Biodiv Sci ›› 2022, Vol. 30 ›› Issue (2): 21282. DOI: 10.17520/biods.2021282
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Zhengliang Huang1,2, Hanlun Liu1,2, Chengjin Chu1,3, Yuanzhi Li1,3,*()
Received:
2021-07-14
Accepted:
2021-09-15
Online:
2022-02-20
Published:
2022-02-28
Contact:
Yuanzhi Li
Zhengliang Huang, Hanlun Liu, Chengjin Chu, Yuanzhi Li. Advances in intransitive competition between organisms[J]. Biodiv Sci, 2022, 30(2): 21282.
Fig. 1 Forms of transitive and intransitive competitive networks between species (different letters) or genotypes/phenotypes (same letter with different numbers). One-way arrow points to the winner, with dash line indicating competitive reversal. Two-way arrow indicates uncertain competitive outcomes. a, Transitive competition between three species; b, Intransitive competition between three species; c, Intransitive competition between three genotypes/phenotypes of the same species; d, Intransitive competition between two species; e, Weak intransitive competition between three species; f, Intransitive odd loop; g, Intransitive even loop; h, An intransitive triplet nested in a six-species intransitive loop; i, A four-species intransitive loop nested in a six-species intransitive loop.
非传递性指标 Metrics of intransitivity | | | |
---|---|---|---|
d (非传递性三元环的数量 The number of intransitive triplets) | 0 | 1 | 5 |
I (转换为等级性竞争所需最少竞争关系转换数 The minimum number of competitive reversals to convert a network to a hierarchy) | 0 | 1 | 3 |
δ' (参与非传递环的竞争关系数量 The number of interactions embed in intransitive triplets) | 0 | 3 | 10 |
v (竞争能力的差异性 The difference of competitive strength) | 0 | 1 | 3 |
u (是否存在绝对优势种 The presence of unbeatable species) | 1 | 1 | 0 |
a (是否存在绝对劣势种 The presence of always-beatable species) | 1 | 1 | 0 |
Table 1 Examples of calculating intransitivity of different competitive networks in different metrics
非传递性指标 Metrics of intransitivity | | | |
---|---|---|---|
d (非传递性三元环的数量 The number of intransitive triplets) | 0 | 1 | 5 |
I (转换为等级性竞争所需最少竞争关系转换数 The minimum number of competitive reversals to convert a network to a hierarchy) | 0 | 1 | 3 |
δ' (参与非传递环的竞争关系数量 The number of interactions embed in intransitive triplets) | 0 | 3 | 10 |
v (竞争能力的差异性 The difference of competitive strength) | 0 | 1 | 3 |
u (是否存在绝对优势种 The presence of unbeatable species) | 1 | 1 | 0 |
a (是否存在绝对劣势种 The presence of always-beatable species) | 1 | 1 | 0 |
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