Universal Patterns in Food Webs?

Benjamin Good

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 exampleof May’s warning againsttheoretical physicistsin biology?

The Model

• “Niche Parameter” chosen byni=random(0,1), i=1,…,S

• Species eat prey in a range given byri=xni wherep(x) = b(1-x)(b-1) , 0 < x < 1, andb=(S2/2L – 1)

• This range centered on ci=random(ri/2, ni)

• Hence, a list of prey or a list of predators can be calculated for each species

Sample Web

The Predictions

• In another paper, they used this model to derive expressions for Pprey(k) and Ppred(k)

• Pprey(k) is the probabilitythat a given species hask or more prey, Ppred(k) isthe probability that aspecies has k or more predators.

Again note the placeof publication…

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!

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!

… and further

• By pooling the data from all 7 webs, they construct a “master plot”:

… again with no fit parameters

Haven’t seen a fit this good since…

… especially when compared to the modelswe have been dealing with so far.

Other predictions… Amazingly, the same model predicts

several other network characteristicsquite well: number of links per species, raverage distance, dclustering coefficient, C

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

Response to this article…

• A later study by Dunne, Williams, and Martinez extended the data to include 16 data sets in total.

Results from Dunne, et al

Three differentfunctional forms(instead of 1)

Yet some similarities remain…

• Confirmed the earlierresults for a certain levelof connectedness

• Also rejected bothscale-free and small-worldhypotheses

• Some of the differencesin functional form attributedto poor data collectionor extremely specializedwebs

The End