Four pigeons were trained in a series of two-component multiple schedules. Reinforcers were scheduled with random-interval schedules. The ratio of arranged reinforcer rates in the two components was varied over 4 log units, a much wider range than previously studied. When performance appeared stable, prefeeding tests were conducted to assess resistance to change. Contrary to the generalized matching law, logarithms of response ratios in the two components were not a linear function of log reinforcer ratios, implying a failure of parameter invariance. Over a 2 log unit range, the function appeared linear and indicated undermatching, but in conditions with more extreme reinforcer ratios, approximate matching was observed. A model suggested by McLean (1991), originally for local contrast, predicts these changes in sensitivity to reinforcer ratios somewhat better than models by Herrnstein (1970) and by Williams and Wixted (1986). Prefeeding tests of resistance to change were conducted at each reinforcer ratio, and relative resistance to change was also a nonlinear function of log reinforcer ratios, again contrary to conclusions from previous work. Instead, the function suggests that resistance to change in a component may be determined partly by the rate of reinforcement and partly by the ratio of reinforcers to responses. (Contains 2 tables and 13 figures.)