Comparing Predator‐Prey Models to Luckinbill's Experiment with Didinium and Paramecium

Abstract

When Leo Luckinbill (1973) grew Paramecium aurelia together with its predator Didinium nasutum in 6 mL of standard cerophyl medium, the Didinium consumed all the prey in a few hours. When the medium was thickened with methyl cellulose, the populations when through two or three diverging oscillations lasting several days before becoming extinct. When he used a half—strength cerophyl medium thickened with methyl cellulose, 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 differential equation predator—prey model with a carrying capacity for the prey and a saturating (Type 2) functional response predicts the outcome of Luckinbill's experiment qualitatively, but does not give a good quantitative fit to the data. Several modifications of this model are tested against the data for the populations grown in the medium thickened with methyl cellulose, using the Marquardt—Levenberg method to obtain the least squares best fit. Neither Leslie type models nor models with a ratio—dependent functional response do well, but adding either predator mutual interference or a sigmoid (Type 3) functional response improves the fit dramatically. Modeling the predator growth rate to depend 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, produced the best models and gave excellent fits to the data. These models are further validated by the fact that changing only one or two parameter values to reflect the unthickened medium or the half—strength medium also gives reasonably good fits to the other data sets. The last model requires a more sigmoid functional response to fit the data 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 densities.