Predator vs. Prey



Our lab’s first model products will be a set of prototypes of the Lotka-Volterra (LV) model of predator-prey competition. If lions (predators) chase gazelles (prey), then there are mathematical relationships that can be expressed to capture the overall population change resulting from this effect. The LV model was proposed in 1910 according to the Wikipedia article as a “theory of autocatalytic chemical reactions,” and then extended in 1920 for organic systems. In the model, we find the fairly general terms present that make the dynamics interesting–growth (birth), decay (death), and interaction effects modeled as a multiplicative effect of the population variables. You’ll find these same terms in many other mathematical models. Returning to the lab, we chose this model out of thin air based on some sketches I made on the office whiteboard seen above. Unfortunately, there are some errors in the design, but it was some sort of beginning.  Despite the confusing juxtaposition of figures, we observe a transition from equation to block model, and then to an analog model based on water flow. The idea for the spherical floats at the surface of the water will be familiar to all those who have had to correct leaky toilets containing older ball-cock supply valves. The redesigns and creative prototypes of LV will be unleashed in future issues of the blog over the next month.