scholarly journals Predator-prey nutrient competition undermines predator coexistence

2019 ◽  
Author(s):  
Toni Klauschies ◽  
Ursula Gaedke
Keyword(s):  
Nutrient Limitation ◽  
Uptake Rate ◽  
Species Coexistence ◽  
Logistic Growth ◽  
Nutrient Competition ◽  
Functional Responses ◽  
Predator Prey ◽  
Natural Systems ◽  
Prey System ◽  
Flow Through

AbstractContemporary theory of predator coexistence through relative non-linearity in their functional responses strongly relies on the Rosenzweig-MacArthur equations (1963) in which the (autotrophic) prey exhibits logistic growth in the absence of the predators. This implies that the prey is limited by a resource which availability is independent of the predators. This assumption does not hold under nutrient limitation where both prey and predators bind resources such as nitrogen or phosphorus in their biomass. Furthermore, the prey’s resource uptake-rate is assumed to be linear and the predator-prey system is considered to be closed. All these assumptions are unrealistic for many natural systems. Here, we show that predator coexistence on a single prey is strongly hampered when the prey and predators indirectly compete for the limiting resource in a flow-through system. In contrast, a non-linear resource uptake rate of the prey slightly promotes predator coexistence. Our study highlights that predator coexistence does not only depend on differences in the curvature of their functional responses but also on the type of resource constraining the growth of their prey. This has far-reaching consequences for the relative importance of fluctuation-dependent and -independent mechanisms of species coexistence in natural systems where autotrophs experience light or nutrient limitation.

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

scholarly journals Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Kankan Sarkar ◽  
Subhas Khajanchi ◽  
Prakash Chandra Mali ◽  
Juan J. Nieto
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Uniform Persistence ◽  
Functional Responses ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Prey System

In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study.

scholarly journals The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Shaoli Wang ◽  
Zhihao Ge
Keyword(s):  
Hopf Bifurcation ◽  
Logistic Growth ◽  
Positive Equilibrium ◽  
Prey Refuge ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Prey System ◽  
Form Theory ◽  
The Stability

The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.

scholarly journals Space race functional responses

2015 ◽  
Vol 282 (1801) ◽  
pp. 20142121 ◽  
Author(s):  
Henrik Sjödin ◽  
Åke Brännström ◽  
Göran Englund
Keyword(s):  
Functional Response ◽  
Community Dynamics ◽  
Simple Structure ◽  
Functional Responses ◽  
Response Models ◽  
Predator Prey ◽  
Prey System ◽  
Space Race ◽  
Functional Response Models ◽  
The Relationship

We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis–Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka–Volterra predator–prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats.

scholarly journals A hybrid predator–prey model with general functional responses under seasonal succession alternating between Gompertz and logistic growth

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lei Hang ◽  
Long Zhang ◽  
Xiaowen Wang ◽  
Hongli Li ◽  
Zhidong Teng
Keyword(s):  
Global Attractivity ◽  
Seasonal Succession ◽  
Hybrid Population ◽  
Logistic Growth ◽  
Ultimate Boundedness ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Theoretical Results

AbstractIn this paper, a hybrid predator–prey model with two general functional responses under seasonal succession is proposed. The model is composed of two subsystems: in the first one, the prey follows the Gompertz growth, and it turns to the logistic growth in the second subsystem since seasonal succession. The two processes are connected by impulsive perturbations. Some very general, weak criteria on the ultimate boundedness, permanence, existence, uniqueness and global attractivity of predator-free periodic solution are established. We find that the hybrid population model with seasonal succession has more survival possibilities of natural species than the usual population models. The theoretical results are illustrated by special examples and numerical simulations.

scholarly journals Permanence of Periodic Predator-Prey System with General Nonlinear Functional Response and Stage Structure for Both Predator and Prey

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Xuming Huang ◽  
Xiangzeng Kong ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Stage Structure ◽  
Functional Responses ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Prey System

We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.

scholarly journals Caching Behavior of Large Prey by Eurasian Lynx: Quantifying the Anti-Scavenging Benefits

Diversity ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 350
Author(s):  
Ivonne J. M. Teurlings ◽  
John Odden ◽  
John D. C. Linnell ◽  
Claudia Melis
Keyword(s):  
Observational Data ◽  
Roe Deer ◽  
Capreolus Capreolus ◽  
Lynx Lynx ◽  
Large Prey ◽  
Functional Responses ◽  
Eurasian Lynx ◽  
Predator Prey ◽  
Prey System ◽  
Prey Items

Large solitary felids often kill large prey items that can provide multiple meals. However, being able to utilize these multiple meals requires that they can cache the meat in a manner that delays its discovery by vertebrate and invertebrate scavengers. Covering the kill with vegetation and snow is a commonly observed strategy among felids. This study investigates the utility of this strategy using observational data from Eurasian lynx (Lynx lynx)-killed roe deer (Capreolus capreolus) carcasses, and a set of two experiments focused on vertebrate and invertebrate scavengers, respectively. Lynx-killed roe deer that were covered by snow or vegetation were less likely to have been visited by scavengers. Experimentally-deployed video-monitored roe deer carcasses had significantly longer time prior to discovery by avian scavengers when covered with vegetation. Carcass parts placed in cages that excluded vertebrate scavengers had delayed invertebrate activity when covered with vegetation. All three datasets indicated that covering a kill was a successful caching/anti-scavenger strategy. These results can help explain why lynx functional responses reach plateaus at relatively low kill rates. The success of this anti-scavenging behavior therefore has clear effects on the dynamics of a predator–prey system.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR–PREY STOCHASTIC MODEL IN A 2D LATTICE

2010 ◽  
Vol 20 (02) ◽  
pp. 309-314 ◽  
Author(s):  
C. ARGOLO ◽  
H. OTAVIANO ◽  
IRAM GLERIA ◽  
EVERALDO ARASHIRO ◽  
TÂNIA TOMÉ
Keyword(s):  
Critical Behavior ◽  
Critical Exponents ◽  
Order Parameter ◽  
Species Coexistence ◽  
Finite Size ◽  
Universality Class ◽  
Square Lattice ◽  
Scaling Analysis ◽  
Predator Prey ◽  
Prey System

We investigate the critical behavior of a stochastic lattice model describing a predator–prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

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