Digital Commons Network^™

Students Rise To The Challenge Of Modeling Yeast Growth Despite Sour Hiccups From Imperfect Data, Alicia Caldwell

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Students rarely receive the opportunity to experience a learning activity involving mathematical modeling. This paper describes a lab in which students in an Applied Mathematics in Biology course observe the growth of Saccharomyces cerevisiae, a yeast strain, in differing sugar concentrations for use in learning modeling. They parameterized the logistic equation and an alternate model, which they themselves constructed, based on the data they collected. I participated in this lab as a student in 2012 then observed and reviewed the work of other students involved. I found that students gained a deeper understanding of limiting factors and the role of …

Evolving Models: A Density-Based Approach To Modeling Sexual Dimorphism And Adaptive Speciation, Audrey Smith

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In this paper, we begin by extending existing deterministic and individual-based ecological models for sexual dimorphism and adaptive speciation into density-based mathematical models describing the density or number of individuals with various trait values, or phenotypes. These density-based models describe the dynamics of a population of males and females using both clonal and sexual reproduction. Each generation, the populations are subject to mating, mutation, and ecological dynamics including infraspecific competition and carrying capacity of the environment. By avoiding individual-based models, we are able to avoid simulations and instead achieve repeatable results.

Implementing these models numerically, we are able to show …

Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …