COMPARING PREDATOR-PREY MODELS TO LUCKINBILLS EXPERIMENT WITH DIDINIUM AND PARAMECIUM

When Leo Luckinbill (1973) grew Paramecium aurelia together with its p redator Didinium nasutum in 6 mt of standard cerophyl medium, the Didi nium consumed all the prey in a few hours, When the medium was thicken ed with methyl cellulose, the populations went through two or three di verging oscillations lasting several days before becoming extinct. Whe n he used a half-strength cerophyl medium thickened with methyl cellul ose, the populations maintained sustained oscillations for 33 d before the experiment was terminated. The data from this experiment provide a rare opportunity to test current predator-prey models. A standard di fferential equation predator-prey model with a carrying capacity for t he prey and a saturating (Type 2) functional response predicts the out come Luckinbill's experiment qualitatively, but does not give a good q uantitative fit to the data, Several modifications of this model are t ested against the data for the populations grown in the medium thicken ed with methyl cellulose, using the Marquardt-Levenberg method to obta in the least squares best fit. Neither Leslie type models nor models w ith a ratio-dependent functional response do well, but adding either p redator mutual interference or a sigmoid (Type 3) functional response improves the fit dramatically. Modeling the predator growth rate to de pend on energy or nutrient storage instead of directly on the rate of consumption of prey, thus creating a delayed numerical response, along with predator mutual interference or a sigmoid functional response, p roduced the best models and gave excellent fits to the data. These mod els are further validated by the fact that changing only one or two pa rameter values to reflect the unthickened medium or the half-strength medium also gives reasonably good fits to the other two data sets. The last model requires a more sigmoid functional response to fit the dat a in the thickened than in the unthickened medium, suggesting that an increase in the cost-benefit ratio of energy spent searching to energy gained capturing prey inhibits the predator searching at low prey den sities.