A Comparison of Methods for Estimating the Functional Response Parameters of the Random Predator Equation

Abstract

(1) Simulations of functional response experiments were used to compare Rogers's linearization, nonlinear least squares, and a new nonparametric parameter space method as means of estimating parameters of the random predator equation. (2) Rogers's linearization gave highly biased estimates of both parameters. These estimates were consistently too low. (3) Nonlinear least squares using the implicit form of the equation, and the nonparametric parameter space method provided equally good estimates for data sets that departed only moderately from the assumptions of homogeneous, normally distributed error. For data sets with greater heteroscedasticity and more extreme nonnormality, the nonparametric procedure performed slightly better than nonlinear least squares. This was especially true for smaller data sets. (4) For both methods, actual frequencies of erroneous rejection of true null hypotheses were usually significantly greater than the nominal 0-05 for the cases studied. Even a moderate amount of heteroscedasticity seems to effect the probability of type I error for both methods. (5) The practice of analysing average values of number of prey eaten at each value of number of prey offered was compared to using individual data points. Use of average numbers eaten did not alter point estimates of parameters, but produced severe underestimates of S.E.s of parameter estimates. Use of average numbers eaten increased probability of type I error by 16 to 42%. (6) Simulation studies such as this may be generally useful to biologists as tools of applied statistics.