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Lecture 28

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

by OC2595580

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**preview**shows half of the first page. to view the full**3 pages of the document.**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

dependent)

• 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

growth

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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