The price of memory

Content on this page:

Introduction
An example
Introduction of suckers
Introduction of cheaters
Introduction of grudgers
But memory has a price
Conclusion
Further work ...

This page is based on an older Norwegian version. At the bottom you will hopefully se a Java applet. I have made it so the readers can test for themselves what I am writing about.

The applet is time consuming and a fast machine is recommended. But I will ask you to wait a little before starting to run it. Let me first explain what the applet is supposed to simulate ...

Introduction

In 1976 Richard Dawkins' The Selfish Gene was published. The book was both disputed and misunderstood. But even when disagreeing with the content, it is an interesting book. (For this page I have used the issue from 1989, ISBN 0-19-286092-5.) The ideas are well explained, and the examples are both simple and good. But I believe the book contains a few few errors and omissions. Did Dawkins forget that memory has a price?

An example

Chapter 10 is about advantages and costs implied by helping others, as can be read from the tittle You scratch my back, I'll ride yours. An example is based on a population infected by something negative. It might be birds parasitized by a particularly nasty kind of tick which carries a dangerous disease. But no matter what this torment might be, one single individual cannot help itself. The birds are depended on other birds to get rid of ticks, at least those on their heads All infected individuals are depended on help from other individuals. But will it pay for a single individual to help others? Not necessarily!

Introduction of suckers

The simplest would of course be if everybody would help everybody in need of help. Such saints can cynically be called suckers. As long as everyone are suckers, there will be almost as a paradise. This can be seen by trying the applet at the bottom. (Go here if the applet is missing!) You can push the green sucker button before selecting start.

You will then see something like the illustration to the right. The population will grow rapidly and be stable on a high level. The dark green color indicates individuals not parasitized by ticks. The lighter green at the top indicates individuals that are parasitized. There will always be some individuals with parasitizes, but they will only constitute a stable minority.

Introduction of cheaters

But this altruistic paradise cannot last. Before or later there will be introduced genes that are selfish. There is a price involved with helping others. It requires both time and energy. If you are running the applet with only suckers, and you push the red cheat button, you will introduce such egoistic genes.

As shown in the illustration to the left, these cheaters will fast gain a large part of the population. So successful will they be, that all the suckers are exterminated. But since there are no altruists left, the number of light red infected cheaters will grow very fast, and the healthy dark red will disappear. The whole population will vanish.

To the right there is an enlarged example of what will happen if we start a population of only such cheaters. They become infected, and are all exterminated shortly after.

Introduction of grudgers

In order to save the population we can introduce the concept of grudgers. These are individuals who helps everybody who helps others. In the book Dawkins made all grudgers play a forgiving tit-for-tat. All the grudgers would initially help everybody else. But when a grudge was in need of help, it would remember anybody who refused to give such help. Such cheaters would not receive any help later. In the applet I have made this a little simpler. The grudgers are smarter since they can recognize a cheaters at once without any previous experience. The difference with Dawkins' grudgers is that my grudgers not even once will help a cheater. Hopefully that will not give a different result.

p/kun_smarte.png To the left we have such a population of only grudgers. It is the same result as if we had only suckers. Everyone helps everyone, and we have a large and stable population. You can test this in the applet by first selecting init. Then you use the blue grudge button before a new start.

p/kun_dumme_og_smarte_uten_kostnad.png If you start with both suckers and grudgers, there will be a more or less stable mix as can be seen to the right. (After a while one of them might be randomly exterminated.)

But if we have such a partly stable mix of suckers and grudgers, and we then introduce cheaters, we will se something interesting. First the cheaters will have a good life exterminating the suckers. But after that they will get no help from the remaining grudgers. The grudgers will be the winners.

So far this applet has behaved according to Dawkins' description.

But memory has a price

Here is the main issue of this page. There is a price on memory! All grudgers must pay something in order to decide if they shall help others. If they are to remember all cheaters according to Dawkins, they need a good memory. If they are to identify a cheater at once, they need both good senses and brain capacity. No matter how much this will cost, it will cost something. What will the consequences be?

Let us return to the example with a stable population of suckers and grudgers. Her we can check the box for mem.cost. Doing that we are introducing a cost for being a grudge. In a population of only suckers and grudges, there will be an advantage to be a sucker. Everyone helps everyone, but a grudge must use extra resources in order to decide if it will give any help. As we can se to the left, the suckers will outlive the grudgers.

n/tre_kamp_uten_vinner.png But what if we again have a stable population of suckers and grudgers, and we then introduce both memory cost and cheaters? To the right we have the beginning of such a simulation. Before or later one of the categories will win. But which category, is unknown. This is a sort of Rock, Paper & Scissor:

suckers loose for cheaters,
cheaters loose for grudgers and
grudgers loose for suckers.

Simulations so far gives a partly chaotic behavior until one of the categories is exterminated. How long this will take, is also unknown.

Conclusion

What does this proof? Nothing! The applet is made only as an interactive and graphical tool in order to show what I describes. Such coding can be made to show anything. For instance did I modify a lot of parameters before the curves were nice and behaved more or less as I wanted.

But my arguments are hopefully good enough, even without an applet. We humans are a good proof that there is a price to pay for a big brain. This was also confirmed when I programmed the behavior of the grudges. That required extra code which filled up memory and made the execution slower. I believe that considerations of such extra cost will make room for new ideas in sociobiology.

Further work ...

... depends on feedback. The source for the applet should for example be verified by somebody else. Please tell me if you want a copy!

It could also be an idea to modify the code in order to make the simulations closer to real life. But then I need information from people with more knowledge in biology.

I am of course open for comments and other suggestions. Feel free to send me an email: rhj@rhj.info. You can write in English, German or any of the Scandinavian languages.

3/1-2002: