Sequential model runs using a first-order auto-correlation structure, and corresponding difference in AIC values.

<p>The P-value of the term removed from each model is given, and the best model is highlighted in <b>bold</b>.</p

Actogram representative of fish activity (acceleration) across diel and tidal periods (a; data are for fish 3 in Table 1, between the dates 20^th June 2011 and 26^th June 2011), and frequency histogram of acceleration values measured in the study (b).

<p>Tidal height (a; secondary <i>y-</i>axis) is represented by the solid black line, and grey shading indicates night and white shading indicates day.</p

Optimisation of the autocorrelation function, showing the auto-regressive (AR, <i>φ</i>_n) and moving-average (MA, <i>θ</i>_n) correlation parameters for models of increasing order.

<p>The AIC for each model was used to select the model which best described the error structure (shown in <b>bold</b>). As increasing complexity failed to produce models with a lower AIC, models with more than 2 auto-regressive and 1 moving average parameters were not run <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080962#pone.0080962-Zuur1" target="_blank">[39]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080962#pone.0080962-Schabenberger1" target="_blank">[44]</a>.</p

Tagging information for yellowfin bream (<i>Acanthopagrus australis</i>) tracked in the Georges River, showing the numbers of days on which data were recorded during the study period, the temporal window within which these data were recorded (e.g. for Fish 1, data were recorded on 89 days within a window of 100 d), and the number of activity and depth measurements from each tag recorded by the receivers shown in Figure 1.

<p>Tagging information for yellowfin bream (<i>Acanthopagrus australis</i>) tracked in the Georges River, showing the numbers of days on which data were recorded during the study period, the temporal window within which these data were recorded (e.g. for Fish 1, data were recorded on 89 days within a window of 100 d), and the number of activity and depth measurements from each tag recorded by the receivers shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080962#pone-0080962-g001" target="_blank">Figure 1</a>.</p

Parameter summaries and associated statistics for best non-ARMA model and the best ARMA model presented in Table 2, fitted to the linear deviation of <i>Argyrosomus japonicus</i> from its average location along the length of the river (<i>Dev</i>).

<p>Parameter summaries and associated statistics for best non-ARMA model and the best ARMA model presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095680#pone-0095680-t002" target="_blank">Table 2</a>, fitted to the linear deviation of <i>Argyrosomus japonicus</i> from its average location along the length of the river (<i>Dev</i>).</p

Tagging information for mulloway tracked in the Shoalhaven River.

1<p>Sex is male (M), female (F), or juvenile (J). Sex could not be conclusively identified for all samples (U).</p>2<p> refers to the model distance-to-sea value determined from the kernel density distributions for each fish (see Methods).</p>3<p>Linear distance (km) along the estuary encompassed by the 50^th and 90^th percentile of the kernel density distribution.</p

Tagging information for mulloway tracked in the Shoalhaven River.

1<p>Sex is male (M), female (F), or juvenile (J). Sex could not be conclusively identified for all samples (U).</p>2<p> refers to the model distance-to-sea value determined from the kernel density distributions for each fish (see Methods).</p>3<p>Linear distance (km) along the estuary encompassed by the 50^th and 90^th percentile of the kernel density distribution.</p

Parameter summaries and associated statistics for best non-ARMA model and the best ARMA model presented in Table 4, fitted to the depth of tagged <i>Argyrosomus japonicus</i> (Table 1).

<p>Parameter summaries and associated statistics for best non-ARMA model and the best ARMA model presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095680#pone-0095680-t004" target="_blank">Table 4</a>, fitted to the depth of tagged <i>Argyrosomus japonicus</i> (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095680#pone-0095680-t001" target="_blank">Table 1</a>).</p

Mean daily position relative to estuary mouth (km), temperature (°C) and conductivity (ms µs⁻¹, primary <i>y</i>-axis, black line, dashed line and light grey line respectively), and mean daily inflow measured at the Grassy Gully gauging station (secondary <i>y</i>-axis, dark grey line) during the study period for Fish 2 (a) and Fish 11 (b).

<p>Mean daily position relative to estuary mouth (km), temperature (°C) and conductivity (ms µs⁻¹, primary <i>y</i>-axis, black line, dashed line and light grey line respectively), and mean daily inflow measured at the Grassy Gully gauging station (secondary <i>y</i>-axis, dark grey line) during the study period for Fish 2 (a) and Fish 11 (b).</p

Histogram of measurements for average daily fish distribution along the length of the Shoalhaven River.

<p>Data distribution is multimodal with peaks that roughly correspond to for each fish (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095680#pone-0095680-t001" target="_blank">Table 1</a>).</p