Abstact
The concept of trophic level comes from ecosystems where the idea was to quantify how many steps in a food chain a species is from the energy source. The catch is that given a preliminary classification into integer levels, one quickly finds that some species eat things from more than one level. A real-valued notion of trophic level was proposed by Levine to take this into account and has become the accepted standard. The notion was rediscovered by economists in supply networks under the name “upstreamness”. It has been applied to many other classes of directed network.
Johnson et al introduced the notion of trophic coherence, measuring the standard deviation of the trophic height differences along the edges in a network, and showed it to be a good predictor of many other network properties, such as stability of contagion processes, numbers of cycles, and non-normality.
Traditional trophic analysis suffers from three defects, however. Firstly, it is over-sensitive to what is included as basal species and cannot be implemented at all if there are none. Secondly, the results are not equivariant with respect to reversing all the edges. Thirdly, it does not allow a natural way to do local trophic analysis.
Our trophic analysis remedies all three defects. The improved trophic levels give useful information and the improved notion of trophic coherence has similar relations to network properties. A special mention will be made about zeta functions for networks.
Event Details
Date/Time:
-
Date:Tuesday, February 4, 2020 - 3:00pm to 4:00pm
Location:
Howey W505
For More Information Contact
Predrag Cvitanovic
