PREDATOR–PREY MODELS WITH ADDED MORTALITY

1977 ◽  
Vol 109 (5) ◽  
pp. 763-768 ◽  
Author(s):  
H. Barclay ◽  
P. van den Driessche
Keyword(s):  
Functional Response ◽  
Prey Density ◽  
Numerical Results ◽  
Predator Prey ◽  
Predator Prey Models

AbstractSeveral predator–prey models are examined to assess the generality of Volterra’s contention that an external mortality imposed simultaneously on both predators and prey results in a decrease in predators and an increase in prey equilibrium numbers. The models indicate that this phenomenon occurs mainly as a result of the lack of predator crowding. If predator crowding occurs, a strong functional response of predators to prey density, or light prey mortality relative to predator mortality, is required for Volterra’s phenomenon to occur. In increasing populations away from equilibrium, numerical results indicate conditions for Volterra’s phenomenon to occur.

scholarly journals Applying predator-prey theory to modelling immune-mediated, within-host interspecific parasite interactions

Parasitology ◽  
2010 ◽  
Vol 137 (6) ◽  
pp. 1027-1038 ◽  
Author(s):  
ANDY FENTON ◽  
SARAH E. PERKINS
Keyword(s):  
Functional Response ◽  
Interspecific Interactions ◽  
Parasite Load ◽  
Multiple Infections ◽  
Functional Responses ◽  
Predator Prey ◽  
Immune Activity ◽  
Parasite Communities ◽  
Immune Mediated ◽  
Predator Prey Models

SUMMARYPredator-prey models are often applied to the interactions between host immunity and parasite growth. A key component of these models is the immune system's functional response, the relationship between immune activity and parasite load. Typically, models assume a simple, linear functional response. However, based on the mechanistic interactions between parasites and immunity we argue that alternative forms are more likely, resulting in very different predictions, ranging from parasite exclusion to chronic infection. By extending this framework to consider multiple infections we show that combinations of parasites eliciting different functional responses greatly affect community stability. Indeed, some parasites may stabilize other species that would be unstable if infecting alone. Therefore hosts' immune systems may have adapted to tolerate certain parasites, rather than clear them and risk erratic parasite dynamics. We urge for more detailed empirical information relating immune activity to parasite load to enable better predictions of the dynamic consequences of immune-mediated interspecific interactions within parasite communities.

Some Characteristics of Simple Types of Predation and Parasitism

1959 ◽  
Vol 91 (7) ◽  
pp. 385-398 ◽  
Author(s):  
C. S. Holling
Keyword(s):  
Functional Response ◽  
Small Mammals ◽  
Prey Density ◽  
Population Regulation ◽  
Predator Prey

In an earlier study (Holling, 1959) the basic and subsidiary components of predation were demonstrated in a predator-prey situation involving the predation of sawfly cocoons by small mammals. One of the basic components, termed the functional response, was a response of the consumption of prey by individual predators to changes of prey density, and it appeared to be at least theoretically important in population regulation: Because of this importance the functional response has been further examined in an attempt to explain its characteristics.

scholarly journals Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Wahiba Khellaf ◽  
Nasreddine Hamri
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Qualitative Behavior ◽  
Uniform Persistence ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Prey System ◽  
Predator Prey Models ◽  
Type Ii Functional Response

We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.

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