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lecture note 15 for BGYB50


Biological Sciences
Course Code
Herbert Kronzucker

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- Despite what politicians and economists would like you to believe, unbridled growth is
not possible all growth in nature has its limits!
- Biological populations grow at widely differing rates, and they can grow exponentially
(or geometrically) for some time, but the rate of increase will ultimately flatten out
(logistic or sigmoidal growth), or the population collapses (irruptive growth); sometimes,
oscillations in population density are observed (partial collapses that are followed by
- Both irruptive and oscillatory growth are common among bacteria and viruses, but also
occur in mammals (e.g. snowshoe hare and Canadian lynx)
- Graphically, geometric growth (Nt = N0 !t; geometric rate of increase: ! = Nt+1/Nt)
results in a J-curve pattern resembling exponential growth (Nt = N0 ert, i.e. ! = er), but the
former is used to describe J-curve-type growth in discretely-growing populations (e.g.
annual plants like many grasses or Phlox, with bursts of seed production, rather then
overlapping generations of reproducing individuals; points in such graphs should NOT be
connected!), while the latter is observed in populations with overlapping generations (e.g.
Scotch pine colonization after the last ice age in Europe, collared doves introduced to
Britain; by definition, the e function can only be used to model continuous growth!)
- Each environment imposes different limits upon natural population increase: this is
known as the carrying capacity (K) of each environment, i.e. the maximal sustainable
number of individuals of a population in that environment
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