Ecological Archives E096-043-A1

Sophie Bestley, Ian D. Jonsen, Mark A. Hindell, Robert G. Harcourt, and Nicholas J. Gales. 2015. Taking animal tracking to new depths: synthesizing horizontal–vertical movement relationships for four marine predators. Ecology 96:417–427. http://dx.doi.org/10.1890/14-0469.1

Appendix A. Coefficient estimates (Table A1), example derivation of the "dive residual" (Fig. A1), and distribution plots showing how the dive variables alter between states (Fig. A2).

Table A1. Coefficient estimates for the relationships between dive variables and the probability of switching into "resident" movement state. Estimate values are given as the posterior mean, s.d. and median, along with the 2.5% and 97.5% credible limits (CL). Also shown is the proportion of posterior samples falling below (above) zero for positive (negative) median parameter estimates (i.e., %<0<). Where this is less than 5% and 10%, respectively, double [++ , -- ] and single [+ , - ] signs are given in the final "Summary" column. Note that a positive (negative) coefficient indicates a reduced (increased) switch probability from directed into resident state, hence are accorded minuses (pluses). Zeros indicate estimates straddled zero by more than 10 %. NC indicates non-convergence.

 Dive Species Batch Coefficient estimate variable Mean S.D. 2.5% CL Median 97.5% CL %<0< Summary Dive residual SES 1 1.52 0.52 0.49 1.53 2.53 0.0005 a -- SES 2 2.6 0.57 1.53 2.57 3.76 0 -- SES 3 1.72 0.75 0.21 1.74 3.15 0.01 -- SES 4 1.57 0.59 0.46 1.56 2.77 0.003 -- WED 1 0.67 0.3 0.08 0.65 1.31 0.014 -- WED 2 -0.67 0.44 -1.56 -0.65 0.17 0.0585 + WED 3 0.68 0.23 0.25 0.67 1.14 0.001 -- WED 4 0.88 0.46 0 0.88 1.79 0.0255 -- AFS 1 0.12 0.49 -0.86 0.14 1.05 0.4 0 CES 1 0.3 2.06 -3.06 0.04 4.9 0.495 0 CES 2 1.28 2.21 -3.58 1.41 5.3 0.252 0 CES 3 1.64 1.68 -1.35 1.58 5.2 0.169 0 Surface SES 1 -1.92 1.02 -3.9 -1.94 0.12 0.0305 ++ residual SES 2 -3.2 0.99 -5.12 -3.23 -1.26 0.0005 ++ SES 3 -1.7 0.87 -3.34 -1.74 0.14 0.0345 ++ SES 4 -1.99 1.14 -4.12 -2.03 0.31 0.0445 ++ WED 1 -0.9 0.41 -1.75 -0.9 -0.14 0.01 ++ WED 2 0.76 1.01 -1.11 0.7 2.77 0.216 0 WED 3 -1.06 0.31 -1.7 -1.05 -0.46 0 ++ WED 4 -1.24 0.60 -2.45 -1.25 -0.04 0.0225 ++ AFS 1 -0.72 0.51 -1.69 -0.73 0.26 0.0795 + Maximum SES 1 -0.23 0.29 -0.83 -0.22 0.32 0.215 0 depth SES 2 0.72 0.27 0.17 0.72 1.25 0.0075 -- SES 3 0.56 0.26 0.02 0.57 1.03 0.022 -- SES 4 0.23 0.31 -0.43 0.24 0.82 0.225 0 WED 1 -0.02 0.13 -0.28 -0.02 0.25 0.4275 0 WED 2 0.23 0.24 -0.23 0.23 0.71 0.1635 0 WED 3 0.26 0.11 0.04 0.26 0.49 0.01 -- WED 4 0.38 0.23 -0.04 0.37 0.85 0.0355 -- AFS 1 1.02 0.72 -0.21 0.96 2.73 0.0535 - CES 1 NC CES 2 1.89 1.82 -0.69 1.63 6.45 0.135 0 CES 3 0.12 0.37 -0.6 0.12 0.86 0.3655 0 Bottom time SES 1 -0.21 0.46 -1.05 -0.25 0.76 0.3085 0 SES 2 0.27 0.64 -0.95 0.25 1.53 0.3465 0 SES 3 -0.8 0.57 -1.92 -0.8 0.32 0.0795 + SES 4 -0.4 0.53 -1.36 -0.43 0.72 0.2055 0 WED 1 -0.76 0.35 -1.46 -0.75 -0.07 0.017 ++ WED 2 0.09 0.74 -1.23 0.05 1.67 0.473 0 WED 3 -0.27 0.28 -0.79 -0.26 0.28 0.1665 0 WED 4 0.16 0.44 -0.67 0.15 1.07 0.3575 0 Dive duration SES 1 0.22 0.25 -0.24 0.21 0.73 0.1925 0 SES 2 1.09 0.32 0.47 1.09 1.74 0.0005 -- SES 3 1.02 0.33 0.42 1 1.71 0.0005 -- SES 4 0.65 0.35 -0.01 0.64 1.38 0.0285 -- WED 1 0.16 0.23 -0.26 0.15 0.61 0.2425 0 WED 2 0.2 0.43 -0.61 0.2 1.08 0.311 0 WED 3 0.41 0.17 0.09 0.4 0.75 0.0035 -- WED 4 0.45 0.33 -0.23 0.45 1.06 0.085 - AFS 1 1.1 0.58 0.12 1.05 2.38 0.0145 -- CES 1 2.12 1.18 -0.35 2.14 4.36 0.0445 b CES 2 -1.06 1.48 -3.76 -1.17 1.89 0.2355 0 CES 3 0.54 0.6 -0.6 0.54 1.72 0.18 0

a Note that since the Bayesian framework is probabilistic, the result for SES in this case can be directly interpreted as a 100 - 0.05 = 99.95% probability of this coefficient being below zero (negative), hence a 99.95% probability this relationship is positive.

b Label-switching on the behavioral state indices occurred in this model run (see Appendix A), such that the estimated positive coefficient actually influences Pr[R|R] and therefore is not comparable with other results.

Fig. A1. Example showing derivation of the "dive residual" dive variable, from the relationship between dive depth and dive duration. The case shown is for Weddell seals (n = 18). A log-log relationship is fitted using a mixed-effect model allowing a random effect for individuals in both the slope (here depth) and intercept terms (see Methods for details). Positive (negative) "dive residuals" are shown in black (gray). The analogous derivation of "surface residual", from the relationship between dive duration and post-dive surface interval, is shown in Fig. 2 (main article) for the case of Antarctic fur seals.

Fig. A2. Distribution plots showing how the five dive variables alter between the two predicted movement states. Panel layout shows the species results by column (a) Southern elephant seals (SES, purple), (b) Weddell seals (WED, orange), (c) Antarctic Fur Seals (AFS, green) and (d) Crabeater seals (CES, red), with up to four SSM batch runs per species. The five dive variables are shown by row: dive residual, surface residual, maximum dive depth, bottom time and dive duration (see Methods for details). For each dive variable, within a batch the distributions within the directed and resident movement states are presented on the left-hand side (light grey) and right-hand side (dark gray), respectively. Data are presented as a traditional boxplot combined with a kernel density plot (R software package vioplot) and resampled to ensure equal representation across animals. Labels above give the relevant signs from the final "Summary" column in Table A1, excepting those batch runs (marked with an X) showing problematic diagnostics (see Appendix B) or non-convergence (NC).

Literature cited

Adler, D. 2005 vioplot: Violin plot. R package version 0.2. See http://wsopuppenkiste.wiso.uni-goettingen.de/~dadler.