Predation and functional responses FISH 458

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Predation and functional responsesFISH 458
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Readings

• Walters, C.J. 1986. Adaptive management of
  renewable resources. Macmillian Publishing Co.
  NY.
• Holling, C.S. 1965. The functional response of
  predators to prey density and its role in mimicry
  and population regulation. Memoirs of the
  Entomological Society of Canada 45 1-60.

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Overview

• Lotka Volterra predator prey equations
• Functional Responses derivation
• Multispecies functional response
• System behavior and isoclines

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The predators and prey
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Simple predator prey theoryLotka Volterra

• Prey governed by logistic growth
• Simplest theory has simple exponential growth
• Predators deaths are density independent, births
  depend upon number of prey eaten
• Prey eaten per predator is proportional to prey
  density

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Lotka (1926) Volterra (1926)
W wildebeest numbers L lion numbers r W
intrinsic rate of increase e lion predation
efficiency m lion natural mortality a lion
assimilation efficiency
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Biological unrealism of Lotka Volterra

• No prey self limitation
• No predator self limitation
• No limit on prey consumption per predator
• Known as functional response

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Dynamic behavior
These models are either unstable or cyclic
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Adding some biological realism
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Dynamic behavior in time
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Predator prey phase diagram
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Predation dynamicsdeveloping a functional
response

• Predators do a random walk, encounter and kill a
  fraction of what prey they encounter.
• Exponential model is used to correct for the fact
  that no prey can be killed and eaten twice.

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Wildebeest Lion model

• A lion walks 10 km per day
• Can see 200 m in either direction
• Thus sees all wildebeest covering 4 km2/day
• This amounts to 1460 km2/year
• Serengeti ecosystem is 90,000 km2
• A lion can chase and catch 1 in 1000 animals it
  sees
• Thus it kills 0.000016 of the population

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Key assumption

• Kill rate proportional to prey abundance
• No self regulation of predator
• No predator saturation

Demo using lion wildebeest model
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The prey isoclinewhen is prey abundance constant?
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The predator isocline
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Increasing predator, decreasing prey
decreasing predator, decreasing prey
decreasing predator, increasing prey
increasing predator, increasing prey
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Experimental components analysis of predation
from Holling

• Total time available TT
• Can be split into searching time (Ts) and
  handling time (Th).
• If predator spends time h handling an individual
  prey and consumes Na prey, then handling time is
• Thh Na

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• Predator searches area a per unit time
• Predator has probability pc of recognizing and
  successfully attacking a prey in the area
  searched
• Average prey density is N
• Predator will on average kill a pc N prey per
  time spent searching
• Na a pc N Ts
• Ts Na/(a pc N )

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• So
• Tt Na/(a pc N )h Na
• solving for number attached we get

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Behavior

• Asymptote - determined by handling time
• Handling time can include digestive pause
• Initial slope - area searched times probability
  of successful attack times density

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What could be added

• Lion functional response with handling time
• Lion self limitation
• Social behavior and group territoriality
• Spatial heterogeneity and migration of wildebeest
• Alternative prey

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Adding additional prey

• Assume that during the random walk the predator
  encounters possible alternative prey

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Additional prey

• For each prey species there is a probability of
  detection, pursuit and killing
• Do the algebra and you get the

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Multiprey functional response
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Uses

• This formulation is the basis for many ecosystem
  based models

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Further issues

• Predators may not search at random
• Predators may develop a search image and
  preferably attack more abundant prey