Lotka–Volterra Equations | Hacker News Reader

Lotka–Volterra Equations

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53 pointsustad22 comments

A lot of people don't get further than Malthus, and don't realize that he was just the first pioneer. They think "Malthus was wrong", and don't realize the rabbit hole that opens up once you start treating population dynamics mathematically.

Speaking of treating population dynamics mathematically… compartmental models are still some of my favorites https://pypi.org/project/epidemik

on the one hand, yes ecology and math bio is cool. On the other, the demographic transition does not fall out of these models whatsoever. Humans decided to do something very weird for whatever reason.

The actual population size during demographic transition looks very logistic-y. You'd be forgiven for thinking Verhulst applies. (though K is very much an empirical constant in that case, since you can't easily predict it from anything I don't think.)

I think the demographic transition overshoot (https://en.wikipedia.org/wiki/Demographic_transition#Stage_f...) we see is unexpected though.

Yeah the demographic transition is something nobody predicted (afaik). On the other hand, LTG (https://en.wikipedia.org/wiki/The_Limits_to_Growth) is a neo-Malthusian prediction that seems to match early data, and a surprising number of people revisit it and find its conclusions seem to hold. We'll be finding out around 2040, give or take. ¯\_(ツ)_/¯

For me, r/k selection applied to human behavior broke my mind.

Once you see it, you can't unsee it. Be it dating or comparing cultural approaches to relationships, etc.

Can you expand on that?

The very short gist of it is a trade-off between (low quality, high quantity) and (high quality, low quantity).

R-selection: emphasis on high numbers / growth.

K-selection: emphasis on high quality.

Just to expand upon this in HN terms:

- R-selection is just a confusing bit of technojargon, really what we're talking is a zerg style build strategy, lots of units for cheap, as far as our organism in the game of life. So organisms with this build strat will raid an ecological niche like it's 2021 and Biden just unlocked the border

- K- selection, another confusing bit of technojargon (K stands for konfusing here), is more of a protoss build, not nearly as many units but higher quality. this is for scenarios where a raid won't work, kind of like a buffed commando type unit in command and conquer

Quantity has a quality of its own.

Malthus was wrong only in that he didn't anticipate the massive store of energy we were about to unleash with coil, oil, and gas. We were able to smash through Malthus' predictions because we added more solar energy (in the form of fossilized carbon) to the system. The Haber-Bosch process cranked it up to 11.

In an alternative world where we left fossil fuels in the ground, we would have hit a population ceiling in the 1800s.

In a future world where fossil fuels are no longer accessible (either through climate policy, depletion, or market forces) this means our energy budget needs to shrink - Malthusian limits to our food production will be of concern again, assuming we make it through the climate bottleneck.

He was wrong in that he was wrong. I don't blame him for not being to predict what happened, but the industrial revolution had already begun. He had to have been aware that technology can increase efficiencies, and he didn't account for that properly in his models.

He was wrong in the sense that Newton was wrong about physics - he accurately captured an important dynamic that held absent extreme violations of stasis - e.g. Newton was wrong about relativity and quantum mechanics. Nothing Malthus did was absolutely wrong - it's just that other forces that were unleashed overcame the dynamics he accurately observed.

I think the correct framing is that it's people who quote Malthusian population shit that are wrong.

Volterra also contributed to materials science, more precisely with dislocations in crystals. Always amaze me how people in the past could make huge impact in totally different fields.

You still can! But expect a lot of pushback from midwits who appeal to authority.

A long time ago I wrote code to run a visual simulation that combines flocking behavior with Lotka-Volterra dynamics

https://www.youtube.com/watch?v=-_JWAh0lP8Q

It's a stochastic simulation (no differential equations), but it produces predator-prey population swings that are pretty close to the Lotka-Volterra model

What is the stochastic part? It looks like the predator/prey behavior is deterministic.

I'm guessing it's somewhat similar to the foxes/rabbits work you were doing a few months ago? https://github.com/kylebebak/foxes_and_rabbits/blob/main/fox...

In each frame of the simulation there's a small random chance that a fox dies (of starvation), and that a rabbit reproduces. The start positions and velocities of the rabbits and foxes are also random

The foxes and rabbits code is the same code in the simulation, I just recently put it on GitHub so I wouldn't lose it

Lotka–Volterra equations -> Logistic function -> Logistic map -> Mandelbrot set for an interesting connection that might not be immediately apparent. The concepts all turn up around the same time once the line of inquiry becomes chaotic recursive systems.

For those interested in this stuff, I strongly recommend Strogatz "Nonlinear dynamics and chaos".

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