In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas are obtained to (...) determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis. (shrink)

The possible differential effects of ABO blood group materno-paternal (fetal) incompatibility on completed reproductive performance were investigated on a sample of 100 couples (100 fathers and 100 mothers) from three villages in the Jind district of Haryana state, India. The average number of live births per mating couple was slightly higher for the incompatible matings (5·32) than the compatible ones (5·05). This advantage was offset by higher postnatal mortality in the former. Consequently, the average number of living children in the (...) compatible matings (4·64) was higher than in the incompatible ones (4·18). With reference to individual ABO matings, the index of relative fertility (Irf) was the highest in A×AB followed by B×A type of incompatible matings. No decrease in live births in O×A and O×B incompatible matings was observed compared with their reciprocal compatible ones, i.e. A×O and B×O matings, as has been hypothesized in previous studies. The total pregnancy wastage was substantially higher in ABO-incompatible matings (24·59%) than compatible matings (8·45%). About 71% of the postnatal deaths took place within one year of the birth in the case of incompatible matings compared with 50% in the case of compatible matings. The study supports the hypothesis that selection is operative at the ABO locus as revealed by the measures of selection intensity. The loss of fitness in the present sample was associated with differential mortality. There were no differences in the proportions of average number of male live births in the compatible (0·55) and incompatible matings (0·58). However, in the individual mating types, there was some evidence of higher or lower proportions of male live births. (shrink)