Role of Quantity of Additional Food to Predators as a Control in Predator–Prey Systems with Relevance to Pest Management and Biological Conservation

2010 ◽  
Vol 73 (10) ◽  
pp. 2249-2276 ◽  
Author(s):  
P. D. N. Srinivasu ◽  
B. S. R. V. Prasad
2020 ◽  
Vol 30 (07) ◽  
pp. 2050102
Author(s):  
Vandana Tiwari ◽  
Jai Prakash Tripathi ◽  
Debaldev Jana ◽  
Satish Kumar Tiwari ◽  
Ranjit Kumar Upadhyay

In this paper, an attempt has been made to understand the role of predator’s interference and additional food on the dynamics of a diffusive population model. We have studied a predator–prey interaction system with mutually interfering predator by considering additional food and Crowley–Martin functional response (CMFR) for both the reaction–diffusion model and associated spatially homogeneous system. The local stability analysis ensures that as the quantity of alternative food decreases, predator-free equilibrium stabilizes. Moreover, we have also obtained a condition providing a threshold value of additional food for the global asymptotic stability of coexisting steady state. The nonspatial model system changes stability via transcritical bifurcation and switches its stability through Hopf-bifurcation with respect to certain ranges of parameter determining the quantity of additional food. Conditions obtained for local asymptotic stability of interior equilibrium solution of temporal system determines the local asymptotic stability of associated diffusive model. The global stability of positive equilibrium solution of diffusive model system has been established by constructing a suitable Lyapunov function and using Green’s first identity. Using Harnack inequality and maximum modulus principle, we have established the nonexistence of nonconstant positive equilibrium solution of the diffusive model system. A chain of patterns on increasing the strength of additional food as spots[Formula: see text][Formula: see text][Formula: see text]stripes[Formula: see text][Formula: see text][Formula: see text]spots has been obtained. Various kind of spatial-patterns have also been demonstrated via numerical simulations and the roles of predator interference and additional food are established.


Author(s):  
Shawna Bellamy ◽  
Barry W Alto

Abstract Non-lethal predator-prey interactions during the immature stages can cause significant changes to mosquito life history traits and their ability to transmit pathogens as adults. Treatment manipulations using mosquitoes Aedes aegypti (L.) and Toxoryhnchites rutilus (Coquillett) were performed during the immature stages to explore the potential impacts of non-lethal interactions on adult susceptibility to infection, disseminated infection and saliva infection of Ae. aegypti following ingestion of Zika virus-infected blood. Treatments inducing density reduction resulted in reduced development time and survivorship to adulthood. However, effects of treatment did not alter infection, dissemination, or saliva infection. These observations indicate that, while non-lethal predation may impact some traits that influence population dynamics and transmission of pathogens, there were no direct effects on mosquito-arbovirus interactions.


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