Random Sequential Generation of Intervals for the Cascade Model of Food Webs

TL;DR

This paper introduces a Poisson-based random sequential interval generation method that models the cascade food web structure, capturing the chain length distribution observed in ecological data.

Contribution

It presents a novel Poisson model for generating food webs that mimics the cascade model's behavior and chain length distribution.

Findings

The model reproduces the chain length distribution of ecological food webs.

It provides a probabilistic framework for food web generation.

The approach offers insights into the structure of ecological networks.

Abstract

The cascade model generates a food web at random. In it the species are labeled from 0 to $m$, and arcs are given at random between pairs of the species. For an arc with endpoints $i$ and $j$ ($i<j$), the species $i$ is eaten by the species labeled $j$. The chain length (height), generated at random, models the length of food chain in ecological data. The aim of this note is to introduce the random sequential generation of intervals as a Poisson model which gives naturally an analogous behavior to the cascade model.