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Natural Selection and CAs

By Bao-Hoi Nguyen

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Research Paper

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The diverse animal kingdom exemplifies nature's complexity. These animals, unique is many ways, incredible in their creative abilities, skills, physical and mental attributes to compete and survive to pass on their genes, astound and at the same time enlighten us to reach new heights in our own evolutionary struggle. DNA and embryonic similarity suggest that all these animals are all common is some way. That we evolved from one source. Nature also displays amazing interactions: predator and prey, different species working together to benefit one another, patterns of evolution and changes in population due to sudden changes in external forces.

Darwin explains this complexity in nature in the concept of natural selection in his book, The Origin of Species. Its basic premise is that all living organisms are continually improving and optimizing: the strongest survive to pass on their genes while the weaker, less competitive die off. Stephen Wolfram, the inventor of Mathematica, holds a different viewpoint of natural selection in his book A New Kind of Science. He believes that natural selection is too simple and cannot fully explain nature's complexity.

Classes of Natural Selection

In this section, I'd like to introduce my classification for natural selection. This classification is derived from Wolfram's classification for CAs.

Like CAs, natural selection patterns can also mimic each category. Class 1 is an example of when a species becomes extinct. Class 2 describes a simple repetitive pattern. The pattern of population growth is an example. A study was conducted by Italian mathematician Vito Volterra in the1920s on the population of sharks and the population of food-fish. The results show a cyclic pattern of ups and downs. As the food-fish population grows, the sharks will breed more readily. At a certain point the shark population will "overflow" and eat up all the food. With little food supply, many sharks will die of starvation. This contradicts the rule of natural selection and optimization. Intuitively, one would suspect that optimization would lead to a balanced and stabled relationship.

Another example of Class 2 behavior is found in a species of salamander and snake. This prey-predator situation is one of competition and evolution. The salamander produces a toxin that defends it against its predators. However, this snake has evolved a tolerance of the poison. The poison doesn't kill the snake, but leaves it paralyzed and vulnerable for a few hours. At the same time, the production of toxin is very energy consuming for the salamander. Through this interaction of species, future generations of salamanders produce more and more of the toxin. And likewise, the species of snake also gradually evolves to become more and more tolerant of the poison. As a result of such competition, today, the situation is such that the salamander's toxin is ridiculously high and is extremely poisonous. This predictable pattern is a clear example of Class 2 behavior.

The inclusion of external forces gives rise to Class 4 behavior. According to the Darwin's theory, the evolution of species progresses towards an optimal peak. If coupled with the ever-changing faces of nature, these animals are forced to adapt to their environment. Thus, the evolution process is predictable but yet can dramatically and instantly change towards a different pattern: the definition of Class 4.

Class 3 behavior in natural selection is very rare. Periods in history where there is wide spread changes lasting for a very long time are examples of Class 3 behavior. For example, the theory of evolution states that the dinosaurs became extinct because a large meteorite hit the earth. This meteorite created an environment that affected the whole earth, and this condition did not revert back to its original state. The population sizes and evolution of all animals during this time was extremely random and chaotic. Population sizes of large animals virtually disappeared. Changes in the environment were dramatic. Many elements were changing concurrently and the rippling effects of each were felt.

This situation is different than that described in Class 4 because it affected all areas of life and prevailed throughout a long period. Class 4 has chaotic patterns but also displays symmetric patterns as well. The external forces in Class 4 are things like hurricanes or earthquakes, which only affects a limited population and does not last very long. And because of this, patterns of animal populations recuperate and return to evolve in a predictable pattern.

Wolfram vs. Darwin

In this section, we will look at Wolfram's viewpoint of CAs and it's correlation with natural selection. Wolfram will dispute the evidences of natural selection and give his reasoning for the complexity that we see in nature. An example will then be given for further clarification.

Too Many Parts

Wolfram argues the significance of natural selection by saying that an organism is too complex. Natural selection cannot determine which characteristic is the better one. That is, organisms are made up of many parts. All these parts are changing at once. There are simply too many of these changes taking place that natural selection cannot pin point one individual part to improve.


Another important point is that animals interbreed. If a mutation occurred and it gives an animal an advantage, it will counterbalance when the advantage character is mixed with a non-advantage character. Let's say, 10 percent of an animal changes for the better, but another 10 percent or even less changes for the worse. This animal will breed with a normal animal that doesn't have this mutation. Or the second animal could have a disadvantage in the parts that the first animal has an advantage over. Thus interbreeding and the fact that there are too many parts to be accounted for causes a balancing effect such that one trait cannot be optimized.

Example: Finches

An example will clarify the above statements. Let's look at the varying species of finches on the Galapagos Island. How did they evolve? According to Darwin, the birds were probably blown in by some storm. There they were isolated from the rest of the world. The finches evolved into many different species of finches: each one with varying beak size and shape. The different shapes and sizes give each finch species an advantage, specializing it to accommodate certain food categories and also reducing competition amongst each other.


Wolfram says this diversity cannot be explained by natural selection. If the bird's beak gradually gets smaller, then this change should be transparent with all the birds. Why did some birds stay the same and some get bigger. If something was an advantage, why do some not change or diverge. Darwin's explanation is that the small beaks gave some birds an advantage while big beaks gave those a different advantage as well. The problem with this explanation is that the species interbreed. Because of this interbreeding, the varying beak sizes should balance each other out. That is, the only way that this divergence can occur is that species were selective in whom their mates were or that somehow the interbreeding stopped. Darwin's explanation is that somehow, these birds were isolated from each other and developed their speciation apart from one another, and thus evolved into different species. And after some time has past, these differences were so great that when the two came together, breeding between them cease to exist. However, for this example, it is hard to imagine that so many of these isolations can take place on an island. These are birds. They fly around and can cover large distances. It's hard to imagine how they can be isolated from themselves on an island.

Too Many Parts

Wolfram also says that even if interbreeding does not take place (assuming the isolation theory is correct), natural selection still cannot explain the varying beak size. The reason, as mentioned earlier, is that there are too many parts that make up the animal. The large number of parts makes it hard for natural selection to distinguish the good part from the bad part. For instance, say one bird had a large beak. Another bird will be lucky and have great speed but a very small beak. However, the second bird survives to pass on its genes because of its great speed. Thus the variations will even out. Natural selection would not work simply because it cannot distinguish or separate the good traits from the bad traits when there are so many traits to consider.


This section will look at natural selection's theory of progressive optimality. First, we will discuss how optimal characteristics are ambiguous. Then we will look at what Wolfram has to say about optimality and CAs.

What does Optimal Mean?

Natural selection says that organisms move towards an optimal state. But what does optimal mean? Does it mean survival and having many offspring? If this is the case as, then viruses and other bacteria are the optimal organisms. That is, we should evolve into them in the future according to the laws of natural selection. But that won't happen. Another important point is that these viruses have existed since the beginning of time. The whole backbone of evolution says that in the beginning of life, there existed simple one-cell organisms and then they evolved into more complex organisms. But why evolve, when you are already "optimal". Why did the virus or bacteria change into something more complicated when they were already "optimal"? The funny thing is, many didn't change and stayed the same.

It is a little tricky to define what is optimal. After all, optimal, in a sense, is perfection, and perfection can never be achieved. The truth is, we don't know what's optimal. But we do know when certain animals have advantages over others. Is that animal moving towards optimality? I would say yes, but Wolfram says no. One thing is for sure, some species clearly have an advantage over other species.

However, there is the opposite case. There are lots of systems that migrate in the opposite direction into simpler organisms. Wolfram gives the analogy of a new technology introduced into the market. At first, this technology is used in many different ways. But eventually, this technology settles down and is used in a conventional way that is much simpler that the ones that were tried.

The fact that it's hard to distinguish what characteristic is optimal and that some viruses evolve to something more complex while the some of the same type of viruses does not, tells us that nature is moving back and forth (simple to complex, complex to simple). Nature might not be moving towards optimality but instead just moving randomly.

But Many Animals have Advantages

Although Wolfram claims that natural selection doesn't advance towards an optimal state, it is evident that many of species are well adapted to complete in their environment. Humans are simply amazed as to the complexity, but more important is the "optimality" that is endowed in each and every species. A couple of examples to clarify are the cheetah with its great speed and the kangaroo with its ability to carry its young in its pouch. They are designed for peak performance in their own special niche. And within all these specialization, we see incredible diversity as each animal compete for survival.

Wolfram's Explanation of Optimality

Wolfram does not deny the existence of optimality. It's more accurate to say that Wolfram acknowledges the fact that some animals have an advantage over other animals. However, he doesn't give the credit to natural selection. The reason that we see animals with advantages over others is because of chance. It is just diversity. And out of this diversity, there will be organism that happens to have an advantage over the next. The key thing here is that Wolfram never agrees to the fact that organisms move towards an optimal state. That is, the organism doesn't "evolve".

As for the diversity that we witness, it is an occurrence of probability and mutation. Wolfram uses CAs to explain the "illusion of optimality" and diversity of nature. Assumed that our DNA strands can be interpreted into a long binary string of bits. Just flipping one random bit will cause major changes in the final outcome. For example, in a 1D CA, we see that completely different patterns arise even from adjacent rules. That is, rule 110 is completely different that rule 111. From this perspective, Wolfram says that a mutation in DNA causes the same type of effect. So that the small bit of a DNA change has the possibility of creating enormous physical change. Thus, it is easy to cause changes and since the change (mutation) does not cause death, it is passed on and we see diversity.

Also, it is evidence against natural selection in that the sudden and drastic changes in so many traits would make it hard for the natural selection theory to work properly. In other words, since there are drastic changes, there are too many characteristics to identify as the primary reason for the advantage. (This was mentioned earlier in the section "To many parts".)

The properties in CAs can be applied to animals. The variations that we see are just random. Somewhere along the timeline, a mutation occurred that drastically changed the animal. The random mutation does not prove fatal to the animal (the animal lives on to reproduce). This animal is not better or worst that before. It's just different. The strongest of each species do survive, but there isn't this progression towards some optimal state. Thus, the high standards that are characteristic of the animal are kept, but the animal does not get faster and faster and faster (the animal does not evolve).

Wolfram goes on to say that higher organism (e.g., humans) has nothing to do with optimality. Again, it is simply a consequence of random strings of mutations. If natural selection causes one to move to more complicated animals, why do there exist organisms that have been subjected to natural selection for over billions of years and have not changed at all. Examples already mentioned are viruses and bacteria.

Only One Type of "Human": An argument against evolution

Natural selection says that we move towards some type of optimality. Every species must progress. But this is not true. When you look at intelligence, humans are far superior to all animals. Why are there no such animals with similar intelligence since greater intelligence means greater ability to survive and dominate. For example, say you have 4 species: A, B, C, and D. And all were of equal intelligence. Why is it that species D mutated (into humans) and achieved greater intelligence while species A, B, and C did not. Species A, B, and C must have observed that species D was getting smarter. They therefore had to adapt and become smarter themselves. One can argue that the mutations are random and that only D was lucky enough to get it. But that's a weak argument. I think the same mutations must also occur in A, B, and C, and therefore, they too will benefit from the greater intelligence, preserve that characteristic, and be able to pass it on. Millions of years ago, of all the animals/fish/insects/etc., there must have been one other species that also mutated to achieve the same level of intelligence as a human. If not the same level at least something close. Why did this not happen? It is obviously to their advantage. And if that mutation occurs, the fundamental principle of natural selection says that that animal will dominate and we would be able to see it today.

This leads me to question the theory that Neanderthals die off. They were much smarter than monkey and therefore had an advantage over competition. They must have been able to compete against monkeys and still live to present day. That is, if there were no humans and only monkeys and Neanderthals, then I would imagine that the Neanderthals would be able to out compete monkeys and still be alive today. The Neanderthals did not die off because of competition from humans because there were plenty of land/territories along time ago. And if they couldn't compete with humans, why didn't they evolve towards a different direction or back into monkeys?

The same arguments can be used for other attributes such as flying. This is a definite advantage. There should be many animals with this ability (just like there should be many animals with human like intelligence). Why is it not the case?

Even worse, some of these animals such as penguins and ostriches lose their abilities to fly? That doesn't make sense. The penguin or ostrich that is able to fly will have a definite advantage over the others and that advantage should carry over to the next generation. Natural selection experts say that they didn't need that characteristic anymore. What? That doesn't make sense that they don't need to fly. The ability to fly is so much greater than not being able to fly (e.g., penguins can easily escape from walruses).

Flying is more optimal that not flying yet instead of evolving, these animals regressed. This point is hard for us to imagine, but if we give an analogy to humans, then it would be very obvious. Human intelligence is a definite advantage, yet can you imagine humans getting dumber? It doesn't make sense for humans to lose their ability to think and regress back into a monkey no matter what circumstances we find ourselves in.

What about the animals that have become extinct? Natural selection says that these animals could not compete. If sabbertooth tigers were still alive, would they not be able to compete against today's tigers? Did the modern tiger progress or regress? Which of the two is more optimal?

The Leopard has an Internal CA

As previously stated, Wolfram does not agrees with the idea of optimality. Wolfram argues this idea by saying that humans "invented" the optimal characteristics and attributed them to animals. For example, we see spots on an animal and we say it's there for a purpose. Or that we see a leaf shaped a certain way and we say it's optimal. The last part of this section talks about the golden angle and shows us that these coincidences are simply coincidences and has nothing to do with being optimal.

All three sections lean on the idea of simplicity in creating new patterns/shapes/etc. Just like the varying beak size of the Galapagos finches, we see diversity in plants and animals because of the ease in the rule in which we can create new patterns.


Animal Patterns

Animal patterns are thought to be complex for most people. Natural selection tries to explain this by claiming that there is a purpose behind it. The spots provide the leopard with camouflage so that it can hide in the tree or grass from enemies or prey. A long time ago, there were leopards that didn't have spots and one mutated. The mutated leopard with spots gained an advantage over the others and passed on his genes. The key thing that distinguishes natural selection with Wolfram's explanation with CAs is that the stronger leopard (the one with spots) has a better chance of survival, and thus, leads into the idea of progression towards an optimal state.

Pattern Created Because of CA

However, this is another one of man's attempt to give reason as to the purpose of the different things that he finds. Man tries to explain and clarify why things are the way they are. The funny thing is, there does not have to be a purpose, and the intricate patterns do not have to be produced by some complicated rule. The spots are there simply because of a rule that governs it. The leopard has an "internal CA" if you will that determine its skin pattern. These are the same patterns that are generated by 2D CAs. The rules used to produce the patterns are also very simple. An interesting fact is that these same patterns are seen in many different types of species and the patterns are almost always stripes and/or spots.


SeaShell Patterns

Natural selection uses the same explanation for seashell patterns and shapes. But wouldn't it be better if the patterns were exactly like that of the environment? Wouldn't that serve as better camouflage? The patterns I see are not exactly like the environment. Some actually make the animals stand out.

There is no reason for the patterns. It's not there to attract mate or prey, either. The difference with seashell and animal patterns is that the seashell patterns are produced one line at a time. The pattern doesn't change. Once it is produced then it is fixed. If the pattern is produced one line at a time, then how are complex patterns created. Either the animal remembers what pattern it has created in the past so it can continue where it left off or that it follows some type of rule to determine the next line. Remembering everything is too complicated. The rule theory is very probable. The patterns seen on seashells are very similar to those seen on 1D CAs. In fact, 1D CAs are created in a similar space-time fashion (one line at a time). The similarity seen on seashells and 1D CAs should not be taken lightly. It is very probable that the patterns are created by some type of 1D CA rule.

The biggest evidence against natural selection, however, is that some mollusc have an extra layer that covers the patterns that it creates. So why go through the trouble of making a pattern (that is suppose to provide it with some type of purpose, designed for its optimal performance) and then making another layer to cover it. The only answer for this is that there is no specific reason for the patterns. They appear by chance mutations. And the variety of patterns is just random changes to the rules. Mollusc can't even see! How are they supposed to recognize the patterns to find their mate? Mollusc eat dead animals, plants, or things like that. How are their patterns going to attract prey?

SeaShell Shapes

The shapes of seashells can also be produced by simple three-dimensional geometric rules. And minor changes to the rules also create all the patterns that we see in nature. Natural selection explains the diverse forms by saying that they allow specialization. That is, the different shapes give the animals an advantage and thus those animals prevail. That is why we see so many different types. They are all in competition with one another. But the fact that the variety of shapes are easily made through minor adjustments in the rules that make them, tells us that the diversity that we see is really coincidental mutations in the rules. And the coincidences create all sorts of different shapes. It's not hard to make a wide range of different shapes. From one shape, one can easily diverge to create many different shapes. The rule that defines the shape just need minor adjustments.


Tree and Leaf Shape

The branching patterns of trees and their leaves are also a result of rules. These patterns can be replicated with simple substitution systems. And by varying the angles of the substituted branches, we can make any tree or leaf shape. It's that simple. The similarity between the branches or leaves created via substitution and the real shapes of trees and branches leads one to have an open mind and the possibility that maybe they are related. It is much easier for a tree to have this rule encoded into its DNA. There is not much information that needs to be store. Natural selection says that we have different tree and leaf shapes because it gives each one an advantage. And the shapes are optimal. At the risk of sounding repetitive, the rules such as CAs and substitutions are much more logical at explaining the diversity and complexity of the leaves or pigmentation (leopard spots). There are two reasons: one is that the rules are simple yet they produce complex patterns, two is that minor changes in the rules produce different patterns, and the range of these rules cover the complete shapes and patterns that are seen in nature. The clear similarity between the patterns produced by these system rules and the same patterns found in real life should make one stop, ponder, and give it a second thought. It is very probable that this explanation is correct.


Another compelling reason that nature follows simple rules is the frequent occurrences of Fibonacci numbers. Here are the facts: lilies have 3 petals, buttercups have 5, delphiniums have 8, corn have 13, asters have 21, and daisies and sunflowers have 34, 55, 89, or 144. There are many more examples where Fibonacci numbers come up. Its frequent occurrences suggest that there are rules that are followed and the diversity that we see is a minor alteration of the rule. One might be incline to say that the numbers occur often because they supply some sort of optimal condition for the plant. But from what we've discussed, this doesn't have to be the case. The golden angle is an example which looks like its there for a purpose, but in fact is just coincidence.

Golden Angle

The Golden angle (137.5) is another number that frequently arises. This is the angle in which new branches grow out of the tree if one were to take a birds-eye view of the tree. This angle almost always comes out to be 137.5. When considering the growing tree, just focus in on the tip. This is where the growing and branching occurs. Since the stem is a cylinder, if one only considers the top of the stem, then it is a circle. Now unwrap that circle and you have a line.

This is how branching works: when chemical concentration reach a level at a certain place in the line, branching at that place in the line will occur, but it will also soak up all the chemical around the surrounding area. Therefore, the next branching point in the line will occur somewhere farther away. When following this rule, the distance at the beginning to not uniform, but after a few steps, the distances are the same and produce an angle of 137.5. That is incredible result. It just happens to work out this way all the time. This angle does not occur in order to achieve any optimality. It just does.

Evidence Against Natural Selection

The Neck of the Giraffe

There is a lot of evidence against natural selection. For one there are many gaps in the fossil records. The fossil records fail to show gradual changes in a species. There are always time jumps from one ancestor to the next. For example, the neck of the giraffe is very long and natural selection says that the animal's neck grew longer and longer as it evolved because the longer necked animal had an advantage of reaching the leaves that others cannot. However, animals with in-between sized necks were never found. Moreover, female giraffes are a meter shorter than male giraffes and there were also baby giraffes. Therefore, there must have been plenty of food at different heights.

Multiple examples

Natural selection says that we evolved from a single cell. But where did that single cell come from. Natural selection says that the single cell is a product of chemical reactions. If this is true, then we should be able to reproduce this chemical reaction and create life (so far we haven't).

But the explanation that life came from inorganic chemicals is very questionable to begin with. All living organism comes from a parent. This is a fact that we see today. Living organisms do not simply appear. Another point is that although the single cell organism, thought of as simple by you and me, has very complex DNA sequences. The probability that these parts coming together to make a living cell is astronomically low. To give an analogy to the degree of low probability, it is like saying that a hurricane passed through a junkyard and the parts amazingly attached to create a Bowing 757.


In conclusion, the basic idea of natural selection is questionable. If things were to continually evolve into bigger and better things, then why haven't we seen dogs the size of horses by now. Breeders know that there are limitations. Try as they might, they can't get a greyhound or horse to run as fast as a cheetah. Wolfram's explanation as to the diversity of animals from the idea of 1D CAs, 2D CAs, and substitution has some validity. There is no push towards optimal performance. Instead there is a haphazard approach given to chance and probability. The higher complex organisms like humans are no more "optimal" than the lower level viruses, we just have more stuff.


[1] Hitching, Francis, The Neck of the Giraffe, Ticknor & Fields, New haven and New York 1982.

[2] Johnson, E. Phillip, Darwin on Trial, Regnery Gateway, Washington D.C., 1991.

[3] Leah, Edelstein-Keshet, Mathematical Models in Biology, Random House, New York, 1988.

[4] Natural Selection and Evolution, Website found at: http://www.sp.uconn.edu/~gogarten/mcb221/class3.htm

[5] KurzweilAI, website found at: http://www.kurzweilai.net/index.html?flash=2

[6] Origin of Life, Website found at: http://christiananswers.net/q-eden/origin-of-life.html

[7] Stewart, Ian, What Shape is a Snowflake?, W.H. Freeman and Company, New York, 2001.

[8] Wolfram, Stephen, A New Kind of Science, Wolfram Media, Inc., 2002.





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