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Exploiter-Victim Relationships. Host-Parasite: Host death need not occur, and often does not; birth rate of host reduced by parasite Host-Parasitoid: Host death always occurs Predator-Prey: Death rate of prey increased by predators Herbivore-Plant: May resemble predation or parasitism.
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Exploiter-Victim Relationships Host-Parasite: Host death need not occur, and often does not; birth rate of host reduced by parasite Host-Parasitoid: Host death always occurs Predator-Prey: Death rate of prey increased by predators Herbivore-Plant: May resemble predation or parasitism
Functional Response Basic forms to consider: Type I: Linear increase in # attacked with increasing # prey (insatiable predator) Type II: Gradual levelling off As predators become satiated Type III: Predators satiable as in Type II, but hunt inefficiently at low prey densities I Change in predator’s attack behavior as prey density increases # attacked/pred/time II III Prey density
Toxorhynchites Functional Response, sympatric & allopatric prey: IL (allopatric) NC (sympatric)
Fraction killed per predator/time Type I Type II Type III Prey Density Type II and III: satiable predators become less effective at controlling prey as prey become more abundant.
Lotka-Volterra Predator-Prey Model: Assume: Random search, producing encounters between prey and predators (and subsequent attacks) proportional to the product of their densities (attack rate = a’) Exponential prey population growth in absence of predator, with constant growth rate, r Death rate of predator is constant = q Birth rate of predator proportional to #prey consumed
Prey growth equation Prey: Without predator, dN/dt=rN If predator searches with attack rate a’, and there are C Predators, then deaths due to predation = a’CN dN/dt = rN - a’CN
Predator Growth Equation dC/dt = (birth rate - death rate)C Death rate assumed constant = q Birth rate: #prey consumed x conversion constant, f = (#prey consumed)x f # prey consumed = a’CN (see prey equation) births = a’CNf birth rate = a’Nf dC/dt = (a’Nf - q)C
Equilibrium Conditions, Prey Too many predators Prey: dN/dt = rN - a’CN = 0 r-a’C = 0 C = r/a’ C = r/a’ C Not enough predators N
Equilibrium conditions, predators dC/dt = (a’Nf - q)C = 0 a’Nf - q = 0 N = q/a’f More than enough prey Not enough prey C N = q/a’f N
Humped Prey curves Change in phytoplankton density at different combinations of Rotifer density and phytoplankton density Rotifer density Phytoplankton density
Why the Prey curve has a Hump Resource limits for prey at high densities (fewer preds needed to keep in check) But, predator is most effective at low prey densities
Effects of a humped prey curve: C N Damped oscillation (stable point) Neutral stability Increasing oscillation (unstable)
Effects of a humped prey curve: C N time Damped oscillation (stable point) Neutral stability Increasing oscillation (unstable)