Fraction of links reproduced correctly for each species.

<p>(a) Number of prey versus <i>f_R</i>, the expected fraction of prey links reproduced correctly and (b) Number of predators versus <i>f_C</i>, the expected fraction of predator links reproduced correctly.</p

MLE parameter Spearman rank correlations and p values.

<p>Entries marked with * have significant correlation (p<0.001) while all other entries have <i>p</i>>0.05 when corrected using false discovery rate control (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012092#pone.0012092-Verhoeven1" target="_blank">[36]</a>).</p

Relationships between maximum likelihood parameters.

<p>(a) Feeding range <i>r_i</i> and (b) centre of feeding range <i>c_i</i> versus niche position <i>n_i</i> and (c) <i>r_i</i> versus <i>c_i</i> for the MLE parameter set of the probabilistic niche model.</p

Appendix A. A comparison of formulas for the estimators of species richness.

A comparison of formulas for the estimators of species richness

Probabilistic niche model results for the Benguela food web.

<p>Feeding links in the empirical data set and feeding probabilities in the probabilistic niche model for the maximum likelihood estimate (MLE) parameter set. On the x-axis, predators are ordered by their estimated (MLE) <i>c_i</i> values; on the y-axis, prey are ordered by their estimated (MLE) <i>n_i</i> values. Model predictions, calculated at the MLE, are shown as the grey circles: the area of each circle is proportional to P(<i>n_j</i>, <i>r_i</i>, <i>c_i</i>), the probability that <i>i</i> eats <i>j</i>. Apparent missing grey circles simply correspond to very low values of P(<i>n_j</i>, <i>r_i</i>, <i>c_i</i>). Observations are shown in black: a black circle is shown for those feeding relationships that have been observed. A match between large grey circles, and the black circles, implies a close match between model and data. Two predators with poorly predicted prey (expected fraction of prey links ≤0.65), <i>other pelagic</i> and <i>chub mackerel</i>, are labelled with arrows. Six prey species with poorly predicted predators (expected fraction of predator links ≤0.65) are labelled with arrows: from bottom to top, <i>gelatinous zooplankton</i>, <i>bacteria</i>, <i>macrozooplankton</i>, <i>snoek</i>, <i>sharks</i> and <i>kob</i>.</p

Food web data for the Sanak Islands, Alaska

The food web data compiled for this study, consisting of 339 quadrats, 39 transects, five sites, four locales, and one archipelago-wide network. The table provides a unique numeric identifier per food web (WebID), the spatial scale (WebScale; distinguishing quadrats [Q], transects [T], sites [S], locales [L], and the archipelago-scale [A]), a sample number (WebUnit; to identify individual transects [quadrat- and transect-scale samples], sites, or locales), and the Integrated Taxonomic Information System's (ITIS) Taxonomic Serial Number (TSN) and name of each predator and prey (PredTSN, PreyTSN, PredName, and PreyName, respectively). Taxa lacking entries in ITIS have a unique custom TSN prepended with “san”

The SNA metrics of the case sites used and compared in this study.

<p>The mean proportion of inter-cluster links is higher in Longyearbyen than in Surselva-Gotthard, indicating lower modularity in Longyearbyen, the same as the modularity values directly show.</p

The relationship between geographic distance and collaboration modules for both the Surselva-Gotthard region in the Alps and Longyearbyen in the Arctic.

<p>The data presented are the mean and standard deviation of geographic distances among all pairs of businesses within vs between each collaboration module identified in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0156028#pone.0156028.g001" target="_blank">Fig 1</a>.</p

The case studies’ geographic and political characteristics.

<p>The case studies’ geographic and political characteristics.</p

Disentangling intrinsic meadow ‘environmental quality’ from its spatial ‘network quality’ with respect to predicted <i>A</i><i>. canorus</i> breeding.

<p>a) Normalized Network Improved breeding probabilities ((Network Boosted probability – Environmental Model probability) / (1 – Environmental Model probability)) for each meadow as a function of the mean Environmental Model probability. Symbol colors represent field survey results (Breeding detected (red), Breeding not detected (blue), and Meadow not visited (black). b-c) Total Influence (G_<i>i</i>) of meadow deletion (the decrease in park-wide breeding probability summed across all meadows after deleting that meadow from the network) as a function of the Environmental Model and the Network-Boosted GLM probabilities. Horizontal dotted lines indicate the 90^th percentile of meadow deletion impact, and solid red symbols are the known breeding meadows within that 90^th percentile. Vertical dotted lines in all panels represent the threshold probability that maximizes both true positives and true negatives predicted by the model.</p