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- W1995048949 abstract "Extending the cascade model for food webs, we introduce a cyclic cascade model which is a random generation model of cyclic dominance relations. Put n species as n points Q 1 , Q 2 ,…, Q n on a circle. If the counterclockwise way from Q i to Q j on the circle is shorter than the clockwise way, we say Q i dominates Q j . Consider a tournament whose dominance relations are generated from the points on a circle by this rule. We show that when we take n mutually independently distributed points on the circle, the probability of getting a regular tournament of order 2 r +1 as the largest regular tournament is equal to ( n /(2 r +1))/2 n -1 . This probability distribution is for the number of existing species after a sufficiently long period, assuming a Lotka-Volterra cyclic cascade model." @default.
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- W1995048949 date "2000-06-01" @default.
- W1995048949 modified "2023-09-25" @default.
- W1995048949 title "Oriented graphs generated by random points on a circle" @default.
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- W1995048949 doi "https://doi.org/10.1239/jap/1014842556" @default.
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