Abstract: Networks of coupled dynamical systems have been used to model biological oscillators Josephson junction arrays excitable media, neural networks spatial games11, genetic control networks12 and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation). The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

Abstract: To examine when and why animals break up fights between others in their group, I modelled whether ‘winner’ and ‘loser’ effects might be one element driving the evolution of intervention behaviour. I considered one particular type of intervention: when the intervener simply breaks up fights between two others, but does not favour either party in so doing. When victories at time T + 1 are more likely given a victory at time T (i.e. winner effects), intervention is often favoured. Intervention is favoured in these circumstances because the intervening party in essence stops others from ‘getting on a roll’ and climbing up any hierarchy that exists. However, when loser effects alone are at work (defeats at time T + 1 are more likely given a defeat at time T), breaking up fights between others is never selected. If both winner and loser effects are operating simultaneously, then the likelihood of intervention behaviour evolving is a function of the relative strength of these two effects. The greater the winner effect relative to the loser effect, the more likely intervention behaviour is to evolve.

Abstract: Plasma cortisol is largely bound to corticosteroid-binding globulin (CBG), which regulates its bioavailability by restricting exit from capillaries. Levels of CBG may be altered by several factors including stress and this can influence the amount of cortisol reaching cells. This study investigated the effect of social instability on plasma concentrations of CBG, total and free (not protein bound) cortisol in horses. Horses new to our research herd ('newcomers') were confined in a small yard with four dominant resident horses for 3-4 h daily for 3-4 (n = 5) or 9-14 (n = 3) days. Jugular blood was collected in the mornings from newcomers before the period of stress began ('pre-stress'), and then before each day's stress. Residents were bled before stress on the first and thirteenth day. Residents always behaved aggressively towards newcomers. By the end of the stress period, all newcomers were subordinate to residents. In newcomers (n = 8) after 3-4 days of social stress, CBG binding capacity had fallen (P = 0.0025), while free cortisol concentrations had risen (P = 0.0016) from pre-stress values. In contrast, total cortisol did not change. In residents, CBG had decreased slightly but significantly (P = 0.0162) after 12 days of stress. Residents and newcomers did not differ in pre-stress CBG binding capacity, total or free cortisol concentrations. However, by the second week of stress, CBG binding capacity was lower (P = 0.015) and free cortisol higher (P = 0.030) in newcomers (n = 3) than in residents. Total cortisol did not differ between the groups. In conclusion social stress clearly affected the adrenal axis of subordinate newcomer horses, lowering the binding capacity of CBG and raising free cortisol concentrations. However, no effect of stress could be detected when only total cortisol was measured. Therefore, to assess adrenal axis status accurately in horses, it is essential to monitor the binding capacity of CBG and free cortisol concentrations in addition to total cortisol levels.