Confidence intervals for the optimum in the Gaussian response function

The optimum of a species on a gradient is an important parameter for ecolog ical interpretation and bioindication. The location of the optimum is easil y estimated in the popular Gaussian response model, but it is more difficul t to assess the precision of the estimated optima. Methods based on the pro file likelihood or quasilikelihood function are presented to find confidenc e intervals for the optimum parameter of the Gaussian response function usi ng generalized linear models. The following four cases are considered: opti mum on one gradient; optimum on one gradient when there are additional stra tifying variables; optimum on an interesting gradient at a certain level of a stratifying variable when the optimum is dependent on the latter; and si multaneous 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.