkill in Tasmania – about one dead animal every three kilometres – is unprecedented worldwide.” (

Unprecedented Worldwide!

Certainly seemed that way to me. And it was very sad.

25 Emmjay January 30, 2012 at 3:05 pm

Our last road trip around Tasmania was about seven or eight years ago. The roadkill was pretty horrific then. So were the monster timber tucks raging around those tiny blacktop strips at something close to Mach II. Co-incidence ?

26 zebra January 30, 2012 at 6:37 pm

@dan – another excellent link. I may try and get in touch with the CSIRO guy.
@emmajay – I was warned about the timber trucks but found very few of those or RVs which I was also warned about. Except the RV that came around the corner on the wrong side and noticed me at the last minute and swerved. Now I know how roadkill feel. Or at least road-near-miss.

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