Motion in the visual periphery of lizards, and other animals, often causes a shift of visual attention toward the moving object. This behavioral response must be more responsive to relevant motion (predators, prey, conspecifics) than to irrelevant motion (windblown vegetation). Early stages of visual motion detection rely on simple local circuits known as elementary motion detectors (EMDs). We presented a computer model consisting of a grid of correlation-type EMDs, with videos of natural motion patterns, including prey, predators and windblown vegetation. We systematically varied the model parameters and quantified the relative response to the different classes of motion. We carried out behavioral experiments with the lizard Anolis sagrei and determined that their visual response could be modeled with a grid of correlation-type EMDs with a spacing parameter of 0.3 degrees visual angle, and a time constant of 0.1 s. The model with these parameters gave substantially stronger responses to relevant motion patterns than to windblown vegetation under equivalent conditions. However, the model is sensitive to local contrast and viewer-object distance. Therefore, additional neural processing is probably required for the visual system to reliably distinguish relevant from irrelevant motion under a full range of natural conditions.