Initiative, Personality and Leadership in Pairs Figure 2. Transition intensities from the Markov Chain model. Transition intensities (best estimates and 95% CI) for leaving and returning to cover, estimated for the bold (red) and shy fish (blue) depending on which individual initiated the trip out of cover and whether it was successful in recruiting its partner. The width of each arrow is proportional to the magnitude of the transition intensity. For each state, the area under cover is shaded, while the exposed area is in white; each state is identified with a number at the top-right corner of the ‘‘tank’’. doi:10.1371/journal.pone.0036606.g002 temperament scores of each bold and shy fish when in isolation were fitted as covariates of the full model. The log-linear effects of covariates were estimated on each transition (b for bold fish, s for shy fish) to investigate how the temperament scores of each individual influenced the transition intensities. To refer to the covariate for a particular transition, we use subscripts with the same convention adopted for q (for example, b1,5 gives the effect of the temperament score of the bold fish on the transition from state 1 to state 5). Results Temperament and Coordination in Foraging Pairs When they could observe one another’s movements through a transparent partition, each fish made 53.963.7 (mean 6 SE) trips out of and back into cover per hour. The Markov model showed that the bold fish in a pair generally had a greater propensity to leave cover than did the shy fish [(q1,5, q2,5, q3,5, q4,5).(q1,9, q2,9, q3,9, q4,9), P,0.001, except q2,5 = q2,9, P = 0.258, q2,5 = q3,9, P = 0.199, q2,5,q4,9, P,0.001, qi,j denotes the transition intensity from state i to state j, see Figure 2] and a lesser propensity to return than did the shy fish [(q6,7, q10,11),(q6,8, q10,12), P,0.001]. Focusing on the influence of the location variables, however, both the bold and the shy fish in a pair were more likely to leave cover when their partner was already out than when it was under cover [bold fish (q7,6, q9,10).(q1,5, q2,5, q3,5, q4,5), P#0.020; shy fish (q5,6, q8,6, q11,10).(q1,9, q2,9, q3,9, q4,9), P,0.001]. Also, both fish were less likely to return to cover when their partner was still out than when their partner was under cover [bold fish (q6,7, q10,12),(q5,1, q8,3, q11,4) P,0.001; shy fish (q6,8, q10,11),(q7,3, q9,2, q12,4), P,0.001]. Evidence for Social Roles within a Trip The full model, distinguishing between social roles based on the memory of which fish led out of cover, gave a significant improvement in fit compared to the constrained, ‘memory-free’ version (x216 = 731.7, P,0.001; DAIC = 699.7). Also, the full model yielded a better fit than a partially constrained model in which transition intensities depend only on the identity of the most recent initiator, but are independent of whether it has yet been joined by its partner (x28 = 261.8, P,0.001; DAIC = 245.8). The full model showed that both members of a pair displayed greater reluctance to remain out of cover when it was their partner who first led the way, but were more resolute when they themselves were the original initiator (for the bold fish: q10,12.q6,7, P,0.001; for the shy fish: q6,8.q10,11, P,0.001). Moreover, individuals were more likely to accede to the termination of a joint trip by their partners and follow them back to cover when it was the partner who had initiated the trip (for bold: q11,4.q8,3, P = 0.002; for shy: q7,3.q12,4, P,0.001). The full model, which allows for longer-term memory of social roles, also yielded a significantly better fit than the one-step memory alternative, in which the effects of leading or following are constrained to persist over no more than one change in location (DAIC = 251.9). Exchange of Roles between Trips Moving on from within-trip effects to between-trip effects, we see that both members of a pair were more likely to initiate a new trip out of cover if they had initiated the previous trip and successfully recruited their partner as a follower, than if it was their partner who had initiated the previous joint trip (bold fish q3,5.q4,5, P,0.001; shy fish q4,9.q3,9, P,0.001). Consequently, if we consider the sequence of initiation events (in which one individual first leaves cover after both fish have returned to safety), we see that individuals tend to have ‘‘runs’’ of consecutive PLoS ONE | www.plosone.org 3 May 2012 | Volume 7 | Issue 5 | e36606