Simulating the Evolution of AggressionYouTube↗  IA↗(long shot)
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in this video we're going to start
В этом видео мы начнем
exploring conflict between creatures to
исследовать конфликт между живыми существами
try to build some understanding here
Чтобы выстроить понимание по этой теме,
we're going to use some simulations and
мы будем использовать некоторые модели и идеи
some ideas from a field of math called
из области математики, называемой Теорией Игр
game theory
(легкая музыка)
okay so in our simulation food will
Итак, в нашей симуляции еда будет появляться каждый день
appear each day and then blobs will appear and go out to eat the food
а потом будут появляться существа, чтобы выйти и её съесть
we'll use the same survival and
Мы будем использовать те же правила выживания и размножения,
reproduction rules as in previous videos
что и в прошлых видео.
eating one piece of food lets a creature
Поедание одного кусочка еды позволяет существу
survive to the next day and eating two
прожить до следующего дня,
pieces of food allows a creature to both
а поедание двух кусочков позволяет
survive and reproduce
еще и завести потомство.
what's different in this simulation
Однако в этой симуляции, в отличии от предыдущих,
though is that food will come in pairs
кусочки еды будут лежать парами
each creature randomly picks a pair of
Каждое существо выбирает случайную пару кусочков еды к которой оно пойдет,
food to walk to so it might get the pair
так, оно может взять оба кусочка
all to itself and get to go home with two food and then reproduce or another
и добраться с ними до дома, где оставит потомство,
creature might find the pair at the same
либо существо случайно попадет в пару с другим существом.
time and when this happens they have to
И если это случится, они должны как-то решить,
somehow figure out how to split things
как ее поделить.
up we'll start off by having only one
Мы начнем, имея только одну возможную стратегию
possible strategy for creatures who run
для существ, которые столкнулись друг с другом.
into each other they'll just share each
Они просто поделятся, каждый взяв один кусочек еды
taking a piece of food and going home to survive to the next day
и пойдут домой, чтобы выжить до следующего дня
and because this strategy is so nice
И поскольку эта стратегия такая милая,
we'll give it the name dove
мы будем называть её "голубь".
all right let's let things run for a bit
Ладно, давайте запустим симуляцию. Надпись: "Только голуби".
[Music] [Music]
"Только голуби"
all right now let's add a new strategy
Ладно, давайте теперь добавим новую стратегию
called the hawk strategy hawks are more
названную "ястреб".
aggressive if a hawk meets a dove the
Ястребы более агрессивны.
hawk will go for the same piece of food
Если ястреб встречает голубя, он сначала возьмет тот же кусок, что и голубь,
as the dove eat half of it and then
откусит от него половину, а затем быстро съест
quickly eat the other piece of food taking it for itself
второй кусок еды, оставив его таким образом себе.
this half food does complicate our
Эта половинка еды немного усложняет
survival and reproduction rules a little
наши правила выживания и размножения.
bit so in this situation adove ends the
В такой ситуации, голубь заканчивает день с половинкой еды,
day with half of food so it'll have a 50 chance of surviving to the next day and
имея 50% шанс выживания до следующего дня
the hawk ends its day with one and a
а ястреб заканчивает день с 1,5 кусочками еды,
half food so it'll survive for sure and
так что он точно выживает,
also have a 50 chance of reproducing
и дополнительно имеет 50% шанс размножения.
so it looks good to be a hawk but it's
Кажется, что ястребом быть хорошо, но это еще и рискованно.
also risky if two hawks meet they'll fight and
Если два ястреба встретятся, они будут сражаться за еду,
fighting is taxing at the very least
а сражение утомляет.
they use a lot of energy and they might
По крайней мере, они затрачивают много энергии,
also get injured so when hawks fight
а так же могут быть ранены.
each one gets a piece of food but they
Поэтому, когда ястребы сражаются, каждый из них получает по куску еды,
spend so much energy fighting that they
но они тратят столько энергии сражаясь,
use up all the benefit of the food right
что сразу же истрачивают все преимущества полученной еды,
away and effectively go home with zero
то есть они будто бы и не ели вовсе,
food meaning they won't survive
что означает, что они не выживут.
so now let's try adding a hot creature
Итак, давайте теперь попробуем добавить одного 'ястреба' в нашу симуляцию,
to our simulation and see what happens
и посмотрим, что получится
now is a good time to pause and predict
Сейчас хорошее время, чтобы поставить на паузу
what you think will happen
и попробовать предугадать, что случится.
[Music] [Music] [Music] [Music]
Надпись: "Голуби и ястребы" "Голуби и ястребы"
all right it looks like we have a
Что-ж, выглядит, будто голуби и ястребы занимает каждый около половины всей популяции, с небольшими отклонениями.
mixture that fluctuates roughly around
половины всей популяции, с небольшими отклонениями.
half and half and there are also fewer
Также, сохраняется примерно статичный размер популяции,
creatures overall even with the same amount of food here's an example of how natural selection doesn't necessarily act for the good of the species
Даже с одинаковым кол-вом еды.
and to cover our bases let's try starting with all hawks [Music] okay not too surprisingly they're
tearing each other apart and their max population size didn't even reach half of the population size of the doves now if we add a dove to the mix in the
next day what do you think will happen [Music] [Music] okay so it took the doves a little while
to gain a foothold here but eventually we end up in a similar situation with a fluctuating mixture of hawks and doves so why do we care well this is a
situation where survival of the fittest doesn't help us understand what's going on there isn't one fittest strategy we can get a better sense for why this
is by translating our conflict rules from before into a table if two doves face each other they'll each get one food
if a dove faces a hawk the dove gets half a food and the hawk gets one and a half or three halves food and if we reverse perspectives if hawk
faces a dove they'll get three halves and one half and when a hawk faces another hawk they'll each end up with zero after they waste all that energy
fighting each other now that we have this table let's imagine blobs that can choose which strategy they want to play say i control
the blob on top and you control the blob on the left say you know that i'm going to play a hawk strategy which of course i am what should you do
well you're better off just backing down and taking your half food that might be annoying since it feels like i'm winning somehow and you might
be tempted to challenge me and also play hawk to teach me that i can't just push you around this could make sense if we were going
to play this game against each other over and over again as two humans might do and that is something we'll talk about in future videos but in this
situation we're just these simple blobs with no social structure interacting once and even if we do see each other again we won't remember it so all that
matters is how much food we take home right now and if you want to maximize your chances of surviving and reproducing you'll play dove discretion
is the better part of valor here let's record this by drawing an arrow if we're in the right hand column because i'm playing hawk the situation
in the upper right square is the best you can do okay in the other case where i'm not so mean you know that i'm going to play the
dove strategy in this case you'll do better playing hawk and here again because you're a very smart human you might be tempted to
think about the future and want to reward me for playing nice and play dove yourself but we're just these really simple blob creatures who might never
see each other again so if you want to maximize your chance of reproducing you'll play hawk and we can record this with another arrow
so now to complete this table we can reverse perspectives and think about what i should do in response to you which i won't go through in detail it's
the same reasoning but we get similar arrows in the rows here these arrows all point to more advantageous strategies and the interesting thing to notice is
that there are two stable situations either you play hawk and i play dove or you play dove and i play hawk if we're in one of those two situations
either one of us would be worse off if we pick a different strategy and by the way this way of analyzing choices is called game theory which is a whole
field of math and a situation where nobody benefits from changing their strategy is called a nash equilibrium named after john nash who some would say
had a beautiful mind so the best strategy isn't hawk or dove it's to do the opposite of what your opponent is doing when there are a lot
of doves it's better to be a hawk and when there are a lot of hawks it's better to be a dove there's some equilibrium fraction of doves that the
population has always pulled toward great so we have the main conceptual point down but we can deepen our understanding by calculating what that
equilibrium fraction should be the population will be in equilibrium if doves and hawks have the same expected average score in a contest right
equilibrium is when on average we don't expect to change one way or the other so we can't have one strategy doing better they're equal
our goal is to find the fraction of doves that makes this condition true on our way there let's first calculate the expected average score for a dove in
a hypothetical example say where the rest of the population is 90 doves so let's see a dove will have a 90 chance of facing another dove in which
case it gets the dub versus dove payoff of one food and a dove also has a 10 chance of facing a hawk right that's just the rest of the creatures in which
case it only gets a half of food so overall when a dove runs into another creature when the rest of the population is 90 doves it'll come away with 0.95
food on average this number is pretty meaningless on its own but once we calculate the expected hawk score we can compare the two to see
whether the equilibrium condition is met so let's do that let's find the expected hawk score it could be good to pause and try to do
this yourself to make sure it all makes sense maybe even rewinding to watch the dove part again okay just like before the rest of the
population is 90 doves and against the dove a hawk gets one and a half or three halves pieces of food and again there's a 10 chance of running into another hawk
in which case our hawk goes home with zero food and this comes out to 1.35 food on average
now notice that 1.35 is more than 0.95 so at 90 doves hawks will do better and we'd expect the fraction of hawks to increase in the next generation so it's
not equilibrium not 90 now to find out what fraction of doves does meet the equilibrium condition we can write the fractions of doves and
hawks as variables instead of just guess against specific numbers and you might be saying right now wow that's a lot of letters which is a fair
point but we're almost there and our next step is actually to get rid of one of those letters so there's a nice treat already
doves and hawks make up all the creatures so their fractions have to add up to one and this means we can replace the small h with one minus small d
and now the expected dove and hawk scores are both written as functions of one variable and the same variable so we can graph them on top of each other
the expected scores are equal when the graphed lines cross and indeed the equilibrium condition is met at 50 doves and if we run a simulation with way more
creatures than before unfortunately too many to animate the randomness smoothes out a bit and we can see that the prediction is true
okay so it might feel like that was kind of a lot of work just to verify what we already thought but the fraction of doves isn't always going to be one half
it depends on the numbers in our payoff grid the most interesting number to play with here is the hawk vs hawk payoff so far we've been saying that the hawks
each get one piece of food but waste all the energy of the food on fighting but what if instead they only waste most of the energy not all of it and go home
with a score of one-fourth plugging that in we see the population move toward one-third doves and again we can see this borne out in the simulation
at this point congratulations we have a pretty detailed understanding of how populations of hawks and doves work and as basic as this model is with only two
simple strategies it's a powerful starting point for analyzing behavior in the real world and before we go i want to give you some teasers for how we'll
build on this to get closer to reality in future videos first creatures in the real world can play more than one strategy so instead of having their
behavior completely determined by a single gene our creatures could have several genes affecting their behavior causing them to have different chances
of playing hawker dove and the game theory term for this is mixed strategies there can also be more complex conditional strategies that act
differently depending who they're facing for example there could be a strategy that fights with hawks but is nice to doves
and there could also be a strategy that tries to threaten a fight but runs away if things get serious and seeing what happens with these kinds
of strategies can help us understand why some animals put on threatening displays while rarely actually fighting or have somewhat ritualistic fights that usually
don't harm anyone next most conflicts are actually asymmetric so far we've been assuming that everyone
has the same amount to gain and lose and that all the creatures are on equal footing but when this changes we can start to understand things like
territorial behavior and dominance hierarchies and last let's go back to our equations and see what happens as the hawk payoff
gets less and less bad say getting to three-fourths now the graphed lines don't cross at all there's no equilibrium at this point even if you
know you're facing a hawk the three-fourths food you get from fighting is better than the one-half you get from being nice so these arrows should
actually flip and it only ever makes sense to play hawk we end up in this tragic situation where everyone's fighting all the time even though they
would do better if they could just cooperate this kind of situation has a special name it's called the prisoner's dilemma it can feel kind of grim but
there are ways out of it which we'll talk about in future videos and i'll see you then okay so now i have some people to thank
first thanks to you for watching to the end second thanks to everyone who's become a patron on patreon your support is what
makes me feel like people actually get value from these videos and gives me the confidence that they'll be funded into the future third i want to thank the
channel three blue one brown who shared the last video and really gave this channel a kick if you like this channel you really should go check out three
blue one brown
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