One of the most common methods of studying insect dispersal is the recapture of members of a population released at a single time from a single location. This procedure especially lends itself to quantitative analysis. Quantitative studies of the dispersal of insects released in this manner may be divided into the following three general categories: (1)statistical studies in which certain dispersal parameters such as average distance flown are estimated without assuming any particular model; (2) curve fits to an empirical model having a predetermined functional form, such as an exponential; and (3) fits to a fundamental biological model such as a diffusion-based model. Each of these methods of analysis serves a purpose. For example, the first and second methods are often useful in developing control strategies for invasive pest species, whereas the third is useful for understanding the biological process driving dispersal. The article presents a quantitative analysis of the dispersal of irradiated Mediterranean fruit flies,Ceratitis capitata(Wiedemann) in a macadamia nut orchard near Hilo, Hawaii. All three of the methods described above are used in the analysis. The article had three primary objectives. The first was to review and contrast the three methods of analyzing data on the dispersal of insects from a point source. The second was to illustrate how these methods may be applied to insect recapture data using the example of released Mediterranean fruit flies. The third was to use the quantitative analysis to compare the results of the present release study with other studies on related species and to draw general conclusions about the nature of the dispersal of released sterile Mediterranean fruit flies. Results indicated that a population of irradiated flies released from a single point dispersed in a manner that may be modeled as if the population consisted of two subpopulations, one of which was dispersing in a diffusionlike pattern and the other was not dispersing, and that the fraction of the population in the nondispersing subpopulation increased. The dispersal pattern appeared to be little influenced by prevailing wind and to remain centered near the release point. The pattern had almost complete circular symmetry.