Most published results concerning deuterium-hydrogen fractionation in plants are in the range 0.8-1, indicating no bioaccumulation of the heavy isotope. In spite this, an updated compilation of litterature data show that 77% of OBT/TFWT ratios measured in terrestrial plants and food items are greater than one, with a mean value of 1.92. On the other hand, OBT/TFWT ratios for aquatic samples do not show such a tritium anomaly, with 81% of the published ratios being less than 1. This strongly suggests that the cause for excess tritium in terrestrial organic matter has to be found in the atmosphere. We have developed a simple model of tritium incorporation during plant growth, forced by the annual cycle of tritium in precipitation taken from the IAEA/ISOHIS database. The simulated distribution of the OBT/TFWT ratios for terrestrial samples shows many similarities with the observed one. Although other processes such as soil moisture with lower tritium content than atmospheric water vapour can be invoked, our results suggest that the annual tritium maximum which occurs in spring, during the growing season, is capable of creating substantial OBT/TFWT enrichments and has to be considered as well.