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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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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 • Population equilibrium point • Function of limiting factors • K is the notation
Positive Density Dependence • Increases in population size increase vital rates • Allee Effect • Decrease:decrease also possible and goes by the same name
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
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
Range: Mainly east of Mississippi River • North to Hudson Bay • South to Texas
Allee effect • Human overexploitation • Habitat destruction • Chestnut blight eliminated chestnut trees & reduced food sources • Fragmented hardwood forest habitat
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
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
Positive and Negative DD Threshold Strength
More thoughts on chaos… • What happens if K varies?
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
What does DD usually look like? • Juvenile survival declines
What does DD usually look like? • Juvenile survival declines • Age at first reproduction increases
What does DD usually look like? • Juvenile survival declines • Age at first reproduction increases • Adult survival declines
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!
Density dependence • Males matter • If sex ratio is changing, a female only model may not catch important issues
Red Deer (Mysterud et al. 2001) Females Males
Red Deer (Coulson et al. 1997) Sample Size: >200,000 resights over 20 years!
Sockeye Salmon Constant Proportion Asymptotic relationship All salmon killed at low density, constant number at high density Quinn et al. 2003
It’s dangerous, be careful! Detecting Density Dependence
Detecting Density Dependence Freckleton et al. 2006
Detecting Density Dependence Freckleton et al. 2006
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