You are dealing with objects that have essentially the same handling time in reality.
I used the disc equation in my MS thesis. As it turned out there were a number of prey antipredator behaviors that led to differences in swallowing time. Your differences are undoubtedly due to differences among these three prey items, and their handling times in the mouth. Skittles are substantially harder to chew than eitehr of the otehr two items. Therefore, your handling time for them is longer because they require longer to chew. Cheezeits require longer to chew than cherios. Further, the "enjoyment factor" may lead to slowing down to enjoy the more attacked food! Preference leads to skittles being attacked more frequently, and they take longer to chew. Cherios are less tasty than either cheezits or skittles, and require way less time to chew. Handling time includes chewing in the mouth!!!! On Fri, Nov 3, 2017 at 4:38 PM, Brown, Christopher <[email protected]> wrote: > 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] > > > -- Malcolm L. 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