Maintaining biodiversity requires direct and indirect interspecific interactions. The study of direct interactions, including
competition, predation, mutualism, commensalism, and parasitism, has greatly promoted the development of species
coexistence theory. However, as a simplified method to explain community assembly, direct interactions alone cannot
adequately explain the coexistence of related species in the absence of indirect interactions. Indirect interactions can be
defined as the impact of one species on another that is mediated or transmitted by a third, and they are considered to be a
more complex and less understood type of interspecific interaction.
During the past two decades, scientists have gradually realized that a type of density-mediated indirect interaction,
known as intransitive competition, is ubiquitous in nature. Intransitive competition can be described as a game of “rockpaper-scissors” in which three species A, B and C have competitive ranks A>B>C>A. In this competitive mode,
competitive exclusion between relative species is counteracted by mutual restrictiveness, and there are no “invincible”
species in the community. Therefore, intransitive competition is an important factor in promoting species coexistence,
which affects species distribution patterns, community structure and ecosystem functions. To summarize the theory of
intransitive competition, this paper discusses the definition, characteristics, and detection methods of intransitive
competition and the main factors affecting intransitive competition as well.
There are five formation modes of intransitive competition. Resource utilization mode occurs when species have
different competitive abilities for resources. Life history mode arises if species cannot maintain an absolute competitive
advantage throughout their life stages. Behavioral trade-off mode follows when species have different ways of acquiring
resources. Competition trade-off mode and allelopathy mode require species to develop both aggressive and defensive
Our paper also explores three characteristics of intransitive competition. First, the populations of species participating in
intransitive competition often exhibit periodic fluctuations in their frequency. which are regulated by dynamic equilibrium.
Second, intransitive competition systems involving an odd number of species can maintain community stability, whereas
systems involving an even number of species will theoretically collapse. Finally, multiple intransitive competition loops
may appear in the community, and intransitive competition may also be nested in other coexistence patterns. This nested
feature makes intransitive competition difficult to detect and measure. Fortunately, current research methods such as
competition matrix, transfer matrix and invasion growth rate model can be used to infer the existence of intransitive
competition and quantify its prevalence and importance.
Competitive rank has been considered as one of the most important factors affecting intransitive competition. The higher
the coefficient of variation of competitive rank among species, the more negative impact on intransitive competition. At the
same time, global-scale environmental changes could also be critical factors: drought increases the intransitive competition
in the community, but eutrophication caused by land-use intensification reduces the intransitive competition. Functional
traits are non-negligible because species traits adapted to high-productivity environments often impede the formation of
intransitive competition. Finally, to promote the understanding of indirect interaction and multi-species coexistence
strategies, we propose that future research on intransitive competition should focus on long-term controlled field
experiments, coupled with theoretical considerations of high-order interactions, complex networks, and ecosystem