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## Predation (Chapter 18)

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**Predation (Chapter 18)**• Predator-prey cycles • Models of predation • Functional vs. numeric responses • Stability in predator-prey models**Two big themes:**• Predators can limit prey populations. This keeps populations below K.**Predator and prey populations increase and decrease in**regular cycles.**A verbal model of predator-prey cycles:**• Predators eat prey and reduce their numbers • Predators go hungry and decline in number • With fewer predators, prey survive better and increase • Increasing prey populations allow predators to increase And repeat…**The Lotka-Volterra Model: Assumptions**• Prey grow exponentially in the absence of predators. • Predation is directly proportional to the product of prey and predator abundances (random encounters). • Predator populations grow based on the number of prey. Death rates are independent of prey abundance.**R = prey population size (“resource”)**P = predator population size r = exponential growth rate of the prey c = capture efficiency of the predators**removal of prey**by predators rate of change in the prey population intrinsic growth rate of the prey**For the predators:**a = efficiency with which prey are converted into predators d = death rate of predators death rate of predators rate of change in the predator population conversion of prey into new predators**Prey population reaches equilibrium when dR/dt = 0**• equilibrium – state of balance between opposing forces • populations at equilibrium do not change • Prey population stabilizes based on the size of the predator population**Predator population reaches equilibriumwhen dP/dt = 0**• Predator population stabilizes based on the size of the prey population**Isocline – a line along which populations will not change**over time. • Predator numbers will stay constant if R = d/ac • Prey numbers will stay constant if P = r/c.**Predators are stable when:**Prey are stable when: Number of Predators (P) Number of prey (R)**Prey are stable when:**Prey Isocline Number of Predators (P) r/c d/ac Number of prey (R)**Predators are stable when:**Predator isocline Number of Predators (P) d/ac Number of prey (R)**equilibrium**Number of Predators (P) r/c d/ac Number of prey (R)**Predation (Chapter 18)**• Finish Lotka-Volterra model • Functional vs. numeric responses • Stability in predator-prey cycles**Number of predators depends on the prey population.**Predator isocline Number of Predators (P) Predators decrease Predators increase d/ac Number of prey (R)**Number of prey depends on the predator population.**Prey decrease Prey Isocline Number of Predators (P) r/c Prey increase d/ac Number of prey (R)**Changing the number of prey can cause 2 types of responses:**Functional response – relationship between an individual predator’s food consumption and the density of prey Numeric response – change in the population of predators in response to prey availability**Lotka-Volterra: prey are consumed in direct proportion to**their availability (cRP term) • known as Type I functional response • predators never satiate! • no limit on the growth rate of predators!**Type II functional response – consumption rate increases**at first, but eventually predators satiate (upper limit on consumption rate)**Type III functional response – consumption rate is low at**low prey densities, increases, and then reaches an upper limit**Why type III functional response?**• at low densities, prey may be able to hide, but at higher densities hiding spaces fill up • predators may be more efficient at capturing more common prey • predators may switch prey species as they become more/less abundant**Numeric response comes from**• Population growth • (though most predator populations grow slowly) • Immigration • predator populations may be attracted to prey outbreaks**Predator-prey cycles can be unstable**• efficient predators can drive prey to extinction • if the population moves away from the equilibrium, there is no force pulling the populations back to equilibrium • eventually random oscillations will drive one or both species to extinction**Factors promoting stability in predator-prey relationships**• Inefficient predators (prey escaping) • less efficient predators (lower c) allow more prey to survive • more living prey support more predators • Outside factors limit populations • higher d for predators • lower r for prey**Alternative food sources for the predator**• less pressure on prey populations • Refuges from predation at low prey densities • prevents prey populations from falling too low • Rapid numeric response of predators to changes in prey population**Huffaker’s experiment on predator-prey coexistence**• 2 mite species, predator and prey**Initial experiments – predators drove prey extinct then**went extinct themselves • Adding barriers to dispersal allowed predators and prey to coexist.**Prey population outbreaks**Population growth curve for logistic population growth Per capita population growth rate ro K Density of prey population**Type III functional response curve for predators**Per capita death rate K Density of prey population**Point A – stable equilibrium; population increases below A**and decreases above A A**Unstable equilibrium – equilibrium point from which a**population will move to a new, different equilibrium if disturbed**Point B – unstable equilibrium; below B, predation reduces**population to A; above B, predators are less efficient, so population grows to C B**Between B & C – predators are less efficient, prey**increase up to C B**Predator-prey systems can have multiple stable states**• Reducing the number of predators can lead to an outbreak of prey