SlideShare a Scribd company logo
PAGE
1
Name:______________________________
HOW DO POPULATIONS GROW?
Student Guide
Thomas Austin was an Englishman who migrated to southern
Australia to farm the land. His property, Barwon Park was
located near Winchelsea, Victoria. In October of 1859,
homesick for his homeland and the hunting he used to enjoy,
Thomas enlisted his nephew, William Austin who still resided
in England, to send two dozen wild English rabbits, which
Thomas then released onto his land. Thomas dismissed the act
as benign, not realizing the drastic consequences of his actions.
Due to the well-known prolific nature of rabbits, and the
suitability of the Australian climate, within 6 years, this
population of 24 rabbits had increased to 22 million. By the
1930’s, Australia’s rabbit populations were estimated to exceed
750 million! How did the populations grow so large, so
quickly? And what might the consequences be on the local
ecosystem?
Procedure
1. Select a partner to work with and obtain 10 pennies. The
pennies represent 10 individual rabbits in a population. Place
the pennies in a container and shake them up. Pour them out
onto a table. Each penny that lands with a tail showing
represents a rabbit that gets to produce an offspring that is
added to the original population of 10. [So chances are that
approximately five individuals got to reproduce and your new
population contains about 15 individuals (i.e., about 15
pennies)]. Now remove 10% of your population representing
individuals that have died. Round down if the number is not an
integer.
2. Repeat this procedure several times until the rabbit
population exceeds 100 individuals. After each episode of births
and deaths (i.e., after each “generation”), record the population
size (i.e., the total number of pennies) in the chart below. Also
record the Idealized population size (given that exactly half of
your individuals reproduced each generation with NO ONE
dying—go ahead and report the idealized numbers in decimals,
but only keep two decimals. I’ve gotten it started for you.)
Flip/Generation Number
Experimental
Population Size
Idealized
Population Size (no death)
0
10
10
1
15
2
22.5
3
33.75
4
5
6
7
8
9
10
3. Using the graph on the next page, plot population size (on the
y axis) versus flip/generation number (on the x axis). Use the
data on your graph to determine the slope during each time
interval (REMEMBER: slope is the change in y over the change
in x, or rise over run; i.e., slope = (y/(x). Record the slopes
below.
Interval
Slope
Between generations 0 and 1
Between generations 1 and 2
Between generations 2 and 3
Between generations 3 and 4
Between generations 4 and 5
Between generations 5 and 6
Between generations 6 and 7
Between generations 7 and 8
4. How do the slopes change? What do they tell you about how
the rabbit population is growing? What if all the slopes were the
same? What would that tell you about population growth? Does
this suggest a reason why the rabbit population grew so rapidly
in Australia? Explain.
5. How does this pattern of growth affect the rate at which the
population is increasing? In other words, in each generation,
what percent increase did the population experience (i.e., the
number of new individuals added divided by the total number of
individuals present)? Did the rate of increase also increase with
each generation? See if you can find out by calculating some
sort of growth rate for each time interval. To simplify the math,
ignore death rates and use the idealized numbers (i.e., 10, 15,
22.5, 33.75, and so on). Record the rate of population increase
for each of the first four time intervals in the table below:
Interval
Growth Rate
Between generations 0 and 1
Between generations 1 and 2
Between generations 2 and 3
Between generations 3 and 4
6. Based on your calculations, how does growth rate vary across
time? Why?
7. How did you calculate growth rate (r)? Can you write a
generic formula that could be used on any population?
r =
Do you suppose that this is a realistic pattern of growth for
rabbits, and can it continue in this fashion indefinitely? Let’s
look at some numbers from a hypothetical population of rabbits
on the island of New Zealand, off the coast of Australia
(Australia does not currently have a reasonable rabbit number
map; currently, recording systems rely on individual reports).
Use the initial generation interval to calculate a value for r.
What value did you get?
Table 1. Initial Growth of a Rabbit Population (in thousands)
____________________________________
Generations
# of rabbits
____________________________________
0
10
1
18
____________________________________
8. Can you predict the size of future generations? Use your r
value to generate expected numbers for the next several time
intervals – at least up to and including interval t = 8. Record
your expected numbers in Table 2.
Table 2. Continued Growth of a Rabbit Population
Generations
Expected Numbers
Observed Numbers
0
10
10
1
18
2
29
3
47
4
71
5
119
6
174
7
257
8
351
9
441
10
513
11
560
12
595
13
629
14
641
15
651
16
656
17
660
18
662
9. How did you decide how many individuals would be added to
each generation? Can you write a generic formula that could be
used on any population, given that we know the growth rate, r?
10. Now plot a graph showing both the expected and observed
numbers. How do they compare? If they do not match, can you
suggest one or more reasons (alternative hypotheses) for the
mismatch? List them below and be prepared to share them with
the class.
11. Our equation for exponential population growth does not
generate expected numbers that match the observed numbers in
Table 2 very well, at least not after the first few time intervals.
This means that we either have to throw out our equation (our
mathematical model) and generate a better one, or modify the
equation to make it better (in the sense that it will generate
expected numbers that do in fact match the observed numbers).
Because our initial equation seems to do a good job for the first
few time intervals, let’s not throw it out but instead let’s see if
we can modify it in some way that might make it work better for
later time intervals. Read on.
12. How might the environment affect population growth? Is
there a limit to how much it can hold, a carrying capacity? Let’s
represent carrying capacity with a K and assume for the sake of
argument we have a growing population with a carrying
capacity of 100. With your partner try to come up with a way to
write an equation to describe how close our growing population
is to its carrying capacity of 100, i.e., how much “room” the
population still has to grow. (See the figure below.)
a) For example, if the population size is 75, how much room
does it still have to grow?
b) Can you write the population’s amount of “room to grow” as
a percent?
c) Suppose another population growing in an environment with
a carrying capacity of 600 is now at 250. How much room does
it have to grow? Express this as a percent and show how you
derived the percent.
d) Now, try to write a general expression for the relationship
using the symbol K for carrying capacity and N for population
size. The expression should describe how much room the
population has to grow before it hits its environment’s carrying
capacity. What is the range of values that your expression can
have? When is the value largest? When is it smallest?
13. Recall our graph of the growing rabbit population. What
appears to be the carrying capacity of this environment?
14. The population grows more slowly as it approaches K. In
other words, with lots of room to grow, the population grows
rapidly. And with little room to grow, the population grows
slowly. Can you write an equation that uses this new “carrying
capacity” issue to predict population growth? [Hint: Start with
your exponential equation and add in our “carrying capacity”
element.] Be prepared to discuss it with the class.
15. Now that you have your equation, let’s test its ability to
model the rabbit population’s growth. First, use your equation
to predict each generation of rabbits. How does your prediction
compare now? Is this equation a better way to predict
population growth?
16. When populations are growing in a limited environment,
when is their growth the largest? (Hint, to figure this out, graph
the amount of individuals added to the population with each
generation.)
17. Around the same time that rabbits were introduced to
Australia, the red fox was also introduced, for the same purpose
of hunting. However, after seeing that it was an efficient
predator to rabbits, additional red foxes were introduced after
1859 to help control rabbit populations. How do you suppose
this will affect rabbit populations? Graph your prediction
below.
18. What do you suppose will happen to the red fox population?
Add a curve representing predator population to the graph
above.
19. As red fox populations increase, what might happen to
rabbit populations? As rabbit populations decrease, what might
happen to red fox populations? Over time, what pattern do you
predict will emerge? Graph it below:
Alfred Lotka and Vito Volterra independently derived a pair of
equations to explain the relationships between predator and
prey. The simultaneous non-linear, differential equations are
now known as the Lotka-Volterra Predator-Prey Model. They
are shown below:
Prey:
– aNP
Predator:
– rd P
Where
rmax= growth rate of the prey
N = prey population size
P = predator population size
a = the probability of dying due to predation
rd = death rate of predator with or without prey present
b = the probability of capturing prey AND converting the
usable energy into offspring
20. Notice that the first part of the prey equation (rmaxN) is the
exponential growth equation. Explain how the addition of the
“aNP” term limits the prey population. Is it a density-
dependent or density-independent factor? How can you tell?
21. Your instructor will show you simulations of the Lotka-
Volterra model using the computer program, Populus. We will
set up a typical fox-rabbit predator-prey relationship using the
following values:
rmax= 1.7
N = 500
P = 20
a = 0.05
rd = 0.10
b = 0.005
Graph the relationship below:
22. How would you simulate an increase in predator skill at
capturing prey? What does this do to our model? Why?
23. How would you simulate a decrease in prey reproductive
ability? What does this do to our model? Why?
24. How would you simulate a decrease in predator numbers due
to a relocation program? What does this do to our model?
Why?
25. Notice in our model that the “b” term is about 10% of the
“a” term’s value. Why is that? Come up with some hypotheses
and be prepared to share them with the class.
PAGE  1Name______________________________HOW DO POPULAT.docx

More Related Content

Similar to PAGE 1Name______________________________HOW DO POPULAT.docx

ESS Topic 8.1 - Human population dynamics guide
ESS Topic 8.1 - Human population dynamics guideESS Topic 8.1 - Human population dynamics guide
ESS Topic 8.1 - Human population dynamics guide
Brad Kremer
 
p. 1Lab 6 Population Genetics Hardy-Weinberg TheoremOBJEC.docx
p. 1Lab 6 Population Genetics  Hardy-Weinberg TheoremOBJEC.docxp. 1Lab 6 Population Genetics  Hardy-Weinberg TheoremOBJEC.docx
p. 1Lab 6 Population Genetics Hardy-Weinberg TheoremOBJEC.docx
alfred4lewis58146
 
ECOL203403 Assignment 1 Age Structure of a Population Using Life.docx
ECOL203403 Assignment 1 Age Structure of a Population Using Life.docxECOL203403 Assignment 1 Age Structure of a Population Using Life.docx
ECOL203403 Assignment 1 Age Structure of a Population Using Life.docx
tidwellveronique
 
Population dynamics
Population dynamicsPopulation dynamics
Population dynamics
CarolinaSoler14
 
Leslie Matrices
Leslie MatricesLeslie Matrices
Leslie Matrices
Lorisha Riley
 
Presentation
PresentationPresentation
Data Visualization for Beginners
Data Visualization for BeginnersData Visualization for Beginners
Data Visualization for Beginners
Nika Aleksejeva
 
popgrowth.ppt
popgrowth.pptpopgrowth.ppt
popgrowth.ppt
VivekChauhan516259
 
popgrowth.ppt
popgrowth.pptpopgrowth.ppt
popgrowth.ppt
brendontodal
 
8.1 Exploring Exponential Functions
8.1 Exploring Exponential Functions8.1 Exploring Exponential Functions
8.1 Exploring Exponential Functions
Kristen Fouss
 
Lab 7 introduction
Lab 7 introductionLab 7 introduction
Lab 7 introduction
Erik D. Davenport
 
Populations
PopulationsPopulations
Populations
tas11244
 
Life Of Galileo Conflict Essay. Online assignment writing service.
Life Of Galileo Conflict Essay. Online assignment writing service.Life Of Galileo Conflict Essay. Online assignment writing service.
Life Of Galileo Conflict Essay. Online assignment writing service.
Nicole Barnes
 
1. A small accounting firm pays each of its five clerks $35,000, t.docx
1. A small accounting firm pays each of its five clerks $35,000, t.docx1. A small accounting firm pays each of its five clerks $35,000, t.docx
1. A small accounting firm pays each of its five clerks $35,000, t.docx
SONU61709
 
Linear Paper final
Linear Paper finalLinear Paper final
Linear Paper final
Charlotte Rose Hamilton
 
Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...
Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...
Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...
Danny Dorling
 
1 The annual growth rate r for population A is 005 The.pdf
1 The annual growth rate r for population A is 005 The.pdf1 The annual growth rate r for population A is 005 The.pdf
1 The annual growth rate r for population A is 005 The.pdf
abdulmajidandco
 
PopulationEcology52.ppt
PopulationEcology52.pptPopulationEcology52.ppt
PopulationEcology52.ppt
Jake933493
 
GEOGRAPHY Population Ecology HSC MAHARASHTRA
GEOGRAPHY Population Ecology HSC MAHARASHTRAGEOGRAPHY Population Ecology HSC MAHARASHTRA
GEOGRAPHY Population Ecology HSC MAHARASHTRA
TwinsIT2
 
Intro to statistics formatted
Intro to statistics   formattedIntro to statistics   formatted
Intro to statistics formatted
aurrico
 

Similar to PAGE 1Name______________________________HOW DO POPULAT.docx (20)

ESS Topic 8.1 - Human population dynamics guide
ESS Topic 8.1 - Human population dynamics guideESS Topic 8.1 - Human population dynamics guide
ESS Topic 8.1 - Human population dynamics guide
 
p. 1Lab 6 Population Genetics Hardy-Weinberg TheoremOBJEC.docx
p. 1Lab 6 Population Genetics  Hardy-Weinberg TheoremOBJEC.docxp. 1Lab 6 Population Genetics  Hardy-Weinberg TheoremOBJEC.docx
p. 1Lab 6 Population Genetics Hardy-Weinberg TheoremOBJEC.docx
 
ECOL203403 Assignment 1 Age Structure of a Population Using Life.docx
ECOL203403 Assignment 1 Age Structure of a Population Using Life.docxECOL203403 Assignment 1 Age Structure of a Population Using Life.docx
ECOL203403 Assignment 1 Age Structure of a Population Using Life.docx
 
Population dynamics
Population dynamicsPopulation dynamics
Population dynamics
 
Leslie Matrices
Leslie MatricesLeslie Matrices
Leslie Matrices
 
Presentation
PresentationPresentation
Presentation
 
Data Visualization for Beginners
Data Visualization for BeginnersData Visualization for Beginners
Data Visualization for Beginners
 
popgrowth.ppt
popgrowth.pptpopgrowth.ppt
popgrowth.ppt
 
popgrowth.ppt
popgrowth.pptpopgrowth.ppt
popgrowth.ppt
 
8.1 Exploring Exponential Functions
8.1 Exploring Exponential Functions8.1 Exploring Exponential Functions
8.1 Exploring Exponential Functions
 
Lab 7 introduction
Lab 7 introductionLab 7 introduction
Lab 7 introduction
 
Populations
PopulationsPopulations
Populations
 
Life Of Galileo Conflict Essay. Online assignment writing service.
Life Of Galileo Conflict Essay. Online assignment writing service.Life Of Galileo Conflict Essay. Online assignment writing service.
Life Of Galileo Conflict Essay. Online assignment writing service.
 
1. A small accounting firm pays each of its five clerks $35,000, t.docx
1. A small accounting firm pays each of its five clerks $35,000, t.docx1. A small accounting firm pays each of its five clerks $35,000, t.docx
1. A small accounting firm pays each of its five clerks $35,000, t.docx
 
Linear Paper final
Linear Paper finalLinear Paper final
Linear Paper final
 
Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...
Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...
Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we ta...
 
1 The annual growth rate r for population A is 005 The.pdf
1 The annual growth rate r for population A is 005 The.pdf1 The annual growth rate r for population A is 005 The.pdf
1 The annual growth rate r for population A is 005 The.pdf
 
PopulationEcology52.ppt
PopulationEcology52.pptPopulationEcology52.ppt
PopulationEcology52.ppt
 
GEOGRAPHY Population Ecology HSC MAHARASHTRA
GEOGRAPHY Population Ecology HSC MAHARASHTRAGEOGRAPHY Population Ecology HSC MAHARASHTRA
GEOGRAPHY Population Ecology HSC MAHARASHTRA
 
Intro to statistics formatted
Intro to statistics   formattedIntro to statistics   formatted
Intro to statistics formatted
 

More from alfred4lewis58146

For this assignment, students will need to observe the activities th.docx
For this assignment, students will need to observe the activities th.docxFor this assignment, students will need to observe the activities th.docx
For this assignment, students will need to observe the activities th.docx
alfred4lewis58146
 
For this assignment, select a human service organization from .docx
For this assignment, select a human service organization from .docxFor this assignment, select a human service organization from .docx
For this assignment, select a human service organization from .docx
alfred4lewis58146
 
For this Assignment, read the case study for Claudia and find tw.docx
For this Assignment, read the case study for Claudia and find tw.docxFor this Assignment, read the case study for Claudia and find tw.docx
For this Assignment, read the case study for Claudia and find tw.docx
alfred4lewis58146
 
For this assignment, download the A6 code pack. This zip fil.docx
For this assignment, download the A6 code pack. This zip fil.docxFor this assignment, download the A6 code pack. This zip fil.docx
For this assignment, download the A6 code pack. This zip fil.docx
alfred4lewis58146
 
For this assignment, create infographic using the Canva website..docx
For this assignment, create infographic using the Canva website..docxFor this assignment, create infographic using the Canva website..docx
For this assignment, create infographic using the Canva website..docx
alfred4lewis58146
 
For this assignment, compare  California during the Great Depression.docx
For this assignment, compare  California during the Great Depression.docxFor this assignment, compare  California during the Great Depression.docx
For this assignment, compare  California during the Great Depression.docx
alfred4lewis58146
 
For this assignment, create a 10- to 12-slide presentation in Mi.docx
For this assignment, create a 10- to 12-slide presentation in Mi.docxFor this assignment, create a 10- to 12-slide presentation in Mi.docx
For this assignment, create a 10- to 12-slide presentation in Mi.docx
alfred4lewis58146
 
For this assignment, begin by reading chapters 12-15 in Dr. Bells t.docx
For this assignment, begin by reading chapters 12-15 in Dr. Bells t.docxFor this assignment, begin by reading chapters 12-15 in Dr. Bells t.docx
For this assignment, begin by reading chapters 12-15 in Dr. Bells t.docx
alfred4lewis58146
 
For this assignment, assume you are the new Secretary of Homelan.docx
For this assignment, assume you are the new Secretary of Homelan.docxFor this assignment, assume you are the new Secretary of Homelan.docx
For this assignment, assume you are the new Secretary of Homelan.docx
alfred4lewis58146
 
For this assignment, address the following promptsIntroductor.docx
For this assignment, address the following promptsIntroductor.docxFor this assignment, address the following promptsIntroductor.docx
For this assignment, address the following promptsIntroductor.docx
alfred4lewis58146
 
For this assignment, analyze the play by focusing on one of the .docx
For this assignment, analyze the play by focusing on one of the .docxFor this assignment, analyze the play by focusing on one of the .docx
For this assignment, analyze the play by focusing on one of the .docx
alfred4lewis58146
 
For this assignment I would like you to answer these questions.docx
For this assignment I would like you to answer these questions.docxFor this assignment I would like you to answer these questions.docx
For this assignment I would like you to answer these questions.docx
alfred4lewis58146
 
For the Weekly Reports I need 2 reports. For the First two weeks the.docx
For the Weekly Reports I need 2 reports. For the First two weeks the.docxFor the Weekly Reports I need 2 reports. For the First two weeks the.docx
For the Weekly Reports I need 2 reports. For the First two weeks the.docx
alfred4lewis58146
 
For the shortanswer questions,you will need to respo.docx
For the shortanswer questions,you will need to respo.docxFor the shortanswer questions,you will need to respo.docx
For the shortanswer questions,you will need to respo.docx
alfred4lewis58146
 
For the sake of argument (this essay in particular), lets prete.docx
For the sake of argument (this essay in particular), lets prete.docxFor the sake of argument (this essay in particular), lets prete.docx
For the sake of argument (this essay in particular), lets prete.docx
alfred4lewis58146
 
For the proposal, each student must describe an interface they a.docx
For the proposal, each student must describe an interface they a.docxFor the proposal, each student must describe an interface they a.docx
For the proposal, each student must describe an interface they a.docx
alfred4lewis58146
 
For the project, you will be expected to apply the key concepts of p.docx
For the project, you will be expected to apply the key concepts of p.docxFor the project, you will be expected to apply the key concepts of p.docx
For the project, you will be expected to apply the key concepts of p.docx
alfred4lewis58146
 
For the past several weeks you have addressed several different area.docx
For the past several weeks you have addressed several different area.docxFor the past several weeks you have addressed several different area.docx
For the past several weeks you have addressed several different area.docx
alfred4lewis58146
 
For the Mash it Up assignment, we experimented with different ways t.docx
For the Mash it Up assignment, we experimented with different ways t.docxFor the Mash it Up assignment, we experimented with different ways t.docx
For the Mash it Up assignment, we experimented with different ways t.docx
alfred4lewis58146
 
For the first time in modern history, the world is experiencing a he.docx
For the first time in modern history, the world is experiencing a he.docxFor the first time in modern history, the world is experiencing a he.docx
For the first time in modern history, the world is experiencing a he.docx
alfred4lewis58146
 

More from alfred4lewis58146 (20)

For this assignment, students will need to observe the activities th.docx
For this assignment, students will need to observe the activities th.docxFor this assignment, students will need to observe the activities th.docx
For this assignment, students will need to observe the activities th.docx
 
For this assignment, select a human service organization from .docx
For this assignment, select a human service organization from .docxFor this assignment, select a human service organization from .docx
For this assignment, select a human service organization from .docx
 
For this Assignment, read the case study for Claudia and find tw.docx
For this Assignment, read the case study for Claudia and find tw.docxFor this Assignment, read the case study for Claudia and find tw.docx
For this Assignment, read the case study for Claudia and find tw.docx
 
For this assignment, download the A6 code pack. This zip fil.docx
For this assignment, download the A6 code pack. This zip fil.docxFor this assignment, download the A6 code pack. This zip fil.docx
For this assignment, download the A6 code pack. This zip fil.docx
 
For this assignment, create infographic using the Canva website..docx
For this assignment, create infographic using the Canva website..docxFor this assignment, create infographic using the Canva website..docx
For this assignment, create infographic using the Canva website..docx
 
For this assignment, compare  California during the Great Depression.docx
For this assignment, compare  California during the Great Depression.docxFor this assignment, compare  California during the Great Depression.docx
For this assignment, compare  California during the Great Depression.docx
 
For this assignment, create a 10- to 12-slide presentation in Mi.docx
For this assignment, create a 10- to 12-slide presentation in Mi.docxFor this assignment, create a 10- to 12-slide presentation in Mi.docx
For this assignment, create a 10- to 12-slide presentation in Mi.docx
 
For this assignment, begin by reading chapters 12-15 in Dr. Bells t.docx
For this assignment, begin by reading chapters 12-15 in Dr. Bells t.docxFor this assignment, begin by reading chapters 12-15 in Dr. Bells t.docx
For this assignment, begin by reading chapters 12-15 in Dr. Bells t.docx
 
For this assignment, assume you are the new Secretary of Homelan.docx
For this assignment, assume you are the new Secretary of Homelan.docxFor this assignment, assume you are the new Secretary of Homelan.docx
For this assignment, assume you are the new Secretary of Homelan.docx
 
For this assignment, address the following promptsIntroductor.docx
For this assignment, address the following promptsIntroductor.docxFor this assignment, address the following promptsIntroductor.docx
For this assignment, address the following promptsIntroductor.docx
 
For this assignment, analyze the play by focusing on one of the .docx
For this assignment, analyze the play by focusing on one of the .docxFor this assignment, analyze the play by focusing on one of the .docx
For this assignment, analyze the play by focusing on one of the .docx
 
For this assignment I would like you to answer these questions.docx
For this assignment I would like you to answer these questions.docxFor this assignment I would like you to answer these questions.docx
For this assignment I would like you to answer these questions.docx
 
For the Weekly Reports I need 2 reports. For the First two weeks the.docx
For the Weekly Reports I need 2 reports. For the First two weeks the.docxFor the Weekly Reports I need 2 reports. For the First two weeks the.docx
For the Weekly Reports I need 2 reports. For the First two weeks the.docx
 
For the shortanswer questions,you will need to respo.docx
For the shortanswer questions,you will need to respo.docxFor the shortanswer questions,you will need to respo.docx
For the shortanswer questions,you will need to respo.docx
 
For the sake of argument (this essay in particular), lets prete.docx
For the sake of argument (this essay in particular), lets prete.docxFor the sake of argument (this essay in particular), lets prete.docx
For the sake of argument (this essay in particular), lets prete.docx
 
For the proposal, each student must describe an interface they a.docx
For the proposal, each student must describe an interface they a.docxFor the proposal, each student must describe an interface they a.docx
For the proposal, each student must describe an interface they a.docx
 
For the project, you will be expected to apply the key concepts of p.docx
For the project, you will be expected to apply the key concepts of p.docxFor the project, you will be expected to apply the key concepts of p.docx
For the project, you will be expected to apply the key concepts of p.docx
 
For the past several weeks you have addressed several different area.docx
For the past several weeks you have addressed several different area.docxFor the past several weeks you have addressed several different area.docx
For the past several weeks you have addressed several different area.docx
 
For the Mash it Up assignment, we experimented with different ways t.docx
For the Mash it Up assignment, we experimented with different ways t.docxFor the Mash it Up assignment, we experimented with different ways t.docx
For the Mash it Up assignment, we experimented with different ways t.docx
 
For the first time in modern history, the world is experiencing a he.docx
For the first time in modern history, the world is experiencing a he.docxFor the first time in modern history, the world is experiencing a he.docx
For the first time in modern history, the world is experiencing a he.docx
 

Recently uploaded

How to deliver Powerpoint Presentations.pptx
How to deliver Powerpoint  Presentations.pptxHow to deliver Powerpoint  Presentations.pptx
How to deliver Powerpoint Presentations.pptx
HajraNaeem15
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
Dr. Shivangi Singh Parihar
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
GeorgeMilliken2
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
AyyanKhan40
 
Cognitive Development Adolescence Psychology
Cognitive Development Adolescence PsychologyCognitive Development Adolescence Psychology
Cognitive Development Adolescence Psychology
paigestewart1632
 
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingYour Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Excellence Foundation for South Sudan
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
Wahiba Chair Training & Consulting
 
The Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collectionThe Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collection
Israel Genealogy Research Association
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Nicholas Montgomery
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
TechSoup
 
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
สมใจ จันสุกสี
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
Dr. Mulla Adam Ali
 
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptxNEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
iammrhaywood
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching AptitudeUGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
S. Raj Kumar
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
Jyoti Chand
 
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptxChapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Denish Jangid
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
Celine George
 
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
imrankhan141184
 
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptxPrésentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
siemaillard
 

Recently uploaded (20)

How to deliver Powerpoint Presentations.pptx
How to deliver Powerpoint  Presentations.pptxHow to deliver Powerpoint  Presentations.pptx
How to deliver Powerpoint Presentations.pptx
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
 
Cognitive Development Adolescence Psychology
Cognitive Development Adolescence PsychologyCognitive Development Adolescence Psychology
Cognitive Development Adolescence Psychology
 
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingYour Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
 
The Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collectionThe Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collection
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
 
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
 
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptxNEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching AptitudeUGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
 
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptxChapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptx
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
 
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
 
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptxPrésentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
 

PAGE 1Name______________________________HOW DO POPULAT.docx

  • 1. PAGE 1 Name:______________________________ HOW DO POPULATIONS GROW? Student Guide Thomas Austin was an Englishman who migrated to southern Australia to farm the land. His property, Barwon Park was located near Winchelsea, Victoria. In October of 1859, homesick for his homeland and the hunting he used to enjoy, Thomas enlisted his nephew, William Austin who still resided in England, to send two dozen wild English rabbits, which Thomas then released onto his land. Thomas dismissed the act as benign, not realizing the drastic consequences of his actions. Due to the well-known prolific nature of rabbits, and the suitability of the Australian climate, within 6 years, this population of 24 rabbits had increased to 22 million. By the 1930’s, Australia’s rabbit populations were estimated to exceed 750 million! How did the populations grow so large, so quickly? And what might the consequences be on the local ecosystem? Procedure 1. Select a partner to work with and obtain 10 pennies. The pennies represent 10 individual rabbits in a population. Place the pennies in a container and shake them up. Pour them out onto a table. Each penny that lands with a tail showing represents a rabbit that gets to produce an offspring that is added to the original population of 10. [So chances are that approximately five individuals got to reproduce and your new population contains about 15 individuals (i.e., about 15 pennies)]. Now remove 10% of your population representing
  • 2. individuals that have died. Round down if the number is not an integer. 2. Repeat this procedure several times until the rabbit population exceeds 100 individuals. After each episode of births and deaths (i.e., after each “generation”), record the population size (i.e., the total number of pennies) in the chart below. Also record the Idealized population size (given that exactly half of your individuals reproduced each generation with NO ONE dying—go ahead and report the idealized numbers in decimals, but only keep two decimals. I’ve gotten it started for you.) Flip/Generation Number Experimental Population Size Idealized Population Size (no death) 0 10 10 1 15 2 22.5 3 33.75 4 5
  • 3. 6 7 8 9 10 3. Using the graph on the next page, plot population size (on the y axis) versus flip/generation number (on the x axis). Use the data on your graph to determine the slope during each time interval (REMEMBER: slope is the change in y over the change in x, or rise over run; i.e., slope = (y/(x). Record the slopes below. Interval Slope Between generations 0 and 1 Between generations 1 and 2 Between generations 2 and 3 Between generations 3 and 4 Between generations 4 and 5 Between generations 5 and 6
  • 4. Between generations 6 and 7 Between generations 7 and 8
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21. 4. How do the slopes change? What do they tell you about how the rabbit population is growing? What if all the slopes were the same? What would that tell you about population growth? Does this suggest a reason why the rabbit population grew so rapidly in Australia? Explain.
  • 22. 5. How does this pattern of growth affect the rate at which the population is increasing? In other words, in each generation, what percent increase did the population experience (i.e., the number of new individuals added divided by the total number of individuals present)? Did the rate of increase also increase with each generation? See if you can find out by calculating some sort of growth rate for each time interval. To simplify the math, ignore death rates and use the idealized numbers (i.e., 10, 15, 22.5, 33.75, and so on). Record the rate of population increase for each of the first four time intervals in the table below: Interval Growth Rate Between generations 0 and 1 Between generations 1 and 2 Between generations 2 and 3 Between generations 3 and 4 6. Based on your calculations, how does growth rate vary across time? Why? 7. How did you calculate growth rate (r)? Can you write a generic formula that could be used on any population? r = Do you suppose that this is a realistic pattern of growth for rabbits, and can it continue in this fashion indefinitely? Let’s look at some numbers from a hypothetical population of rabbits on the island of New Zealand, off the coast of Australia (Australia does not currently have a reasonable rabbit number map; currently, recording systems rely on individual reports). Use the initial generation interval to calculate a value for r. What value did you get?
  • 23. Table 1. Initial Growth of a Rabbit Population (in thousands) ____________________________________ Generations # of rabbits ____________________________________ 0 10 1 18 ____________________________________ 8. Can you predict the size of future generations? Use your r value to generate expected numbers for the next several time intervals – at least up to and including interval t = 8. Record your expected numbers in Table 2. Table 2. Continued Growth of a Rabbit Population Generations Expected Numbers Observed Numbers 0 10 10 1 18 2 29 3
  • 25. 651 16 656 17 660 18 662 9. How did you decide how many individuals would be added to each generation? Can you write a generic formula that could be used on any population, given that we know the growth rate, r? 10. Now plot a graph showing both the expected and observed numbers. How do they compare? If they do not match, can you suggest one or more reasons (alternative hypotheses) for the mismatch? List them below and be prepared to share them with the class.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40.
  • 41.
  • 42.
  • 43. 11. Our equation for exponential population growth does not generate expected numbers that match the observed numbers in Table 2 very well, at least not after the first few time intervals. This means that we either have to throw out our equation (our mathematical model) and generate a better one, or modify the equation to make it better (in the sense that it will generate expected numbers that do in fact match the observed numbers). Because our initial equation seems to do a good job for the first few time intervals, let’s not throw it out but instead let’s see if we can modify it in some way that might make it work better for later time intervals. Read on. 12. How might the environment affect population growth? Is there a limit to how much it can hold, a carrying capacity? Let’s represent carrying capacity with a K and assume for the sake of argument we have a growing population with a carrying capacity of 100. With your partner try to come up with a way to write an equation to describe how close our growing population is to its carrying capacity of 100, i.e., how much “room” the population still has to grow. (See the figure below.) a) For example, if the population size is 75, how much room does it still have to grow? b) Can you write the population’s amount of “room to grow” as a percent?
  • 44. c) Suppose another population growing in an environment with a carrying capacity of 600 is now at 250. How much room does it have to grow? Express this as a percent and show how you derived the percent. d) Now, try to write a general expression for the relationship using the symbol K for carrying capacity and N for population size. The expression should describe how much room the population has to grow before it hits its environment’s carrying capacity. What is the range of values that your expression can have? When is the value largest? When is it smallest? 13. Recall our graph of the growing rabbit population. What appears to be the carrying capacity of this environment? 14. The population grows more slowly as it approaches K. In other words, with lots of room to grow, the population grows rapidly. And with little room to grow, the population grows slowly. Can you write an equation that uses this new “carrying capacity” issue to predict population growth? [Hint: Start with your exponential equation and add in our “carrying capacity” element.] Be prepared to discuss it with the class. 15. Now that you have your equation, let’s test its ability to model the rabbit population’s growth. First, use your equation to predict each generation of rabbits. How does your prediction compare now? Is this equation a better way to predict population growth? 16. When populations are growing in a limited environment, when is their growth the largest? (Hint, to figure this out, graph the amount of individuals added to the population with each generation.)
  • 45.
  • 46.
  • 47.
  • 48.
  • 49.
  • 50.
  • 51.
  • 52.
  • 53.
  • 54.
  • 55.
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 61.
  • 62. 17. Around the same time that rabbits were introduced to Australia, the red fox was also introduced, for the same purpose of hunting. However, after seeing that it was an efficient predator to rabbits, additional red foxes were introduced after 1859 to help control rabbit populations. How do you suppose this will affect rabbit populations? Graph your prediction below.
  • 63.
  • 64.
  • 65.
  • 66.
  • 67.
  • 68.
  • 69.
  • 70.
  • 71. 18. What do you suppose will happen to the red fox population? Add a curve representing predator population to the graph above. 19. As red fox populations increase, what might happen to rabbit populations? As rabbit populations decrease, what might happen to red fox populations? Over time, what pattern do you predict will emerge? Graph it below:
  • 72.
  • 73.
  • 74.
  • 75.
  • 76.
  • 77.
  • 78.
  • 79.
  • 80. Alfred Lotka and Vito Volterra independently derived a pair of equations to explain the relationships between predator and prey. The simultaneous non-linear, differential equations are now known as the Lotka-Volterra Predator-Prey Model. They are shown below: Prey: – aNP Predator:
  • 81. – rd P Where rmax= growth rate of the prey N = prey population size P = predator population size a = the probability of dying due to predation rd = death rate of predator with or without prey present b = the probability of capturing prey AND converting the usable energy into offspring 20. Notice that the first part of the prey equation (rmaxN) is the exponential growth equation. Explain how the addition of the “aNP” term limits the prey population. Is it a density- dependent or density-independent factor? How can you tell? 21. Your instructor will show you simulations of the Lotka- Volterra model using the computer program, Populus. We will set up a typical fox-rabbit predator-prey relationship using the following values:
  • 82. rmax= 1.7 N = 500 P = 20 a = 0.05 rd = 0.10 b = 0.005 Graph the relationship below:
  • 83.
  • 84.
  • 85.
  • 86.
  • 87.
  • 88.
  • 89.
  • 90.
  • 91. 22. How would you simulate an increase in predator skill at capturing prey? What does this do to our model? Why? 23. How would you simulate a decrease in prey reproductive ability? What does this do to our model? Why? 24. How would you simulate a decrease in predator numbers due to a relocation program? What does this do to our model? Why? 25. Notice in our model that the “b” term is about 10% of the “a” term’s value. Why is that? Come up with some hypotheses and be prepared to share them with the class.