What percentage of all life do humans make up on earth?

[scr4]

@smam

The coin is not tossed for each individual life. It’s a random pick until half the total is reached

All life is in a bucket, there is a total number

The claw stops grabbing at half that number

Same thing. If the “claw” starts killing a random life form one at a time until it has killed half of them, then each life form has a 50% chance of being killed before the 50% number is reached.

If there are 10,000 trillion ants and 8 billion humans, then when the killing is over, there will be 5,000 trillion ants and 4 billion humans left alive. Assuming the selection is random, it would not pick 5,000 trillion 4 billion ants to kill and spare all humans. “Random” means each human is as likely to be killed as an ant.

[smam]

Thanks to everyone and the inevitable power of math in the tombola of life. I still feel lucky though

[septimus]

The mean rate of human deaths will clearly be 50% in OP’s scenario, but what about the variance? Will you get the same distribution as if a coin were tossed for each human?

If the number of non-humans were zero, then the death rate would be exactly 50% in OP’s scenario, but instead that number is huge. With the human population thus dwarfed I think the distribution to expect is the same as for the coin-tossing experiment, but I don’t know a clear proof for this besides waving my hands and babbling about “large numbers.”

[RioRico]

@smam

Not mass. Number. If 50% of all life were to die in one moment and all animals from single celled upwards counted as 1 life then how many humans would be expected to die?

Q: If you count a tail as a leg, how many legs does a dog have?
A: Four, because calling a tail a leg does not make a tail a leg.

>> “…all animals from single celled upwards counted as 1 life…”

Counting all animals as one life does not make them so. And one human or other visible lifeform is not a single creature. We are filled with bacteria; your inhabitants outweighs the bits of you with “your” DNA.

Q: What percentage of all life do humans make up on earth?
A: A vanishingly small fraction, based on either biomass or count.

Biomass (ecology)

…biomass is measured as the mass of organically bound carbon (C) that is present. The total live biomass on Earth is about 550–560 billion tonnes C, and the total annual primary production of biomass is just over 100 billion tonnes C/yr.
<snip>
Humans comprise about 100 million tonnes of the Earth’s dry biomass…

For comparison, ants are up to 100 million tonnes, cattle about 150 million tonnes, earthworms over 2000 million tonnes, and prokaryotes (bacteria) up to 70,000 million tonnes. For every pound of YOU are 20 pounds of earthworms. Yes, worms rule.

[Wendell_Wagner]

The weight of bacteria in each person is not more than the weight of the person when one considers just the human cells. The number of bacteria in each person is indeed more than the number of human cells in that person. I presume that when you say that ‘your inhabitants outweighs the bits of you with “your” DNA’ that you are talking about the weight, not the number of cells.

[Great_Antibob]

@septimus

The mean rate of human deaths will clearly be 50% in OP’s scenario, but what about the variance? Will you get the same distribution as if a coin were tossed for each human?

It’s the same distribution as a coin flip in the limiting case.

But in the particular case of the OP where it’s exactly 50%, the chances are not good to hit 50% exactly with coin flips.

I think I gave the example of 10 flips above. With 10 flips, hitting exactly 5 only takes place 24.6% of the time. But hitting between 4 and 6 happens over 67% of the time.

With 1000 flips, hitting exactly 500 is very rare, but hitting between 400 and 600 is basically guaranteed.

So, yes, variance matters. This is one of those weird bits about the Law of Large Numbers. If the selection was based on coin flips instead of an exact 50% selection, the result would not be EXACTLY 50% but it would be within a “small” (for given definition of ‘small’) neighborhood of exactly 50% with a very high probability.

When you flip the coin 1 trillion times, getting 1 million more heads than tails is basically a rounding error. So the number of times the result varies from the perfect 50% behavior can get big in absolute terms. But the percentage it varies from the perfect 50% behavior gets arbitrarily close to 0 at the same time.

@septimus

With the human population thus dwarfed I think the distribution to expect is the same as for the coin-tossing experiment, but I don’t know a clear proof for this besides waving my hands and babbling about “large numbers.”

Arbitrarily dye some of the coins blue. Label the blue coins “humans”. That’s the proof, basically.

After that, re-label the blue coins “non-humans”. Unless you have a very small number of blue coins (like less than 100), they’ll get selected with the same 50% behavior.

The trick is the independence of selection. We are assuming (supported by the OP) that “life” is chosen 1 at a time until half are reached. And we are assuming things are uniformly mixed so the probability ‘blue’ life is chosen at the same proportion it represents in the bucket.

As before, things only break down when that assumption is violated - the number of samples gets so small that the same proportionality no longer holds.

[Telemark]

If 50% of my gut bacteria are killed off in the snap then I’m more likely to die even I wasn’t one of the chosen ones.

[Buck_Godot]

@Telemark

If 50% of my gut bacteria are killed off in the snap then I’m more likely to die even I wasn’t one of the chosen ones.

Cite? While a thriving microbiome is important to health, I am pretty sure that we could survive a temporary 50% reduction of this.

[Telemark]

@Buck_Godot

Cite? While a thriving microbiome is important to health, I am pretty sure that we could survive a temporary 50% reduction of this.

I’m sure most healthy people could. But the elderly, ill, or otherwise compromised may fall prey to dehydration, sickness, etc. I don’t think you could say any specific person would die, but statistically the death rate would go up, no?