To all, On a lazy Friday afternoon, I have a semi-trivial question that the list just doesn't seem to see much of anymore! Every year in my ecology lab I have the students test Holling's equation relative to a predator's functional response:
Pe = aNT / (1 + aNh), where Pe is # of prey eaten, N is # of prey available, a is attack/encounter rate between predator and prey, T is available search time, and h is handling time. A number of years ago, an article in Bulletin of the ESA showed that you can invert this equation and use it to have the students estimate attack rate and handling time as a simple linear equation: 1/Pe = (1/aT)*(1/N) + h/T If you plot 1/Pe vs. 1/N, then the slope = 1/aT and the Y-intercept = h/T. The students have a bunch of N and Pe numbers, and T is constant, so they can plot this and estimate attack rates and handling times. So far, so good. However, every year I do this it comes out that prey that are eaten more easily (i.e., that have higher Pe counts) end up with lower attack rates than prey that have lower Pe counts. For example, this year my values of "a" estimated this way were 0.0212 for Skittles, 0.0158 for Cheez-Its, 0.0133 for M&Ms, and 0.0121 for Cheerios... which is the exact opposite of what I and the students expect! Cheerios have the highest consumption rate, yet the lowest attack rate; Skittles have the lowest consumption rate, yet the highest attack rate. Essentially, when plotting the data this way, prey that have higher #s consumed have steeper slopes, which leads to lower estimates of attack rate. I've always thought that there's some obvious reason, either mathematical or biological, for this that simply continually escapes me. For example, maybe this equation just doesn't "work" for this particular situation, but the reason why it wouldn't isn't clear to me. Does anyone have an explanation for this apparent conundrum?! CAB ************************** Chris Brown Associate Professor Dept. of Biology, Box 5063 Tennessee Tech University Cookeville, TN 38505 Email: [email protected]<mailto:[email protected]>
