The simulaton life is a rich life experience provided by training our
minds to consider simulations of natural and human phenomena often
in order to gain depth in understanding, awareness, and compassion.
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biotic evolution simulation case study
Our second case study looks at simulation approaches to simulate evolutionary biology in plants. The theory of how plants evolve through genetic processes is simulated quite readily via a variety of approaches. Growth models do a satisfactory job of simulating a plant growing as it expresses its genetic information. The simulations provide our brains the opportunity to develop insights and deepen our understanding of evolutionary process in general.
Before we get into the details of the technical simulation tools available for use in this chapter, let's take a step back to see where they have come from historically. Gregor Mendel first solved the mystery of inheritance by experimenting with pea plants in the 19th century, leading to the eventual addition of the words allele, dominant, recessive, and diploid to common English vocabulary. Gregor Mendel started his life by following his ancestors in maintaining a family farm through gardening and beekeeping at a young age. After a formal university education and study for the priesthood, he lived at St Thomas's Abbey in St. Brno where he worked at plant breeding — watching the process across generations of plants closely. With the patience required of watching plants grow generation after generation between 1856 and 1863, he cultivated and tested some 29,000 pea plants and reported that one in four pea plants had purebred recessive alleles, two out of four were hybrid and one out of four were purebred dominant. His experiments led him to make two generalizations, the Law of Segregation and the Law of Independent Assortment, which later became known as Mendel's Laws of Inheritance.
Because the mathematics aligned well for such a large sample size of plants, those who read his published papers had the opportunity to imagine what possible vehicle in a pea plant would pass on that potential expression in future generations. But, sadly, Mendel's work was rejected at first and not widely accepted until after he died — the evidence was too revolutionary for those who clung to existing theories to accept. It would be ninety years after Mandel finished his pea plant experiments until the discovery of the structure of DNA in 1953. By then, a strong healthy competition was underway to find the physical structures in plants that could explain genetic expression over generations. Documentaries that track the work Watson and Crick performed to find the structure of DNA show the power that physical artifacts provided in helping arrive at strong candidates for DNA structure. Today, Watson and Crick would have had a tremendous number of virtual artifact approaches they could have relied on to help them discover DNA structure. These virtual artifacts are helping humanity study protein folding and other structures critical to plant development and health.
While Mendel started a trajectory of research into plant genetics, Aristid Lindenmayer started a trajectory of research into plant growth and development with his work with yeast and filamentous fungi and studies of growth patterns of various types of algae, such as blue-green bacteria. Generalizations of the growth process led Lindenmayer to develop a type of formal language called L-systems (or Lindenmayer Systems) in 1968. L-systems were devised to provide a formal description of the development of simple multi-cellular organisms, and to illustrate the neighborhood relationships between plant cells. From a basic starting base, L-systems have been extended to describe higher plants and complex branching structures associated with their growth.
Together Mendel and Lindenmayer initiated paths towards human understanding of how plants store information and then use those stored instructions to express their form during growth. Biological modeling and visualization researchers like Dr. Przemyslaw Prusinkiewicz at the University of Calgary have been working to apply understanding towards the generation of graphics that represent plants faithfully. As a case study in this chapter, we'll play with some software that let's us get a sense of what biological modelers do with software that can simulate plant growth over generations. We can then discuss possible directions to take the software for those of us who want to explore specific aspects of the simulation such as the work others have done previously.
In 1992, Deborah Fowler investigated the use of collisions while implementing the process of Spiral Phyllotaxis as a guideline to creating virtual plant models. Phyllotaxis is a well-documented phenomenon in plants that determines where primordia (seeds, petals, nuggets etc.) are located on a receptacle (sunflower, coneflower, corn ear) using a fixed divergence angle of 137.5 degrees. Primordia are packed following the rules of phyllotaxis until they collide with each other. Phyllotaxis has been incorporated into all plant development simulation systems as a result of Fowler and others' work. In 1996, Radomir Mech devised a system design where virtual plants could be modularly developed through interaction with other environmental modules. Using such a system, virtual plants don' t grow in a vacuum, but instead have their growth parameters affected by dynamic environmental parameters. For example, if the environment experiences a drought, plant growth is stunted and body structures wilt. The communication goes in both directions. If a species of plant becomes successful in growing and respiring, additional oxygen is passed back to the environment. In 1998, Oliver Deussen led a team that focused on realistic modeling of plant ecosystems. Starting with a terrain specification and environmental characteristics such as soil humidity, the researchers' virtual plant engine distributed plant species across the terrain. With the engine running on a supercomputer array, a computer interface afforded a user the ability to zoom in and zoom out while investigating the component wildflowers that had grown to fill the terrain.
Once procedural plant models are driven by parameters to a virtual plant growth engine, nature can provide additional inspiration in evolving new plants from existing parameter lists. The simulation process mimics nature by repackaging parameter lists into psuedo-genomes that then simulate physical plant genomes. Once the parameters are in a genome format, the forces of evolution can be written algorithmically in the virtual plant application engine to provide a variety of plant offspring. Chris Colby of Boston University classifies observed phenomena of genome evolution into five processes: mutation, recombination, gene flow, genetic drift, and natural selection. All five processes can be simulated in lines of code. A quick mention of each is warranted here.
Mutation occurs when some external process (such as a cosmic ray) interferes with the normal functioning of DNA within a living cell and forces a change in its chemical makeup. The changed structure then can change the mutated structure's function. Mutation usually does more harm than good to the affected entity but in nature, on average, only about 1 x 10-11 mutations occur per base pair of DNA per generation.
Recombination occurs most spectacularly through meiosis during sexual reproduction. During meiosis, the mother provides half the offspring's genetic material and the father provides the other half. So, the next generation's DNA varies quite dramatically from that DNA of the mother or father's individual.
Gene Flow occurs when some process (such as a mosquito drawing blood) transfers genetic material from one species to another and that material makes its way into the DNA of the target species. The process has been documented between species of fruit flies with a parasitic mite as carrier.
Genetic Drift occurs as a purely statistical process. As a gene pool reproduces and survives in an environment where death is caused by events outside its control, chance determines which genes continue to reproduce and which genes die out.
Natural Selection refers to the process where a gene pool's makeup changes based on reproducing and surviving in an environment where the individual does have some control over their survival. Those individuals with genes that are better suited to the environment tend to reproduce more often than those less suited. Volumes have been written about the sub processes of natural selection: ability to feed, ability to avoid predators, sexual selection, etc. as Charles Darwin intrigued the world with his study of life's struggle in the Galapagos Islands of South America.
All five processes of genetic evolution can be added to a biotic evolution simulation. To demonstrate the genetic processes, we decompose the L-system into components that can be controlled by genetic representation. Take a look at a simple example of an L-system. The model presented on the left is created by the L-system described on the right.
L-Systems incorporate recursion to grow plant structure iteratively. For each recursive processing of the L-system rules, the output of a previous process run is fed as input to the next. The L-system includes rules to apply at each iteration that defines the process by which petals and leaves are generated. As a result, the leaves and petals are similar with the difference being that leaves are created in earlier iterations and are colored green, while petals are created in later iterations and are brightly colored at the red and violet ends of the color spectrum (not that virtual plants have to conform to the stereotypes of physical plants). Alternatively, the petals and leaves can be generated by separate L-system instructions.
L-system examples are available from many different sources. You can learn from exploring each approach to generating plant structure. If you do, as I have done in the past, you will gain insights into how each L-system instruction (in the representation above, each instruction is also called a rule) contributes to overall growth. Eventually, you can pick and choose the best generation techniques and tie them to a genetic representation that identifies which L-system rules to activate for each gene (or group of genes). Through an iterative process of trial and error, my choice for a simulated plant genome became structured to contain a plant expression like the following:
YY|NN|3|0.3 0.3 0.0|0.5|YY NN YN NY|2|4|YY NN YN NY|3|0.2 0.6 0.15|10|1|YY NN YN NY|4|0.6 0.2 0.1
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