# BIO205H5 Chapter Notes - Chapter 12: California Quail, Exponential Growth, Protist

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School
UTM
Department
Biology
Course
BIO205H5
Professor BIO205
Chapter 12: Population growth and dynamics (corresponding to lecture 8)
Population dynamics: changes in population size
Demography: study of population
Under ideal conditions, populations grow rapidly
o The exponential growth model
A model of population growth in which the population increases
continuously at an exponential rate
Nt = N0ert
Growth rate: individuals produced individuals die
Intrinsic growth rate (r): the highest possible per capita growth rate for a
population
Figure 12.1: The exponential growth model. Over time, a population living under
ideal conditions can experience a rapid increase in population size. This
produces a J-shaped curve. Human Population growth is an example.
Rate of growth at any point in time is the derivative of the exponential
growth model
DN/Dt (change in pop/unit of time)= rN
High intrinsic growth = greater change in pop size
A constant intrinsic growth rate results in increasing numbers of
individuals in a population and the population experiences
exponential growth
o The geometric growth model
NOT applied to species that reproduce throughout the year (humans)
Most species and plants have discrete breeding seasons due to resources
(birds, mammals birth in spring and then decrease in size due to deaths)
Figure 12.2: The discrete breeding events of the California quail. Each
generation of new quail produced each spring is represented by a
different colour. Because births only happen in the spring, the growth of
the California quail is better modelled by a geometric growth model than
by an exponential growth model.
The geometric growth model: a model of population growth that
compares population sizes at regular time intervals
Allows comparison of sizes at yearly intervals for example
Nt=N0λt
o Nt is the population at time t
o N0 is the population at time 0
o λ is the ratio of the population size between intervals
(growth rate)
o t is time in years
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Unlock all 7 pages and 3 million more documents. Example a population of quail is initially 100. Their growth rate is
1.5. After 5 years what is the size of the population?
o Nt=N0λt
o N5=(100)(1.5)5
= 759
N=N0(λt-1) ……………the change in population between time
intervals
Comparing the exponential and geometric growth models
Geometric and exponential growth are related by
λ = er
When this relationship is graphed, we can come to some
conclusions
Figure 12.3. Comparing the growth of populations using the
exponential and geometric growth models. Exponential model
uses continuous data and geometric model uses discrete data.
Even so, the two models reveal the same increase in population
size over time.
Figure 12.4. A comparison of λ ad r alues he populatios are
decreasing, increasing, or constant
o Dereasig: λ <  ad r < 
o Increasing: λ =  ad r = 
o Costat: λ >  ad r > 
Population Doubling Time
Doubling time is the time required for a population to double in
size
For exponential models: t= loge2 / r
For geometric models = t = loge2 / loge λ
loge2 = 0.69
** note that t is in years
Populations have growth limits
o Density-Independent Factors: factors that limit population size regardless of the
populatio’s desity
Others: extreme temp, droughts
Note that the size of the populatio does’t affet the deaths
Using density independent factors to estimate abundance is quite
accurate (figure 12.5)
Figure 12.6: Bark beetles. Many of these lodgepole pines in central British
Columbia have been severely damaged by bark beetles, which consume
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## Document Summary

Intrinsic growth rate (r): the highest possible per capita growth rate for a population: figure 12. 1: the exponential growth model. Over time, a population living under ideal conditions can experience a rapid increase in population size. Each generation of new quail produced each spring is represented by a different colour. After 5 years what is the size of the population: nt=n0 t, n5=(100)(1. 5)5. = 759: n=n0( t-1) the change in population between time intervals, comparing the exponential and geometric growth models, geometric and exponential growth are related by. = er: when this relationship is graphed, we can come to some conclusions, figure 12. 3. Comparing the growth of populations using the exponential and geometric growth models. Exponential model uses continuous data and geometric model uses discrete data. Even so, the two models reveal the same increase in population size over time: figure 12. 4.