Name: 模擬為了家庭犧牲的演化！ (Simulating the Evolution of Sacrificing for Family)
Uploaded: 2025-11-19T02:04:50.000Z
Duration: 20 min 49 s

The basic idea of natural selection is that if a gene does an above average job at helping its host creatures survive and reproduce, it'll tend to become more common as creatures compete with each other over the generations.

自然選擇的基本概念是，如果一個基因在幫助宿主生物生存和繁殖方面做得比平均好，隨著世代間的競爭，這個基因就會變得越來越普遍。

基礎被動語態

This tendency to survive and reproduce is called fitness, and

這種生存和繁殖的趨勢就叫做適應度，

you'll often hear natural selection summarized as survival of the fittest.

你常常會聽到自然選擇被簡化為適者生存。

But one day, a clever, newly mutated gene realized another strategy was possible.

但有一天，一個聰明的、新突變的基因發現了另一種策略是可行的。

If copies of the gene exist in multiple different creatures, the gene can do better by causing the creatures to help each other rather than mercilessly competing with each other.

如果基因的複本存在於多個不同的生物體中，這個基因可以透過讓這些生物體互相幫助，而不是無情地互相競爭，來做得更好。

This concept is known as inclusive fitness.

The only problem is the copies of a gene are hidden inside the creatures and they can't see each other.

唯一的問題是，基因的複本藏在生物體內，牠們彼此看不到。

So if the copies of the gene want to help each other, they have to gamble, sometimes helping the competing genes by accident.

所以，如果基因的複本想要互相幫助，牠們就得冒險，有時會不小心幫助到競爭的基因。

So the question is, how can a gene strategize around inclusive fitness without the whole plan backfiring?

是以問題來了，一個基因如何在不讓整個計畫適得其反的情況下，針對包容適應度進行策略規劃呢？

The condition for making inclusive fitness gambling work is called Hamilton's Rule, and

讓包容適應度賭局奏效的條件叫做漢彌爾頓法則，

這也是我們今天要建立的目標。

It's a pretty simple looking inequality, and

這是一個看起來相當簡單的不等式，

if you've learned about Hamilton's rule before, you might be wondering why the heck this video is so long.

如果你之前學過漢彌爾頓法則，你可能會想說，為什麼這個影片這麼長？

Well, it turns out that the simplicity of Hamilton's rule is a bit deceptive, or at least it deceived me at first.

嗯，事實證明，漢彌爾頓法則的簡單性有點騙人，至少一開始騙了我。

So this video is going to go slowly, starting with the general requirement for gambling to be beneficial and then applying that idea to simulations of increasingly complex biological systems.

所以這個影片會慢慢來，先從賭局獲利的普遍要求開始，然後將這個概念應用到越來越複雜的生物系統模擬上。

在我們建構的過程中，有些東西會出錯。

And when it does, you might not realize it.

而當它發生時，你可能不會意識到。

It'll get fixed before the end of the video, but

在影片結束前，這個問題會被解決，但

consider it a challenge to follow closely enough to see what's going wrong before I tell you about it.

把它當成一個挑戰，看你能不能仔細跟著，在我告訴你之前就發現哪裡出錯了。

如果擲出六，你就會贏得七枚硬幣。

Let's let this blob play for a bit while we try to predict what will happen.

我們就讓這個小東西玩一陣子，同時我們試著預測會發生什麼事。

Okay, so there are six possible outcomes, and

好的，所以總共有六種可能結果，而且

we can summarize each with an equation where the payout minus the cost equals the net gain.

我們可以用一個方程式來總結，其中支付減去成本等於淨收益。

If the die lands on a number from 1 to 5, the payout is 0 and the cost is 1, leading to a net gain of negative 1 in each case, or a loss of 1, if you prefer to say it that way.

如果骰子擲出 1 到 5 的數字，支付是 0，成本是 1，這樣每種情況的淨收益都是負 1，或者說，如果你比較喜歡這樣說，就是損失 1。

If the die lands on a six, though, the payout is seven.

So the net gain for that case is six on a fair die.

所以這種情況的淨收益是六個硬幣。

These six possible results are all equally likely.

這六種可能結果的機率都一樣。

So we can combine the equations together and divide everything by six to get the average payout cost and net gain.

所以我們可以把這些方程式合併，然後全部除以六，來得到平均支付、成本和淨收益。

One way to read this equation is to say you have a one in six chance to win the benefit of seven coins.

這個方程式的一種讀法是，你有六分之一的機會贏得七個硬幣的獎勵。

And it costs one coin to play, so you expect to win one sixth of the coin per time you play.

玩一次要花費一個硬幣，所以你預期每次玩都能贏得六分之一的硬幣。

The coins only come in whole numbers, but the average is a fraction.

硬幣只有整數，但平均值是個分數。

An average predicted result like this has a special name.

像這樣預測的平均結果有一個專有名稱。

And since the expected value here is positive, the blob should gain money over time by continuing to play.

因為這裡的期望值是正的，這個小東西應該會透過持續玩遊戲來隨著時間賺錢。

It looks like the blob is actually doing way better than 1/6 of a coin on average.

看起來這個小東西平均贏的硬幣比六分之一還多。

That's good for the blob, but not so good for our prediction.

這對小東西來說是好事，但對我們的預測就不太妙了。

It's only been a few rolls, though, so maybe the blob is just getting lucky.

不過才滾了幾次而已，也許小東西只是運氣好。

If our prediction is good, it should start to look more accurate with a larger number of rolls.

如果我們的預測是準的，滾動次數越多，預測應該會越準確。

So let's enlist some more blobs to see if that happens.

所以我們來找更多小東西來看看是不是這樣。

It can sometimes take surprisingly long for random events to even out, which is my favorite excuse whenever I'm getting my butt kicked in a board game.

有時候隨機事件要平均下來需要很長的時間，這也是我每次在桌遊被電爆時最喜歡的藉口。

We can use variables to write this out in a way that will apply to a broader set of situations.

我們可以用變數來寫出這個公式，讓它適用於更廣泛的情況。

The benefit of winning times the probability of winning minus the cost to play is the expected value of a gambling game.

贏的收益乘以贏的機率，減去玩的成本，就是賭博遊戲的期望值。

If the expected value is positive, it's usually a good idea to gamble.

如果期望值是正的，通常賭博是個好主意。

And when the expected value is negative, like.

Like in every single casino game, for example, you should expect to lose money.

就像在每個賭場遊戲裡，你應該預期會輸錢。

You might notice that this looks basically the same as Hamilton's rule already.

你可能會注意到，這看起來跟漢彌爾頓法則差不多了。

So let's try applying it to a biology simulation to see how it works.

那我們來試著將它應用到一個生物系統模擬，看看它是怎麼運作的。

We'll start with the same basic structure from the video on Green Beard Altruism.

我們會從綠鬍子利他主義那支影片裡，使用相同的基本架構開始。

Each day, blobs will go out to the forest to eat some fruit.

每天，這些小點點會去森林裡吃水果。

Some of the trees have predators in them, though.

And if the blobs are unlucky enough to visit a tree with a predator in it, they'll think get eaten.

如果這些小點點不幸去到有掠食者的樹，牠們就會被吃掉。

But if they don't get eaten, they'll head to one of the homes and reproduce, creating a puddle of three new identical blobs in their place.

但如果牠們沒被吃掉，就會回到其中一個家並繁殖，原地創造出一灘由三個新的、一模一樣的小點點組成的群體。

And yes, a group of blob siblings is officially called a puddle.

對，一群小點點的兄弟姊妹，正式名稱就叫做一灘。

And after the blobs reproduce, the cycle repeats.

然後這些小點點繁殖後，循環就會重複。

Also, when it's time to go home, there might not be enough homes to go around.

另外，到了該回家的時候，可能會沒有足夠的家讓牠們回去。

In which case some randomly determined blobs won't get to go home and reproduce.

在這種情況下，有些隨機決定的小點點就無法回家繁殖。

In case you've seen that Greenbeard video, I want to highlight the key difference here.

如果你看過 Greenbeard 的影片，我想強調這裡的關鍵差異。

This time, the siblings always stick together in their puddle when they go out to a tree.

這一次，這些兄弟姊妹外出到樹上時，總是會待在牠們那一灘裡。

let's make this a bit bigger and let it run for a while to understand how the simulation works in this baseline case.

我們來讓這個情況稍微擴大一點，讓它跑一段時間，以便了解這個基準情況下的模擬是如何運作的。

Alright, it turns out that the blobs thrive in this environment and the limiting factor ends up being the supply of houses.

好的，結果發現這些小點點在這個環境中蓬勃發展，而限制因素最終變成了房屋的供應。

The blobs should really figure out a way to build more housing, but

這些小點點真的應該想辦法建造更多房屋，但是

comments like that belong in the economic series.

這種評論比較適合放在經濟系列裡。

Okay, now let's add the ability to be altruistic again.

好的，現在我們來重新加入無私行為的能力。

This will be pretty similar to what we saw in the Greenbeard video.

這會跟我們在綠鬍子影片裡看到的很像。

When the blobs go to a tree with a predator in it, one of them will notice the predator and it'll have two options for how to react.

當這些小點點走到有掠食者的樹旁時，其中一個會發現掠食者，牠會有兩種反應方式。

The first option is to just run away, leaving the other blobs to die.

第一種是直接逃跑，讓其他小點點去死。

我們會把這種稱為懦弱的行為。

The second option will be to make a bunch of noise to warn the other blobs, but

第二種選擇是發出很大的噪音來警告其他小點點，但

in the process attract the predator's attention and end up getting eaten.

同時也會吸引掠食者的注意，最後被吃掉。

Because these blobs are sacrificing themselves to help others.

因為這些小點點是犧牲自己來幫助別人。

我們會把這種稱為無私的行為。

The behavior will be controlled by a gene which has two versions or alleles.

這種行為將由一個基因控制，這個基因有兩個版本或稱等位基因。

The cowardly allele will be blue, and the altruism allele will be orange.

膽小基因會是藍色，而無私基因會是橘色。

The blobs can't actually see the genes, but

這些小點點其實看不到基因，但是

we're going to use these colors to graph the frequency of each allele over time.

我們要用這些顏色來繪製每個基因隨時間變化的頻率圖。

I mention this in basically every video, but I can't say enough how.

我幾乎每個影片都會提到，但還是不夠強調。

In real life, the cause of behaviors is very complex.

在現實生活中，行為的原因非常複雜。

And the genetic part itself is a lot more complicated than this model we're using here, where just one gene controls this one kind of behavior.

而基因的部分本身比我們這裡使用的模型複雜得多，在這個模型裡，只有一個基因控制著一種行為。

We're just using a simple model to explore one small piece of the very large picture of behavior.

我們只是用一個簡單的模型來探討行為這個巨大圖景中的一小部分。

But with that said, let's run this simulation.

但話雖如此，我們來運行這個模擬吧。

We'll start with equal numbers of each allele.

我們將從兩種基因數量相等開始。

Before we hit go, though, what do you think will happen?

不過，在我們開始之前，你覺得會發生什麼事？

Try using that expected value idea we talked about earlier.

試著用我們之前討論過的預期值概念來想想看。

And keep in mind that the puddles stay together when they go to find food.

還有，記得牠們去找食物時，水窪會聚集在一起。

This graph shows the frequencies of each allele over time, stacked on top of each other at the beginning it's half and half.

這張圖顯示了每個基因隨時間的頻率，一開始疊加在一起時是各佔一半。

But over time, the orange altruism allele drove the other allele to extinction.

但隨著時間過去，橘色的利他基因把另一個基因逼到滅絕了。

Let's see if we can make sense of why the altruism allele did so well.

讓我們來看看為什麼利他基因表現得這麼好。

Just like before, we'll look at the benefit of the behavior times the probability of getting the benefit, minus the cost of the behavior to get the expected value.

和之前一樣，我們會看行為的好處乘以獲得好處的機率，減去行為的成本，來得到預期值。

But instead of coins, we're worried about copies of the altruism allele.

但這次我們關心的不是硬幣，而是利他基因的複製品。