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Questions?. Density Dependence. Density dependence. Influence of population density on the vital rates of individuals Negative Positive Competition Interference or contests Food, mates, territories … Winners and losers Exploitative and scrambles Everyone loses. Carrying capacity.

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  1. Questions?

  2. Density Dependence

  3. Density dependence • Influence of population density on the vital rates of individuals • Negative • Positive • Competition • Interference or contests • Food, mates, territories… • Winners and losers • Exploitative and scrambles • Everyone loses

  4. Carrying capacity • Population equilibrium point • Function of limiting factors • K is the notation

  5. Logistic Growth

  6. Ricker Discrete Logistic

  7. Positive Density Dependence • Increases in population size increase vital rates • Allee Effect • Decrease:decrease also possible and goes by the same name

  8. Allee Effect • Mechanisms? • Minimize predation • Detection & defense • Predator confusion • Predator swamping • Foraging advantage • Access to food • Cooperative resource defense • Reproductive success • Finding mates • Conditioning of environment

  9. Overexploitation and Allee effects in the Passenger pigeon • In the pigeon & dove family, but more closely related to tropical fruit pigeons than to other North American columbids. • Low reproductive rate, long lived • 3-5 billion passenger pigeons when Columbus arrived • Current population of ALL birds in U.S. approximately 6 billion

  10. Range: Mainly east of Mississippi River • North to Hudson Bay • South to Texas

  11. Allee effect • Human overexploitation • Habitat destruction • Chestnut blight eliminated chestnut trees & reduced food sources • Fragmented hardwood forest habitat

  12. Allee effect • Passenger pigeons needed large flocks for courtship ritual, synchronization of mating condition • Were never successfully captive bred • Last one died in 1914, at age 29

  13. Including + & - density dependence

  14. Positive and Negative DD Only negative density dependence Weak Allee effect K = Carrying capacity Strong Allee effect Realized per-capita growth rate Abundance A = Allee effect threshold

  15. Positive and Negative DD

  16. Positive and Negative DD Threshold Strength

  17. Positive and Negative DD

  18. More thoughts on chaos… • What happens if K varies?

  19. Variation in K

  20. Variation in K

  21. Component Density Dependence

  22. Vital rates are not equal • DD effect on one rate does not necessary = DD effect on λ • Correlations and compensation may further cloud the picture

  23. What does DD usually look like?

  24. What does DD usually look like? • Juvenile survival declines

  25. What does DD usually look like? • Juvenile survival declines • Age at first reproduction increases

  26. What does DD usually look like? • Juvenile survival declines • Age at first reproduction increases • Adult survival declines

  27. What does DD usually look like? • Juvenile survival declines • Age at first reproduction increases • Adult survival declines • Look out, adult survival can have a big impact!

  28. Density dependence • Males matter • If sex ratio is changing, a female only model may not catch important issues

  29. Examples of Density dependence

  30. Red Deer

  31. Red Deer (Mysterud et al. 2001) Females Males

  32. More Red Deer

  33. Red Deer (Coulson et al. 1997) Sample Size: >200,000 resights over 20 years!

  34. Red Deer (Clutton-Brock et al. 1987)

  35. Sockeye Salmon

  36. Sockeye Salmon Constant Proportion Asymptotic relationship All salmon killed at low density, constant number at high density Quinn et al. 2003

  37. Sockeye Salmon

  38. It’s dangerous, be careful! Detecting Density Dependence

  39. Detecting Density Dependence Freckleton et al. 2006

  40. Detecting Density Dependence Freckleton et al. 2006

  41. Detecting Density Dependence • Sampling variance can cause the appearance of density dependence • Problem grows with larger variance • Splitting population can cause the appearance of density dependence

  42. Next: Predation

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