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

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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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• 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 ad r alues he populatios are

decreasing, increasing, or constant

o Dereasig: λ < ad r <

o Increasing: λ = ad r =

o Costat: λ > ad 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 desity

▪ Common: tornadoes, hurricanes, floods, fires

▪ Others: extreme temp, droughts

• Note that the size of the populatio does’t affet 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.