the seed. This exercise will attempt to replicate experiments first done by G.F. Gause in the 1920s and early 1930s and reported in his book, The Struggle for Existence, published in 1934. He was attempting to show experimentally that the relationships described by the Pearl-Verhulst and Lotka-Volterra equations on population growth and species interaction were correct. These equations will be described later in the exercise. At present, suffice it to say that these two sets of demographers (students of populations, especially humans) had developed mathematical equations which they felt described populations growing in natural conditions, the effect of two species in competition for the same resources and the outcome of the interaction between predators and their prey. Their equations fit the theory of the time (and are still about the best we have), but most populations have so many things affecting them besides simple competition and there is so seldom a single predator/single prey situation in nature that it was difficult to show that the equations ever had any validity in field studies.

So Gause set up a series of experiments in microcosms containing protozoans (single-celled, eukaryotic heterotrophs) that ingeniously mimicked the assumptions of the mathematicians.

He used ciliates, protozoans which are fairly large and use cilia for locomotion, of three species. Paramecium aurelia and P. caudatum are both protozoan "grazers," feeding on yeast, bacteria and smaller protozoans in their medium, so Gause felt they would be in direct competition for food. There is a slight difference in size, P. caudatum being somewhat larger, but Gause's assumption proved to be quite correct in the long run. This set of experiments led to the conclusion the "no two species can remain in competition for exactly the same niche indefinitely: which has become known as Gause's Principle or the Principle of Competitive...