1. Universal Patterns in Food Webs? Benjamin Good

2. What is the evidence? Paper by Camacho et al. claims to demonstrate some traits common to all food web networks Uses the niche model to make theoretical predictions and then compares predictions to data from 7 different food webs Perhaps an example of May’s warning against theoretical physicists in biology?

3. The Model “Niche Parameter” chosen by n i =random(0,1), i=1,…,S Species eat prey in a range given by r i =xn i where p(x) = b(1-x) (b-1), 0 < x < 1, and b=(S 2 /2L – 1) This range centered on c i =random(r i /2, n i ) Hence, a list of prey or a list of predators can be calculated for each species Sample Web

4. The Predictions In another paper, they used this model to derive expressions for P prey (k) and P pred (k) P prey (k) is the probability that a given species has k or more prey, P pred (k) is the probability that a species has k or more predators. Again note the place of publication…

5. Initial Results Using data from the St. Martin Island web, with an empirically measured value for z, the data fit the model quite well. No fitting parameters at all!

6. Taking the idea further… Instead of the distribution of number of prey, they use the “scaled number of prey” k/2z and the “scaled number of predators” m/2z and obtain: Now the same function works for all 7 food webs – and still without any fitting parameters!

7. … and further By pooling the data from all 7 webs, they construct a “master plot”: … again with no fit parameters

8. Haven’t seen a fit this good since… … especially when compared to the models we have been dealing with so far.

9. Other predictions… Amazingly, the same model predicts several other network characteristics quite well: number of links per species, r average distance, d clustering coefficient, C

10. Compared to older studies Rejects the scale-free hypothesis that had been established earlier Also rejects the small world hypothesis for food webs Hypothesizes a single functional form for various food web properties

11. Response to this article… A later study by Dunne, Williams, and Martinez extended the data to include 16 data sets in total.

12. Results from Dunne, et al Three different functional forms (instead of 1)

13. Yet some similarities remain… Confirmed the earlier results for a certain level of connectedness Also rejected both scale-free and small-world hypotheses Some of the differences in functional form attributed to poor data collection or extremely specialized webs

14. The End