Very interesting. Seems like the growth rate equations are off. Since the trees die off after giving off their seeds, population is just (mp)^2 after two generations. In steady state, mp will always have to be about 1, which puts a somewhat high bar on s to make it worth it (can you really double seed production by waiting twice as long?).
And where do the bamboo store all these seed producing resources for so long?
You’re right! Corrected. As where the extra resources are stored, I don’t know enough about botanic to tell, but here’s what they say in the paper: “First, plants that wait longer to flower may accumulate greater energy resources to invest in producing more seeds, and/or seeds that are better protected (Fenner 1985). (The latter scenario, involving better-protected seeds, seems less applicable to bamboos, whose ancestral fruit type is a caryopsis, i.e. fruits with seeds that are generally less well protected than those of many other flowering plants.) In bamboos, this investment might, for example, take the form of increased shoot production between masts”. So, at least from that paper, it doesn’t look like there’s a clear mechanistic explanation, aside from more bamboo.
I agree, it should be (mp)^2. But you will just need 1+s>mp for the delay to be an advantage, which in steady state means we just need s to be positive.
That looks right mathematically but seems absurd. Maybe steady state isn’t the right situation to think about this in? It’s weird that the strategy of “never reproduce” would be just as good as the usual, since not reproducing means not dying. Or we need to model the chance that the bamboo dies due to illness/fire/animals prior to getting a chance to reproduce?
Yes, I’m pretty sure there is some diminishing return after some decades (though, apparently, they hit pretty late for bamboos). Now if we stick to the absurd model with no diminishing returns, we can imagine a mutant that almost never reproduces, but when it does, it suddenly covers the entire planet, erasing all the other strains that have been growing exponentially in the meantime. The limit where it doesn’t reproduce at all is when a bamboo in a forest appears dead, but will eventually turn the entire universe into copies of itself when comes the Armageddon.
Very interesting. Seems like the growth rate equations are off. Since the trees die off after giving off their seeds, population is just (mp)^2 after two generations. In steady state, mp will always have to be about 1, which puts a somewhat high bar on s to make it worth it (can you really double seed production by waiting twice as long?).
And where do the bamboo store all these seed producing resources for so long?
You’re right! Corrected. As where the extra resources are stored, I don’t know enough about botanic to tell, but here’s what they say in the paper: “First, plants that wait longer to flower may accumulate greater energy resources to invest in producing more seeds, and/or seeds that are better protected (Fenner 1985). (The latter scenario, involving better-protected seeds, seems less applicable to bamboos, whose ancestral fruit type is a caryopsis, i.e. fruits with seeds that are generally less well protected than those of many other flowering plants.) In bamboos, this investment might, for example, take the form of increased shoot production between masts”. So, at least from that paper, it doesn’t look like there’s a clear mechanistic explanation, aside from more bamboo.
I agree, it should be (mp)^2. But you will just need 1+s>mp for the delay to be an advantage, which in steady state means we just need s to be positive.
That looks right mathematically but seems absurd. Maybe steady state isn’t the right situation to think about this in? It’s weird that the strategy of “never reproduce” would be just as good as the usual, since not reproducing means not dying. Or we need to model the chance that the bamboo dies due to illness/fire/animals prior to getting a chance to reproduce?
Yes, I’m pretty sure there is some diminishing return after some decades (though, apparently, they hit pretty late for bamboos). Now if we stick to the absurd model with no diminishing returns, we can imagine a mutant that almost never reproduces, but when it does, it suddenly covers the entire planet, erasing all the other strains that have been growing exponentially in the meantime. The limit where it doesn’t reproduce at all is when a bamboo in a forest appears dead, but will eventually turn the entire universe into copies of itself when comes the Armageddon.