Why Simon Singh is wrong: 5 does predate 6

In promoting his new book, author Simon Singh put together a short “quiz” of math jokes for The Guardian. I was initially tickled to see an ecological type problem in the very first question:

“1.Why did 5 eat 6?

  1. Because 1, 2, 3
  2. Because 7, 8, 9
  3. Because 5 predates 6″

There is a well-known joke that goes more like, “Why was 6 afraid of 7?” The answer to that is quite obviously, “Because 7, 8, 9!” Such predator avoidance behaviors as 6 being afraid of 7 and perhaps fleeing from it are ubiquitous in animals, as anyone knows who sees sparrows flutter away at your approach in the parking lot. There is a growing body of mathematical theory demonstrating the effect that these avoidance behaviors can have on the actual population dynamics of the prey species, led by scientists such as Peter Abrams and John Orrock. These results are readily demonstrated in experiments:  Oswald Schmitz and his colleagues have demonstrated how grasshoppers reduce their feeding and thus slow their population growth rates by avoiding nutritious leaves where spiders may lurk – and the reduced grasshopper population growth rate occurs even when they glue spider mouth parts shut! The effect of fear on the prey species can even transform entire biological communities and their ecosystems.

Well, 7 eating 9 is a great reason for 6 to be afraid of 7, especially if 6 looks anything like 9 (and it sure does to me). But that’s not a good reason for 5 to eat 6. What on earth do we learn about 5 from this other interaction? (Well, it’s prime, like 7, I suppose, so maybe they have similar predaceous traits.) Predators that are coexisting in a community (of integers less than 10?) are quite likely to partition prey in some way as a trade-off that prevents one from excluding another.

But, as Abrams and other theoretical and empirical studies point out, adopting behavior to avoid one predator may make a prey item easier to capture by a predator hunting by a different mode. So if 6 is afraid of 7, it may crowd closer to 5, who, predating it in an ordered number line, can also then prey (or predate) the 6.

Imagine my indignation, then, when I clicked on the end of the quiz to see my answers, only to discover this subtlety completely overlooked by Singh. He had set the answer to this unusually phrased variant of the classic to the well known answer, which frankly, in this scenario, made far less sense.

So since 5 does predate 6, that is a far better reason for 5 to then eat 6, than because some other number like 7 ate the far off 9. I rest my case, sir!

A song of ice and fire

High in the Sky Islands, sunsets are epic and forest fires and freezes more common than on the basin floor in Tucson.
High in the Sky Islands, sunsets are epic and forest fires and freezes more common than on the basin floor in Tucson.

Freezing and frequent fires are both more prevalent in the Sky Islands than in Tucson. Sky Islands are the forest capped mountain ranges dotting the low lying desert sea of the southwestern United States and northern Mexico. Over the last two days, I helped to investigate which would contribute more to weathering: the fires or the freezes?

This project was the work of five Environmental Science students at Tanque Verde High School who spent their fall break attending the new University of Arizona Sky School, a residential science school located at the summit of Tucson’s most accessible Sky Island: Mount Lemmon. It was co-advised by myself (a doctoral candidate in Ecology and Evolutionary Biology) and Phil Stokes (a doctoral candidate in Geosciences). Needless to say, this project built substantially on Phil’s expertise, and I learned a lot.

For example, I learned that weathering is the process of rocks breaking down, while erosion is the transportation of those particles. I learned that having five students lean around a fire and watch intensely through their safety goggles as a crack in a rock widens visibly a millimeter feels like success.

We collected 3 types of rock to test the effects of freezing and fire: schist, quartzite, and granite.
We collected 3 types of rock to test the effects of freezing and fire: schist, quartzite, and granite.

To test the severity of weathering by freezing and by fire, we collected 3 types of rock, and subjected them to 4 treatments. The rock types were schist, quartzite, and granite. The treatments were repeated short freezing cycles, repeated short fire cycles, a long freeze, and a long burn. Rocks were soaked in warm water before treatments, and between freeze or burn cycles.

As the members of Team Tough Schist presented in the Second Sky School Symposium, ice and fire work differently on weathering rock. A very general explanation they provided was that water seeps into existing cracks, then expands when frozen, widening them. Fire, however, heats the many minerals in the rock, busting them apart and creating new cracks. This additional surface area opened by fire allows more weathering.

Armed with this understanding of weathering mechanisms, and the evidence of more cracks in the roasted rocks than the frozen rocks, Team Tough Schist also concluded that schist is not so tough. Anyone who has picked up the papery flakes laced with mica may have also observed this. And when those papery layers curl up when expanding due to heat, they stay crinkled like a book that once wetted, never lies perfectly flat. As you might also imagine, repeated freeze-thaw cycles wedge cracks wider and wider more than one long freeze. But one long and intense fire may expand and crack a rock more than repeated short fires.


Rocks were grilled on charcoal to simulate forest fires, and placed in the freezer to simulate winter.
Rocks were grilled on charcoal to simulate forest fires, and placed in the freezer to simulate winter.

Although overall fire was determined by Tough Schist to be a more severe weathering agent, freezing occurs every year all over the tops of Sky Islands, and fires near any given rock are less frequent, even under historical more frequent fire regimes. So they left their audience with further questions: Which weathering agent, ice or fire, should be contributing more to weathering processes on Mount Lemmon overall?

On a final note, I was obviously disappointed none of the students were fans of George R.R. Martin, given their choice of research question.

The gecko was still alive.

Dr. Brittany Barker, a post doctoral researcher at the University of Arizona, recently photographed another example of an invertebrate tackling and eating a vertebrate, this one from Sabino Canyon in the Santa Catalina mountains:


She writes:

“The spider apparently attacked the baby gecko – they appear to be sit and wait predators. Gecko was still partially alive – I could see his/her eyelids moving – but not moving. The stuff I see here in Tucson is crazy!”

Interestingly, sit-and-wait predators that ambush their prey tend to have larger effects on prey behavior, according to experiments with spiders and grasshoppers that appeared in the journal Ecology.  Prey are much more cautious and avoid areas from which predators might ambush them. I know I avoid large rocky outcroppings where a mountain lion could be lying in wait when I hike alone at dusk.  This avoidance behavior, though, can change the way they forage on the landscape either by where they forage or how much they eat, and that has effects on their resources in turn. Cool to think about, right? I wonder if geckos are instinctively avoiding places that look like spider ambush points, and if so, did this one just get unlucky? Or is it something they have to learn, and this individual was too young and naive?


[Update: Brittany writes that after some research, she believes the spider is a funnel-web wolf spider in the genus Sosippus. Can you find evidence to confirm that or to determine what species it is?]