Chapter 18: Dynamics of Predation

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Chapter 18 Dynamics of Predation

• Robert E. Ricklefs
• The Economy of Nature, Fifth Edition

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Population Cycles of Canadian Hare and Lynx

• Charles Eltons seminal paper focused on
  fluctuations of mammals in the Canadian boreal
  forests.
• Eltons analyses were based on trapping records
  maintained by the Hudsons Bay Company
• of special interest in these records are the
  regular and closely linked fluctuations in
  populations of the lynx and its principal prey,
  the snowshoe hare
• What causes these cycles?

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Some Fundamental Questions

• The basic question of population biology is
• what factors influence the size and stability of
  populations?
• Because most species are both consumers and
  resources for other consumers, this basic
  question may be refocused
• are populations limited primarily by what they
  eat or by what eats them?

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More Questions

• Do predators reduce the size of prey populations
  substantially below the carrying capacity set by
  resources for the prey?
• this question is prompted by interests in
  management of crop pests, game populations, and
  endangered species
• Do the dynamics of predator-prey interactions
  cause populations to oscillate?
• this question is prompted by observations of
  predator-prey cycles in nature, such as Eltons
  lynx and hare

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Consumers can limit resource populations.

• An example populations of cyclamen mites, a pest
  of strawberry crops in California, can be
  regulated by a predatory mite
• cyclamen mites typically invade strawberry crops
  soon after planting and build to damaging levels
  in the second year
• predatory mites invade these fields in the second
  year and keep cyclamen mites in check
• Experimental plots in which predatory mites were
  controlled by pesticide had cyclamen mite
  populations 25 times larger than untreated plots.

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What makes an effective predator?

• Predatory mites control populations of cyclamen
  mites in strawberry plantings because, like other
  effective predators
• they have a high reproductive capacity relative
  to that of their prey
• they have excellent dispersal powers
• they can switch to alternate food resources when
  their primary prey are unavailable

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Consumer Control in Aquatic Ecosystems

• An example sea urchins exert strong control on
  populations of algae in rocky shore communities
• in urchin removal experiments, the biomass of
  algae quickly increases
• in the absence of predation, the composition of
  the algal community also shifts
• large brown algae replace coralline and small
  green algae that can persist in the presence of
  predation

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Predator and prey populations often cycle.

• Population cycles observed in Canada are present
  in many species
• large herbivores (snowshoe hares, muskrat, ruffed
  grouse, ptarmigan) have cycles of 9-10 years
• predators of these species (red foxes, lynx,
  marten, mink, goshawks, owls) have similar cycles
• small herbivores (voles and lemmings) have cycles
  of 4 years
• predators of these species (arctic foxes,
  rough-legged hawks, snowy owls) also have similar
  cycles
• cycles are longer in forest, shorter in tundra

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Predator-Prey Cycles A Simple Explanation

• Population cycles of predators lag slightly
  behind population cycles of their prey
• predators eat prey and reduce their numbers
• predators go hungry and their numbers drop
• with fewer predators, the remaining prey survive
  better and prey numbers build
• with increasing numbers of prey, the predator
  populations also build, completing the cycle

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Time Lags in Predator-Prey Systems

• Delays in responses of births and deaths to an
  environmental change produce population cycles
• predator-prey interactions have time lags
  associated with the time required to produce
  offspring
• 4-year and 9- or 10-year cycles in Canadian
  tundra or forests suggest that time lags should
  be 1 or 2 years, respectively
• these could be typical lengths of time between
  birth and sexual maturity
• the influence of conditions in one year might not
  be felt until young born in that year are old
  enough to reproduce

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Time Lags in Pathogen-Host Systems

• Immune responses can create cycles of infection
  in certain diseases
• measles produced epidemics with a 2-year cycle in
  pre-vaccine human populations
• two years were required for a sufficiently large
  population of newly susceptible infants to
  accumulate

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Time Lags in Pathogen-Host Systems

• other pathogens cycle because they kill
  sufficient hosts to reduce host density below the
  level where the pathogens can spread in the
  population
• such cycling is evident in polyhedrosis virus in
  tent caterpillars
• In many regions, tent caterpillar infestations
  last about 2 years before the virus brings its
  host population under control
• In other regions, infestations may last up to 9
  years
• Forest fragmentation which creates abundant
  forest edge tends to prolong outbreaks of the
  tent caterpillar
• Why?
• Increased forest edge exposes caterpillars to
  more intense sunlight ? inactivates the virus ?
  thus, habitat manipulation here has secondary
  effects

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Laboratory Investigations of Predators and Prey

• G.F. Gause conducted simple test-tube experiments
  with Paramecium (prey) and Didinium (predator)
• in plain test tubes containing nutritive medium,
  the predator devoured all prey, then went extinct
  itself
• in tubes with a glass wool refuge, some prey
  escaped predation, and the prey population
  reexpanded after the predator went extinct
• Gause could maintain predator-prey cycles in such
  tubes by periodically adding more predators

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Predator-prey interactions can be modeled by
simple equations.

• Lotka and Volterra independently developed models
  of predator-prey interactions in the 1920s
• dR/dt rR - cRP
• describes the rate of increase of the prey
  population, where
• R is the number of prey
• P is the number of predators
• r is the preys per capita exponential growth
  rate
• c is a constant expressing efficiency of
  predation

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Lotka-Volterra Predator-Prey Equations

• A second equation
• dP/dt acRP - dP
• describes the rate of increase of the predator
  population, where
• P is the number of predators
• R is the number of prey
• a is the efficiency of conversion of food to
  growth
• c is a constant expressing efficiency of
  predation
• d is a constant related to the death rate of
  predators

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Predictions of Lotka-Volterra Models

• Predators and prey both have equilibrium
  conditions (equilibrium isoclines or zero growth
  isoclines)
• P r/c for the predator
• R d/ac for the prey
• when these values are graphed, there is a single
  joint equilibrium point where population sizes of
  predator and prey are stable
• when populations stray from joint equilibrium,
  they cycle with period T 2? / ?rd

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Cycling in Lotka-Volterra Equations

• A graph with axes representing sizes of the
  predator and prey populations illustrates the
  cyclic predictions of Lotka-Volterra
  predator-prey equations
• a population trajectory describes the joint
  cyclic changes of P and R counterclockwise
  through the P versus R graph

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Factors Changing Equilibrium Isoclines

• The prey isocline increases if
• r increases or c decreases, or both
• the prey population would be able to support the
  burden of a larger predator population
• The predator isocline increases if
• d increases and either a or c decreases
• more prey would be required to support the
  predator population

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Other Lotka-Volterra Predictions

• Increasing the predation efficiency (c) alone in
  the model reduces isoclines for predators and
  prey
• fewer prey would be needed to sustain a given
  capture rate
• the prey population would be less able to support
  the more efficient predator
• Increasing the birth rate of the prey (r) should
  lead to an increase in the population of
  predators but not the prey themselves.

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Modification of Lotka-Volterra Models for
Predators and Prey

• There are various concerns with the
  Lotka-Volterra equations
• the lack of any forces tending to restore the
  populations to the joint equilibrium
• this condition is referred to as a neutral
  equilibrium
• the lack of any satiation of predators
• each predator consumes a constant proportion of
  the prey population regardless of its density

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The Functional Response

• A more realistic description of predator behavior
  incorporates alternative functional responses,
  proposed by C.S. Holling
• type I response rate of consumption per predator
  is proportional to prey density (no satiation)
• type II response number of prey consumed per
  predator increases rapidly, then plateaus with
  increasing prey density
• type III response like type II, except predator
  response to prey is depressed at low prey density

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The Holling Type III Response

• What would cause the type III functional
  response?
• heterogeneous habitat, which provides a limited
  number of safe hiding places for prey
• lack of reinforcement of learned searching
  behavior due to a low rate of prey encounter
• switching by predator to alternative food sources
  when prey density is low

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The Numerical Response

• If individual predators exhibit satiation (type
  II or III functional responses), continued
  predator response to prey must come from
• increase in predator population through local
  population growth or immigration from elsewhere
• this increase is referred to as a numerical
  response

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Several factors reduce predator-prey oscillations.

• All of the following tend to stabilize predator
  and prey numbers (in the sense of maintaining
  nonvarying equilibrium population sizes)
• predator inefficiency
• density-dependent limitation of either predator
  or prey by external factors
• alternative food sources for the predator
• refuges from predation at low prey densities
• reduced time delays in predator responses to
  changes in prey abundance

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Destabilizing Influences

• The presence of predator-prey cycles indicates
  destabilizing influences
• such influences are typically time delays in
  predator-prey interactions
• developmental period
• time required for numerical responses by
  predators
• time course for immune responses in animals and
  induced defenses in plants
• when destabilizing influences outweigh
  stabilizing ones, population cycles may arise

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Predator-prey systems can have more than one
stable state.

• Prey are limited both by their food supply and
  the effects of predators
• some populations may have two or more stable
  equilibrium points, or multiple stable states
• such a situation arises when
• prey exhibits a typical pattern of
  density-dependence (reduced growth as carrying
  capacity is reached)
• predator exhibits a type III functional response

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Three Equilibria

• The model of predator and prey responses to prey
  density results in three stable or equilibrium
  states
• a stable point A (low prey density) where
• any increase in prey population is more than
  offset by increasingly efficient prey capture by
  predator
• an unstable point B (intermediate prey density)
  where
• control of prey shifts from predation to resource
  limitation
• a stable point C where
• prey escapes control by predator and is regulated
  near its carrying capacity by resource scarcity

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Implications of Multiple Stable States

• Predators may control prey at a low level (point
  A in model), but can lose the potential to
  regulate prey at this level if prey density
  increases above point B in the model
• a predator controlling an agricultural pest can
  lose control of that pest if the predator is
  suppressed by another factors for a time
• once the pest population exceeds point B, it will
  increase to a high level at point C, regardless
  of predator activity
• at this point, pest population will remain high
  until some other factor reduces the pest
  population below point B in the model

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Effects of Different Levels of Predation

• Inefficient predators cannot maintain prey at low
  levels (prey primarily limited by resources).
• Increased predator efficiency adds a second
  stable point at low prey density.
• Further increases in predator functional and
  numerical responses may eliminate a stable point
  at high prey density
• Intense predation at all prey levels can drive
  the prey to extinction

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When can predators drive prey to extinction?

• It is clearly possible for predators to drive
  their prey to extinction when
• predators and prey are maintained in simple
  laboratory systems
• predators are maintained at high density by
  availability of alternative, less preferred prey
• biological control may be enhanced by providing
  alternative prey to parasites and predators

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What equilibria are likely?

• Models of predator and prey suggest that
• prey are more likely to be held at relatively low
  or relatively high equilibria (or perhaps both)
• equilibria at intermediate prey densities are
  highly unlikely

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Summary 1

• Predators can, in some cases, reduce prey
  populations far below their carrying capacities.
• Predators and prey often exhibit regular cycles,
  typically with cycle lengths of 4 years or 9-10
  years.
• Lotka and Volterra proposed simple mathematical
  models of predator and prey that predicted
  population cycles.

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Summary 2

• Increased productivity of the prey should
  increase the predators population but not the
  preys.
• Functional responses describe the relationship
  between the rate at which an individual predator
  consumes prey and the density of prey.
• The Lotka-Volterra models incorporate a type I
  functional response, which is inherently
  unstable.
• Type III functional responses can result in
  stable regulation of prey populations at low
  densities.

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Summary 3

• Type III functional responses can result from
  switching.
• Numerical responses describe responses of
  predators to prey density through local
  population growth and immigration.
• Several factors tend to stabilize predator-prey
  interactions, but time lags tend to destabilize
  them.
• Predator-prey systems may have multiple stable
  points.