Probabilistic Evolution in Dynamic Equilibrium
Jonathan Yong Zhi Zhou, Andrew Juno Jung
Pinetree Secondary School, Walnut Grove Secondary
Floor Location : S 201 P

The purpose of Probabilistic Evolution in Dynamic Equilibrium is to mathematically determine trends of population growth in an idealized ecological setting. This project is primarily focused on Lowest Number Wins, a simple probability game modeled after population growth of a species. By analyzing the progressive outcomes of the game, we hoped to demonstrate that a species's growth rate is in an equilibrium state with various factors, a phenomenon we called "Probabilistic Evolution". We defined these factors as variables of population growth, and created a simulation of the game through a computational software, Mathematica. From the simulated data, we found the statistical effects of variables such as time, population, and probability of participation. We observed that a graph of population versus species varies logarithmically, and the population that produces maximum growth occurs reciprocally against the probability of participation. These trends verified our hypothesis that population growth evolves dynamically and in equilibrium with its variables. With Calculus, we were able to mathematically explain these observations and determine the growth rate as a combinatorial function of its population. rnrnThis project provides a greater insight into the dynamic mechanics of population growth. It also establishes the mathematical significances of various variables in population growth and evolution.