Predator-Prey Interaction in Structured Models

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Predator-Prey Interaction in Structured Models

• Glenn Ledder
• J. David Logan
• University of Nebraska-Lincoln
• gledder_at_math.unl.edu

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Simple Holling type II dynamics
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Simple Holling Type II Dynamics

• Time is split between searching and feeding
• U prey density R(U) overall predation rate
• s search speed h handling time

food total t
search t total t
space search t
food space
search t total t
feed t total t
------- --------- --------- -------
--------- 1 -------
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Simple Holling Type III Dynamics

• Time is split between searching and feeding
• Searching is density-dependent
• U prey density R(U) overall predation rate
• s maximum search speed h handling time

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Simple Holling Type II Dynamics

• Time is split between searching and feeding
• U prey density R(U) overall predation rate
• s search speed h handling time

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Holling type IIMultiple Prey

• Time is split between searching and feeding
• Ui prey densities Ri(Ui) overall
  predation rates
• si search speeds hi handling times

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Full Model 1 Predator Class

• Ui prey densities Ri(Ui) overall
  predation rates
• si search speeds hi handling times ci --
  conversion
• G per capita growth M per capita
  mortality

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Multiple Prey and Predators

• Ui prey densities Pk predator
  densities
• sik search speeds hik handling
  times
• cik conversion efficiencies

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Continuous Structure

• x prey class y
  predator class
• u(x, t) prey density p(y, t)
  predator density
• s(x, y) search speed h(x, y)
  handling time
• I(y) set of prey consumed by predators of size
  y
• K(x) set of predators capable of consuming prey
  of size x
• dF(x, y, t) predation of (y, ydy) on (x, xdx)