The article below my snowflake example of self-organization describes a computer model for evolution. It is from five years ago, but it is still interesting.
“How can something as complicated and beautiful as ourselves happen by chance?”
The fairly new science of self-organizing systems has the answer: Small local rules–for example, charges which cause atoms to attract or repel–lead spontaneously to large scale order and complexity, including reproduction and evolution.
This is very hard for most people to grasp or even to believe. How can order be created from chaos without a designer? One example of self-organization in the real world is crystal growth.
Who builds each snowflake? Isn’t something as orderly and complicated as a snow flake evidence that some intelligent being designed each one?
There is no intelligent designer of snowflakes. No one sketches out each pattern. Snow crystals grow by themselves without blueprints, with no plan.
Snowflakes are groups of 2 to 200 snow crystals. They occur when dust particles give water vapor in clouds at cold temperatures a surface on which to form ice.
As they bounce around, molecules will stick to a rough surface more often than a smooth surface. This is because a rough surface offers more sites where a new molecule can bond. The blue circle on the top of is more likely to bond than the one at the bottom.
If you look even closer (image left), you will see that water molecules are attracted to each other because Oxygen (red in the model picture) has an overall negative charge, and Hydrogen an overall positive charge.
If you zoom out (image right), you can see that ordinary ice forms a crystal structure based on these attractions of water molecules.
Snowflake shape depends on the temperature and on how the flakes spin as they fall.
“Snowflake formation is a dynamic process. A snowflake may encounter many different environmental conditions, sometimes melting it, sometimes causing growth, always changing its structure.” – about
To sum it up: Small local rules (not a snowflake designer in the sky!), lead to the complexity and order from chaos we are able to observe in snowflakes.
The DNA in our bodies is similar to a snowflake because it self-organizes based on the properties of attractions of the Carbon, Hydrogen, Oxygen, Nitrogen and Phosphorus atoms involved. DNA is more complicated than snow because new rules apply as the crystals of our DNA form complicated 3 dimensional structures.
Now you can read the article with an understanding of how it can apply to the real world:
It has taken more than five decades, but the electronic computer is now powerful enough to simulate evolution. Researchers from Michigan State University have used software to prove Charles Darwin’s postulation that small, seemingly inconsequential changes over thousands of generations can result in the evolution of complex functions.
They also uncovered a twist on conventional evolutionary thinking — it seems that some mutations that are harmful in the short run may boost long-term potential.
A better understanding of evolution promises to improve software and provide new ways to address engineering challenges.
The researchers’ simulation involves bits of software that self-replicate, but not perfectly. When the digital organisms make copies of themselves they sometimes make random errors, just as DNA is subject to mutations when it replicates. Many of the mutations are neutral or harmful. “But occasionally a variant comes along that replicates faster or even performs some logic operation,” said Richard Lenski, a professor of microbial ecology at Michigan State University.
The organisms compete to get the energy — in the form of computer time — required to replicate. The organisms perform any of nine logic operations, and if they perform them efficiently enough, they gain computer time. “Digital organisms that solve a problem get an extra boost in their reproductive rates,” said Lenski.
The researchers studied 50 different populations, or genomes, of 3,600 individuals. Each individual began with 50 lines of code and no ability to perform logic operations. Those that evolved the ability to perform logic operations were rewarded, and the rewards were larger for operations that were more complex.
After 15,873 generations, 23 of the genomes yielded descendants capable of carrying out the most complex logic operation: taking two inputs and determining if they are equivalent. The lines of code that made up these individuals ranged from 49 to 356 instructions long. The ultimately dominant type of individual contained 83 instructions and the ability to perform all nine logic functions that allowed it to gain more computer time.
In principle, 16 mutations coupled with three instructions that were present in the original digital ancestor could have combined to produce an organism that was able to perform the complex equivalence operation.
What actually happened was more complicated. The equivalence operation appeared anywhere from 51 to 721 steps along the evolutionary tree, and the organisms used anywhere from 17 to 43 instructions to carry it out.
The most efficient of the evolved equivalence functions was just 17 lines of code — two fewer than the most efficient code the researchers had come up with beforehand. Evolving even as few as 17 lines involved a lot of incremental changes.
Because the population evolved in software, the researchers were able to trace the exact genealogy from an ancestor that was able only to replicate to progeny able to perform multiple logic functions requiring the coordinated execution of many instructions.
In order to follow the exact genealogy, the researchers developed a pair of software tools. The first tool continuously purged genotypes that lacked living descendants. This reduced the number of genotypes the researchers had to study more carefully from many millions to just a few hundred.
The second tool mapped out which of the lines of code that made up a particular organism were needed to perform any particular function. The tool shows the effect on all of the organism’s performance capabilities by eliminating — one at a time — each instruction, said Lenski.
The simulation proved that digital organisms could, over many generations, acquire the many separate steps ultimately needed to perform a complex logic operation.
In one case, 27 of the 35 instructions that an organism used to perform the logic operation were derived through mutations, and all but one of them had appeared in the line of descent before the complex function was performed.
The results broadly supported the hypothesis that biologists since Darwin have held, said Lenski. “Complex features arise by building on simpler features. The functions use bits and pieces of older functions, then tweak them here and there to get the new function,” he said.
When digital organisms were rewarded for solving simple puzzles with more CPU time — and thus an increased ability to send their genes forward to future generations — they eventually evolved a way to solve even the most complex problem they were challenged with, said Lenski.
The researchers’ results also show that this is the only way organisms can evolve, said Lenski. “Calculations imply [that] the probability of the digital organisms getting that complex all at once is astronomically small,” he said.
The birds-eye view on evolution also showed a twist, said Lenski. “Biologists usually assumed that the evolution of new mutations is an uphill climb — one in which the winners are descended from the most fit organisms in earlier generations, rather like a mountaineer that is always moving up — or at least sideways,” he said.
The researchers found that among the ancestors of the eventual winner, some had mutations that were harmful in the short run. Taking two steps back sometimes provided a better route. “Some of these harmful mutations worked well in combination with other mutations that came later,” said Lenski. So while most deleterious mutations were eliminated, some were passed on, turning a short-term handicap into a long-term advantage as the subsequent evolution unfolded, he said. – trnmag
More info about water:
In one water molecule the hydrogen atoms stick to the Oxygen atoms with a double bond. This is called a covalent bond because the atoms share electrons in their valence shell.
Bohr in 1922 received the Nobel Prize in physics for his model that electrons exist around the nucleus of an atom in different shells or orbits. Each shell can only hold a certain number of electrons before it is “full” and then new electrons will form a higher shell. A shell which is not yet full attracts other electrons, including those which can be shared from other atoms.
For this reason, a single water molecule has positive and negative areas and single shared electrons between two water molecules form. These “hydrogen bonds” are weaker bonds than the two shared electrons which bind the hydrogen and oxygen atoms.
Water takes different forms at different temperatures because heat is the amount of vibration (bouncing around) done by the entire system, including the electrons. At higher temperatures, with more vibration, there is less chance for temporary weaker hydrogen bonds to form.