ICA 8 POPULATION GROWTH: PROBLEM SET 2
1) A moth species breeds in late summer and leaves
only eggs to survive the winter. The adult die after
laying eggs. One local population of the moth,
increased from 5000 to 6000 in one year.
Does this species have overlapping generations? Explain.
No; all adults die after they lay eggs so only one
generation is alive at any one time.
What is  for this population? Show calculations.
Nt+1 =  = Nt+1 / Nt
Geometric
Nt+1 = Nt (growth over 1 time unit)
Nt = tNo (growth over many time units)
Exponential
dN/dt = rN
Nt = Noert
Logistic
dN/dt = rN (K-N)/K
Nt+1 = 6000/5000 = 1.2
Predict the population size after 3 yrs. Show calculations.
Nt = tNo
Nt = 1.23 (5000) = (1.2 x 1.2 x 1.2 (5000) = 8640
What is one assumption you make in predicting the future population size?
Environment is constant. Birth and death rates do not change. No limiting resources.
2. A. Draw a logistic growth curve. Indicate
where the carrying capacity is on the axis.
Label axes and label K See book. X = time; Y = population size; K = point on Y
axis where population size stabilizes.
B. Put an X on the curve at the point at which
population growth rate is at its maximum. X goes on the curve at the ‘inflection point’
separating accelerating and decelerating parts of the curve.
What is the population size at this rate of
growth? = K/2
C. A fisheries biologist is maximizing her fishing yield by maintaining a population of
lake trout at exactly 500 individuals. (Hint: At maximum growth rate, N = K/2). What is the
value of K, the carrying capacity of this lake? K/2 = 500, so K = 1000.
r for the trout is 0.005 individuals/ individual/ day. Predict the population growth rate if the
population is stocked with an additional 600 fish.
Write down the formula you will use to solve this problem. dN/dt = rN (K-N)/K
(Hint: Choose the formula used for the type of growth curve above)
Solve it by showing your math.
dN/dt = .005 (1100) ((1000 – 1100)/ 1000) = -0.55 fish per day
D. Is the population increasing or decreasing in size? It is decreasing.
What is causing this direction of change in growth? Population has exceeded its carrying
capacity.
3) In a population of mice in the successional plots we studied, 50% of each
age class of females survive to the following breeding season, at which time they
give birth to an average of three female offspring. This pattern continues to the end
of their third breeding season, when the survivors all die of old age.
A. Fill in this cohort life table.
x
nx
0-1
1000
(mx = # births per female in each age class x)
lx = nx/no
mx
lxmx
xlxmx
1.0
0
0
0
1-2
500
0.5
3
1.5
1.5
2-3
250
0.25
3
0.75
1.5
3-4
125
0.125
3
0.375
1.125
0
RO = 2.625
∑ = 4.125
B. Is the population increasing or decreasing? Show formula used? RO = ∑ lx mx Increasing.
C. How many female offspring does a female mouse have in her lifetime? RO = 2.625
At what precise age does a mouse have her first child? 4.125/2.625 = 1.57
Show formula used. T = ∑ xlxmx / ∑ lx mx
D. Draw the survivorship curve for this mouse population. Use log scale on y axis.
Label axes carefully. Is death rate constant? What type of curve is it? (I, II, III) Explain how
you reached your answer. X axis = time; Y axis = lx Death rate is
constant until the end. The curve is Type 2. The death rate being constant results in
a linear slope (on a log scale).
4. Below is the projection of age distribution and total size through time for a population.
Age class
Time = 0
0
1
2
3
Total N
66
24
10
0
100
Prop in age
class
0.66
0.24
0.10
0.10
1.00
Time = 1
143
33
19
5
200
Prop in age
class
.715
.165
.095
.025
1.00
A. Calculate the total population size at both times.
B. What is ? Show formula used and calculation.  = Nt+1 / Nt = 200/100 = 2.0
C. Is the population increasing or decreasing? The population is incrasing.
D. Calculate the percent in each age class at each time.
E. Has the population reached a stable age distribution? No
F. Can a population with a SAD continue to grow? Yes At what rate does it grow? It grows at a
constant rate of ;