1963
DOI: 10.1086/282272
|View full text |Cite
|
Sign up to set email alerts
|

Graphical Representation and Stability Conditions of Predator-Prey Interactions

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

12
1,096
0
15

Year Published

1999
1999
2018
2018

Publication Types

Select...
5
4

Relationship

0
9

Authors

Journals

citations
Cited by 1,715 publications
(1,123 citation statements)
references
References 8 publications
12
1,096
0
15
Order By: Relevance
“…We now turn our attention to the specific case of ecological systems. In general, interactions among species can be described by a set of dynamical equations: dx i /dt ¼ f ðx i Þ þ gðx i ;xÞ, where x i is the density of a given species i, f(x i ) describes the effect of its density on population growth and gðx i ;xÞ is the contribution to growth from interactions with other species in the system [20][21][22] . We can divide the interaction term between two species, gðx i ;xÞ, into two parts: the frequency of interactions g i,j x i x j , and the effect of each interaction hðx i ;xÞ, and so gðx i ;xÞ ¼ P j g i;j x i x j hðx i ;xÞ.…”
Section: Resultsmentioning
confidence: 99%
“…We now turn our attention to the specific case of ecological systems. In general, interactions among species can be described by a set of dynamical equations: dx i /dt ¼ f ðx i Þ þ gðx i ;xÞ, where x i is the density of a given species i, f(x i ) describes the effect of its density on population growth and gðx i ;xÞ is the contribution to growth from interactions with other species in the system [20][21][22] . We can divide the interaction term between two species, gðx i ;xÞ, into two parts: the frequency of interactions g i,j x i x j , and the effect of each interaction hðx i ;xÞ, and so gðx i ;xÞ ¼ P j g i;j x i x j hðx i ;xÞ.…”
Section: Resultsmentioning
confidence: 99%
“…Population stability and species co-existence The idea that behavioral and physiological plasticity can affect population dynamics was suggested O20 years ago (reviewed in [3,30]). However, there is an increasing interest in the effects of plasticity on population dynamics, and early ideas are being re-discovered or investigated for different types of plasticity.…”
Section: Altered Interactions Have Consequences For Populations and Cmentioning
confidence: 99%
“…Here the point (R c , C c ) corresponds to the intersection of the prey isocline of model (5) and, by definition (the prey isocline consists of points in the prey-predator density phase space where prey population neither increases nor decreases, Rosenzweig and MacArthur, 1963), this half-line must be a part of the prey isocline of the Gause model. Thus, the prey isocline of the Gause model is L-shaped (the thick dashed line in Figure 2).…”
Section: The Gause Modelmentioning
confidence: 99%
“…Hereafter I will refer to this model as the Gause model. Models with a saturating functional response were introduced to theoretical ecological literature later on by e. g., Rosenzweig and MacArthur (1963) who replaced the linear functional response in the Lotka-Volterra model by the Holling type II (Holling, 1959) functional response. Besides the fact that the Rosenzweig-MacAthur model assumes negative density dependent prey growth, another difference between these two models is the jump in the functional response in the Gause model.…”
mentioning
confidence: 99%