Mathematical models were developed to characterize the physiological bases of the responses of tomato (Lycopersicon esculentum Mill. cv T5) seed germination to water potential (psi) and abscisic acid (ABA). Using probit analysis, three parameters were derived that can describe the germination time courses of a seed population at different psi or ABA levels. For the response of seed germination to reduced psi, these parameters are the mean base water potential ( psi(b), MPa), the standard deviation of the base water potential among seeds in the population (sigma(psib), MPa), and the "hydrotime constant" (theta(H), MPa.h). For the response to ABA, they are the log of the mean base ABA concentration ([unk]ABA(b), m), the standard deviation of the base ABA concentration among seeds in the population (sigma(ABA) (b), log[m]), and the "ABA-time constant" (theta(ABA), log[m].h). The values of psi(b) and [unk]ABA(b) provide quantitative estimates of the mean sensitivity of germination rate to psi or ABA, whereas sigma(psi) (b) and sigma(ABA) (b) account for the variation in sensitivity among seeds in the population. The time constants, theta(H) and theta(ABA), indicate the extent to which germination rate will be affected by a given change in psi or ABA. Using only these parameters, germination time courses can be predicted with reasonable accuracy at any medium psi according to the equation probit(g) = [psi - (theta(H)/t(g)) - psi(b)]/sigma(psib), or at any ABA concentration according to the equation probit(g) = [log[ABA] - (theta(ABA)/t(g)) - log[[unk]ABA(b)]]/sigma(ABA) (b), where t(g) is the time to radicle emergence of percentage g, and ABA is the ABA concentration (m) in the incubation solution. In the presence of both ABA and reduced psi, the same parameters can be used to predict seed germination time courses based upon strictly additive effects of psi and ABA in delaying the time of radicle emergence. Further analysis indicates that ABA and psi can act both independently and interactively to influence physiological processes preparatory for radicle growth, such as the accumulation of osmotic solutes in the embryo. The models provide quantitative values for the sensitivity of germination to ABA or psi, allow evaluation of independent and interactive effects of the two factors, and have implications for understanding how ABA and psi may regulate growth and development.