James Farley

Professor Underwood

Seminar D5

11/4/07

Log 2- The Everyday Math of Evolution: Chance, Selection, and Time

Synopsis:       

Chance, Selection, and Time are the key ingredients to the theory of evolution. The evolutionary process consists of a series of small changes that are believed to lead to significant difference over time. The process of natural selection can best be thought of in the real-world applicable terms of compounding interest. With interest, the amount gained after a set amount of time may be small. However, when the amount of money in addition to its interest rate is compounded year after year, the sum of money gained from interest over a large amount of time is significant. In short, small differences have a profound impact over time.

            Studying and representing changes over time can be difficult. In his works, Darwin started off with keeping things simple by illustrating his theories with a common bird…pigeons. He did this because everyone in his time knew what a pigeon was and were quite used to seeing them in everyday life. By making the theory familiar, Darwin appealed to a greater audience. In his studies, he looked at small variations in pigeons and predicted that these micro-variations over time would lead to macro-differences. The predictions of his studies have thus been widely accepted by the scientific community.

            Darwin took his findings and got the second opinion of expert pigeon breeders who were skilled in breeding techniques that produced different desirable variations. The major question amidst the research was whether adaption exists in small variations in individuals or large variations existing within the group dynamic. Darwin’s personal belief was that the evolutionary process was one of small steps (adaption) that led to a larger process (evolution).

            Many others challenged, tested, and built off of Darwin’s original ideas. Scholars such as William Bateson, and William Castle pioneered research to further ascertain and solidify evidence for variation and the evolutionary process. Bateson’s worked attempted to prove that “selection acted on large differences among individuals, and that Darwin’s picture of evolution occurring in small increments was wrong” (Caroll 46).  His work ultimately led him to the belief that he disproved Darwin’s idea that the evolutionary process occurred in small increments over large periods of time.

            Bateson’s theories were later disproved as William Castle’s work solidified the case for Darwin. Castle worked with breeding hooded rats. He found that the rats broke the boundaries of controlled variation experimentation and “modified by selective breeding beyond the limits of the patterns of starting parental lines” (Caroll 47). The studies showed that the rat offspring displayed traits that were not characteristic of the original parents. Thus, the evidence was clear in showing that genetic variation was occurring beyond the human selective process designed in the experiment.

            From the work of these individuals, the study of adaption over time began to further spill into the experimental field of upper mathematics. R.C. found that the processes of evolution and selection were much faster than originally proposed. The system set in place to measure the process consists of two major and essential components, competition and frequency. Competition is a key variant of mathematical computation because it prevents selection and evolution from being measured in the form of exponential growth. Regulation of the populace through competition serves as a natural control mechanism. The second part to the mathematical computation process is fitness. Fitness is a measurement of the advantages and disadvantages of having a trait based on the total differences of those organisms possessing the trait.

            Authorities such as J.B.S. Haldane, R.A. Fisher and Sewall Wright further pioneered evolutionary arithmetic by creating a series of formulas to understand and organize data in an efficient manner in. These formulas were more specifically rendered in order to explain the relationship between evolution, selection, and time. Dually noted, the two most difficult things to measure are time and the quantity of measurements. The population must be big so that variations in populations can successfully be identified. This study of documentation takes great discipline. Multiple experiments must also be conducted in order to account for difference in variation over multiple years.

            In a study of predator-prey interaction of peregrine falcon vs. pigeon, Alberto Palleroni discovered that a specific breed of pigeon held an advantage in variation. Palleroni hypothesized that the white patch on the back of the white-rumped pigeon enabled it to have a greater survival rate than other pigeons. He observed that when the white-rump pigeon rolls to evade the falcon’s dive, the white patch seems to distract the falcon. The population of the white-rumped pigeon has thus increased significantly.

            In the case of the stickleback fish of North American, population of saltwater Stickleback has decreased whereas the population of freshwater Stickleback increased. This development can be attributed to the freshwater Stickleback’s decrease in armored plating over time. “The selective advantage of plate reduction in lakes and streams may be due to greater body flexibility and maneuverability while swimming” (Caroll 56). Change and variation is relatively rapid because it has to be in order for the organism to survive in the new environment.

            In the creation and processing of DNA, mistakes in DNA sequencing and production, when not addressed, create mutation. Mutations can be both good and bad. “There are an estimated 175 new mutations among the 7 billion DNA letters in every individual…these variations in size, shape, color and other physical and chemical properties are what make each of us unique. This is the raw material for evolution” (Caroll 58). Mutations should not be looked down upon because they provide the variation by which genetic differences and abnormalities give way to the process of adaption. By using the DNA code, the study of mutation can further explain the process of change through adaption.

            In the 1960’s ground breaking and innovative work was being conducted by an evolutionary biologist known as Motoo Kimura. Kimura used neutrality as a base to measure change. When change deviated from neutrality, Kimura noted that the process of selection then began. This discovery was revolutionary to the process of further understanding adaption and variation in the evolutionary process.

Time serves as the interactive agent between chance and selection. Chance must arise from the change in order for selection and adaption to occur over time. The probability and rate of change is both limited by and dependent upon the change in the environment. Probability is also dependent on time due to the fact that a considerable amount of time is needed to turn up notable changes in variations and results through the passing down of traits through generations. Mathematics is known far and wide as the language of science. By taking a stated hypothesis and analyzing it in a mathematical sense, many conclusions based trends found throughout the various numbers and test results can be made with sheer objective data as well.

Take Away Idea:

I never thought about the importance of mathematics in supporting evidence. I always thought of math as “just numbers”. Algebra was my least favorite subject in high school. Now I am beginning to see the trends in numbers and what inferences, deductions, and conclusions can be made from the data. I want to know more about how mathematics can be used to further understand the world around me.  Math is now alive to me. I’m not the greatest mathematician, but my skills are getting better and better everyday.

Most Challenging Concepts:

The most challenging concept is understanding the idea of probability and the formula for average time for variation. (t=(2/s) natural log (2Ne) generations) It’s a simple formula but I couldn’t grasp its conceptual depth. Everything else in the reading I was able to understand fairly easily. Nothing stood out as unbearingly difficult. I enjoyed the chapter and found it very interesting. I’m working hard to understand the logic of math.

Aesthetic Awareness:

It is important to note that time must be taken to not only examine the initial subjects being studied, but the environment in which they are being studied in as well. Aesthetic Awareness is important because it provides appreciation for the objects being tested. Numbers and data can be very boring alone. In many cases, a visual aid may not be needed, but it is certainly helpful to putting a “face” to the study. Life is not about being dull and boring; it is about appreciating the beauty and magnitude of the world around us.

If aesthetic awareness is lost parts of the world, whether they are large or small, will be devaluated and eventually lost. For example, take a factory that produces pollution and dumps it in a major river. If the owners of that factory are not educated and informed to appreciate the wildlife and habitat of the environment around them, much life will be lost in the process of careless waste and the excessive dumping of pollution. Aesthetic awareness and appreciation breeds responsibility. Responsibility, in turn, produces good stewardship.

Critical Thinking:

            Questioning the world around us is the overall learning experience of life. Critical Thinking and analysis is essential to understanding just how and why things work. All the individuals involved in this study were intelligent men who questioned things for themselves and understood through the logical experimental process of trial and error. Examining and analyzing is the first step. Questioning and forming intelligent ideas about that which is being examined is the second part of the process. The third part consists of testing those ideas and hypothesis in order to determine if they are true.

            Darwin’s first observations came from years of studying pigeons and critically thinking about their variations. Mendel thought about different variations in his plants and reproduced them using the critical thinking process in order to ascertain desirable traits. All experiments that have taken place in genetics research have been extensively thought over. Humans will always question the world around them. Critical Thinking produces greater understanding and broader discovery.

Connection:

            In NCLC 120, we have gone through the process of both carbon dating and mapping billions of years of information on a calendar. These experiences have used math to represent and work with the evidence to the proposed theory of evolution. The book provides greater understanding for the concepts in class. By having real-world and modern evidence of adaption, as well as working with numbers to determine the frequency of variation, the student is able to gain a full and broad perspective of the concepts being taught. This chapter did an excellent job in emphasizing the relationship between chance, selection, and time.

Vocabulary:

            Salutations- large discontinuous differences among individuals

            Selection- coefficients- genetic form of measurement thought of as interest rates

            Fitness- relative measure of positive or negative values of selection coefficients

Key Concepts:

Small differences make huge differences in the long run-small changes may not seem like much but over time small changes accumulate into big and significant differences

Mathematics as a tool to further explain evolution- Mathematics can further examine and prove hypotheses concerning the theory of evolution

Time and large population essential to studying variation- A large population is needed to study in order to note a wider variety of significant difference. Time is also needed to document the changes of adaption over multiple years.

Bibliography

The Making of the Fittest: DNA and the Ultimate Forensic Record of  Evolution by Sean Carroll, W.W. Norton; Reprint edition (September 10, 2007)