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# Ch11 Population Growth and Regulation3.pdf

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University of Toronto St. George

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UNI101Y1

Spencer Barrett

Winter

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there is another reason to express pop. growth as an exponential function
whereas the change in absolute # of indiv. depends on the pop. size, the change in the
logarithm of pop. size is linear over time
if we plot the natural logarithm (ln) of N as a function of time, we obtain a straight
line whose slope is the value of r
we can see this by taking the logarithm of the expression for the exponential growth,
N(t) = N(0)e , which is ln[N(t)] = ln[N(0)] + rt
o this is the eqn for the straight line w/ an intercept at t = 0 of ln[N(0)] and a slope
of r
the growth rates of diff pop., or of a single pop. over time, can be compared readily by
plotting the logarithm of pop. size over time
Calculating Population Growth Rates from Birth and Death Rates
exponential growth: the indiv. contribution to pop. growth (r) is the diff. b/w birth rate
(b) and death rate (d) calculated on a per capita basis, thus r = b – d
geometric growth: the per capita growth rate per unit of time (R) is the diff. b/w the
per capita rates of birth (B) and death (D) per unit of time, thus R = B – D & λ = 1 + R
in the case of individuals moving b/w subpopulations: r = b – d + i – e
immigration (i), emigration (e)
birth and death rates pertain to populations not to indiv.
ex. an indiv. groundhog dies only once, it can’t have a personal death rate
when birth and deaths are averaged over a pop., they take on meaning as rates of
d

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