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Robert Wendt

Registered: Sep 2003
Posts: 2

NKS and the Origins of Biological Complexity

I have marveled at the superfluity of mechanisms producing the same effect in an organism, and wondered why so much fine tuning was needed, in particular during the formation of organs in embryos. Maybe natural selection has allowed gratuitous mechanisms to persist as long as they were noncompeting.

M. Mitchell Waldrop wrote in Complexity: The Emerging Science at the Edge of Order and Chaos, that Stuart Kauffman wanted to discover the driver for increasing complexity in biological evolution. I thought the driver might be the need for hybrid vigor to prevent extinction. This thought lacked the elaboration you provide, that any change is likely to introduce new complexity.

An advantage of having gratuitous mechanisms would be the increase in opportunity for hybrid vigor in a species.

...

Lately I have wondered whether natural selection in biology favors the genes which produce a complex expression. I remember reading in US News and World Report in the summer of 1996 that birds with complex birdsong were found to produce more offspring. On January 31, 2003, I sent you an e-mail with my idea of why redundant mechanisms for the same effect may be favored in biology.

My present hangup about A New Kind of Science is that if God is a computer programmer, computer programming should be used consistently for modeling of nature. What I have found useful with my experimental data has been double regression analysis with the allometric relationship lnC = M(lnB) + N(lnA). I do not see a way of using statistics with my data if I model by computer programming.

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09-30-2003 03:20 AM

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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

You wrote -

Lately I have wondered whether natural selection in biology favors the genes which produce a complex expression.

It is possible, but NKS suggests it should not really be necessary.

In the past, an elaborate mechanism like natural selection was typically thought necessary to explain how complexity could arise in biology. But complexity can arise from simple underlying rules without any such winnowing, as NKS shows. Give a class of simple rules, some portion will typically yield complex behavior, as soon as the complexity of interrelations in the system rises above a (quite low) threshold. If nature is using simple rules from that class, complex behaviors will arise just from random rules.

So one should first consider as a "null" hypothesis the possibility that complex results may arise simply from the nature of the simple programs the biological system uses, without requiring any selection effect to weed out simple ones. The way you can test whether this is the case is to examine a whole spectrum of outcomes, and see if similar biological forms "populate" that hole spectrum, or only the complicated ones occur.

There are two examples of this procedure given in NKS - shell patterns and leaf shapes. The "parameterization" was much harder for the leaf shapes, but still possible. And what one finds is that different species have different pigmentation (shells) or leaf shapes, yes, but there is no reason to suppose those have been selected for those particular species. Because some species can be found that show practically every simple outcome produced by the same class of rules.

Yes there are shells with complex patterns. But there are others with simple ones. And no reason to think the two arise for fundamentally different reasons, or either is the result of any elaborate selection. Rather, pigment is laid down according to simple rules. When those rules happen to produce simplicity, the shell pattern is simple. When they happen to produce complexity, the shell pattern is complex. Some leaves have this angle between stems leading to that overall leaf shape. Others have this other angle leading to that other leaf shape. The cause of the variety seen is typical variation seen in the behavior of simple rules, not different selection pressures pushing in different directions.

Gould hypothesized that there was a whole possibility space of forms, and natural selection chose among them by getting rid of some and keeping others. But in the case of leaf shapes and shell pigments, nature has not in fact gotten rid of any to speak of. Other than a few "structurally unsound" ones for outliers among leaves, they are all there.

Selection tends to push toward single optima. It was never terribly clear just how it would give rise to variety, as opposed to some sort of optimality. Implicitly, complexity was being imported from the environment - the idea of various "niches" in some complex "fitness terrain". Selection just explained how, if the fitness terrain happened to be complex and "many hilled", stuff might be attracted to its peaks. Fundamentally the basic idea behind selection is a "fixed point" theorem out of calculus thinking. But it never explained why the fitness terrain should be complex or many hilled. As Gould pointed out, in pure reproduction numbers and longevity on earth terms, the simplest single celled organisms are by far the "most successful".

What NKS adds is an explanation of where underlying complex variety may be coming from. Not from selection or imported hypothetically from beyond the system being explained, but directly and internally, as a direct consequence of nature using simple rules. Simple rules (if not *too* simple), just easily and typically give rise to behavior of arbitrarily high complexity. The "motor" of variety is algorhythmic.

Selection may then "winnow" that variety, certainly. But it seems to me at least as likely it winnows it toward uniformity as the opposite. Engineering designs tend to vary widely early in the history of some invention, and then to get into a few grooves and optimize. Similarly, the evolutionary history seems to show rapid periods of very large scale innovation, followed by long slow periods dominated by stable types, even declining in numbe (more refined). Why not read this "punctuation" as "algorhythmic variety culled by optimizing selection" - at first rapidly "damped", then slowly (as the stuff that gets through the early culling has something going for it)?

The point is, once you have a seperate "motor" making underlying complexity for reasons entirely distinct from natural selection, there is no reason to expect selection to operate toward complexity rather than away from it. You will get away from uniformity regardless, simply because the simple rules "motor" is always there.

Whenever rules of some type arise, you should expect pretty much all of them to be tried, and a giant populated range of possibilities as a result, some of them inevitably complex. When there isn't subsequent selection *against* that variety, it will remain. As apparently happens with leaves and shell patterns.

...

if God is a computer programmer, computer programming should be used consistently for modeling of nature.

Perhaps, at the lowest levels or for the greatest detail. But all formal modeling is about something shared across a wide range of systems. And that can arise because of parallels in the internal construction of systems, even if the underlying programs are different. Take compound interest and radioactive decay. One isn't even a natural system, but a human artificial one. They certainly share nothing in terms of underlying components.

But since both are processes that with a simple dependence of a rate of change on how much of something you've got at a given time, they both follow essentially the same law (one is a time reflection of the other, or exponential decrease vs. increase, but that is a quibble). Whenever we notice one of these formal regularities, there will be places where it applies, places where whatever the underlying program is doing is close enough to the formal abstraction being used. Whether that formal abstraction is mathematical or computational. Computational models are just an extension of the same basic idea. Instead of the regularities of typical mathematical functions seen in simple ODEs, you see regularities of typical varied output types (e.g. classes of behavior) seen from simple programs.

What I have found useful with my experimental data has been double regression analysis with the allometric relationship lnC = M(lnB) + N(lnA).

Allometric equations arise whenever the underlying system is balancing rates, especially when some finite set of system resources is being parcelled out between alternatives according to constant ratios. (Bertanlaffy) So what you'd want to do is find a simple rule that partitions whatever in a similar ratio. It should then give rise to behavior in which an allometric relationship will emerge as a consequence. Just as a radioactive decay model would have an addition or spreading rate depend on how much you have, and that alone would result in an exponential behavior as an emergent property.

What kinds of formal properties of a simple rule might correspond to partitions of a limited system "resource" in constant ratios? Black vs. white cells, rates of spread in different directions. Depending on the type of formal system you use, it could be something else.

Does this mean you'd stop using statistics to look at your data? No, it means you don't stop there. Rather, if the statistics are actually capturing something - meaning there really is an allometric relation going on down there, not just an S shape drawn through noise - then it should be possible to find some simple rule that produces that relationship as one of its emergent properties.

You then want to find one that corresponds as closely as possible to what you think the underlying system is actually doing. Ideally, something that makes sense of the squiggles and misses from the allometric curve. Or that makes sense as a mechanism for producing the relationship, using the components the system has to work with.

And then there will be cases where you see a complicated relationship, one that fits badly with the hypothesis of partition rates. Instead of putting a square peg in a round hole with some badly fitting S through noise, if it looks mostly like noise, you then want to consider a rule that gives rise to more complex behavior. Class 3 behavior makes good noise. It may let you see where what looks like noise is coming from - e.g. perhaps you can get it with only a small change from a similar rule that produces an allometric relationship in a closely related biological case. Then you've got a good guess as to the "bit" that "got flipped" to go from one behavior to the other.

Get used to the idea of running stats on computer models as well as on your data. And then tweaking the computer model to get the stats reasonably close. It isn't easy to come up with the right computer model to try - that is something of an art, and requires detailed knowledge of the system you are working with and what about it you are trying to capture. But it is worth the effort. When in doubt, start simple, building in as little as possible. You will generally be surprised how easily useful stuff emerges, even when you didn't try to put it there.

I hope this helps. Fine questions by the way.

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09-30-2003 03:22 AM

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Robert Wendt

Registered: Sep 2003
Posts: 2

I found the comments of Jason Cawley of the Wolfram Science Group extremely helpful regarding algorithmic modeling beyond finding allometric relationships by statistics.

There is a point in his discussion of genes for complex expression on which other scientists have not agreed. He wrote, "The point is, once you have a separate 'motor' making underlying complexity for reasons entirely distinct from natural selection, there is no reason to expect selection to operate toward complexity rather than away from it."

The second sentence of my e-mail on which he was commenting said, "On January 31, 2003, I sent you an email with my idea of why redundant mechanisms for the same effect may be favored in biology." The gist of the earlier e-mail was that the need for hybrid vigor in biology may be the driver of increasing complexity in biological evolution.

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09-30-2003 03:24 AM

Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Thanks for your note. I will try to clarify what I was saying. I had said -

"The point is, once you have a seperate 'motor' making underlying complexity for reasons entirely distinct from natural selection, there is no reason to expect selection to operate toward complexity rather than away from it."

Notice, I did not say it can't ever operate toward greater complexity. It might, it this or that case. But the reason to suppose natural selection must be capable of generating all the complexity we see, disappears when that complexity is adequately explained by another mechanism.

You said -

my e-mail on which he was commenting said, "On January 31, 2003, I sent you an e-mail with my idea of why redundant mechanisms for the same effect may be favored in biology." The gist of the earlier e-mail was that the need for hybrid vigor in biology may be the driver of increasing complexity in biological evolution.

Yes, I understood the point. Something redundant in A may be useful in A crossed with B, and therefore help A have more descendents without ever helping A directly. I restate the point so you can see I got it.

But it is one thing to show that redunancy may sometimes convey a selective advantage, and other to establish that (1) it generally does (2) that this outweighs optimizing improvements that may reduce complexity (3) that natural selection, operating on whatever level of selective advantage complexity confers, has actually caused all of the complexity (not just organism to organism differences, but complexity of structure or form within individual types) we see in the natural world.

If, instead, biological systems use simple programs from some limited class to perform a given construction, then one expects the variety those programs exhibit to be exhibited by those biological systems, without any more ado and long before any selection comes in. Selection might then favor redunancy too. Or it might prune out a few of the simple program behaviors as unfit. Or optimize slightly for this or that niche. But the complexity would already be there, natural selection would be operating on it, and would not be the underlying cause.

For example, shell fish aren't adaptively selected for widely varied pigmentation patterns, some of them of extreme intricacy. It isn't that shell fish with plain patterns don't make it - there are scads of those too. Nor that only a variety of patterns allow exploitation of a variety of niches. There is really no evidence it makes any difference to any of them, frankly. Instead, all the patterns made by a class of simple programs of one definite type are used.

The whole class of organisms has some "hack" for their shell patterns, and which switches are in which position are essentially random from species to species. Many of those switch position combinations give simple behavior. Some give complicated behavior. Why? Just because that mix is what simple programs typically do, so they do it here, too.

How can we tell this is what is going on in the case of the shell patterns, rather than some elaborate selection favoring complicated rather than simple patterns? Because essentially the entire parameter space is populated by one species or another. There is no sign certain types have been dropped by natural selection. Nothing is missing. The space of the simple program outcomes (with the right parameters) and the space of the shell patterns match.

If instead we looked and saw that only the complicated patterns remained, and the simple ones were missing, *then* we could say that complexity had been selected for, and that the complexity we see is the result of natural selection in favor of complexity. In some other biological case, maybe that happens -and your sort of explanation of a survival value to redunancy through hybrids working might describe why that is happening, perhaps. But sometimes there is no need for it.

Now, back to my quote from my previous. I say "no reason to suppose" natural selection tends toward complexity rather than away from it. That does not mean there is no possible situation or cause whereby natural selection might favor a complicated outcome in case N. It means I can see possible situations or causes whereby it might favor complexity in case N (say redunancy value in hybrids), and others whereby in might favor simplicity (say some optimized wing shape, always exactly "so") in case M. Which way does it go, net? That is an empirical question. I don't know, a priori.

Before I had the algorithimic means of generating complexity, I had a reason to suppose natural selection favored complexity, net. Not based on one mechanism that might do so (e.g. redundancy confering survival value) - that is from the model side, if you get me. But before, I had a reason to suppose it must, from the data side. I didn't have anything else to ascribe the existing complexity I can see in the data, to.

(Kauffman's random spillover into an "adjacent possible" is about it, otherwise. Or another version of much the same thing, Gould's observation that it started simple so where else could it go, just randomly walking?). It is obviously there. Something is causing it.

Before I saw it could come from the nature of the simple programs that life happens to be using, I had to ascribe it to natural selection as the only plausible cause available. Now, I don't. I can match the data without that assumption. It has gone from something I thought had to be so a priori to something that may or may not be so empirically.

Now, look also at the fossil record and think about the rates at which these things seem to happen. You've got survivals forever like the bacteria. No sign of a strong force weeding out the simpler types there. The simple types are still around. In raw numbers, generations, time on earth, they are the most successful organisms. Without any of the later hacks, with less redunancy than higher sexual animals, etc.

Then we've got the Cambrian explosion - all these widely varied types in a tiny geological window, from practically nothing just before. Then no great incease in types for a long time, and even some pruning of the bushy tree of types. Is that the pattern one expects from natural selection operating in favor of redunancy, everywhere and always?

But suppose, hypothetically, that you just reached a programming level with 10-100 new switches, then you'd expect every possible combination of those switches very soon. n^10 or n^100 new forms, bang (some so close we wouldn't distinguish them, to be sure). Some are unsound and disappear. A giant possibility space is already populated. Natural selection then goes to work on an already bushy tree of types. Maybe it favors redundancy and keeps certain things around, maybe it optimizes for a few niches in this or that case.

Which fits cases like the Cambrian better? Or cases like the shell patterns?

Obviously, both can be going on. But which is really causing the variety we see, and complicated rather than simple individual forms, is an empirical question. We can address it, though loosely, by seeing which fits the data in more plausible ways. You may very well find cases where a survival value to redundancy is clearly the cause of some level of remaining variety - wherever it originally came from. You may even find a case where it is clear that is where it originally came from, too (though that is harder to see or to establish).

But what was there before and isn't there anymore (post NKS I mean) is the notion that natural selection has to be the mechanism and we only have to figure out how it could possibly favor complexity. It doesn't have to be the mechanism. Natural selection doesn't *have to* operate, on average, in favor of complexity. If it *does*, that is an additional and empirical result to try to establish, and requires more than arguing it could because sometimes it has a survival value.

I hope this helps.

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09-30-2003 03:26 AM

Brad McFall
The Trainer
Ithaca, NY

Registered: Oct 2003
Posts: 3

I have wondered if Mendel's "rules" and 'simple programs' may be more than correlationally affective.

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10-21-2003 09:10 PM

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alphasun

Dublin, Ireland

Registered: Oct 2003
Posts: 2

Re: NKS and the Origins of Biological Complexity

Originally posted by Robert Wendt
I have marveled at the superfluity of mechanisms producing the same effect in an organism, and wondered why so much fine tuning was needed, in particular during the formation of organs in embryos. Maybe natural selection has allowed gratuitous mechanisms to persist as long as they were noncompeting.
.

Indeed-- why would natural selection affect a non-competing mechanism unless it was attached to something that was competing?
I recall an embryological epigram: 'Ontogeny repeats phylogeny', which is based on the well-known fact that there is a sort of apparent recapitulation of evolution in the embryo (not to be taken literally). This seems to encourage the kind of cybernetic approach put forward in NKS. There appears to be massive spare capacity in the simple sequence-based structures of DNA, and the analogy with a computer language is striking, especially when one considers the earliest stages of evolution.

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10-22-2003 02:11 PM

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Tony Smith
Meme Media
Melbourne, Australia

Registered: Oct 2003
Posts: 167

Variation c.f. selection, a new example

For more than ten years, I've been trying to make the case that the mechanisms of variation are at least as important as Darwinian selection in accounting for the facts of evolution.

Today I stumbled across an article which immediately had me looking for this thread because it says something important about how variation will more typically act on vital functions of a more complexly connected biological system than those familiar NKS examples: shapes of leaves and patterns on shells.

That article stresses the understated importance of variation c.f. selection with emphasis on how a simple increase in in-utero testosterone levels of the spotted, or laughing, hyena produces the unusual but clearly successful combination of matriarchal organisation, infantile fratricide and external genitalia which are almost indistinguishable by sex.

There have long been suggestions that the convoluted dynamics of the regulation of gene expression tie together and thus constrain evolutionary possibilities, such as, by way of obvious example, the structure of our hands and feet, with clear implications for those essential human characteristics of bipedalism and manual dexterity.

So maybe one of the real challenges to advancing the NKS way of thinking into such areas is to find simple systems that have a capability to regulate multiple effects. That looks like a minimum starting point for tackling the question raised in the HOX thread over at the applied NKS forum.

These are quite simple mechanisms with ultimately very complexly connected effects.

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