Figure 1.
Diagram of original and probabilistic niche models.
Diagram of the original niche model, in which species i consumes all species within the range ri, and the probabilistic niche model, in which the probability that species i consumes species j is defined by the probability P(nj, ri, ci).
Figure 2.
Probabilistic niche model results for the Benguela food web.
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) ci values; on the y-axis, prey are ordered by their estimated (MLE) ni values. Model predictions, calculated at the MLE, are shown as the grey circles: the area of each circle is proportional to P(nj, ri, ci), the probability that i eats j. Apparent missing grey circles simply correspond to very low values of P(nj, ri, ci). 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), other pelagic and chub mackerel, 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, gelatinous zooplankton, bacteria, macrozooplankton, snoek, sharks and kob.
Table 1.
Comparative performance of models.
Figure 3.
Fraction of links reproduced correctly for each species.
(a) Number of prey versus fR, the expected fraction of prey links reproduced correctly and (b) Number of predators versus fC, the expected fraction of predator links reproduced correctly.
Figure 4.
Relationships between maximum likelihood parameters.
(a) Feeding range ri and (b) centre of feeding range ci versus niche position ni and (c) ri versus ci for the MLE parameter set of the probabilistic niche model.
Table 2.
MLE parameter Spearman rank correlations and p values.
Figure 5.
Relationships between maximum likelihood parameters and body size.
(a) Niche position ni (b) feeding range ri, and (c) centre of feeding range ci versus log(body mass) for the for the MLE parameter set of the probabilistic niche model.