Download Question 1: (1 point) - University of Nebraska–Lincoln

Population Dynamics on-line testbank
by Andrew J. Tyre, School of Natural Resources, University of Nebraska-Lincoln
atyre2 @ unl . edu
This testbank was developed based on questions used in my class, NRES 450/850,
Biology of Wildlife Populations. Many questions are based on questions from Nicholas
Gotelli's excellent book, A Primer of Ecology (3rd Edition, Sinauer). All equations were
created using MathType 5, and all figures were drafted by myself using Microsoft
Powerpoint or Excel.
In what follows I indicate the answers to questions with x, or * if it depends on the
randomization. I use the EDU functions rand() or rint() in italics to describe the
randomization features of each question.
Exponential Growth
Question 1: (1 point)
A population of deer has a discrete time growth rate of λ = rand(0.9,1.1) with dynamics given by
.
This population will
*
(a) decrease over time.
*
(b) increase over time.
*
(c) stay the same over time.
Question 2: (1 point)
A population of groundhogs is presently at a population density of rand(0.5,10) / ha with a
discrete time growth rate of λ = rand(0.9,0.99) with dynamics given by
.
At what population density will this population stabilize at, given sufficient time
answer: 0
Question 3: (1 point)
An island population of muskoxen is presently at a population density of rand(2,10) / ha with a
discrete time growth rate of λ = rand(0.9,1.1) with dynamics given by
.
How many years will it take for the population to {increase above, decline below} a population
density of {depends on N0 , λ, and Δt=rint(5,10)}?
answer: Δt
Question 4: (1 point)
You are studying a population of beetles of size 3000. During a one-month period, you record 400
births and 150 deaths in this population.
(a)
Estimate r in the exponential growth equation Nt = ertN0.
answer: 0.08
(b)
Using your estimate of r, project the population forward six months.
answer: 4849
Question 5: (1 point)
A population of annual grasses increases in size by 12% every year. What is the approximate
doubling time?
answer: 6.12 years
Question 6: (1 point)
Eight pheasants (Phasianus colchicus torquatus) were introduced to Protection Island off the
coast of Washington state in 1937. There were no predators, and the island is far enough from
the mainland that natural migration is zero. By 1938 the population had increased to 30. Thus the
growth rate λ = 30 / 8 = 3.75. Assuming the population grows exponentially at this rate we have
the following plots
with exponential growth shown in pink, and estimates of the population size at six month intervals
in blue.
What are some reasonable hypotheses about why the observed population sizes deviate from the
expected population size assuming exponential growth?
x
(a)
The food supply decreased in response to a drought, causing adult mortality to
increase.
(b) Adult pheasants began to lay fewer eggs in response to crowding.
(c) Foxes migrated to the island, causing adult and chick mortality to increase.
(d) The population exceeded the available food supply, causing chick mortality to increase.
Question 7: (1 point)
You are conducting an experiment on the growth of Daphnia magna (water fleas) in an algal
culture. You seed the culture with 25 individuals. Each week for the next six weeks you measure
the following number of individuals 41, 75,118,199,302, and 511. Estimate r of the discrete
exponential growth equation by plotting the logarithm (base e) of population size against time.
answer: 0.5 ± 0.02
Logistic Growth
Question 8: (1 point)
On this phase plane diagram of the discrete logistic equation:
The pink line is the 1 to 1 replacement line; the blue line is the logistic map. Select the point on
the blue curve that corresponds to the carrying capacity of the population.
answer: the point where the blue and pink curves intersect
Question 9: (1 point)
(a)
Click on the region of the graph that corresponds to the parameter r in the logistic model.
answer: the distance between the red and green curves along the y-axis
(b)
If the influence of population size on birth rates changes to the dashed red line, what will
happen to the parameters K and r? (Click all descriptions that apply.)
x
(a) r will decrease.
(b) r will increase.
(c) K will increase.
(d) K will stay the same.
x
(e) K will decrease.
(f) r will stay the same.
Question 10: (1 point)
Suppose a population of butterflies is growing according to the discrete logistic equation. If the
carrying capacity is 500 butterflies and r = 0.1 individuals / (individual . month), what is the
maximum possible growth rate for the population?
answer: 12.5
Question 11: (1 point)
A fisheries biologist is maximizing her fishing yield by maintaining a population of lake trout at
exactly 500 individuals. Predict the initial growth rate if the population is stocked with an
additional 600 fish. Assume that r for the trout is 0.005 individuals / (individual . day).
answer: 0.0005
Question 12: (1 point)
A long term study has measured the per capita birth and death rates of a territorial lizard as a
function of population density (individuals / ha). The lizard lives in isolated fragments of forest in
an agricultural landscape. The results of the study are summarized in the following plot:
For the past few years the population in one patch fluctuated between 30 and 35 individuals. This
past summer a drought drove the population down to 4 individuals, two of each sex. What do you
expect the population to do over the next few years?
(a) Increase slowly back to the population sizes observed prior to the drought.
x
(b) Decline to zero because of the Allee effect on birth rates at low population sizes.
(c)
Fluctuate between 5 and 10 individuals because of the low equilibrium point where birth
and death rates are equal.
Life Tables
Question 13: (1 point)
Here is a hypothetical life-table for a population of snails. Complete the life table by calculating
the survivorship curve l(x) and the annual survivorship probabilities p(x).
Age in years (x)
K(x)
b(x)
l(x)
p(x)
0
500
0.0
{ 1}
{0.8}
1
400
2.5
{0.8}
{0.1}
2
40
3.0
{0.08}
{0.0}
3
0
0.0
{0.0}
answers in italics in table.
Metapopulation Dynamics
Question 14: (1 point)
An endangered species of frog, Onthe precipisius, has a single remaining population of 100
individuals. Recent demographic work estimates the annual extinction probability of this
population at 10%, because of occaisional failures of rainfall to fill the pond sufficiently to allow
reproduction. One proposal for conserving this population is to translocate 2/3 of the individuals to
create a total of three populations of 33 individuals each. Based on the demographic models, you
know that a population of 33 individuals has an extinction risk of 50% per year. What is the overall
risk of extinction of this proposal?
answer: 12.5%
Question 15: (1 point)
The checkerspot butterfly (Euphydryas editha bayensis) is only found in serpentine grasslands in
a small area of California. There is a large population of several hundred thousand butterflies at a
site called Morgan Hill. To the south and west of Morgan hill are nearly a hundred patches of
serpentine that support much smaller populations of checkerspots. Several of these populations
are known to have gone extinct, and at least one recolonisation has been observed in the past
few decades. Assume that Morgan Hill is the only source of colonists for the small patches of
habitat, that extinctions on the small patches are independent, the probability of immigration pi =
0.2, and the probability of extinction pe = 0.4. What is the expected fraction of small patches
occupied by the butterfly?
answer: 0.33
Question 16: (1 point)
A metapopulation of butterflies has a propagule rain and a rescue effect, with parameters pi = 0.3
and e = 0.5. Forty percent of the population sites are occupied. Which equation best describes
this system, and is this metapopulation expanding or shrinking?
x
(a) Expanding
(b) Staying the same
(c) Shrinking
x
(d)
(e)
Question 17: (1 point)
Which of the following differential equations for the fraction of occupied patches, f, represents a
system with independent extinctions and colonization only from within the metapopulation?
(a)
x
(b)
(c)
(d)
Question 18: (1 point)
A population of lizards on a group of small tropical islands has been demonstrated to have a
rescue effect on local extinction, and frequent colonization from a nearby larger island. Thus the
rate of change in the fraction of occupied islands is given by
If pi = 0.1 and e = 0.35, what is the expected fraction of islands occupied by lizards?
answer: 0.288 ± 0.02
Competition
Question 19: (1 point)
Two species of short tailed shrew (Blarina) compete in grassland habitats in southern Nebraska.
Supposing that their interaction can be described with a Lotka-Volterra competition model:
and that α = 1.5, β = 0.5, and K2 = 100. What is the minimum carrying capacity for species 1 that
is necessary for coexistence?
answer: 150
Question 20: (1 point)
Two species of short tailed shrew (Blarina) compete in grassland habitats in southern Nebraska.
Supposing that their interaction can be described with a Lotka-Volterra competition model:
and that α = 1.5, β = 0.5, and K2 = 100. How large must K1 be for species 1 to win the
competition?
answer: 200
Question 21: (1 point)
Gallagher and colleagues experimentally estimated the parameters of a Lotka-Volterra
competition model:
for an interaction between a polychaete worm (species 1) and an oligochaete worm (species 2)
feeding on diatoms. They found K1 = 64.2, α = 1.408, K2 = 50.7, and β = 0.754. If the two
populations start at densities of 15 individuals each, tick all boxes with relevant predictions from
the model.
(a) Oligochaetes decrease in density initially.
x
(b) Ultimately, polychaetes decrease to extinction.
(c) Ultimately, both species coexist.
(d) Polychaetes (species 1) decrease in density initially.
x
(e) Oligochaetes increase in density initially.
x
(f) Polychaetes (species 1) increase in density initially.
(g) Ultimately, oligochaetes decrease to extinction
Predation
Question 22: (1 point)
The most basic predator-prey model is the Lotka-Volterra model given by:
Tick all boxes next to assumptions of this model.
(a) Predators can persist in the absence of this prey.
x
(b) Predator and victim encounter one another randomly in an homogenous environment.
(c) There is a maximum rate at which predators can consume prey.
x
(d) Individual predators can consume an infinite number of victims.
(e) The victim population is limited by other factors in addition to predation.
x
(f) The predator is a specialist that can persist only if the victim population is present.
(g) Predators actively seek prey.
x
(h) Growth of the victim population is limited only by predation.
Question 23: (1 point)
A predator-prey model with a victim carrying capacity is given by:
Tick all boxes next to assumptions of this model.
(a) Predators actively seek prey.
x
(b) Individual predators can consume an infinite number of victims.
(c) Growth of the victim population is limited only by predation.
(d) There is a maximum rate at which predators can consume prey.
(e) Predators can persist in the absence of this prey.
x
(f) Predator and victim encounter one another randomly in an homogenous environment.
x
(g) The victim population is limited by other factors in addition to predation.
x
(h) The predator is a specialist that can persist only if the victim population is present.
Question 24: (1 point)
A predator-prey model where the predators have a Type II functional response is:
Tick all boxes next to assumptions of this model.
x
(a) The predator is a specialist that can persist only if the victim population is present.
x
(b) There is a maximum rate at which predators can consume prey.
x
(c) Growth of the victim population is limited only by predation.
x
(d) Predator and victim encounter one another randomly in an homogenous environment.
(e) Predators can persist in the absence of this prey.
(f) Individual predators can consume an infinite number of victims.
(g) Predators actively seek prey.
(h) The victim population is limited by other factors in addition to predation.
Question 25: (1 point)
A population of spiders eating a population of flies have a trajectory determined by Lotka-Volterra
predator-prey model:
with the following coefficients: r = 0.1, q = 0.5, and α = β = 0.001. Their initial population sizes are
200 spiders and 600 flies.
What are the short term dynamics of predicted by the model?
x
(a) The spiders will increase in abundance.
(b) Both species will stay at the initial population sizes.
x
(c) The flies will decrease in abundance.
(d) The spiders will stay constant.
(e) The flies will increase in abundance.
(f) The spiders will decrease in abundance.
Island Biogeography
Question 26: (1 point)
The theory of island biogeography predicts the number of species on an island as a function of
immigration from a "source pool" and local extinction. In the diagram below, the green line
represents the rate of colonization, and the red line represents the rate of local extinction.
What is the equilibrium number of species expected on an island with these curves? (click on the
image)
answer: the point labeled S
Question 27: (1 point)
The theory of island biogeography predicts the number of species on an island as a function of
immigration from a "source pool" and local extinction. In the diagram below, the green line
represents the rate of colonization, and the red line represents the rate of local extinction.
What is the number of species on the island when the immigration rate is a maximum? (click on
the image)
answer: zero, click on the origin of the plot.
Question 28: (1 point)
The theory of island biogeography predicts the number of species on an island as a function of
immigration from a "source pool" and local extinction. In the diagram below, the green line
represents the rate of colonisation, and the red line represents the rate of local extinction.
Click on the point that represents the total number of species in the pool that can immigrate to the
island.
answer: the point labeled P
Question 29: (1 point)
The theory of Island Biogeography predicts the number of species on an island as a function of
immigration from a nearby source pool of species (on a "mainland"), and local extinction. The
graphical version of the model is
where the green line is the rate of immigration from the source, and the red line is the rate of local
extinction. Select all of the assumptions of this model from the list below.
x
(a) The probability of a population becoming extinct is inversely proportional to its size
x
(b)
The probability of colonization is inversely proportional to isolation or distance from the
source pool.
(c)
Immigration rates are normally distributed with a variance proportional to the distance
from the source pool.
(d) The population of a species decreases with the number of other species on the island.
x
(e)
Colonization and extinction of local poulations is independent of species composition on
the island.
x
(f)
An island potentially can be colonized by a set of P source pool species with similar
colonization and extinction rates
x
(g) The population size of a given species is proportional to the area of the island.
Question 30: (1 point)
The formula for the simplest version of the theory of Island Biogeography is:
Where S is the number of species on a particular island.
Hinchinbrook Island in the Great Barrier Reef off the coast of Queensland in Australia currently
has 20 species of bird nesting on the island. The species pool of birds on the mainland that could
nest on the island is estimated at 60 species, and work elsewhere in the Great Barrier Reef
system has lead to estimates of the maximum immigration rate of 0.1 species / year and the
maximimum extinction rate for an island the size of Hinchinbrook of 0.2 species / year.
Developers plan to expand the resort on the island, which would reduce the area of nesting
habitat for these birds to half of its present size. What is the equilibrium number of nesting
species that will occur on the island if this plan is implemented?
answer: 12 species