Lectures6-7_4pp

# 5 an elephant has a volume of about 5 cubic meters

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Unformatted text preview: a volume of about 5 cubic meters! Darwin: After 500 yrs there would be 15 million elephants (more like 16,000)… not such a great mathematician, but:! After 2500 yrs, there would be 73 x 1018 elephants! Which would occupy 1/3 of the volume of the Earth! (actual population size currently around 500,000)! so, something is limiting Density dependent regulation: per individual birth and death rates depend on density! ! As density increases:! #Per individual birth rate decreases! #Per individual death rate increases! carrying capacity (K) is the maximum population size that can be supported by available resources or physical space! What causes birth and death rates to change with increasing density?! Resource depletion (energy limitation):! Decreases per individual birth rates (fecundity)! Decreased individual growth (fewer offspring)! Increased death rate due to starvation! Waste product accumulation! Space limitation! Predators! #intraspeciﬁc (cannibalism)! #interspeciﬁc (predation or disease)! Dispersal or emigration! Growth rate decelerates as K is approached and popuation stabilizes at K! Maximum growth rate is reached! Paramecium in lab culture dishes shows logistic growth… why? What limits population growth of Paramecium in the lab?! Growth starts nearly exponential! Logistic population growth: including density dependence! dN/dt = rN [1-(N/K)]! Exponential growth! *K = carrying capacity! Fraction of K remaining! In words: population growth equals the amount expected under exponential growth multiplied by what percent of the carrying capacity is left [understand this!]! If N is very close to K, then population growth will be slow! ! How do we get this type of growth?! If N is very small...
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