A Lotka–Volterra symbiotic model with cross-diffusion

Delgado, Manuel; Montenegro, Marcelo; Suárez, António

doi:10.1016/j.jde.2008.10.032

Cited by 19 publications

(26 citation statements)

References 22 publications

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“…The simplest model for studying symbiotic relationships is described by Murray (2002) and consists of two interacting populations, similarly to the classic Lotka-Volterra predatorprey system. Symbiotic models based on the Lotka-Volterra formulation have attracted the interest of many mathematicians (Korman and Leung, 1987;Lou, 1996;Delgado et al, 2000;Pao, 2005) because they are suitable for studying existence, non-existence, uniqueness or multiplicity of solutions using various techniques (Delgado and Suárez, 2009).…”

Section: Introductionmentioning

confidence: 99%

A Trait-Based Model for Describing the Adaptive Dynamics of Coral-Algae Symbiosis

2017

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The survival of many ecological communities relies on the symbiotic relationships formed by various organisms. An example of a symbiotic association that is often described as mutualistic is the one between corals and algae. Since the algae are located within coral epidermis, they are referred to as "endosymbiont" (more generally "symbiont") whereas the corals are referred to as "host." This association is based on the exchange of photosynthetically fixed carbon from algae to corals and inorganic nutrients, acquired from animal waste metabolites or directly from seawater, from corals to algae. The evolution of this symbiotic relationship has enabled the emergence of highly productive and diverse coral reef ecosystems in nutrient-poor waters of the tropical oceans. Here we present an adaptive, trait-based model that describes the temporal dynamics of this association. Given that corals control the flux of inorganic nutrients to the algae, we focus on the adaptation of a hypothetical trait expressed by the coral population: investment of energy in the symbiotic relationship. Investment of energy produces losses for the corals that reflect costs for algal photosynthetic efficiency and for sustaining and maintaining the symbiont population. The fitness of the coral is modeled as the net benefit obtained by the symbiotic association. The model features a decrease in the fraction of energy invested by the corals with increasing symbiont to host biomass ratio. Our sensitivity analyses show that the best conditions for the survival of the simulated coral-algae community occur for a broad range of symbiont to host biomass ratio if the costs of symbiosis are low. With increasing costs, the survival region narrows down to a smaller range of symbiont to host biomass ratio. Finally, a break down of the symbiotic relationship and a consequent collapse of the coral-algae system occur under shock changes in algal abundance.

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Section: Introductionmentioning

confidence: 99%

A Trait-Based Model for Describing the Adaptive Dynamics of Coral-Algae Symbiosis

2017

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“…Hopf bifurcations of coexistence steady states have been analyzed by Kuto [83]. The existence and nonexistence of coexistence steady states of the mutualistic model was analyzed by Pao [118], later generalized by Delgado et al [32]. In recent years, several works were considered with three-species cross-diffusion systems providing sufficient conditions for the existence of nonconstant positive steady states, see [24,52,95,128,129].…”

Section: Cross-diffusion Population Modelsmentioning

confidence: 99%

Diffusive and nondiffusive population models

Jüngel

2010

Modeling and Simulation in Science, Engineering and Technology

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“…For more details on the backgrounds of this model, the readers are refered to Okubo and Levin [7]. Pao [8] in 2005, and Delgado et al [4] in 2008 have obtained some results on the existence of global solutions of the elliptic cross-diffusion systems with cooperative …”

Section: Introductionmentioning

confidence: 99%