Predatorprey dynamics

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Predator-prey dynamics
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Snowshoe hare and lynx dynamics
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(No Transcript)
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Conceptual model predation regulation
Predation prey density predator density
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Conceptual model growth and mortality
growth
mortality
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Simple Lotka-Volterra model
It has two variables (P, H) and several
parameters H density of Herbivore prey (Food
in reader)P density of Predator (Consumer in
reader) r intrinsic rate of prey population
increasea predation rate coefficient (clearing
rate) e reproduction rate of predators per prey
eatenm predator mortality rate
Lotka, A. J. 1925. Elements of physical biology.
Baltimore Williams Wilkins Co.Volterra, V.
1926. Variazioni e fluttuazioni del numero
d'individui in specie animali conviventi. Mem. R.
Accad. Naz. dei Lincei. Ser. VI, vol. 2.
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Assumptions simple Lotka-Volterra model

• r independent of prey density (exponential
  growth
• a independent of prey density (ever hungry
  predator

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Steady states

• F dependent on m and ea,
• C dependent on r and a

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Phase-plane analysis
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Results of L-V-predation model
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Limits to growth Logistic growth of the prey
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Steady states

• F still dependent on m and ea (predator
  characteristics)

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Phase-plane analysis
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Incorporating functional response for the predator
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Limits to growth

• Holling type II response for predator
• a search rate for prey
• h handling time
• m conversion factor prey to predator

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Compare with Monod
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Rosenzweig-MacArthur model
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Steady states
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Phase-plane analysis
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Selective grazing
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Food web models
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Parasite modelling