Linear mixed-effects model estimates of change in telomere length (CTL) during the nestling period in relation to mass gain, brood size, and sibling order.

<p>Linear mixed-effects model estimates of change in telomere length (CTL) during the nestling period in relation to mass gain, brood size, and sibling order.</p

Relationship between mass gain and change in telomere length during the nestling period.

<p>The red circles represent singleton chicks. The green triangles and blue squares represent older and younger siblings, respectively. The solid lines connect siblings. Dashed lines represent regression lines for singletons (red), older siblings (green), and younger siblings (blue), respectively.</p

Telomere length of chicks at hatching and fledging.

<p>The red circles and boxes represent single chicks. The green triangles and boxes and blue squares and boxes represent older and younger siblings, respectively. In the scatter plot, the line between a triangle and a square connects siblings from the same nest. The dotted line represents equality of the telomere lengths: in which chicks over the line experienced telomere lengthening from hatching to fledging, whereas chicks below the line experienced telomere attrition. The siblings had shorter telomere length at hatching and fledging and experienced more drastic telomere attrition than singletons during the nestling period.</p

Linear mixed-effects model estimates of initial telomere length (ITL) in relation to brood size and sibling order.

<p>Linear mixed-effects model estimates of initial telomere length (ITL) in relation to brood size and sibling order.</p

GPS trajectory of an adult <i>Calonectris leucomelas</i> breeding on Sangan Island.

<p>The bold lines represent the 15 selected flight sections (F1–F15), while the gray lines represent other flying trajectories. The arrows indicate the entire observed flight direction GPS coordinates when the bird appeared to be on the sea surface are not displayed, and the two flights are connected by the thin line.</p

Example 2: homeward flights.

<p>(A) GPS trajectories of F14 and F15 (bold lines), 5 examples of simulated trajectories of each selected model (thin lines), and 100 examples of final locations of 1000 simulated trajectories produced by each selected model (green: F14, red: F15, throughout). The gray lines indicate 5 examples produced from the model that were not selected for F15 (setting the island as the focal point). The inset enlarges the takeoff section. (B, C) Heading distribution; the observed heading distribution (─•─), and mean (bold line) and 95% confidence envelopes (thin lines). (D) The red thin, red bold, thin, and dotted lines represent the regression curves, modes, medians, and 25% and 75% quartiles of the selected model for F15, respectively. Dots are points from the scatter diagram indicating the direction of heading (Θ<i>_t</i>_–1, Θ<i>_t</i>). The four rotated curves indicate the density functions of the Kato–Jones distributions for θ<i>_t</i> when θ<i>_t</i>_–1 is π/4, π/2, 3π/4, and π. (E) A scatter diagram showing the relationship between the direction of heading and observed speed (<i>T</i> = 1) and the expected speed when <i>V_t</i>_–1 = {the mean over each flight section} and Θ<i>_t</i> – Θ<i>_t</i>₋₁ = 0.</p

Examples of trajectories simulated by the movement model.

<p>(A) Examples of the transformation θ<i>_t</i> = <i>M</i>(θ<i>_t</i>_–1; α, <i>w</i>) (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050309#pone.0050309.e009" target="_blank">equation (5</a>), α = 0). (B) Examples of the probability density functions of the von Mises distribution (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050309#pone.0050309.e017" target="_blank">equation (7</a>), μ = 0). (C) Examples of trajectories produced by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050309#pone.0050309.e007" target="_blank">equation (3</a>) using the heading model (4) with the transformation in (A) and the von Mises distribution in (B). (D) An example of trajectory produced by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050309#pone.0050309.e007" target="_blank">equation (3</a>) using the heading model (12). In (C) and (D), speeds were fixed at 1, the grid unit is 10, and the first 50 steps are shown. The same random samples from the von Mises distribution of κ = 6 were used for the four red trajectories.</p

Distributions of the maximum likelihood estimates.

<p>The horizontal axes indicate the classes of each parameter, and the vertical axes show the frequencies from 200 simulations. Shaded: F14, white: F15. The arrows indicate the true parameter values.</p

Example 3: searching flights.

<p>(A, C) Observed GPS trajectory of F7 (A) and F10 (C). The bold lines are observed trajectories and the thin lines are five examples of simulated trajectories for each selected model. The insets enlarge each takeoff section. (B, D) The thin, bold, dashed, and dotted lines represent the regression curves, modes, medians, and 25% and 75% quartiles of each selected model, respectively. The dots represent points from scatter diagrams between Θ<i>_t</i>_–1 and Θ<i>_t</i> for every 4 s (B) and 3 s (D). The four rotated curves are the density functions of the Kato–Jones distributions for θ<i>_t</i> when θ<i>_t</i>_–1 is −π/3, 0, π/3, and 2π/3 (B) and 0, π/3, 2π/3, and π (D).</p

Example 1: outward flight.

<p>(A) Observed GPS trajectory of F2 (bold line, the final location is indicated by the large gray circle), five examples of simulated trajectories (thin lines), 100 examples of the final locations (dots) of 1000 simulated trajectories produced by the selected model. (B) Black dots: Points from the scatter diagram showing the relationship between speed and direction of heading. White dots: Predicted speeds by the selected model from (Θ<i>_t</i>, <i>V_t</i>_–1, cos(Θ<i>_t</i> – Θ<i>_t</i>_–1)) plotted on Θ<i>_t</i>. Bold line: The expected speed as a function of the direction of heading when the previous speed was fixed as the mean over the flight section and angular velocity was 0. (C) The heading distribution: Observed trajectory (─•─), and mean (bold line) and 95% confidence envelopes (thin lines) derived from 1000 simulated trajectories.</p