Lion, wildebeest and zebra: A predator–prey model

Fay, Temple H.; Greeff, Johanna C.

doi:10.1016/j.ecolmodel.2006.02.026

Cited by 26 publications

(20 citation statements)

References 9 publications

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“…This solution could represent the way herds act as a defensive mechanism for preys 20,21 . Also, large herds of zebras or wildebeest seem to be stable in time; in 22 the authors presented data of the Kruger National Park, in South Africa, that showed a stable and increasing populations of zebras and wildebeest (more than 10,000 individuals) over a period of twenty years, with an also a more or less stable population of lions (around 400 individuals). Or the effects of intraspecific competition can act as a regulatory mechanism.…”

Section: Discussionmentioning

confidence: 99%

A general model of population dynamics accounting for multiple kinds of interaction

Stucchi

Pastor

García-Algarra

et al. 2020

Preprint

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Population dynamics has been modelled using differential equations almost since Malthus times, more than two centuries ago. Basic ingredients of population dynamics models are typically a growth rate, a saturation term in the form of Verhulst's logistic brake, and a functional response accounting for interspecific interactions. However intraspecific interactions are not usually included in the equations. The simplest models use linear terms to represent a simple picture of the nature, meanwhile to represent more complex landscapes, it is necessary to include more terms with higher order or analytically more complex. The problem to use a simpler or more complex model depends on many factors: mathematical, ecological, or computational. To address it, here we discuss a new model based on a previous logistic-mutualistic model. We have generalised the interspecific terms (for antagonistic and competitive relationships) and we have also included new polynomial terms to explain any intraspecific interaction. We show that by adding simple intraspecific terms, new free-equilibrium solutions appear driving a much richer dynamics. These new solutions could represent more realistic ecological landscapes by including a new high order term. 2/183/18 10/18

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Section: Discussionmentioning

confidence: 99%

A general model of population dynamics accounting for multiple kinds of interaction

Stucchi

Pastor

García-Algarra

et al. 2020

Preprint

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“…We let x(t) denote the population of wildebeest and y(t) denote the population of lions, measured in thousands. A predator-prey model has been developed [9] using data from park records to estimate coefficients…”

Section: Vmentioning

confidence: 99%

On Solving Systems of ODEs Numerically

Fay¹,

Joubert²,

Mkolesia³

2005

AJUR

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Many beginning courses on ordinary differential equations have a computer laboratory component in which the students are asked to solve initial value problems numerically. But little attention in texts is given to the question of how accurate such solutions are. In this article we offer a simple procedure that not only can provide a measure of accuracy, but also often produces superior numerical results.

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“…Consider the following system of wildebeest and zebra without the presence of lion as proposed in Fay and Greeff (2006) by incorporating proportional harvesting to illustrate the theory discussed previously …”

Section: Numerical Simulationmentioning

confidence: 99%

“…Some common examples of twospecies mutualism include zebra and wildebeest (Fay and Greeff, 2006), yucca moths and yucca plants (Starr et al, 2015) and damselfish and sea anemone (Benz, 2000). In a thorough review of the natural history of mutualisms, Janzen (1985) has argued that most mutualisms can be classified into four types; seed dispersal mutualisms, pollination mutualisms, digestive mutualisms and protection mutualisms.…”

Section: Introductionmentioning

confidence: 99%

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Global stability of two-species mutualism model with proportional harvesting

Ahmad

2017

Int. j. adv. appl. sci.

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This paper deals with the study on a mathematical model consisting of mutualistic interactions among two-species with proportional harvesting. Harvesting function is introduced to describe the rate of removal of the species. The local stability analysis shows that the unique positive equilibrium point is asymptotically stable when certain conditions are satisfied. Global stability is discussed by constructing Lyapunov function. It has been shown that the unique positive equilibrium point is globally asymptotically stable. Finally, numerical simulations supporting theoretical results are also included.

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Lion, wildebeest and zebra: A predator–prey model

Cited by 26 publications

References 9 publications

A general model of population dynamics accounting for multiple kinds of interaction

A general model of population dynamics accounting for multiple kinds of interaction

On Solving Systems of ODEs Numerically

Global stability of two-species mutualism model with proportional harvesting

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