A Mathematical Model on the Dynamics of Hardseededness of Trifolium repens L. Seeds Following the Retention in the Bovine Rumem

Abstract

Seeds of Trifolium repens with a wide variation in their hardseededness were placed into the rumen of a fistulated steer in nylon bags to investigate the population dynamics in the rumen. After the seeds were retained in the rumen for 0 (control), 1, 2, 3, 7, 14 days, and then germination tests were carried out over 42 days at 20℃ on all the seed recovered from the nylon bags. The seeds were classified into 4 groups as follows. Hard seeds (H) were defined as seeds which remained intact and ungerminated after the 42 days (germination test). In germination test for control, short-term soft seeds (SS) were defined as seeds which germinated within the germination peak during the first 7 days, long-term soft seeds (SL) as seeds which germinated between 8 and 42 days (after the germination peak), and dead seeds (D) as the remainder. According to the characteristic pattern of the change in soft seeds for the first day in the rumen, SS would be equivalent to the seeds which changed into D within 1 day in the rumen, and SL would be equivalent to the seeds which were viable and germinateble when recovered from a rumen. The model of the seed population dynamics in the rumen was constructed with simultaneous differential equations as follows. dH/dt=-k_1 H, dSL/dt=k_1 H-k_2 SL, dSS/dt=k_2 SL-k_3 SS, dD/dt=k_3SS Values of the parameters were estimated, and predictions from the model closely agreed with the data from the experiment. The long-term soft seeds (SL) that possess some degrees of characteristic of hard seeds are likely to contribute to seed dispersal via ruminants and to germination and establishment on dung pats. There seems to be a close correlation between the distribution of germination rate in the germination test on seeds before placement in the rumen and that of death rate of seeds in the rumen.