BLOW-UP IN A FRACTIONAL LAPLACIAN MUTUALISTIC MODEL WITH NEUMANN BOUNDARY CONDITIONS

In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.

Emerging directions in the study of the ecology and evolution of plant-animal mutualistic networks: a review

The study of mutualistic plant and animal networks is an emerging field of ecological research. We reviewed progress in this field over the past 30 years. While earlier studies mostly focused on network structure, stability, and biodiversity maintenance, recent studies have investigated the conservation implications of mutualistic networks, specifically the influence of invasive species and how networks respond to habitat loss. Current research has also focused on evolutionary questions including phylogenetic signal in networks, impact of networks on the coevolution of interacting partners, and network influences on the evolution of interacting species. We outline some directions for future research, particularly the evolution of specialization in mutualistic networks, and provide concrete recommendations for environmental managers.

Dynamics of a Mutualistic Model with Diffusion

This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.

From Mutualistic Partner to Hunted Prey?

Sharks and sharksuckers maintain a mutualistic symbiotic relationship;thus, it is surprising to observe a lemon shark, Negaprion brevirostris, killing a sharksucker, Echeneis lucrates, which has been recorded during a dive with lemon sharks. Does this observation indicate that the symbiosis between the two species may shift occasionally? The awkwardness of the recorded kill, combined with its comparatively long duration, suggests this bout be a freak incident, rather than a common occurrence;thus, the mutualistic relationship needs not be questioned. What triggered the bout, however, can only be speculated. Although the caloric value of the killed sharksucker is not known, a feeding-oriented behavior can likely be rejected as the potential cause based on the teleost’s rather small size, and an irritation related issue is more likely to have triggered this bout.

Internal Stabilization of a Mutualistic Reaction Diffusion System

We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different internal controllers to stabilize different steady-state solutions. The controllers axe provided by considering LQ problems associated with the lineaxized systems at steady-state solutions.

Intracellular Interactions in the Reproduction Control of Introgressed Strains Involving Species from Drosophila saltans Group(Sophophora Subgenus)with Emphasis to the Effect of Wolbachia Infection

Interspecific hybrids and constructed research models have provided infor-mation on intracellular interactions. We used two introgressed, chromosomally differentiated strains (H4 and H2) derived from F1 hybrids of crosses between D. prosaltans females and D. saltans males. In H4, the D. prosaltans chromosomes were eliminated. In H2, a mixture was maintained, preserving the entire genome of D. prosaltans (except the Y chromosome) and parts of the D. saltans genome. The IIR arm and a segment of chromosome III were eliminated. A third strain, used for comparison, was a normal D. prosaltans strain (P). This study aimed primarily to analyze the effect on the reproductive char-acteristics productivity (number of progeny) and sex-ratio caused by Wolbachia infection in interaction with different chromosome constitutions. For this, infected and uninfected flies were used in intrastrain cross combinations. Firstly, we analyzed the productivity of intracrosses of uninfected parents, in each strain, in order to detect the effects of intracellular interactions, in flies carrying different chromosome constitutions and sharing a Wolbach-ia-free, D. prosaltans cytoplasm. Data indicated that the chromosome parts that were eliminated, in H2, carry the isolating genes that impair productivity in hybrids of the two species, and suggested the occurrence of a nuclear/nuclear interaction. The analysis of Wolbachia-infected flies showed that the three strains presented different responses, depending on the chromosome constitution. As to productivity, the infection was harmful in P strain, in H2 behaved as mutualistic, and, in H4, produced the effect cytoplasmic incompatibility. As to sex-ratio, intracrosses showed significant differences in P and H4 strains. These results, associated with the cytological characteristics of the strains, pointed to the fundamental importance of host chromosome constitution to define the interactive process host/Wolbachia, and showed the flexibility of the endo-symbiont manifested in different forms of self-preservation.

Asymptotic profile of a mutualistic model on a periodically evolving domain

In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.

Coexistence in a mutualistic model with cross-diffusion in a heterogeneous environment

To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.

The spreading fronts in a mutualistic model with delay

This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indi- cate that two free boundaries tend monotonically to finite or infinite limits at the same time, and the free boundary problem admits a global slow solution with unbounded free boundaries if the intra-specific competitions are strong, while if the intra-specific competitions are weak, there exist the blowup solution and global fast solution.

Arbuscular Mycorrhizal Symbiosis Requires a Phosphate Transceptor in the Gigaspora margarita Fungal Symbiont

The majority of terrestrial vascular plants are capable of forming mutualistic associations with obligate biotrophic arbuscular mycorrhizal （AM） fungi from the phylum Glomeromycota. This mutualistic symbiosis provides carbohydrates to the fungus, and reciprocally improves plant phosphate uptake. AM fungal trans- porters can acquire phosphate from the soil through the hyphal networks. Nevertheless, the precise func- tions of AM fungal phosphate transporters, and whether they act as sensors or as nutrient transporters, in fungal signal transduction remain unclear. Here, we report a high-affinity phosphate transporter GigmPT from Gigaspora margarita that is required for AM symbiosis. Host-induced gene silencing of GigmPT ham- pers the development of G. margarita during AM symbiosis. Most importantly, GigmPT functions as a phos- phate transceptor in G. margarita regarding the activation of the phosphate signaling pathway as well as the protein kinase A signaling cascade. Using the substituted-cysteine accessibility method, we identified residues A146 （in transmembrane domain [TNID] IV） and Va1357 （in TMD VIII） of GigmPT, both of which are critical for phosphate signaling and transport in yeast during growth induction. Collectively, our results pro- vide significant insights into the molecular functions of a phosphate transceptor from the AM fungus G. margarita.

Arbuscular mycorrhizal fungi are necessary for the induced response to herbivores by Cucumis sativus

Aims Although ecological interactions are often conceptualized and stud-ied in a pairwise framework,ecologists recognize that the outcomes of these interactions are influenced by other members of the com-munity.Interactions(i)between plants and insect herbivores and(I)between plants and mycorrhizal fungi are ubiquitous in terrestrial ecosystems and may be linked via common host plants.Previous studies suggest that colonization by arbuscular mycorrhizal fungi(AMF)can modifty plants'induced responses to herbivore attack,but these indirect effects of fungal symbionts are poorly understood.I investigated the role of AMF in induced plant response to a gen-eralist herbivore.Methods|manipulated AMF status and herbivory in Cucumis sativus L.(cucumber,Cucurbitaceae)in a greenhouse to investigate induced responses in the presence and absence of the mycorrhi-zal fungus Glomus intraradices(Glomeraceae).Spodoptera exigua Habner(Noctuidae)were used to manipulate prior damage and later as assay caterpillars.I also measured G.intraradices and her-bivory effects on plant N and effects on plant growth.Impor tant Findings AMF status affected the induced response of C.sativus,underscor-ing the importance of incorporating the roles of plant symbionts into plant defense theory.Assay caterpillars ate significantly more leaf tissue only on mycorrhizal plants that had experienced prior damage.Despite more consumption,biomass change in these cat-erpillars did not differ from those feeding on plants with other treat-ment combinations.Leaf N content was reduced by G.intraradices but unaffected by herbivory treatments,suggesting that the observed differences in assay caterpillar feeding were due to changes in defensive chemistry that depended on AMF.

Potential role of lava lizards as pollinators across the Galápagos Islands

Lizards have been reported as important pollinators on several oceanic islands.Here we evaluate the potential role of Galápagos lava lizards(Microlophus spp.)as pollinators across their radiation.Over 3 years,we sampled pollen transport by 9 lava lizard species on the 10 islands where they are present,including 7 single-island endemics.Overall,only 25 of 296 individuals sampled(8.4%)transported pollen of 10 plant species,the most common being Prosopis juliflora,Exodeconus miersii,Sesuvium sp.and Cordia leucophlyctis.At least 8 of these plant species were native,and none were confirmed as introduced to the archipelago.Despite the low overall proportion of individuals carrying pollen,this was observed in 7 of the nine lizard species,and on 8 of the ten main islands(Española,Fernandina,Floreana,Isabela,Marchena,Pinta,Santa Cruz and Santiago),suggesting that this is a widespread interaction.The results reported here support the potential role of lava lizards as pollinators across their radiation,although they may represent a relatively modest contribution when compared with birds and insects.However,we cannot discard that lizards may be ecologically significant for particular plant species and ecosystems given the specific climatic condition and functional diversity of each island.