Bamboo mathematicians – phenomena: the loom
This remarkable cycle would be fascinating enough on its own. But it turns out a number of other species of bamboo grow flowers on cycles lasting decades, too. A species called Bambusa bambos flowers every 32 years, for example. Phyllostachys nigra f. henonis takes 60 years.
Three biologists at Harvard got puzzled by these cycles and recently set out to find an explanation for how they evolved. In the journal Ecology Letters, they offer up a tantalizing hypothesis: bamboo cycles have reached their remarkable lengths through some simple arithmetic.
Like all scientists, these biologists (Carl Veller, Martin Nowak, and Charles Davis) stand on the shoulders of giants. Or one giant in particular-the ecologist Daniel Janzen, who over the years has cast off a huge number of creative, influential ideas with unsettling ease.
In the mid-1970s Janzen came up with an explanation for why bamboo plants would flower in synchrony. He noted that rats, birds, pigs, and other animals devour colossal numbers of bamboo seeds. Each gobbled-up seed represents the loss of a potential offspring. If there are enough seed-predators, and they are hungry enough, they can wipe out a bamboo plant’s entire set of seeds.
Bamboo plants might fare better, Janzen argued, if they flowered at the same time. They would overwhelm their enemies with food. Even if they gorged themselves to bursting, they would still leave some seeds untouched. Those surviving seeds would then have enough time to grow into plants that could defend themselves with tough fibers and bitter chemicals.
Once bamboos fell into flowering lockstep, it would be hard for them to slide out. If a few bamboo plants flowered a few years too early, animals would feast on their seeds, and their out-of-sync genes would fail to make it into future generations.
Other scientists have found support for Janzen’s idea. Swamping enemies with seeds really does lower the overall harm that seed-eaters cause to each individual plant. But Veller and his colleagues still had questions. How did the bamboo plants get into those beneficial flower cycles to beginВ with? And how did various species end up with such long-and such different-flowering rhythms?
The scientists developed a mathematical model based on what’s known about bamboo biology. They started out with a bamboo forest in which almost all the plants flower annually, as some bamboo species do.
But the population also contained some mutants. They had mutations in their flower-timing genes, so that they needed two years to flower instead of one. Some of the two-year mutants flowered in even years, while others flowered in odd years. Spending two years between flowering instead of one could have some advantages for bamboo plants. The plants could have more time to gather more energy from sunlight, which they could use to make more seeds, or give their seeds more defenses against predators.
As more of the forest becomes two-year plants, there are fewer plants releasing their seeds every year. Eventually, Veller and his colleagues found, a year arrives when the annual bamboo plants can’t produce enough seeds to survive the onslaught of animals. In one fell swoop, they’re wiped out. If it’s an odd year, then the odd-year two-year plants can get wiped out, too. If it’s an even year, the even-yearedВ plants take the fall. Either way, the whole forest getsВ abruptly synchronized into flowering every two years.
It’s also possible that the forest wouldn’t just have two-year mutants, but mutants that took three years or more to flower. Veller and his colleagues found that in their mathematical model, bamboo plants with longer flowering cycles could also take over. Exactly which cycle won out was partly a matter of chance, because how many seeds bamboo plants successfully produce in a given year can fluctuate due to the weather and other unpredictable conditions. Whichever cycle emerges as the dominant one, the whole forest then evolves to stay synchronized. Any outliers flowering out of sync get wiped out, just as Janzen had proposed.
There is one exception, though: a mutant bamboo plant can evolve a new cycle that’s a multiple of the original one. Imagine that a two-year bamboo turns into a four-year one. Every year it flowers, it’s protected by the two-year plants flowering at the same time. And it’s got an advantage over them: it can spend the extra time making more seeds.
Even though the four-year flowers need twice as long to produce their seeds, the scientists found, under some conditions they can still become increasingly common over a few centuries. Eventually, the whole forest will lock onto the four-year cycle.
But bamboo can’t evolve the other way, the scientists found. If a four-year forest produces a two-year mutant, it will flower half the time in yearsВ when it has no protection from predators. The only direction it can go is towards longer cycles. If a four-year forest produces an eight-year mutant, it can have the same advantage that the four-year plants originally had: well-protected time.
Veller and his colleagues realized that they could test this model. Over millions of years, they reasoned, species should have multiplied their flowering cycles. It’s likely that they could only multiply the cycles by a small number rather than a big one. Shifting from a two-year cycle to a two-thousand-year cycle would require some drastic changes to a bamboo plant’s biology. Therefore, the years in a bamboo’s cycle should be the product of small numbers multiplied together.
The mathematics of bamboo offers some promising support. Phyllostachys bambusoides has a cycle of 120 years, for example, which equals 5 x 3 x 2 x 2 x 2. Phyllostachys nigra f. henonis takes 60 years, which is 5 x 3 x 2 x 2. And the 32 year cycle of Bambusa bambos equals 2 x 2 x 2 x 2 x 2.