bat (M. lucifugus)(Figure 2), integration of the tail-membrane and wings varied across the first three wing-beat cycles and in this case, most oscillation offsets occurred in wing-beat cycles two and three. For the fringed myotis (M. thysanodes), similar degrees of oscillation offset occurred across all five wing-beat cycles with similar intensity (Figure 3). There were also two main ways in which bats produced oscillation offsets between wings and the tail-membrane. Most commonly, lagging the downstroke of the tail-membrane relative to the wings was achieved by what we term ‘stroke-initiation- offsets’ wherein the tail-membrane was held at its top position as the bat initiated its wing downstrokes (Figure 2). However, once the tail-membrane downstroke was initiated, the cycle speed was very similar to that of the wings. A second method involved what we term ‘stroke-tempo-offsets’ wherein the initiation of the downstroke of the wings and tail-membrane were synchronized, however, the tail-membrane and wings were cycling at different tempos (Figure 3). Performance at takeoff and very slow flight speeds Wing performance in bats at very slow flight speeds differs from performance at higher flight speeds [18,19] and analysis of trailing vortices indicate that the lift and thrust generated during the wing’s upstroke are minimal at very slow flight speeds (1–3 m s21) [17]. Although we currently do not have data on the amount of thrust produced by the tail-membrane during horizontal takeoffs at very slow flight speeds (,1 m s21), the offset oscillations produced by delayed initiation or slower relative downstroke speed and the high level of tail-membrane fanning effort (Video S4) would logically indicate that the tail-membrane is providing an important contribution to takeoff acceleration. Analysis of digitized tracings (Figure 4) of the left wingtip path and tail-tip path for little brown myotis (Myotis lucifugus) showed variation of stroke planes as related to takeoff trajectories. An individual with a relatively steep takeoff trajectory for this species A Hind-Wing in Bats (Figure 4A, 34u to the horizontal) displayed a shallow wing stroke plane relative to the body plane (b = +62.5u) and the tail- membrane stroke plane exhibited a relatively moderate degree of fanning motion (dorsal tail-membrane extension, h = 60u, ventral tail-membrane flexion, h9 = 249u with 109u total sweep degrees). An intermediate takeoff angle of 24u to the horizontal (Figure 4B) by another individual produced a wing stroke plane (b) of 62u, and a degree of dorsal tail-membrane extension and ventral flexion angles (h) of +65.3u and (h9) of 257u respectively, resulting in 122.5u of total tail-membrane fanning motion. An individual with a takeoff angle horizontal to the platform (Figure 4C, 0u) displayed a wing stroke plane angle (b) of 68u and the least degree of tail-membrane fanning motion (h = +41u , h9 = 231u, total tail- membrane sweep was 72u). The average extent of dorsal tail-membrane extension mea- sured as degrees above the horizontal axis of the body in 14 male little brown myotis (M. lucifugus) was 48.5u (range 32.7u–49.2u, SD = 8.3u). Extent of dorsal tail-membrane motion above the body-axis as logN-logN plotted against body mass (g) showed a significantly positive correlation (Figure 5, R2 = 0.33, R = 0.59, P = 0.02). Total degrees of arc regarding tail-membrane fanning motions in M. lucifugus ranged from 72.5u to 134.9u and these data did not significantly correlate with body mass (R2 = 0.13, R = 0.368, P = 0.30). Thus it appears that dorsal extension of the tail-membrane is a primary way in which vespertilionid bats increase thrust support during horizontal platform takeoffs. There was also a change in the relationship between upstroke versus downstroke oscillation offsets between wings and tail- membrane motions in relation to body mass in M. lucifugus (Figure 6A). At lower body mass, upstroke offsets between the wings and tail-membrane were greater than observed in downstroke offsets. However, when mass was greater than 6.8 g, downstroke offsets became more pronounced than upstroke offsets. Regression analysis (Figure 6B) showed the switchover in offset timings between upstrokes and downstrokes of the wings and Figure 3. Stroke tempo offsets. Stroke tempo offsets between left wing and tail-membrane as illustrated by plots of the digitized motions of the wrist (blue line) and tail tip (red line) for the fringed myotis (Myotis thysanodes) across wingbeat cycles one through five. In this example, the individual showed little to no stroke intiation offsets, but instead used differential flap rates between the wings and tail-membrane to afford asynchrony of motion. The angles of the red and the blue arrows indicate oscillation offsets via stroke tempo. doi:10.1371/journal.pone.0032074.g003 PLoS ONE | www.plosone.org 4 February 2012 | Volume 7 | Issue 2 | e32074