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.
Github: github.com/Hel...
Special thanks to supporters on Patreon, especially:
Jordan Scales
世珉 匡
Eric Helps
Ben Kamens
Christy Serbus
Sean Barker
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More on logistic growth on Khan Academy:
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License information:
Creative Commons 4.0 (CC-BY-NC). More info at creativecommon...
Speaking of attribution:
The 3D bunny model comes from the Stanford Computer Graphics Laboratory: graphics.stanfo....
The music is "Summer Days" by Kai Engel, distributed under a CC-BY-NC license via the Free Music Archive. freemusicarchiv...
Several other inputs into the graphics are from public domain contributions to www.blendswap.com.

[@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.) 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!

[@mehdibouchaffra868]

Thanks!

[@homeyworkey]

new subscriber here, whatever u put out i think im going to watch either way :)

[@SaganIII]

More of this ! 🤤

[@2haha447]

But dosn't this also influence the "death rate" because blue lose every mutation one who can not replicate you could maybe give both yellow and green a 1% mutation rate to get blue idk it is just an idea

[@Kamushy]

Primer wow

[@KDNG105]

sometimes youtube algorithm really gives you the good stuff like this

[@Blobbyboi986]

You are correct

[@timbo3406]

Yeah!

[@thinboxdictator6720]

if it is sometimes,then it is more likely a mistake

[@nicosalsa21]

Then we get actually happened videos only

[@dsi-films1264]

Yeah your right

[@BoneAppleTea]

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

[@eclipserepeater2466]

At which point that whole "logistics curve" thing would quickly bring the population back up to carrying capacity. No matter how powerful the snap, its effects are ultimately temporary. :P

[@BoneAppleTea]

@@eclipserepeater2466 I know, Thanos was not a mathematician haha

[@Wm7forthewin]

+DEMON XD sorry boys we took over the planet and have gone to the moon and invented the internet

[@brendaajamu7152]

Love that sub

[@rage_2000]

*Orange blobs appear* Blue blobs: _I don’t feel so good_

[@scares009]

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

[@MystGames]

nigga

[@bestbread3446]

rude

[@MystGames]

@@bestbread3446 not really, since it's not directed at anyone or anything. CHECK YO' PRIVILEGE, SON

[@vanthonvenus]

would you drop your child?

[@MystGames]

LillyCookies DDAENG no, but im sure you were dropped as a child.

[@googly4038]

The way the blobs wiggle their hands.

[@Isvoor]

The way the blobs win our hearts.

[@henryg.8762]

'hands'

[@williamhuynh869]

The derp.... I love derpy stuff, like Quagsire and these blobs

[@awhahoo]

They vibin

[@bigmoniesponge]

@@henryg.8762 I need to watch his video now “5 ways NOT to think.”

[@gnikola2013]

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

[@bodbn]

Blue blobs being sore losers

[@AltAccount-ko3pp]

I'm pretty sure he has done this in a later video now

[@biglefteye5017]

Kiritsu yes

[@ChaosAbandon]

He did

[@miniaturejayhawk8702]

@MsBizzyGurl na its more like gis first natural selection simulation. There he made it that when a blob was 20% bigger than the others it could simply eat them.

[@kurzed4904]

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

[@MarkAlcarezBoston]

Yes

[@aquaphoenix-mt2iv]

He'd have to increase birth rates for almost all creatures (except humans, since they're the problem-) And increase how quickly plants grow (to sustain current human populations, and the soon to be increased animal populations from increasing their birthrates) And since he can't do both of those in one snap (those are seperate actions after all), he'd have to snap twice. Which would kill him more than likely. Also those variables would have to be very precisely changed So.. no, he really couldn't fix it that way. I do agree that decreasing population size was the dumbest possible solution though

[@TooHarshForYou]

Even if he didnt add , there was still a n equilibrium point , the thing is humans modified earth to increase ita carrying capacity to their own good and thus they influenced their own stats and caps

[@matyaskassay4346]

but don't forget that in real life the "stats" are determined by the environment of the creatures, and aren't fixed unconditionally.

[@user72974]

This guy literally just debunked Thanos.

[@NickNLouie]

I'm a fan for the excited orange blob

[@cgmelody6422]

Nick Louie bandwagon fan

[@Ziess]

I'd like this but it's at orange blob's favourite number, 69.

[@Poffean]

@@Ziess 87, let's get it to 420

[@extaponts2402]

Me too

[@outofcontext728]

You mean scp 999

[@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

[@erwinmoreno23]

Hahah your last sentence is what all of us think but couldnt quite express

[@rogeronslow1498]

That's the problem with most universities. They produce graduates that are good at remembering stuff, not necessarily understanding stuff.

[@poofy6959]

Collage btw

[@cqrcin0]

*College :\

[@umbuchscui]

College* And I’m 10

[@rhysmartins8936]

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

[@colleen9493]

Yeah same. Simulating natural selection just showed up in my recommended.

[@cartor7892]

Same just found this channel yesterday

[@ellathon2277]

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

[@yzraeloa]

ellathon22 this actually shows how futile Thanos strat is. Population would grow back in no time and even promote a higher replication ratio

[@TheRedMooncorp]

@@yzraeloa Plus you have an initial universal famine, since most logistics will be severly damaged due to the loss of half the officials, half the technicians, half the farmers etc. Thanos never really thought this through at all^^

[@IamCoalfoot]

@@TheRedMooncorp It took me about five seconds of thought when I heard his plan to realize he'd spent about zero seconds on it.

[@TheRedMooncorp]

@@IamCoalfoot I feel you. I mean even choosing specifically half is so stupid. Even if Thanos would be right, the optimal number of deaths would differ from world to world, but sure let's treat a well organized society with population controlls, a new colony with 500 people and a sprawling over populated world of slums the same 😂😅

[@cooperwright9515]

TheRedMooncorp population controls are a meme

[@oceanman_8370]

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

[@purple_sky]

I believe it's a flat plane viewed from above, and they are just looking up because they know how to smile at the camera

[@blacknoir2404]

Ooh differential equations in disguise

[@PrimerBlobs]

Shh

[@buygeorgeivegotit7203]

I will reply to not shh

[@buygeorgeivegotit7203]

And use my home account tomorrow

[@awhahoo]

@@buygeorgeivegotit7203 F

[@Arkos.Knight]

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

[@theominouspigeon]

°vine boom°

[@availablekjp0609]

"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)

[@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.

[@PrimerBlobs]

++ Thanks for spelling it out. :)

[@hubierti]

Help me out here, if dN/dt = aN, then the integral of dN/dt with respect to t is N. Thus, integral of aNdt = aNt = N, right? What am I missing?

[@XenophonSoulis]

Thank you!

[@kvackkvackfrisk]

​@@hubierti No, since N actually is a function of t itself (you could write our differential equation as N'(t) = aN(t)) you can't just leave it be when you integrate with respect to t - what we're looking for is a function whose derivative has the original function as a factor. And in fact, the only function f(t) whose derivative f'(t) = some constant * f(t) is the exponential function, and the derivative of e^ax = a*e^ax so the solution must be, like Vincent stated, N(t) = e^at + C since this gives N'(t) = a*e^at = a*N(t).

[@Kryo_Ghost]

I am smol brain and i have no ide wat haf of dis is

[@alfon375]

Thanos should watch your videos.

[@professionalmemeenthusiast2117]

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.

[@alkali5841]

TELL US

[@conoroneill8067]

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.

[@PrimerBlobs]

Thanks, I really appreciate the kind words.

[@munzeralseed]

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

[@PrimerBlobs]

Haha, thanks for the enthusiasm. Rest assured that more are coming. I'm getting impatient too. :P

[@munzeralseed]

:D

[@theprofessor1554]

@@PrimerBlobs :D

[@Hansgilhaus]

Plz do a video on simulation of life and why these ameobas are pear shaped

[@Hansgilhaus]

They ameobas cuz they look squidgy and there hands stretch from their bodies so there pseudopods

[@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.

[@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.

[@vantutri9571]

This white haired guy is right

[@PrimerBlobs]

I didn't add a label for the mutation rate, but I did say that orange and green each come out of 1% of blue's mutations. So blue is still 98% as good as the written stats suggest.

[@vantutri9571]

@@PrimerBlobs yeah 98% is only for one generation though. Blue is destined to extinction

[@vantutri9571]

@@PrimerBlobs oh your videos are lovely and almost unique btw. Can you make a video about yourself, how do you make these videos and how long does it take? Thanks a lot

[@georgplaz]

@@PrimerBlobs You are right. I missed that! And yes, 1% is pretty negligible. The mutation rate does really "feel" a lot higher though. But I'll take your word!

[@Nexonium]

KZbin recommendations want me to learn. How much money did Miss Johnson give you?

[@h_3795]

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.

[@b1rd1e81]

I knew that it was exponential only from integration, cool to see the visuals though

[@h_3795]

B1rd1e yeah I know how to integrate it but it didn’t make sense conceptually.

[@dvirkomlosh4152]

@@h_3795 can you maybe explain? I really wanna know how to get the function of N from the Delta function

[@h_3795]

dvir komlosh shoot idk man. I can give you the proof with integration but idk conceptually. But here’s what I think. The reason why tho that dN/dt=N is exponential is that it doesn’t have to move to the right in order to increase faster. Simply increasing makes it increase faster. With dN/dt=t, which results in a quadratic, much slower, you have to increase t in order to increase faster, which lowers the slope.

[@h_3795]

dvir komlosh oh I’ve just figured it out. You know that the derivative of y=e^x is e^x, so dy/dx e^x=e^x. Since y=e^x, dy/dx=y

[@jobliar937]

5:47 Green survives because blue creature offspring can turn into green but green creatures offspring can't turn into blue creatures as a result a blue creature has a result the offspring rate for blue decreases and is added onto the green

[@Eggy-ty9vx]

where can i get this program?

[@atilacorreia]

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

[@Bananappleboy]

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

[@carlosbarzottowirti1895]

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

[@tymorgan2107]

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.

[@zersetzung8550]

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!

[@peterlewis2178]

I love how you condescendingly call people who are less mathematically gifted or educated "baboon-tier". It says a lot about you that you consider people to be tiered in that way, and consider yourself in a superior "tier".

[@mangjyz6336]

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

[@Sephirothfrank]

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

[@pnpgod7904]

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!

[@vithushanjegatheeswaran5317]

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

[@DodgeThatAttack]

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

[@EugeneAyindolmah]

G E K O L O N I S E E R D

[@mememachine3029]

Trump is Orange

[@dezynjikReal]

@@mememachine3029 you are an orange

[@amireinav1]

0:50 why use x as multiply, wouldn’t that be confusing?

[@Yato_q]

Episode 56 How the cReAtUrEs population goes on when you include anxiety, suicide, civil wars, revolutions, alcohol problems and the fact that the creatures are constantly using fossil energy instead of sunlight and water even though greenhouse effect does obscure damage to the creatures because of a lack of oxygen ps.: i like the videos :D

[@MNoelMusic]

Does anyone have good book recomendations on this kind of thinking? This channel and its videos are superb!

[@jacobr7729]

Just a hypothesis: the reason that green did better then blue was because blue had no way to "get founded" out of another species. When blue turned yellow or green, and eventually died out, it had no way of coming back. If green dies out though, it gan be brought back with blue.

[@Jazzafritsch]

Dear God biology economics and maths. I love this channel 😍

[@ok-kk3ic]

Jazza Fritsch / Do you actually find economics interesting? How interesting? (seriously asking btw)

[@Jazzafritsch]

@@ok-kk3ic very I never took the class but I would've if I had more units too my friends becoming a economist so it's great hearing him talk about it and now these videos

[@caoduyhoang8383]

*sees cute blobs* *subs*

[@YEETSWORLDWIDE]

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

[@hstera]

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

[@alejandrolaguna203]

Who are the three monsters who disliked the video, please correct your mistake, find some redemption

[@demetraeconomou6096]

Just 37 Australians

[@39401JLB]

I have encountered people in the USA who, incredibly, treat the concept of 'understanding' something with hostility. Simply admitting that you are able to comprehend an idea (which they have been indoctrinated to believe is evil) automatically makes you the untrustworthy enemy. I am not proud of the abysmal state of education in my country.

[@josepablolunasanchez1283]

They must be bad teachers not liking the video because they feel they are better.

[@joshuahudnut4992]

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

[@EnjoyCocaColaLight]

6:04 Also the blue always has a chance to mutate, whereas the green and orange cannot mutate and devolve back into a blue. So the blue will ALWAYS die out eventually. You forgot this part :(

[@HelloIAmAnExist]

2:37 short name? Then call it Dan or something

[@NuggetNugget-ld7wr]

Most people watching these videos probably have no idea what what these equations are 😂😂

[@twstf8905]

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

[@Someone-cr8cj]

At 1:01 I'm pretty sure that the integral of a linear function is a quadratic one... You have messed up something

[@proton4938]

looks like you're going to the shadow realm, jimbo.

[@johnnyi1337]

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

[@justakid8215]

If you combined what Primer experimented, we might explain the meaning of Life

[@tony_yt5967]

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

[@randomizer01j23]

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

[@henryg.8762]

1:50 Mojang inventing entity cramming

[@eduardofreitas8336]

Looooooooove this

[@vlgado3895]

Hi. You have very nice content on your channel and it is very easy to understand. Personally I think you use the term "evolve" a little to much when "adapt" would be more appropriate. I see your point of view at 6:20 when the blobs turn into rooster and rabbit. I think the species barrier cannot be broken since all mutations are bad (if you ask a doctor instead of a biologist), and all attributes need to be there in the first place. Thank you again for your nice posts, I cannot wait for the next one.

[@APerson-14]

5:20 I expect 70 orange In the end lol

[@jackalzyt3804]

Who is having this at their recommendation section

[@ringanmajumdar1949]

"The most likely outcome doesn't always happen."

[@redbeard8532]

You should make this into an app! So people can run their own simulation it would make bank! Charge whatever.

[@Zoova]

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.

[@danizk0]

I love how enthusiastic he sounds about creatures dying at 3:16

[@ggentertainment2737]

I was abel to recreate this in excel and added a virus. doing things like setting a chance of death or chance of loosing the virus for people who have the virus or saying if infected people can reproduce or not etc. really gives some interesting results!

[@AndrewFaberProperty]

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

[@harmitchhabra989]

Hey guys Delta is Just rate of change of N with time So you can write it as dN/dt and solve the differential eqiation yourself to get N as a funcation of time This allows you to experiment with the crowding death rate Say you want it to be dependent in the square of population Also you can try adding a food competition death rate ans solve to get a new function of N in time. Have Fun! The whole simulations is based upon this central idea of buildind dN/dt using terms we can comprehend and in a way tgat the rate makes sense to us And then we let the math do the magic tk get N as a fn of time. But also to implement this simulation you would have to apply a chance or probability fn too. Then you can make differential equation for all 3 blobs. Heck you van use OOP Classes to do so.

[@stephenlujan8512]

Surprised the math this guy used wasn't explained a bit more. You can solve for the crowding coefficient with algebra, plug 0 in for delta and any number you want as your equilibrium stable maximum population for N, and you can calculate the crowding coefficient that gets you there. Also the delta curve is the derivative of the population curve, while the population curve is the integral of the delta. With the formula for either you can use basic calculus to get the other.

[@authomat6236]

Fuck, I think I was finally tricked into learning math. But Im already out of school.

[@milkman2962]

Imagine that the creature in this simulation are somewhat like us. That we are somehow a simulation for someone bigger. Trying to learn how life was formed too

[@kfcchicken1610]

And the creatures creating us read ur comment as and r watching you right now

[@bingbong8761]

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 KZbin- thank you so much!

[@saophhire]

I remember watching this before highschool maths and not understanding anything, now I come back and still understand nothing

[@mandoanimations9056]

Make an "inbreeding" problem, that makes them pale and slow. Increases ded chance.

[@jiffylou98]

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)

[@YitzharVered]

I see integration here, why not call it by it's name?

[@PrimerBlobs]

The concept didn't require calc. Why use a tool you don't need? Plus I figured folks like you would see the connection anyway. :)

[@uMaud]

6:03 "There's always a chance for unlikly events to happen" -Connor, Detroit become human

[@Mikkerd12]

Actualy green was going to survive longer than blue becouse they can come from blue and not the other way around

[@whiteboard1335]

Cool channel and nice representations. one of my favorite channel after 3Blue1Brown

[@PrimerBlobs]

:) I wouldn’t presume to usurp 3b1b!

[@MrDoodleDood]

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

[@thegalwhosayswoo_881]

very interesting FORTNITE SUCKS

[@BiIlDipperIy]

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

[@simunator]

this basically supports thanos in every way

[@eget4144]

Green beat blue because blue can turn in to orange and green but green&orange cant turn back. So number of blues are actualy birth rate for others and turning non-blue is failed birth for blue. Edit: 5:35

[@PrimerBlobs]

True, but the effect is small enough to not overpower the better underlying replication rate. Running more sims, green consistently loses, but to decided to animate the first sim for the lesson about surprising results.

[@matthewbergeron3641]

this is kinda similar to the fear of over population many people think we will have to face, even though we won't. Every single country, regardless of personal or political views, follow a very very specific birth rate route. Going from having ton of children, due to fear of child mortality, to continuing to have that amount of children as medicine gets better, that group of people have less children due to child mortality getting less likely, then the next group averages a little over 2 children, which balances death rates and puts population growth to a standstill. This has happened and is currently happening to every single country on the planet, though specific countries are at different stages, which is why we see such massive spikes in population growth. However as more and more countries reach that last stage, other countries have been getting there faster and faster. Iran was in the first stage less than 100 years ago, and is now stable and in the last stage. All countries will reach stability, however certain countries face decreasing populations, such as Japan, but that's not due to lack of resources or birth rate routes, but are instead affected by local issues, such as lack of progression, which leads to overbearing societal pressures and expectations, racism, sexism and lack of immigration. Mathematicians and economists have calculated the global population, many many times, and claimed that the 12 billionth person will never be born, and by a simple examination of birth rates over the years, it's apparent that the rate is now slowing down. The rates from 1950 - 1970 are massive, 1970-1990, massive but slightly less, 1990- 2010, still growing but less than the last one, and 2010- now it's slowing still. Many graphs only graph things on large scales, and not spaced 20 years apart, which leads to misinformation, but it is slowing, slowly but surely. When all countries reach that last stage, which they will eventually, assuming there isn't some nuclear war that sets them back, the world population almost assuredly not exceed 12 billion, 13 billion at the absolute most, assuming medical progress is forcefully stopped in a population growth area, but even 13 billion is fully sustainable both land and food wise, pretty much forever. The only non-sustainable things would be our planet, since global warming will need to be fixed or we will die off since land will continue to dry up like it already has been, starting from the equator and moving outward. Besides that, everything from food to energy, and precious metals, are 99% sustainable. In which the only factors we need for long long term survivability is to come up with solutions to quell global warming, hopefully, stop it, and to find ways to create materials efficiently, such as the hydron collider, which can create any element, but on a much larger scale, or to find a way to mine asteroids.

[@General12th]

I approve.

[@tristanshah9716]

How did you code all of this? Python?

[@PrimerBlobs]

Yep, there's a (painfully disorganized) github repo in the description

[@icecream6256]

This video is great. But it made me think. We live in a world where overpopulation is just on the corner. Meanwhile, our death rate is going lower and lower as healthcare improves and technology advances. Im wondering how many people can be born before the equilibrium state of human is reached.

[@PrimerBlobs]

This used to bother me a lot too, but affluent societies tend to have fewer children by choice, so if we solve poverty, it will go a long way toward solving overpopulation. That's not simple, nor will it solve everything, but it gives me hope.

[@LucreDenouncer]

You should do a video on what happens when the carrying capacity is exceeded (overshoot)

[@afjelidfjssaf]

what do you mean? the crowd coefficient makes the death rate high enough so that the blobs die more than they reproduce thus it evens out at about 50 blobs in this example, that is the carrying capacity which cannot be exceeded.

[@Plazard_YT]

I don't need school, this guy would be like an A level teacher

[@CyberSaurian]

Orange blob looks like SCP-999

[@azariaasleep7621]

Me during this whole video: *....WHAT???? I DON'T UNDERSTAND THE LANGUAGE OF MATH HALP*

[@Posh1G]

3:51 not exponential but ok.

[@oldveryveryoldmanfromthe1900s]

I can’t understand a single thing but I like the videos

[@genvievesplayhouse8670]

Enderdragooon i thought I was the only one 😭

[@pillarshipempireemployee0142]

6:44 How? Didn't you not kill all the blue ones by hand?

[@erinnlynn7]

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

[@lowfy0]

I’m wondering how much this guy feels like god/thanos/actually decent math teacher!

[@konokaiza]

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

[@Scullgaming962]

4:30 when the blobs come out

[@beanieteamie7435]

2:44 you basically just added decease.

[@liamcourtney390]

You are the only KZbinr of quality