CONFIDENCE INTERVALS FOR THE OPTIMUM IN THE GAUSSIAN RESPONSE FUNCTION

Abstract

The optimum of a species on a gradient is an important parameter for ecological interpretation and bioindication. The location of the optimum is easily estimated in the popular Gaussian response model, but it is more difficult to assess the precision of the estimated optima. Methods based on the profile likelihood or quasilikelihood function are presented to find confidence intervals for the optimum parameter of the Gaussian response function using generalized linear models. The following four cases are considered: optimum on one gradient; optimum on one gradient when there are additional stratifying variables; optimum on an interesting gradient at a certain level of a stratifying variable when the optimum is dependent on the latter; and simultaneous confidence region for the joint overall optimum on two gradients. The methods are illustrated with two species of testate amoebae (Protozoa: Rhizopoda) in Finnish mires. The first two cases were also analyzed using Fieller's theorem, although it produced generally wider limits.