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The Need for a Quantifiable Model of Evolution J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas THE NEED FOR A QUANTIFIABLE MODEL OF EVOLUTION Elizabeth A Siewert*1 and Thomas A Siewert2 1Retired from University of Colorado & 2Retired from NIST (Received on Date: 6th August 2017 Date of Acceptance: 18th September 2017) ABSTRACT When Charles Darwin first published his book, the origin of the species, he explained his theory by appealing to analogy. He observed that man can develop desirable traits in domestic plants and animals by selectively breeding for these traits. In a similar way, nature can develop desirable traits in plants and animals – not by intention, but by an undirected process of natural selection acting on random variation. Unfortunately, much of evolutionary theory today is still explained using only descriptive arguments. There have been few attempts to develop a quantitative model of this undirected process. We describe two attempts at a quantitative model – one by Sir Fred Hoyle and the other by Dr. Richard Dawkins. While most models modify a previously-existing, functional, complex structure, both of these models are attempts to quantify the ability of evolution to innovate rather than modify. We critique these two models, and present our quantitative model. Specifically, we hypothesize a primitive version of Chlamydomonas reinhardtii, a simple single-celled green alga, which does not yet have a functional eyespot. We then calculate the probability of developing an eyespot that is functional enough to confer an evolutionary benefit assuming all components are pre-existing, except a few proteins. We conclude by encouraging others to become involved in developing quantitative evolutionary models Keywords: evolution, quantitative model, eyespot, Chlamydomonas No: of References: 8 2017 September Edition |www.jbino.com | Innovative Association J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas INTRODUCTION In his book, The Origin of the Species, (e.g., being able to run faster if you‟re a Charles Darwin speculated that the wide wolf or, for that matter, a deer) might be variety of beaks seen on birds of the inherited by some unknown mechanism – Galápagos Islands developed their thus allowing a continuous gradual different shapes and sizes (depending change from one generation to the next. upon the type of food available to them Darwin praised Lamarck in his Origin of the on each island) through a series of Species, saying “Lamarck was the first man incremental changes in much the same whose conclusions on the subject excited way that desirable traits of domesticated much attention” and calling him a “justly plants and animals are developed through celebrated naturalist.” (Darwin, 1859) husbandry. He proposed that while man So, considering the state of scientific breeds and selects for traits that he desires knowledge at that time, Darwin could only in his plants and animals, the variation of argue intuitively from what he knew. He traits seen in nature is due to an undirected saw the adaptations in organisms that process of natural selection acting on favored survival (eg., green leaf-eating random variation. He further extended this insects, mottled-grey bark-feeding insects), undirected process of developing variation he observed the obvious relationships within a species to the development of the among the species based on gross various species, themselves – thus the title anatomies, and he understood the of his book, The Origin of the Species. In his practice of selective breeding to obtain concluding remarks, he states, “Thus the desirable characteristics in domestic plants small differences distinguishing varieties of and animals. On these observations, he the same species steadily tend to increase, proposed his theory of the origin of the till they equal the greater differences species through an undirected process of between species of the same genus, or natural selection acting on random, even of distinct genera.” (Darwin, 1859) incremental (and at that time, not It‟s important to understand that in 1859 understood) variation among individuals. when Darwin published his theory, the cell Today, we know much more about the was thought to be a fairly simple bag of complex structure of the cell, the source of protoplasm; its internal structure was not variation among individuals, and the discovered until the advent of the electron genetic relationship among the species. microscope in the 20th century. The However, Darwin‟s theory is still mostly mechanism for inheritance was also presented using only descriptive unknown until the structure of DNA was arguments. Although this gives some discovered in 1953. In the early 1800s, intuitive understanding of his theory, it lacks Lamarck had proposed that acquired traits 2017 September Edition |www.jbino.com | Innovative Association J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas rigor. What is needed is a quantifiable Hoyle‟s model dramatically illustrates the model to provide mathematical precision “outrageously small” probability of the to his theory. There have been multiple “origin of life by chance” problem. attempts to quantify the probability that However, evolutionary theory states that complex structures can develop via a complexity is built up slowly step by gradual process of random variation and incremental step–not all at once and selection. We provide two of these suddenly. This model, although attempts – a very large-scale one from the quantifiable, is too complex to represent a astronomer, Sir Fred Hoyle, and a small- single, incremental evolutionary step. scale one from evolutionary biologist, Dr. Richard Dawkins, on the other hand, has Richard Dawkins. While most models presented a much simpler model. In his modify a previously-existing, functional, book, The Blind Watchmaker, he proposed complex structure, both of these models a model of developing the phrase, are attempts to quantify the ability of “METHINKS IT IS LIKE A WEASEL” in evolution to innovate rather than modify. incremental steps. (Dawkins, 2006) In this Fred Hoyle, along with many scientists of case, at each iteration he randomly the mid 1900s, was a proponent of the generated letters and spaces for each of Steady State Theory, proposed by Sir Isaac the 28 positions, kept the letters and Newton in 1687, which postulated an spaces that matched the target phrase, infinite age of the universe. He is credited and regenerated the letters and spaces with giving the Big Bang theory its name as that did not match the desired phrase until a pejorative because he objected to the all matched. He calculated that if he had implication that a finite universe put too tried to generate this phrase in a single much restriction on the ability of life to step, the probability would be one chance occur by chance. In his book, Evolution in 2728 or 1040 – an extremely low from Space, he states, “Life cannot have probability. However, by keeping any had a random beginning … The trouble is letters and/or spaces that agreed with the that there are about two thousand target phrase, “METHINKS IT IS LIKE A enzymes, and the chance of obtaining WEASEL” at each step, he showed that he them all in a random trial is only one part in could reach the 100% match in only a 1040,000, an outrageously small probability small number of iterations. that could not be faced even if the whole universe consisted of organic soup.” (Hoyle and Wickramasinghe , 1981) 2017 September Edition |www.jbino.com | Innovative Association J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas Generation 01: WDLTMNLT DTJBKWIRZREZLMQCO P Generation 02: WDLTMNLT DTJBSWIRZREZLMQCO P Generation 10: MDLDMNLS ITJISWHRZREZ MECS P Generation 20: MELDINLS IT ISWPRKE Z WECSEL Generation 30: METHINGS IT ISWLIKE B WECSEL Generation 40: METHINKS IT IS LIKE I WEASEL Generation 43: METHINKS IT IS LIKE A WEASEL While this example illustrates the process of goal. For example, one approach might achieving complexity via random, be to define success as matching any incremental steps, it does not correctly word in the dictionary, and possibly model an undirected process. Dawkins including grammar and syntax rules to had a predefined goal and retained letters determine whether a coherent sentence until they all matched that defined goal. or phrase could be formed. He knew, as the programmer, what phrase A. Proposed Quantifiable Model of he wanted to reach and defined each Darwin’s Theory incremental “success” with respect to that predefined goal. In other words, in this With today‟s knowledge of molecular model, Dawkin‟s blind watchmaker had biology, and the development of the resulting phrase firmly in sight. mathematical modeling of biological systems, it is no longer justifiable to present Methods and Results Darwin‟s theory using only descriptive Neither of the two previous models fairly arguments. This is an important issue and represents Darwin‟s theory of evolution. should be modeled quantitatively. In this While Hoyle‟s model is much too complex paper, we propose a biological model for and thus fails to be an incremental step in one incremental, undirected, random step evolution, Dawkins‟s model pre-defines the in evolution that is quantifiable. final goal, and thus fails to be undirected. Specifically, we propose to quantify the We need an example that is simple occurrence of one small component of a enough to depict the small incremental primitive eyespot assuming all other steps of evolution, and undefined enough components already exist. We chose the to model an undirected process of eye, as it seems to be a popular example evolution. One possibility would be to by both the critics and the proponents of improve Dawkin‟s “METHINKS IT IS LIKE A Darwin‟s theory. In fact, Darwin, himself, WEASEL” program by restricting each presented the eye as a testable example success to be independent of the final 2017 September Edition |www.jbino.com | Innovative Association J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas of his theory.
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