Extinction risk and structure of a food web model.
We investigate in detail the model of a trophic web proposed by Amaral and Meyer [Phys. Rev. Lett. 82, 652 (1999)]. We focus on small-size systems that are relevant for real biological food webs and for which the fluctuations play an important role. We show, using Monte Carlo simulations, that such webs can be nonviable, leading to extinction of all species in small and/or weakly coupled systems. Estimations of the extinction times and survival chances are also given. We show that before the extinction the fraction of highly connected species ("omnivores") is increasing. Viable food webs exhibit a pyramidal structure, where the density of occupied niches is higher at lower trophic levels, and moreover the occupations of adjacent levels are closely correlated. We also demonstrate that the distribution of the lengths of food chains has an exponential character and changes weakly with the parameters of the model. On the contrary, the distribution of avalanche sizes of the extinct species depends strongly on the connectedness of the web. For rather loosely connected systems, we recover the power-law type of behavior with the same exponent as found in earlier studies, while for densely connected webs the distribution is not of a power-law type.
Pekalski
Andrzej
A
Institute of Theoretical Physics, University of Wrocław, place M. Borna 9, 50-204 Wrocław, Poland. apekal@ift.uni.wroc.pl
Szwabiński
Janusz
J
Bena
Ioana
I
Droz
Michel
M
D000818:Animals; D044822:Biodiversity; D003198:Computer Simulation; D004463:Ecology; D017753:Ecosystem; D053476:Extinction, Biological; D020387:Food Chain; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D009010:Monte Carlo Method; D011157:Population Dynamics; D012306:Risk