The rapid rate of expansion of the disciplines of biotechnology, genomics, and bioinformatics emphasizes the increased interdependency between computer science and biology, with mathematics serving as the bridge between these disciplines. This paper demonstrates this interrelationship within the context of a computational model for a biological process. We designed and implemented a lesson plan for an interdisciplinary science course that examines the evolutionary process from biological, mathematical, and computer science perspectives. The observations obtained from this lesson can be used to augment studies in mathematics with emphasis on arithmetic functions, probability, and generating series.
Computer simulations of a process can be used to gain insight to that process. Many are familiar with the gains of biological sciences from increased computational power such as longitudinal drug studies, (Dennis et al, 2000); genome sequencing, (Collins et al, 2003); cell tracking, (Culler, 2003); and visualization, (Ma et al, 2002). However, not as obvious to some are the computational designs that are inspired by biological processes (Paun and Cutkosky, 2002). One of the developments of this bi-directional relationship was in the realm of evolutionary computation (Sawai et al, 2003). In this article we present a lesson in which students examine an evolutionary process, first from the biological perspective and then as a simulation from the computer science perspective.
Very often it is mathematical processes and concepts that bridge the gap between science and the computer simulation of a scientific process. In his book How Children Fail, John Holt (1964) tells of a student who was paid to tabulate scores at a bowling alley, but could not perform arithmetic in class; there was no connection being made between the classroom and the real world. By giving a student an interdisciplinary experience, the class work can take on more meaning. It is the hopes of the authors that the discussions within will inspire students from different disciplines to understand the influences that different subject matters have on each other.
This article emphasizes the mathematical and computer science aspects of the genetic algorithm along with the relevant biological concepts necessary for understanding the former in the context of the living organism and biological evolution. While the lesson presented here was originally created to show remedial and introductory mathematics students an interdisciplinary application of basic arithmetic, probability and summation of numbers, it can easily be adapted to meet the needs of various levels of students depending on their background. In fact, it has been presented as a workshop, once for high school teachers (none of whom were mathematics or biology teachers), and once for college biology professors.
The lesson begins with relevant biological terminology and the biological perspectives of Darwinian evolution as discussed in Section 2. Then in section 3 the same process is presented from a computer science point of view. The mathematics required to model Darwinian evolution is presented in sections 4 and 5. The details of the computer simulation and the extrapolation of the mathematical process to biological relevance are illustrated using the data generated during one simulation. Finally, in the last section, a concluding summary is provided.
2. AN INTRODUCTION TO DARWINIAN EVOLUTION
The art of simple and clear observations in many different complex environments gave rise to the core of Darwinian Theory (Magner, 2002). Evolution results from the introduction of heritable traits that produce a survival advantage of some type in the individuals of a species possessing them (Darwin, 1859). This "advantage" allows a particular group of organisms to proliferate in a selective environment. Over time, this group of organisms (the population) might become geographically isolated and will reproduce successfully in a particular habitat due to the distinctive inheritance of features that provide the organisms with that advantage. …