Monte Carlo empirical square coefficient of error and corresponding mean predictors.

<p>(A, B, C) Monte Carlo results corresponding to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.g001" target="_blank">Fig 1A</a>, for fundamental box side lengths <i>T</i> = 200,250,300 pixels, respectively, and for different quadrat side lengths in each case. The equivalent mean sample sizes are also shown. The empirical square coefficient of error (= error variance divided by <i>N</i>²) is represented in blue, whereas the corresponding mean predictors obtained with Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.e009" target="_blank">(2)</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.e016" target="_blank">(3)</a>, are represented in red and black colour, respectively. Grey dots represent all the replicated values of <math><mrow><msubsup>ceCav<mn>2</mn></msubsup><mo>(</mo><mi>N</mi><mo>^</mo><mo>)</mo></mrow></math>. The dark grey dots lie between the 2.5% and 97.5% quantiles. The broken horizontal lines correspond to 5% and 10% coefficients of error, respectively. (D, E, F) Analogous data for Fig 7b of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.ref013" target="_blank">13</a>]—here <i>T</i> = 120,150,180 pixels, respectively.</p

Quadrats used to estimate the total number of people in Fig 5.

<p>Magnified version of the 50 quadrats marked in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.g005" target="_blank">Fig 5</a>.</p

A practical protocol for systematic quadrat sampling.

<p>Aerial view of an emperor penguin colony on November 2nd, 2012. Photograph by Robin Cristofari, from an altitude of ca. 1,000 feet, Fig 3 of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.ref001" target="_blank">1</a>]. Picture size: 2359 × 2808 pixels. The adopted quadrat grid with <i>T</i> = 200, <i>t</i> = 30 pixels was superimposed uniformly at random with a tilting of 45° to reduce error variance, see text.</p

Empirical, Monte Carlo histograms of crowd number estimates.

<p>(A) Empirical distributions of the number estimator given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.e004" target="_blank">Eq (1)</a>, obtained for <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.g001" target="_blank">Fig 1A</a> from 1024 Monte Carlo superimpositions of quadrat grids of different sizes. The side length of the fundamental box was <i>T</i> = 250 pixels. As expected, the histogram means always coincide with the true crowd size because the estimator is unbiased. (B) Analogous data for Fig 7b of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.ref013" target="_blank">13</a>]. Here <i>T</i> = 150 pixels.</p

Systematic quadrat sampling and unbiased counting rule to estimate feature number in the plane.

<p>(A). Spectators in a football match (Bilbao, 1966), (original picture taken from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.ref014" target="_blank">14</a>]; with permission of the author). A square grid of quadrats was superimposed uniformly at random to estimate the total head number. The quadrat marked with a yellow arrowhead is magnified in (E). Size of the entire picture: 1796 × 1200 pixels. (B) Corresponding associated points—as used in our Monte Carlo automatic resampling—with the same grid superimposed on them (quadrat side length <i>t</i> = 50, fundamental box side length <i>T</i> = 250 pixels). (C) Forbidden line rule to remove edge effects in manual counting [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.ref011" target="_blank">11</a>]. The green particles are counted in the quadrat, the red ones are not because they hit the extended forbidden edge (in red). (D) Application of the forbidden line rule to each of the four quadrats shown, yields the total correct count of one particle. (E) With the latter rule, only arrowed heads are counted.</p

Individual quadrat counts and preliminary calculations corresponding to Fig 1B.

<p>Individual quadrat counts and preliminary calculations corresponding to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.g001" target="_blank">Fig 1B</a>. ‘o’ and ‘e’ refer to odd and even numbered quadrats, respectively, within the slices.</p><p>Individual quadrat counts and preliminary calculations corresponding to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141868#pone.0141868.g001" target="_blank">Fig 1B</a>.</p

Plot of the volume (a-f), circularity form factor (g-k), and thickness (l) for the twelve studied cases; regression equation, correlation significance, and regression lines that fits the data are displayed.

<p>Hemispheric correlation (right and left) are shown in top, for MRI study. Correlation between MRI and histological measurements are shown at bottom, for right hemisphere. GM: Grey matter; WM: White matter; A: Amygdala; Hp: Hippocampus; LV: Lateral ventricle; TL: Temporal lobe; Th: Thickness (entorhinal cortex).</p

Size descriptors plot of the piamater, white matter, amygdala, hippocampus and temporal horn of the lateral ventricle by age group (LT and GT), in both MRI and histological studies, and for both right and left hemispheres.

<p>Data are mean and standard deviation.</p

Study cases.

<p>Case indicates the anonymous ordinal number of autopsy. M, man; W, woman. Age’s group: LT (lower than), less or equal to 65 years; GT (greater than), 65 years.</p><p>* (asterisk): the two cases marked (with alcoholism) did not differ in results with respect to other cases, without significant changes in results.</p><p>Study cases.</p

Plot of the size descriptors for the piamater, white matter, amygdala, hippocampus and temporal horn of the lateral ventricle sorted by groups of age (LT, lower than 65 years, and GT, greater than 65 years, see text) in both MRI and histological studies, as well as for both right and left hemispheres.

<p>Data represent mean and standard deviation.</p