Simulating Competition and Logistic Growth

Resource limits bend exponential curves into S-shaped logistic curves. The fourth in a series on evolution.

Made with Blender and python.

Special thanks to supporters on Patreon, especially:
Jordan Scales
世珉 匡
Eric Helps
Ben Kamens
Christy Serbus
Sean Barker

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Streaming myself working on these monstrosities:

More on logistic growth on Khan Academy:

License information:

Speaking of attribution:

[PrimerBlobs]

A number of people have commented that at 5:22, the green population should be expected to beat out the blue population because the blue population suffers from mutations while the green population benefits from them. That effect is real, but it's too small to tip the scales, and I determined it was too complex for the main message of the video. But because some people are interested, I thought I'd lay it out in more detail here.

Only 1% of replications by blue creatures produce a green creature (4:52), and another 1% produce orange creatures. This means blue's replication rate is effectively only 98% of the stated value. 9.8% instead of 10%. The green population gets an expected influx of creatures each time step equal to 0.001 (a tenth of a percent) times the number of blue creatures.

Here's a desmos graph of the expected changes per time step for blue and green, from the equation in the video. (The green equation has an added term for bonus creatures from blue's mutations.)
x is the number of blue creatures, and there are sliders for the other parameters if you want to play with them. N is the total, and N-x is the number of green creatures.
We can see that when there are 49 or more blue creatures we expect to gain green creatures and lose blue creatures. And if there are 44 or more blues, we expect to lose more blues than greens. But for any number of blues less than this, we expect green to do worse. Green is never expected to outnumber blue.
This all assumes no oranges. The fact that the functions add to less than zero for any value reflects the fact that orange is gaining in any of these scenarios.

So it's true that in this setup blue suffers losses from mutations to different colors while green benefits, but the magnitude of this effect with the given parameters is too small to make up the difference in base replication chance between green and blue. Additional sims I ran reflect this fact, with green regularly losing, but I chose to animate the first sim I ran because it was a good reminder of how chaotic this system is.

I appreciate folks commenting with a critical eye, and this will help me know what to explain more clearly vs what to gloss over in future videos. It was also kind of fun to make the desmos graph. If you like it and want to see more desmos graphs when relevant to other videos, please reply to this comment and tell me so!

[KDNG]

sometimes youtube algorithm really gives you the good stuff like this

[scares]

This is one of the only channels that I will drop everything to watch when a new video comes out. Love it!

[budzikt]

My God, In collage I was unable to figure out from where numbers comes out and memorize all stuff related to logistic growth without understanding it at all just to pass my matlab laboratories. It's so hard to explain this so simple. Thank you, channels like this deserve gold medal and monetization factor of x100

[NickNLouie]

I'm a fan for the excited orange blob

[rhysmartins]

Can't believe I've missed out on this superb content until now ! Keep up the good work man !

[BoneAppleTea]

If it's too crowded, you could also just snap your fingers

[VincentZalzal]

Clear and very well animated!
For the mathematically inclined, you can read delta as the derivative of N with respect to time, since it is the variation of N. Thus, before adding the crowding term, you get dN/dt = aN, a differential equation whose solution is indeed exponential, N = exp(at) + c. By adding the crowding term, you get dN/dt = aN^2 + bN, and the solution to that differential equation is the logistic function, as stated.

[undead_boi]

This reminds me of some of my favorite teachers over the years. You take the time to explain a concept in detail, and show every step of your work, while explaining WHY it's changing and how it's affecting everything else. You also recap things we've gone over before, and recap when you finish a concept. It's wonderful, and honestly, has pushed me to add physics classes to the bio classes i was planning on when I return to school. You've rekindled my love of math, and I applaud you for it. Thank you.

[oceanman_]

I love how when you run the simulations it's 3d models just sliding along a wall

[conoroneill]

Thanks - I've been looking forward to this video for a while - you have a style that makes it very easy to listen to and understand. I'm looking forward to what comes next.

[gnikola]

You should simulate the predator-prey model I think it would be really fun

[kurzed]

so thanos should've just modified creature's stats to reach the ideal equilibrium at some point in time instead of killing the half of everything which is only a temporary solution. not so smart huh

[Arkos.Knight]

"Sorry, buddy."

Orange blob: *blank face*

[tymorgan]

Sooo... you spent the first 3/4 of this video explaining the very basics of calculus? I'm not complaining. In fact I'm very glad you are doing this because it is very useful in explaining these kinds of situations where the rate changes over time. So good job, plus you made it more interesting than any lecture could be.

[ellathon]

Thanos’ plan layout when trying to *save the universe* .

[availablekjp]

"We've seen that creatures can grow exponentially-" (flip flop)
"But in the real world-" (stop)
"A realistic growth curve would look something like this." (HOW CAN YOU DO THIS TO ME)

[bingbong]

I'm horrible at maths and science so I don't always understand all the numbers in these videos but all the concepts are really well explained and easy to grasp with a second watch and well-worded google searches. The simulations are also really interesting, easy to follow, and incredibly entertaining, and all of this combines to make your videos some of the best I've seen on YouTube- thank you so much!

[georgplaz]

*Edit* : read response by channel before liking my comment ;)
I doubt that green won because of luck in the simulation at 5:19.
Blue loses offsprings to mutation (both orange and green) which makes blue worse than the stats suggest. Additionally green has a higher birthrate as blue mutates into green. Although I have to admit that you didn't show the mutation rates, so they could be small enough to be negligible.

I think for a better comparison both orange and green could mutate back to blue with the same likelyhood.

[FrankHoneycord]

I absolutely adore this series of videos, I can't watch enough of them! please keep making them