Lecture 10 Predator-prey dynamics (s) PDF

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BISC 204 Dynamics)of)Predation) ! A) Several!general!questions!concern!studies!of!predator-prey!interactions,!and!their! subsequent!effects!on!population!dynamics!and!community!structure:!) ) Do!predators!or!consumers!reduce!the!densities!of!prey!populations!below!the!level! defined!by!their!own!resources!(i.e.,!carrying!capacity)?! ! Do!predator-prey!interactions!cause!populations!to!oscillate!in!time!and!space?) ) ) B) Predators!often!reduce!prey!below!their!carrying!capacity.!! ! C))Predator-prey!systems!sometimes!cycle.!The!most!well-known!example!was!documented! by!Charles!Elton!in!the!early!1900s—fur!records!of!lynx!and!hares!from!the!boreal! forest!from!the!Hudson’s!Bay!Company’s!records!! ) ) *There!are!many!other!examples!of! predator-prey!cycles!in!rodents,!fishes,! insects,!plankton,!bacteria,!and!a!variety! of!other!taxa.! ! ! • causes!of!these!cycles!are!not!always! entirely!clear! ! ! • but!often!occur!when!there!is!a! strong!single!predator-single!prey! interaction! ) What)hypotheses)have)been)put)forward)to)explain)these)cycles?) ) ) ) ) ) D))Predator-prey)interactions)can)be)modeled)with)simple)math.)The!simplest!and! best!understood!model!is!referred!to!as!the!Lotka-Volterra!predator-prey!model! ) **similar)to)the)equations)we)learned)about)simple)population)dynamics)for) continuously)reproducing)populations)(exponential)and)logistic)) ) )

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BISC 204 Prey)equation)(V))

Predator)equation)(P))

! dV/dt!=!aV!–!bVP! ! where:!a!is!the!prey!growth!rate,!b!is!the!capture! efficiency!of!the!predator) ! dP/dt!=!dVP---cP! ! where:!d-is!the!predator!conversion!efficiency!(given!a! defined!capture!efficiency),!and!c!is!the!predator!death! rate)

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! Although!these!models!are!mathematically!very!simple,!they!produce!complicated! dynamics,!some!of!which!resemble!real!predator-prey!cycles!observed!in!nature!and!in! experiments.! ! Like)all)models,)they)make)assumptions,)what)are)they)and)how)realistic)are)they?) ) ) ) ) If!a!population!is!in!a!relatively!stable!state!it!is!said!to!be!in!equilibrium!–!this!keeps! populations!within!sustainable!ranges.!! ! Models!can!be!used!to!assess!the!impact!of!changes!to!a!population!or!populations.!A! population!model!is!basically!a!set!of!rules!that!determine!the!way!a!population!behaves.! ! !

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BISC 204 Mechanistic)explanations)for)cyclic)behaviour.) ) ) ) E))Modifications)to)Lotka-Volterra)can)yield)greater)realism)(in)terms)of)how)some) predator-prey)systems)actually)behave).)) ) ) ) Prey)equation)(V))with) ! ! carrying)capacity)of) dV/dt!=!aV[1-V/K]!–!bVP! ! prey) ! ! where:!a!is!the!prey!growth!rate,!b!is!the!capture! ! efficiency!of!the!predator) ! Modification)to)prey) ! ! isocline)(Rosenberg) ! and)MacArthur)) ! P ! ! ! ! K) V ! ) ! ! ! ! Lab!experiments!with!predatory!mites!and!their!prey!conducted!by!Huffaker!show!! In!a!simple!environment!predator!prey!populations!are!unstable!–!they!go!extinct.! ! In!a!more!complex!environment!predator!prey!populations!go!through!stable!cycles.! Complex!environments!provided!prey!with!a!refuge!because!predators!were!unable!to! disperse!as!fast!as!their!prey!and!predator!numbers!therefore!lagged!behind!their!prey! However,!the!severity!of!this!predator!control!of!prey!varies!widely!among!taxa,! ecosystems,!and!through!time.!! ! ! ! ! ! ! !

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