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Lecture 28

BIOLOGY 1M03 Lecture Notes - Lecture 28: Whooping Crane, Exponential Growth, Carrying Capacity

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Ben Evans

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Biology 1M03 Lecture 28
Intrinsic Rates of Increase
Idea that different populations and different species will have different rates of growth
o E.coli rmax = 60/individual x day
o Homo sapiens rmax = 0.0003/individual x day, 0.11/individual x year
At a point in time under real conditions, populations grow at the per capita growth rate r (not rmax)
Real World Situations
Actual growth is often interrupted by catastrophic reductions in population sizes (not density
If conditions remain constant (r does not change over time), the population experiences
exponential growth
o Very high r has a bigger curve on a graph, whereas very low r is almost straight
Real World Limits to Growth
Density dependent factors
o Examples:
Food or shelter limited by competition
Sunlight limited by shading of other plants
Increased predation rate (predators tracking prey increase)
Density dependent factors reduce growth rates
o Increased death rates
o Decreased birthrate
Sigmoidal-shaped growth curves are a result of density dependence
o Growth rate slows at high density
Carrying capacity
o The maximum population size that a particular environment can sustain
Logistic Growth Model
Should decrease growth as density increases
Let K=carrying capacity
o K-N/ K
As N approaches K, term approaches 0
o Growth rate slows to almost nothing
As N approaches 0, the term approaches 1
dN/dt= r0N *((K-N)/K), or dN/dt= rmaxN *((K-N)/K)
o r0 = rate of growth when a population is very small (close to 0)
o Important to not use generic "r", which can be measured at any stage in a population's
Whooping Crane Example
Hunting and habitat loss reduced whooping crane population
Conservation efforts has brought population up, but still far from carrying capacity
Cranes breed once a year, therefore have a discrete growth (as opposed to continuous growth,
which is not tied to a particular annual season)
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