BILD 3 Lecture Notes - Lecture 22: Exponential Growth, Logistic Function, Bild
13 Jun 2018
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BILD 3 Lecture 22
5/25/2018
• Rate of growth= (number of births/population)-(number of deaths/population) in a
given time period
• Unrestricted growth over multiple intervals is exponential, like compounding interest
• Why do we model exponential growth?
o Recognizes the multiplicative nature of population growth
o Key to the Theory of Natural Selection because of overproduction of offspring
and thus competition
o May occur in phases when resources are temporarily unlimited
• Do real populations ever grow exponentially? Yes, in some circumstances, but
populations will never grow exponentially for long
o Colonization of a new habitat
o Recovery after catastrophe
o Pulse of new nutrients
o Introduced species
• Populations cannot grow exponentially for long because the increasing population size
gives rise to
o Food shortages and other limiting resources
o Greater intraspecific aggression
o Increased attention from predators
o Greater risk of disease outbreaks
▪ These factors will lower birth rates and increase death rates
• Populations exhibiting logistic growth are directly or indirectly regulated by their own
density
o Carrying capacity (K) is the maximum population size that the environment can
support. Stable populations tend to fluctuate around K
o K id determined by the availability of resources, and the amount of
disease/predation/parasites etc.
o Ex: when sheep were initially introduced into Australia in the 1800s
o
▪ N=number of individuals
o Whe a populatio surpasses it’s arryig apaity (whe N>K), the population is
in decline and has a negative (1-(N/K))
• The maximum growth rate of a population is 40%. What will be its growth rate when the
population has reached half of its carrying capacity?
o 20%
▪ Population reduced down to the simplest fraction is ½. So then, N/K is
0.5. 1-0.5=.5→50%. So (50%)(40%)=20% because the maximum growth
rate is 40%
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Yes, in some circumstances, but populations will never grow exponentially for long: colonization of a new habitat, recovery after catastrophe, pulse of new nutrients. Introduced species: populations cannot grow exponentially for long because the increasing population size gives rise to, food shortages and other limiting resources, greater intraspecific aggression. What will be its growth rate when the population has reached half of its carrying capacity: 20, population reduced down to the simplest fraction is . So (50%)(40%)=20% because the maximum growth rate is 40: population growth begins to slow at the point of inflection, community ecology. Is the scientific study of the interactions between species in communities: a community is an assemblage of populations that occupy a particular area or habitat. The populations interact to form their own system: ecological niche. Is the su(cid:373) total of a(cid:374) orga(cid:374)is(cid:373)"s use of (cid:271)ioti(cid:272) a(cid:374)d a(cid:271)ioti(cid:272) resour(cid:272)es i(cid:374) its environment.
