Experiments and simulation studies on the system Lolium perenne - Tylenchorhynchus dubius

The host/parasite system Lolium perenne L./ Tylenchorhynchus dubius (Bütschli, 1873) Filipjev, 1936 was studied in experiments and by simulation, to elucidate the nature and functioning of the relationship between pasture and ectoparasitic nematodes.The influence of temperature and soil moisture on the system and the incidence of tolerance and resistance in the host were studied in experiments under controlled conditions.A mathematical simulation model was developed for the host/parasite system; preliminary models for the population dynamics of the nematode and the influence of the nematode on plant growth are presented.Measurements and simulations indicate that the ratio of nematode numbers to young roots is a main determinant of the effect of the nematodes on plant growth. The role of T.dubius and other ectoparasitic nematodes in the failure of reseeded pastures is discussed

Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata

We give new sufficient ergodicity conditions for two-state probabilistic cellular automata (PCA) of any dimension and any radius. The proof of this result is based on an extended version of the duality concept. Under these assumptions, in the one dimensional case, we study some properties of the unique invariant measure and show that it is shift-mixing. Also, the decay of correlation is studied in detail. In this sense, the extended concept of duality gives exponential decay of correlation and allows to compute explicitily all the constants involved