General > Biology

Natural Selection as an abstraction for game theory

<< < (4/6) > >>

Numsgil:
An addendum, at present the theory of natural selective abstraction is incomplete.  I don't have a a consistant way to determine if an abstraction ceiling exists.  That is, if there is an upper limit on the evolutionary stability of the number of levels of abstraction.  Or put another way, if complexity will increase.

My guess at the moment is that additional levels of abstraction require that "winning" the current abstraction layer adds some new rules to the game.  A successful replicator will now have to contend with the fact that other individuals will quickly exist that share any innovations it makes (close genetic relatives after a few generations).  This creates a race condition to develop innovations first, or otherwise be outcompeted (wether by being hunted or lacking physical space).  The thumb screws are tightened.

Any abstraction layer where winning does not create new rules will collapse back onto itself as mutations cause a splitting in the only surviving agent but nowhere to vent that splitting effect.  The current abstraction layer's game will simply eventually be played again with the mutated parts of the winning agent.  For instance, a planetary government would eventually collapse from in-fighting if constrained on our little Earth, because a world government seems to reduce the rule set instead of increasing it (wars are no longer an evolutionary pressure, and growth will eventually level off.)

In essence, my guess is that a new abstraction layer seems to form (that is, there is no abstraction ceiling) when you have these conditions:

1.  No other players in your current top level abstraction's game.

2.  Massive population increase / size growth.  Locality is reduced.

3.  There is Nash equilibrium type incentive for the sole surviving agent/player to fracture into new players / agents.  That is, cohesive forces are severely reduced.  Agents are rewarded for diversifying.

4.  Being the only player to survive the last game has somehow added a new rule to the game.  Most likely because you're game is larger in scope from the growth in #2 above.  Rules that were of little consequence before are now important.  For instance, a theoretical multicellular creature the size of Earth now has to deal with internal gravitational forces from its own mass.

Another example is oxygen producing algae having to deal with their own toxic output.  In some way, winning has changed the game.

------------------------
Using these 4 criteria I think it should be possible to examine any ALife simulator that suffers from little runaway complexity (like just about every simulator ever run) and determine a course of action to correct this.

In Darwinbots, the bottleneck is #3 and a little #4 I think.  There's certainly population explosions and competition driven extinction.

Testlund:

--- Quote from: Numsgil ---I don't think all altruism in nature is tit for tat.  Certainly some of it is, but not all organisms have the capacity to remember the past actions of the other members in its group.

This is a good article about this very topic! Article.
--- End quote ---

That's an interesting article, though I don't agree with what it says about the monkeys and alarm calls. In nature ALL predators relies on the element of surprise at some degree. If a jaguar will be able to catch a monkey in the Amazon jungle the monkey has to be unaware about it's approach. If a monkey discovers it and start to give alarm calls it means it will be on guard and have much easier to escape from the jaguar. The jaguar instinctevly knows that and give up. It's probably not even worth it to try and find a silent monkey in all that noice.  

Numsgil:
I think the idea is that the time spent being wary of predators has some fitness cost.  If you rely totally on others to tell you if there's a predator, you can spend more time digging for grubs.

Of course, if others learn this too and no one spends time watching for predators, everyone dies.

Numsgil:
I'm totally reformatting the "theory" above into very plain language in an attempt to make it more accessible to people who haven't had the mathematical and bilogical background I have.  As follows is a presentation of it that should be written in very plain terms without jargon.  You should be able to use this post and understand the comments I've made prior in the thread if you haven't been able to yet.

Natural selection is fundamental.  Basically, it says that organisms that are less capable of passing their essence to the next generation will be replaced by ones that are.  Natural selection is well observed and supported.  But it has a very area where it is useful.  Natural selection is difficult to apply in its direct form to understanding the nature of politics, economies, ecological forces, and other "macro", or large scale, phenomena, even though undoubtedly it is at the heart of these systems.

An interesting idea in the mechanics of natural selection came with Dawkin's selfish gene "framework".  I use the term framework instead of theory for a very important reason.  My first premise is that saying natural selection works on individuals trying to pass their genes to the next generation, and saying that genes are acting to propogate themselves are equivelant statements.  They're simply different ways of viewing the same phenomenon, and can be used interchangably depending on which one makes the most sense for the given question at hand.

An interesting consequence of this is kin selection, that is, performing benevolent acts towards another member of your family.  Since the other member of your family shares some of your genes, helping them survive and propogate also helps you spread your genes indirectly.

All organisms alive today are thought to have descended from a single ancestor.  If you were to follow this first ancestor, its kids, their kids, on and on until the present day, you could construct a phylogenic tree, also called a family tree.  All organisms alive today are related at least in some degree.

Game theory is a mathematical model that allows theorists to examine situations in which multiple agents, which can also be understood as "players" in a "game", interact strategically to maximize their wins, or alternatively, to minimize their losses.  I will be using the terms "game", which means a set of rules with consequences, and "agents", meaning players of a "game".  In this simple context, biological competition can be seen as a game, as can wars, economies, and just about everything that's ever been made into any sort of video game

What I propose is a framework for understanding the circumstances for certain observed facts in both real biology and Darwinbots evolutionary simulations.  The basic framework is something like this: agents in a game that do not manage to survive are ill represented in any slice of time.  Or put more simply, things that don't survive don't exist.  This is a generalization of the central tenant of natural selection to all processes, and forms the central tenant to my framework which I'll call abstract natural selection.  The premise is almost a tautology; it should be easily accepted.  The world around us is made of things that are good at existing. Things that aren't good at existing aren't very numerous.  Unstable crystals don't persist, unstable isotopes radioactively decay into stabler ones.

This should bring up a fundamental question in your mind.  How exactly am I defining "good at existing"?  A radioactive isotope with a half life of 100 years might seem stable from a human perspective but unstable from a geological time frame.  Is the isotope stable or not?  This is the second premise of the framework for abstract natural selection: the ability for an agent to survive in a game depends on the time frame your considering.  Or put another way, the ability for something to exist is a relative, qualitative term, and depends on the context in which you're using it.

Reality is made up of a hierarchy of different time frames you can observe the universe from.  If you view the universe in cosmological time, on the scale of the death and birth of stars, nothing is really all that permanent.  Stars are constantly birthing and dying.  Even black holes slowly evaporate into nothing through electron tunneling.  The next step up is geologic time, involving the development of crystals and minerals in the crust of the Earth.  In this time frame, the universe seems stabler, with stars lasting long enough for planets to form and their crusts to harden, etc.  Above geologic time is simple life, like bacteria.  Above that is the more complex life forms and their evolution.  Above that is ecology and the succession of grasses to trees in an area, and on up until you get to many human constructs such as economies and nations that have a cycle lifespan measured in centuries or decades or even just a few years.

Each time frame has specific rules unique to that time frame.  The goal for agents that play in these time frames is to exist.  Those that do are represented and exist.  Those that don't aren't.  Again, it's almost a tautology.  The universe is populated predominantly by very old, slow burning stars because the fast burning ones don't exist as long, and die out unrepresented, not existing.  The different rules come from the fact that the a force on one time scale might be insignificant, but on another time frame could be very important.  For instance, plate techtonics isn't all that important for the political life of nations, but it's had profound impacts on long term evolutionary development.

All these timeframes might have different rules, but they're also interacting.  If a star dies, any life on a planet around it dies.  There is constant feedback between the timeframes' games.  The universe can be seen as a large hierarchy of games being played in different time frames with different rules.  The outcome of games on one level of the heirarchy can effect the outcome of games on another

Now, back to our idea of a phylogenic tree.  Imagine grouping all the individuals that are related by being either parents or children of each other.  Groups will overlap, but you'll be able to do it.  Imagine treating these groups as new entities in a new phylogenic tree.  Imagine doing it over and over, creating larger and larger groups.  Eventually you'll have all life ever developed on Earth in a single group.  Now imagine the time frame that each group represents.  Singe generations are considerably shorter lived than, say, the entire group of 300 generations to which it belongs.  Each of these time frame's groups can be seen as agents in that time frame's game.  This means that agents that might be in direct competition in one time frame's game might be the same agent in another.  This is the fundamental lever point for my idea.  Depending on how you group life forms, you can change the rules by which those life forms are interacting, and even wether they're competing or cooperating.  Life can cooperate on one level and compete on another at the same time.

Note that not all agents in a time frame's game are necessarily competing.  Not all games are "zero-sum", where the winners winning comes at the expense of a loser.  In general if agents are competing, I'll say they are competing for a specific niche, where niche is another generalized term and simply means a limited resource.

Last, notice that games that occurr on shorter time frames have a faster pace.  Again, this is almost a tautology.  For instance, if a bacteria is killed by another bacteria, it's not really going to matter if it happens to live on a planet around a sun that's going to die in 3 billion or 8 trillion years.  Dead is dead, non existance is non existance.  Games that are played in shorter time frames have more weight than games that are played in longer time frames, because their paces are faster and their effects more immediate.

-----------------------------------------------------------------

That defines the base of my idea in its entirety.  Some of the basic premises might be unfounded, but alot of it is simply reorganizing existing facts to allow us to look at data in a new way.  It is particularly useful for explaining some rather peculiar things I've seen that would seem to contradict Dawkins claim that selection at the level of organisms or populations almost never overrides selection on genes.  For instance:

Cannibalism and the leagues - There is something of a pardox to the following fact: conspec recognition in leagues is important for success.  Bots that eat their children or other members of the species will not do as well against another species that doesn't.  However, in evolutionary simulations, this conspec recognition always, except in extremely contrived situations, is selected against and disappears.  What's odd is that it usually follows a reverse pattern to kin selection: when it first appears, it's almost always indiscriminate eating of everything, and is usually first directed at fellow siblings and even the parent, and only later is the bot able to find less related bots to much on.  These bots also seem less able to bear young successfully, with the number of successful reproductions much lower than the unmutated forefather.

Using the Framework of Abstract Natural Selection (FANS) allows us to state and understand the phenomenon on very real terms.  When a bot species is fighting another bot species, the entire battle usually is measured in the low thousands of cycles.  "Cannibots" usually appear after some time of mutations has occurred, somewhere on the order of hundreds to low millions of cycles.

Battling against other species occurs in a slightly different time frame.  In this time frame, the two species are battling for a single niche (victor of the round).  All bots of a single species are essentially the same agent, and it would not be wise for an agent in a zero sum game to fight against itself, which is why cannibalism doesn't work in the leagues.

In the longer term, however, the fight for the niche will long be over, and only a single bot species will survive.  In this long term there is no more game to play in the shorter term, since it's already been played and won.  The most significant game is now the battle between individuals to survive (not even to necessarily pass on their genes.  That's a longer term, multigenerational game).  At first, since they have a conspec recognition gene and all bots are essentially identical, the only way to survive better and have more kids than someone else is to be lucky enough to either stumble onto a fresh veggy patch or have a veggy spawn right next to you.  If you are always crowded out of these new veggies, you will die.  Dumb luck really.  And since no one is being actively hunted by anything, life span can be very long.

However, eventually a cannibot will develop.  This cannibot has a huge advantage in the game of surviving because it actively destroys other agents.  It no longer needs to get lucky and find a new veggy patch or have one spawn, because it's eliminating any other potential rivals for food.  And it's easy pickings because they don't fight back.  What I'm saying is that cannibots develop not because it's a new food source (although that's an important plus), but because it's a trait for eliminating rivals.

In essence, cannibots don't work in the leagues because in that time frame, the species are the agents and cannibalism would be like suicide.  Cannibalism works after a league is done, in longer term evosims where all the bots are basically very similar, because the time frame and thus the rules of the dominant game and the definition of an agent, change.

To test if this idea is true or not, we'd have to figure out some way to rig up a league round with mutations enabled that would last longer than it usually takes for cannibots to develop and dominate the sim, but isn't setup in such a way that the bots co-exist.  One needs to eventually win.  If the cannibots still develop, spread, and belong to the species that wins the round, this would disprove this explanation.  If they don't, that would be strong circumstancial evidence.

Big berthas - Big berthas are very large, very sterile bots that constantly shoot.  They used to develop in evo sims before I increased the problems associated with waste.  Basically, a bot would break its gene to reproduce, and would instead constantly acquire nrg and body.  The body would make it stronger and basically unkillable by the smaller, reproducing bots.  5 or 6 Big berthas would eventually kill all strains of reproducing bots, causing a mass extinction event when the big berthas eventually died.  What's interesting is that these 5 or 6 big berthas would all be independant mutations since the big berthas never reproduced.

Reconciling this with natural selection presented me with some problems.  These bots would appear "fitter" since eventually they'd replace all the reproducing bots.  But there was no hope their genes being passed on to the next generation or even surviving indefinately, since eventually costs would kill the big bertha and its genes with it.  It was the very definition of dead end.

However, if you use FANS this makes sense.  Big berthas were unkillable.  Usually a single hit from one of its shots would kill another bot.  Similar to cannibots, their survival in the contest against other individuals was all but insured.  In their young life they had to contend with other bots' crowding them out for food, accidentally killing them with stray shots, and even being hunted by smaller cannibots.

However, once they were monstrous, other bots simply couldn't kill it.  They had effectively won the more dominant game of surviving against other individuals.  Unfortunately, the selective pressures for this game also caused them to adopt a strategy that wasn't beneficial in the less dominant game of long term survival of the genome.  But these longer term selective pressures didn't get to act until the big berthas had decimated all other kinds of bots, and by then it was too late.  Again, shorter term games have stronger pressures.  Bots will sacrifice success in the longer term games for success in the more immediate moment, mostly because evolution isn't forward thinking, and doesn't know better.

These two examples show how FANS can be used to understand why you see evolution proceed along paths that in the long term are less effective.  It can be used to explain why you see bots "devolve" in long term simulations.  To understand the other half of my idea, about the "abstraction ceiling" try reading the other posts again after reading this.

Jez:
Sorry about the previous spelling and grammar errors in my previous posts, it led to some misunderstandings and I blame it all on my keyboard.

I've done a little bit of reading on games theory/Nash/Evolutionary stable strategy/Evolutionary games strategy/Muller's ratchet etc, in the hope of understanding what I'm talking about a little better.

I'm not going to attempt to reply to everything you have raised all at once either. I'm pretty much just going to make some cursory replies to your last post.

First though, the definition of Altruism particuarly in ethology and evolutionary biology : Altruism

"Altruism refers to behavior by an individual that increases the fitness of another individual while decreasing the fitness of the actor."
"Recent developments in game theory have provided some explanations for apparent altruism, as have traditional evolutionary analyses."
Also a more expansive explanation of the slime mould altruism;
"An interesting example of altruism is found in the cellular slime moulds, such as Dictyostelium mucoroides. These protists live as individual amoebae until starved, at which point they aggregate and form a multicellular fruiting body in which some cells sacrifice themselves to promote the survival of other cells in the fruiting body"
"In the context of biology, the "Tit for tat" strategy is also called reciprocal altruism or Mutual Aid"

Plus the maths bit;
"If a gene copy confers a benefit B on another vehicle at cost C to its own vehicle, its costly action is strategically beneficial if pB > C, where p is the probability that a copy of the gene is present in the vehicle that benefits. Actions with substantial costs therefore require significant values of p. Two kinds of factors ensure high values of p: relatedness (kinship) and recognition (green beards). (Haig, 1997, p. 288)"

Cannabilism and the leagues
That non DB evolutionary sims usually select against cannabilism isn't that surprising, I do think that a cannibot in DB does tend to pick on it's children and kin first simply because they are closer and easier to get at. As it tends to eat its babies it also shows a lower succesful repro rate. In that sense and considering some of the first league bots, which were cannibals, I think that it is the size of (homo species) sims that causes them to be a relatively succesful evolution.
I think cannibots evolve as a way of exploiting a new food source, there isn't anything to stop it becoming omnivorous. Bots like doing the smallest amount of work for the largest reward. Rivals would have to include copies of its own code for that to be the reason it formed, that seems self defeating genetic evolution. It is not a good way for genes to increase the numbers of copies of their genetic code.

To test out evolution over a multi species competition you would need to start with a large sim, plenty of veg and bots that aren't very good at getting enough food to eat. They couldn't be cooperative bots nor a bot that was capable of a sim dominating max pop. Good luck, I've tried doing similar things in the past.

Big Berthas
Had a thought, perhaps this is because there is no disadvantage to being big, no reason to shed excess energy or body. If we started adding disadvantages, and I'm sure there must be biological comparisons, for getting over a certain amount of energy of body mass. More so than the energy required to move that we have atm. Perhaps the problem would be more self defeating, bots would need to reproduce to lose the excess baggage.
Again though, because of the slowness of the Berthas, their stationary existance, perhaps the size of the sim has a part to play in their formation. A few Berthas can succesfully dominate a sim before death rebalances the problems caused by their sterility.

I'm probably being pedantic again I know, I like the idea of having a more structured framework with which we can analyse bot evolution though.  

I guess I'll go and read a bit about FANS now, so much for speedy answers.  

Navigation

[0] Message Index

[#] Next page

[*] Previous page