BIOLOGY 1B Lecture Notes - Lecture 4: Exponential Growth, Song Sparrow, Logistic Function
12 Jun 2018
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Lecture 4
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• No population grows forever
o Many exhibit S shaped growth curves with more or less stable max population size
o Carrying capacity
• Fur seals- hunted a lot
o Fluctuating population; Recovery of population
o Declined to very low level, protections put in place, recovery and then stability
• Logistic growth model
o dN/dt= rN((K-N)/K)
▪ r= intrinsic rate of increase
• depends how quickly population will increase starting at low density
• K= carrying capacity- max pop at which N stabilizes
o S shaped curve
o Population growth declines towards zero as N approaches K
o The absolute number of individuals is greatest when slope is greatest
o The population grows exponentially when N is small
o In exponential, per capita growth rate is r
o In logistic, per capita growth rate is r((K-N)/K)
o R does not change as N approaches K
o R and K don’t change; only N changes
o When population is really small, the model simplifies to exponential
• Density dependent factors that influence population dynamics
o Ex. song sparrow
▪ Fluctuating around an average
▪ Inverse relationships between number of young and juvenile mortality
• Birth rate and death rate are dependent on each other
• Larger population, fewer born, less die
o Per capita rates: per individual
o B= b/N; D=d/N per capita
o R= b-d ; if r=0 constant rate
• Human population growth
o Close to exponential till industrial revolution
o Steady growth till industrial revolution then shoots up; steep slope
o In late 20th century to present; continued exponential growth
▪ Slowly declining
• Density independent factors that influence population dynamics
• Life history
o Suite of traits related to a speiceis lifespan and timing and pattern of reproduction
o R and K selected populations
▪ K selected: density dependent selection; selects for life history traits that enhance
an individuals fitness when a population is fairly stable
• Late age of reproduction, many reproductions, lot of parental care
• Long life span, long maturation, low mortality, few offspring
▪ R selection: density independent selection; selects for life history traits that
maximize reproduction and the ability for population to increase rapidly at low
density
• Early age of reproduction, short life span, fast maturation, high mortality,
lots of offspring, few reproductions, no parental care
▪ Elephant vs. rabbit
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