Sampling design of the Long Term Monitoring Program showing the hierarchical levels of observation for the Cooktown-Lizard Island sub-region, one of six sub-regions of Australia's Great Barrier Reef.

<p>The sub-region is divided into three shelf-positions or habitats (inner reef (red arrows), mid-shelf reef (orange arrows), and outer reef (green arrows)). Each habitat is sampled on three sites (green dots) in each of two or three reefs. We highlight three sites at Carter reef from the outer reef habitat. Modified from original satellite images © Landsat and MODIS satellite imagery courtesy of NASA Goddard Space Flight Center and US Geological Survey.</p

Estimation of the uncertainty in the three hierarchical stages of the model.

<p>The measurement error <i>σ_ε</i> corresponds to the uncertainty at the data stage, and all other variance components <i>σ</i> account for uncertainty in the process model, decomposed into the variability in trend (intercept and slope) of coral cover at the three spatial scales of habitat, reefs and sites.</p

Observed (dots) and fitted (curves) <i>Acropora</i> dynamics and associated parameter estimates and uncertainties.

<p>Coral dynamics are modelled at the three spatial scales within the sub-region of Cooktown-Lizard Island; with plotted lines for: habitats (top); reefs (middle); and sites (bottom). Shaded areas encompass 95% posterior predictive intervals around estimated coral trajectories and 95% credible intervals around model parameters. Top-right inserts on plots illustrate the linear and non-linear components of coral trajectories extracted from equations for <i>f_h</i>, <i>f_r</i> and <i>f_i</i>. Top-left inserts illustrate posterior distributions of linear parameters (from the top to the bottom, plotted lines are for: <i>θ₀</i> and <i>θ₁</i>, <i>δ₀</i> and <i>δ₁</i> respectively; refer to Fig. 2, see equations in main text). Intercept terms were indexed by 0 and slope terms by 1 and shown with their 95% credible interval. Thin black lines on reef- and habitat-scale plots (mid- and top-line) show the fitted dynamics of nested individual sites. Note different y-axis scales in inserted graphs. Estimates of coral cover trajectories are illustrated at the three sites at Carter Reef from the outer reef habitat depicted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0110968#pone-0110968-g001" target="_blank">Figure 1</a>.</p

Directed Acyclic Graph showing how <i>Acropora</i> cover <i>y_ij</i> at a site <i>i</i> and time <i>j</i> is fitted in three stages.

<p>Here, the transformed data <i>y_ij</i> are modelled using a normal distribution with an expected value <i>µ_ij</i> and variance σ_ε. The expected value <i>µ_ij</i> is a function of four spatial scales (sub-region <i>f_s</i>, habitat <i>f_h</i>, reef <i>f_r</i>, and site <i>f_i</i>). Linear trends at sub-region and habitat scale are modelled using fixed effects (<i>β</i>, <i>γ</i>). At the site and reef scale, trend parameters (<i>θ</i>, <i>δ</i>) are considered as random. Trend parameters are denoted with the subscript 0 corresponding to the intercept and 1 corresponding to the slope. Random effects require specification of a variance component (<i>σ</i>), specified for each spatial scale of the model. Refer to the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0110968#s2" target="_blank">methods</a> section for equations.</p

Simulated expert assessments fitted to all four distributions.

<p>Each value of the best guess (<i>B</i> a sequence between 100 and 200 incremented by one; x-axis) was fitted to scaled Beta (blue solid line), lognormal (red dot), Normal (orange dashed) and mirror lognormal (green dash dot) distributions. For each value of <i>B</i>, the simulated value of the lower (<i>L</i>) and upper (<i>U</i>) bounds are 100 and 200, respectively. The y-axis is the encoded value of <i>X</i>, i.e. total <i>N</i> number of species. For each distribution, the middle line is the encoded mode, the lower line is the encoded value of <i>L</i>, and upper line is encoded value of <i>U</i> based on 80% level of sureness (<i>P</i> = 0.80).</p

(a) Skewness and (b) RMSE for each simulated best guess for all four distributions.

<p>For each simulated best guess value between 100 and 200 (x-axis), a) skewness (<i>γ</i>_<i>B</i>(0.5))and b) the RMSE is displayed on the y-axis from encoding the scaled Beta (blue solid) and Normal/lognormal (lognormal (red dot line), Normal (orange dashed) and mirror lognormal (green dash dot)) distributions. In a) the horizontal grey solid line denotes skewness at zero, ie. symmetric. The level of sureness <i>P</i> is 0.80, minimum is zero and maximum is 500.</p

The estimated total number of species for Malacostraca and the sub-taxa.

<p>All components of all experts were encoded using (a) scaled Beta distribution and (b) Normal/lognormal distributions. The solid line is the total number of species (if there were multiple experts, then this line represents the total number of species over both experts). The dash and the dash dot lines represent the total number of species for expert one and two, respectively.</p

The taxonomic hierarchy of Malacostraca.

<p>The number within a circle represents the number of experts elicited from in each taxon within the class.</p

Three examples of expert data from case study (class Malacostraca) and comparison of the fits between the scaled Beta and Normal/lognormal distributions.

<p>(a) an example of extreme positively skewed expert data, where the best guess equals the lower number; (b) symmetric expert data; and (c) left skewed expert data. The first row shows box plots of the expert data; the second row shows the fitted distributions from the scaled Beta distribution, and the last row shows the fitted distributions from (a) lognormal, (b) normal and (c) mirror lognormal distributions. For the box plots (first row), the outer two lines are the minimum and maximum (expert almost 100% sure the number of species is between these two values); the box represents the lower and upper number elicited; and purple dashed line is the best guess. Second and third row shows the fitted distributions, the solid black vertical lines are the encoded lower and upper, and purple dashed line is the encoded mode.</p