Simulating Competition and Logistic Growth 

sometimes youtube algorithm really gives you the good stuff like this

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.) www.desmos.com/calculator/zhig0dcftg 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!

The way the blobs wiggle their hands.

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

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

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

I'm a fan for the excited orange blob

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

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

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

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

"Sorry, buddy." Orange blob: *blank face*

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.

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.

"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)

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

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.

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.

Thanos should watch your videos.

It's been 50 days! We miss your videos!

Wowwww I wished my calc teacher taught it like this when we learnt logistical functions. Never realized why dN/dt=N is exponential and dN/dt=-N^2 logistical.

Ooh differential equations in disguise

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 RU-vid- thank you so much!

Oh how my AP Calculus teacher ruined variable specification for me, I know that if I didn't specify N' = Delta when doing a project like this I'd have gotten tossed out a window or something for not defining my variables sufficiently. Other than that petty observation which most people would just be able to figure out if they're not baboon-tier, this video is genuinely an excellently animated, excellently voiced, and phenomenally descriptive example of the fact that there truly are still amazing content creators on this platform. This will be the first patreon that I support, and I wholeheartedly look forward to your next videos in the future!

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

I should be studying... but as a former biology student, and as I'm fascinated by genetics, I just can't stop watching this series

Never forget that he retconned where the orange blobs came from. Personally, I prefer the original lore, and I'm not calling it 'Legends' or some dumb name like that.

Thanks for giving me a solid base to my next simulation game.

*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.

0:12 *_"Sorry buddy."_*

I have my BA in biology I wish a few of my professors would have used something like this, a lot of people have a hard time understanding population growth. Very informative

I just stumbled upon these videos and I really /really/ enjoy how simplified they are. I enjoy watching these kind of things. Keep up the good work

0:28 could of been a really nice city landscape ya know

I never understood graphs and stuff, like parabels (i don't know if that's the right word, i'm german, so i don't know the special terms for that) in school, but you are really outstanding when it comes to explaining something. Great job man!

Please don't stop making videos, your videos are the beauty of RU-vid and are really satisfying, enjoyable and interesting.

Those videos are amazing, very high quality. Thank you and great work!

Man your videos are fantastic, I'm sure many people would kill for more frequently released episodes

I wish there were more of these videos! They’re very interesting and informative.

This is an awesome way to grasp derivatives too wow this is an insanely clear explanation too thank you 🙏🏽❤️

I like how you explain these differential equations in such an intuitive way.

I love how this RU-vidr just sprouted up with confidence and good quality. Most people start nervous and slow with no audio or something like that. I'm not saying that's a bad thing, I'm just saying that this is way better. It's awesome.

0:06 even though we have limits in the real world it’s still nice to see that the human population looks similar to that graph over the past 150-200 years

This is one of the best channels on RU-vid. Huge fan.

I would like to say that I absolutely LOVE this. I also love the fact that so many people are on board with this series, this topic, and this channel! It actually surprises me how many people like this stuff besides me. Thanks Primer!!! Also since you're going this high so fast you might want to put that face reveal at a higher sub level. Just saying.

I love your videos! This is going to be useful in for future for sure :) It's nothing to complicated, but you always go over things that are easy to overlook.

These videos are so simple, yet SO entertaining

Excellent quality for the visuals and commentary - great stuff!

This is so entertaining, calming and educating. Great job!

These videos are so chill and fun to watch. I'm glad I clicked on one when it was randomly recommended. I love watching the adventures of these little blobs!

Just found this channel, fantastic videos! I’ve been looking for a good educational economics channel for a while

The video, the music and the presentation of the information are excellent

I can say that this is helping me with my trapping course because you talk about the carrying capacity. Keep it up, your vids are epic.

I am so glad I found this channel It’s funny and I’m learning about something that is extremely complex easily

So calming and easy to enjoy. This is so satisfying

Really enjoying this series. Great work

I love this stuff, please keep doing it, I think your style is awesome

I always love coming and watching your videos because I always learn something from it :3

Excellent material. Very clear and informative. Great work!

So far I am loving this series.

This is like 3Blue1Brown standard quality! Good stuff man!

This guy could write codes for old school RuneScape. Lots of equations like this. Really helped me get good at math as a kid. Great vids

Finally RU-vid recommended something stimulating... Keep up the great content

I’m in a calc 2 class rn and just had a test on differential equations (of which logistic growth is one) and it just occurred to me that logistic growth is just the next polynomial step up from direct growth (adding one term)

Wow! I just love watching the blobs. Great animation by the way!

shoutout to my guy for putting so much work for 7 minutes of goodness

This quality videos are the reason why RU-vid is an amazing place

Would love to see your take on something like the rabbit and fox problem, or some other version of populations that have growth rates variant of eachother. Love the videos!

I have multiple questions: Which programming language do you use ? How do you visualize all these stats ? Where can I learn/read more about genetic algorithms, which is related to this topic? Thank you so much for the videos I like each and every one of them

RU-vid recommended me your videos, and I've been binging since. I've been reading a lot about world leaders, especially the suffering going on in North Korea. I've always wondered how one person can end up on top like that, and it would be really interesting to see a simulation based on these structures. I'm still getting through these videos, so I might come across it, but I've just been so fascinated in the way that the world works, which has taken me 25 years to get to this level of curiosity. I saw the doves and hawks video, and I am wondering if it's a derivative of that, but at a way larger scale. Thank you for these videos, so much food for thought. I look forward to any videos you might make in the future :~)

Nice too see all the math about probability etc. in action^^

these are really interesting videos, little tibits like this can make a morning so much better :D

Ur channel is awesome. Keep up the interesting lovely stuff!

5 seconds and I subscribed. God bless youtube recommendations for this good stuff!

You are the only RU-vidr of quality

Why are these videos so fun to watch

this is the best channel to procrastinate to.

Fantastic series!

I'm binge watching all primers videos

I love your channel! awesome content. Thank you!

Very well presented. Thank you

Love your videos!

OMG these animations are soo neat

I came back to watch it again since now I understand this math!

Your content is great! Please keep on doing videos❤❤❤

All I've picked up from these vids so far is that orange is the superior race

i'm really mad you didn't simplify the bell curve into a quadratic equation. im so invested in how beautiful functions look

Fantastic channel. This will grow, a lot.

i love this channel so much

These videos make math exciting for me

This channel is amazing

Please more videos like these, from Uruguay

I learned about this channel from 3blue1brown's website, in his FAQ, the first question he answers is what does he use to animate his videos? He mentions you as an example of not only someone who took inspiration from him, but did the best in coming up with your own unique style, so I thought you were worth checking out based on that. I'm glad I did, and what's more, I liked this video so much that I've just subscribed :)

A good lesson about logistic growth without a single mention of calculus.... Impressive. Clearly calculus is still evident, but the idea was presented flawlessly without it. Good job!

I love your videos! They are pretty lovely!

Man, your content is addictive.

It's better to watch the videos in this playlist in their intended sequence. 🤜💥🤛

i love this channel bc it sceince/maths but i understand it and its fun bc its about things i will click on XD keep it up!!!!

I really hope you're a teacher somewhere. I learn more in these short videos than I did sitting in a high school class lol. The simulations and animations are top notch

Amazing videos. Question. What did you program these simulation models with? What program/coding. Thanks.

I couldn't tell at first but yes the Crowd does include the mutations. Could change based on type of eating/digestive systems.