The Probabilistic Niche Model Reveals the Niche Structure and Role of Body Size in a Complex Food Web

The niche model has been widely used to model the structure of complex food webs, and yet the ecological meaning of the single niche dimension has not been explored. In the niche model, each species has three traits, niche position, diet position and feeding range. Here, a new probabilistic niche model, which allows the maximum likelihood set of trait values to be estimated for each species, is applied to the food web of the Benguela fishery. We also developed the allometric niche model, in which body size is used as the niche dimension. About 80% of the links in the empirical data are predicted by the probabilistic niche model, a significant improvement over recent models. As in the niche model, species are uniformly distributed on the niche axis. Feeding ranges are exponentially distributed, but diet positions are not uniformly distributed below the predator. Species traits are strongly correlated with body size, but the allometric niche model performs significantly worse than the probabilistic niche model. The best-fit parameter set provides a significantly better model of the structure of the Benguela food web than was previously available. The methodology allows the identification of a number of taxa that stand out as outliers either in the model's poor performance at predicting their predators or prey or in their parameter values. While important, body size alone does not explain the structure of the one-dimensional niche

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

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

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

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