put vertically in front of each feeding plate to prevent fish at the deep end from seeing food on the plate at the shallow end. Prior to the experiments, we ran three one-hour-long training sessions, to acclimate the fish and train them to expect food at the feeding site. At the beginning of each session, a single medium-sized bloodworm was placed on the feeding plate, and fish were introduced individually at the deep end of each lane. After 30 min, an observer checked the food on the feeding plate, and a second bloodworm was placed on the feeding plate if the first had been consumed. At the end of each session, fish were returned to their individual holding tanks. For fish that failed to consume all the allotted food, the remainder was placed on the feeding plate in the holding tanks to ensure equal feeding among individuals. Assessment of Individual Temperament After the training sessions, we ran two one-hour-long sessions during which no food was provided in the experimental tank, in order to assess the temperament of each fish. Following a 5-minute acclimation, fish behaviour was recorded from the top of the tank with a digital video camera (Sony SCR-35E, Sony, Japan). After recording, individuals were returned to their holding tanks and fed one bloodworm daily. Fish that failed to consume any food during the training sessions were excluded from the temperament assessments. While watching the videos (speeded up at 46 normal speed), we recorded the times at which each individual left or returned to cover using a custom-made data logger. The time series of location transitions for each individual (from cover to exposed area, and vice-versa) was modelled as a continuous-time Markov chain with two states, either under cover or exposed (using msm v0.9.7 by Christopher Jackson in R2.11.1 by the R Core Development Team, as used in [11,12]). Using this approach, we can estimate the transition intensities between the two locations, providing a measure of the tendency of a fish to leave and return cover. Individual temperament was defined as the ratio of the transition intensity for leaving cover to the transition intensity for returning to cover (higher temperament scores indicate ‘‘bolder’’ behaviour). This measure has been used in other studies as a reliable indicator of temperament [11,13]. Collective Movements in Pairs After one additional training session, during which fish were again rewarded with food at the exposed end of the experimental tank, 40 individuals were haphazardly paired (n = 20 pairs). The movements of each pair were then video-recorded in the experimental tank twice with an opaque partition and twice with a transparent partition (through which the fish could observe each other and interact) for one hour each over four days. Individuals were returned to their individual holding tanks after each Figure 1. Diagrammatic represenation of the experimental set- up. doi:10.1371/journal.pone.0036606.g001 Initiative, Personality and Leadership in Pairs experiment. No food was provided during this period of observation, so as to eliminate any influence of changes in physiological state on an individual’s social role as leader or follower [8,14]. The timings of leaving and returning to cover were again recorded for each individual from the videos. For the experiments with an opaque partition, locations of individuals were categorized as either under cover or exposed, and individual temperament scores were calculated from the transition intensities between the two states in a continuous-time Markov model as described above. The temperament scores from this experiment were used for the later analyses, as they were highly correlated with those estimated during the previous week (r = 0.61, n = 40, P,0.001). In the analysis of Harcourt et al. [9], for the experiment with a transparent partition, the location of each individual at any given moment was categorised as either covered or exposed, yielding four possible states for a pair: bold fish exposed and shy fish covered, bold fish covered and shy fish exposed, both exposed and both covered. The transition intensities estimated for this model provided biologically meaningful quantities that allowed, for example, to compare the tendency of the bold fish to leave cover alone when compared to the shy fish (a measure of leadership), or the tendency of either fish to join their partner out of cover (a measure of followership). Here, we refine this characterisation of pair state to distinguish between distinct states based not only on the current location of each fish (covered or exposed) but also on the identity of the individual that initiated the most recent trip out of cover (bold fish or shy fish), and whether or not it has yet been joined by its partner (i.e. it was successful at leading). The state of a pair is thus defined by four binary variables: the location of the bold fish and the location of the shy fish (together referred to as ‘location variables’), and the identity of the most recent initiator and whether its partner has yet joined it in leaving cover (together referred to as ‘status variables’). Since not all combinations of these variables are possible, there are only 12 feasible states (numbered 1 to 12), illustrated in Figure 2. The rates (transition intensities) of all possible transitions among these 12 states were estimated by fitting the continuous-time Markov model shown in the figure. In the text, to refer to a given transition intensity, we use the notation qi,j, where i represents the old state and j the new state (thus, q1,5 is the transition intensity from state 1 to state 5). These rates provide a tendency of each individual’s movement from one state to another in response to both the position of its partner and interactions (i.e. who initiated the most recent trip and whether or not it has yet been joined by its partner). Confidence intervals for transitions intensities and for their ratios (used to compare the magnitude of different transitions) were estimated by bootstrapping (1000 runs). To test whether the status variables affected the response of a fish to its partner, we fitted a simplified model in which transition intensities were constrained such that only the two location variables mattered (i.e. a model identical to that used by Harcourt et al. [9], see Figure S1). The full model (including all location and status variables) was compared to the simplified model using a log- likelihood ratio test. To test whether a leader held its status within a trip, we considered an alternative, ‘one-step memory’ model in which we distinguished among eight distinct pair states, based on the current values of the location variables and on the values they took prior to the most recent state transition (see Figure S1). In this alternative model, the effects of leading or following are constrained to persist over no more than one change in location. Since the full model and the ‘one-step memory’ model are not nested, we compared the fit of these two models using the Akaike Information Criterion (AIC). To investigate in more detail how the effects of social role interact with an individual’s temperament, the PLoS ONE | www.plosone.org 2 May 2012 | Volume 7 | Issue 5 | e36606