Abstract: Social interactions between individual horses were observed in two herds each comprising a stallion and a number of mares. In one herd, the animals were observed whilst grazing and resting; in the other, nearest neighbours were recorded when the animals were grazing, and social interactions were noted when the animals were feeding on hay.
In both herds, the horses showed marked preferences for the company of specific individuals when they were grazing. In one herd, the associations were mainly between individuals that had been associated prior to being put in the herd. In the other herd, this was not the case. A new statistic was produced for testing for specific company preference. In both herds, the stallion was dominant over all mares and never received any aggression.
The complete social hierarchy could not be determined for the herd which was observed only when grazing because social contact was restricted to that within groups or pairs that associated together. In the herd to which hay was fed, a non-linear hierarchy existed. Statistics were produced to quantify both the general level of dominance of a horse and its specific dominance or subordination to every other horse. It is suggested that these statistics, and one for quantifying the general aggressiveness of a horse, could be widely used.
A principal component analysis allowed the horses to be characterised socially according to aggressiveness, their attitude to other horses and their attractiveness to other horses.

Abstract: An understanding of patterns of leadership during grazing movements is important where the management of grazing cattle is concerned. This paper describes the leadership displayed by grazing cattle by recording the spatial relationship (grazing style) among herd members as the group progressed slowly through a field. Grazing style was divided into “A”, “B” and “C”, meaning following, independence and leading, respectively. The results revealed the following features: (1) the frequency distributions of grazing style and grazing formation used by the herd varied with the seasons; (2) the individual animal variation in grazing style did not fundamentally change with the seasons; (3) there was negative linear correlation between Styles A and C and between Styles A and B. The more any cow followed the grazing movement, the less likely it was to lead the grazing movement or to be independent. Styles C and B tended to be positively related; (4) high, medium and low ranking animals in social dominance showed tendencies to behave in Styles C, A and B, respectively; (5) grazing style and weight gain were not clearly related; (6) the cows that tended to lead, be independent or follow less, tended to get out of their paddocks. The observations suggested (1) that the leader-follower-independent relationship, although modified in each season, did not vary fundamentally, (2) that the active movement of high ranking animals and the independent movement of low ranking animals governed the voluntary formation in grazing, and (3) that as grazing cattle that behaved in a single group and did not escape from their paddock were much easier to manage, the grazing style that expressed these characteristics was one of the significant indices for management of grazing cattle.

Abstract: Most of the experimental observations on facilitated transport have been done with millipore filters, and all the theoretical studies have assumed homogeneous spatial properties. In striated muscle there exist membranes that may impede the diffusion of the carrier myoglobin. In this paper a theoretical study is undertaken to analyze the transport in the presence of membranes in the diffusion path. For the numerical computations physiologically relevant values of the parameters were chosen. The numerical results indicate that the presence of membranes tends to decrease the facilitation. For the nonlinear chemical kinetics of the reaction of oxygen with the carrier, this decrement also depends on the location of the membranes. At the higher oxygen concentration side of each membrane the flow of combined oxygen is transferred to the flow of dissolved oxygen. The reverse process occurs at the lower concentration side. Jump discontinuities of the concentration of the oxygen-carrier compound at each membrane are associated with these transfers. The decrement of facilitation is due to the cumulative effect of these jump discontinuities.