Knowledge and prediction of seasonal weed seedling emergence patterns is useful in weed management programs. Seed dormancy is a major factor influencing the timing of seedling emergence, and once dormancy is broken, environmental conditions determine the rate of germination and seedling emergence. Seed dormancy is a population-based phenomenon, because individual seeds are independently sensing their environment and responding physiologically to the signals they perceive. Mathematical models based on characterizing the variation that occurs in germination times among individual seeds in a population can describe and quantify environmental and after-ripening effects on seed dormancy. In particular, the hydrothermal time model can describe and quantify the effects of temperature and water potential on seed germination. This model states that the time to germination of a given seed fraction is inversely proportional to the amount by which a given germination factor (e.g., temperature or water potential) exceeds a threshold level for that factor. The hydrothermal time model provides a robust method for understanding how environmental factors interact to result in the germination phenotype (i.e., germination pattern over time) of a seed population. In addition, other factors that influence seed dormancy and germination act by causing the water potential thresholds of the seed population to shift to higher or lower values. This relatively simple model can describe and quantify the germination behavior of seeds across a wide array of environmental conditions and dormancy states, and can be used as an input to more general models of seed germination and seedling emergence in the field.