GP mean functions for one realisation of populations s1…s9.

<p>These can be considered the GP estimates of the intensity maps in the previous figure, inferred from the sparse transect data provided to the model.</p

Parameter estimates with alternative sampling designs.

<p>Mean and standard deviation (in parentheses) of GP parameter estimates from 100 simulated runs, for population s3 with different sampling strategies.</p><p>Parameter estimates with alternative sampling designs.</p

One realisation of Neyman-Scott processes for populations s1…s9.

<p>The Neyman-Scott parameters used to generate each population are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111522#pone-0111522-t001" target="_blank">Table 1</a>. 100 realisations of each population were randomly generated and used to test the GP estimator.</p

Covariance structure of GP models.

<p>The solid black line shows the mean covariance between quadrats on the true intensity map, plotted against separation (binned into unit intervals). The dotted grey lines show the standard deviation in the covariance. The solid red line shows the GP squared exponential function with the learnt hyperparameters.</p

Sensitivity of method to sample size.

<p>Summarised results of 100 runs of GP modelling of population s3, for 6 transect sample designs with varying numbers of evenly spaced transects. The error bars show one standard deviation from the mean estimate.</p

Results of run 1 for GP modelling of population s3, with various sampling designs.

<p>Left column: the actual population. Centre column: GP mean estimate of the intensity function with different sampling strategies. Sample locations are marked with a white x. Right column: Corresponding GP variance.</p

GP variance for one realisation of populations s1…s9.

<p>Note how the uncertainty increases from distance increases with distance from the vertical transects where measurements are taken.</p

Intensity per unit quadrat for one realisation of populations s1…s9.

<p>The point process is converted into the intensity map by dividing the survey into unit quadrats and counting the number of events lying within each quadrat.</p

Example survey transects showing different bottom types.

<p>The figures show the photo-realistic 3D mosaic and also the depth mapped bathymetry for each transect. The small red circles show the start and end points of the chain () that was laid out over the terrain. (A) shows a highly rugged patch (, ). It also shows the same patch from an oblique perspective. (B) shows a relatively flat patch (, ) and (C) shows a patch with medium relief (, ). There is also a zoomed in view of the start and end of the chain shown in (C).</p

Illustration showing systematic translation of virtual chain placement.

<p>The start and end points of the chain were moved from the original measured locations by 5 cm, 10 cm, 20 cm and 40 cm, at 12 different points spanning a full circle with increments. This results in a total of 49 virtual chains per transect, all with similar length and orientation. The figure shows the original measured chain positions (big red points in centre of circles), and three examples of the 48 additional translated virtual chains connecting the corresponding start and end points.</p