BIOE 20C Lecture Notes - Lecture 13: Logistic Function, Exponential Growth, Carrying Capacity
12 May 2018
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Exponential growth
• dN/dt = rN means that growth rate is constant
• Produces exponential growth pattern
o Plot has chape of a parabola
o Population increases by steadily increasing amounts
• In reality, as population increases, resources become more limiting
Logistic Growth
• Most populations in nature reach a stable (ie long term) size over time
• Produces an S shaped plot
o Rapid growth at first
o Growth rate slows until it stabilizes (becomes 0)
• Carrying capacity (K) = maximum number
Logistic Growth Equation
• dN/dt = rN x (K - N)/K
• If N is small, r is close to rmax
• As N increases, r decreases
Exponential vs Logistic Growth
• Exponential growth: r constant over time
o r does not change with density
o Density dependant
• Logistic growth: r changes as a function of density
o r decreases with increasing density
o Density dependent
Factor Limiting Pop Growth
• Density independent
o Net affected by population size
o Typically abiotic factors
• Density dependent
o Becomes more pronounced with increasing density
o Typically biotic factors
R vs K Selected Species
• r selected species
o Refers to intrinsic growth rates
o Rapid growth
o Good dispersal
o Short life span (low survivorship/ high fecundity)
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Document Summary
Exponential growth: dn/dt = rn means that growth rate is constant, produces exponential growth pattern, plot has chape of a parabola, population increases by steadily increasing amounts. In reality, as population increases, resources become more limiting. Logistic growth: most populations in nature reach a stable (ie long term) size over time, produces an s shaped plot, rapid growth at first, growth rate slows until it stabilizes (becomes 0, carrying capacity (k) = maximum number. Logistic growth equation: dn/dt = rn x (k - n)/k, as n increases, r decreases. If n is small, r is close to rmax. Exponential vs logistic growth: exponential growth: r constant over time r does not change with density, density dependant, logistic growth: r changes as a function of density r decreases with increasing density, density dependent. Factor limiting pop growth: density independent, net affected by population size, typically abiotic factors, density dependent, becomes more pronounced with increasing density, typically biotic factors.
