7 - The Chemostat with Periodic Washout Rate

Summary

Introduction

The results of Chapters 1 and 2 demonstrate that coexistence cannot occur in the chemostat with constant values of the operating parameters (the washout rate D and the input nutrient concentration S⁰). Roughly speaking, in a temporally homogeneous (constant operating parameters) and spatially homogeneous (well-stirred chemostat) environment, the model predicts competitive exclusion. Of course, real environments are far from being homogeneous, either in space or in time. In addition to the day–night variability in the environment, there are both seasonal effects and random effects caused by the variable climate. In this chapter, the simple chemostat model of competition will be modified to create a periodically varying environment, and it will be shown that coexistence of the two competitors can occur.

There are two basic ways to modify the chemostat model to create a periodic environment – make the reservoir nutrient concentration S⁰ vary periodically in time, or make the washout rate D vary periodically. The first modification was studied by Hale and Somolinos [HaS], Hsu [Hsu2], Smith [S1], and Stephanopoulos, Fredrickson, and Aris [SFA]. This study is natural from the ecological point of view, as nutrient levels in many ecosystems might be expected to vary with the day–night cycle or with the season. The second modification was studied by Butler, Hsu, and Waltman [BHW2] and in [SFA].