Experimental studies on predation: Dispersion factors and predator-prey oscillations

Huffaker, C. B.

doi:10.3733/hilg.v27n14p343

Cited by 1,206 publications

(692 citation statements)

References 12 publications

Supporting

Mentioning

655

Contrasting

Unclassified

Order By: Relevance

“…This, however, contradicts Gause's classic observation of mutual extinction in the protozoans, Paramecium and its predator Didinium (Gause(1934), Luckinbill(1973), Abrams and Ginzburg(2000)), and the well cited experimental observation of Huffaker (Huffaker(1958)). Until very recently, both ecologists and mathematicians chose to ignore the rich dynamics provided by the strict ratio-dependent models, especially that on the boundary and close to the origin (the origin is a singular equilibrium, which renders direct local stability analysis impossible).…”

Section: Introductionmentioning

confidence: 74%

Rich dynamics of a ratio-dependent one-prey two-predators model

Hsu

Hwang

Kuang

2001

Journal of Mathematical Biology

113

View full text Add to dashboard Cite

Abstract. The objective of this paper is to systematically study the qualitative properties of a ratio-dependent one-prey two-predator model. We show that the dynamics outcome of the interactions are very sensitive to parameter values and initial data. Specifically, we show the interactions can lead to all the following possible outcomes: 1) competitive exclusion; 2) total extinction, i.e., collapse of the whole system; 3) coexistence in the form of positive steady state; 4) coexistence in the form of oscillatory solutions; and 5) introducing a friendly and better competitor can save a otherwise doomed prey species. These results reveal far richer dynamics compared to similar prey dependent models. Biological implications of these results are discussed.

show abstract

Section: Introductionmentioning

confidence: 74%

Rich dynamics of a ratio-dependent one-prey two-predators model

Hsu

Hwang

Kuang

2001

Journal of Mathematical Biology

113

View full text Add to dashboard Cite

show abstract

“…The oscillations observed in many data series of natural predator prey populations are normally not as vigorous as the fluctuations predicted by mathematical models. In contrast, populations of predators and prey that are kept in laboratory environments, where the amount of space available is much smaller than in a natural population, often do show oscillations which drive the populations to extinction (Gause, 1934;Huffaker, 1958;Maly, 1969). This suggests that spatial interactions are an important element in the regulation of populations which have a tendency to oscillate in isolation.…”

Section: Introductionmentioning

confidence: 89%

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

155

110

View full text Add to dashboard Cite

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator prey metapopulation or as a spatially explicit predator prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator prey populations can be regulated through the interplay of local dynamics and migration. ]

show abstract

“…IS,no. 3 destabilized the predator/prey system, while in Huffaker's (1958) laboratory study patchiness was necessary to prevent prey extinction.…”

Section: Importance or Interactions Between Plants And Generalist Enementioning

confidence: 99%

“…Huffaker (1958), in a classic laboratory study, showed that the ability of predatory mites to coexist with their herbivorous mite prey was dependent on environmental complexity and dispersal rates of predator and prey. Until recently, spatial heterogeneity has been incorporated into models of enemy/victim dynamics only to the extent that internally homogenous patches differ in prey density.…”

Section: Importance or Interactions Between Plants And Generalist Enementioning

confidence: 99%