Name:__________________________________________
Student No.:____________________________
Equations you may need for the midterm exam:

e x  ( Li ) / l x
i x
Lx 
l x  l x 1
2
qx 
l x  l x 1
lx

R0   l x m x
x 0
N t  N 0 e rt  N 0 t


x 0
x 0
G  [ xlx m x ] /  l x m x
GRR =  mx

1   e  ri li mi
Ba = Bp + P/C
i 0
Cx 
Bi /Bs = 1-P/
e  rx l x

S = CAz
 e rili
i 0
Vx 
e rx
lx
log S = log C + z log A

e
 ry
yx
P = 1 – /c
l y my
Py = (1-pe)y
Pn = 1- (pe)n
Fx  p x mx
Pˆ H  3
N t 1  L N t
e rx
Vx 
lx
l
p x  x 1
lx
dN
KN
 rN
dt
K
C = e-d
w = C x d-a
kx = log10Nx - log10Nx+1
Y = Y0Mb
de ( b  d ) t  d
P0 (t )  ( b  d ) t
be
d
or
P0 (t )  bt /(1  bt ) 
n0
or
d 
P0 (t )   
b
n0
1

e
ix
 ri
li mi
Name:__________________________________________
Student No.:____________________________
Population Biology - 55-324
First Midterm
October 13, 2011
Answer all questions of this exam on the exam pages in the space provided. Answers written outside that
space will not be graded unless permission is specifically granted. Time should not be a constraint on this
exam, so think through what was asked and what must be provided in your answer. In answering all
calculation questions, show your work so that partial credit can be given when a ‘wrong’ answer is the result
of simple mistakes in making the calculations.
The first group of questions is an exercise in matching terms from the left hand column to definitions in the
right column. Place the letter preceding a term in the blank preceding each definition. (1 mark/ term)
1. _e_ turnover
2. _g_ Allee effect
3. _j__ semelparous
4. _b_ stationary age
distribution
a. the number of organisms in a population that have reached age x, but die prior to
their next (or x+1) birthday
b. an age distribution in which the rate at which organisms enter and leave each age
class are equal, so that the age classes remain at fixed numerical size
c. production of a plant’s offspring in two or more events during its lifetime
5. _l_ elasticity
d. the average number of female offspring produced by a female living through all of
the reproductive age classes
6. _c_ polycarpic
e. change in the species comprising an equilibrium community resulting from
continuing immigration and extinction
7. _i_ life cycle
graph
8. _p__ fertility
9. _m_ cohort
10. _d_ Gross Reproductive Rate
11. _k_ stable age
distribution
f. a life table constructed by recording the age at death of a large number of
individuals by taking a ‘snapshot’ of survival within a population during a short
interval of time and the average reproduction of individuals in each age class during
that time interval
g. a reduction in reproduction and/or survival that can occur in population occurring
at low density
h. the proportion of organisms in a population that have reached age x, but die prior to
their next (or x+1) birthday
12. _h_ qx
i. a graphical representation of the life cycle of a species constructed by dividing its
life history into phases or stages and quantifying the probabilities of transition
between those phases
13. _n_ demographic
stochasticity
j. producing only a single litter of offspring during the lifespan of a parent
14. _f_ static life table
k. an age distribution in which the rate at which organisms enter and leave each age
class remain constant, so that the age classes remain at fixed proportions in the total
population
l. the proportional change in  that occurs as a result of a proportional change in a
vital rate or statistic
m. a group of offspring born to parents in a population during a single, short period
n. randomness in the order and rate of occurrence of births and deaths in a population
o. a life table constructed by following the survivorship and reproduction of a group
of individuals born over a short interval until all members of the group have died
p. the actual reproductive performance under prevailing environmental conditions
q. none of the above define the term
2
Name:__________________________________________
Student No.:____________________________
Circle the letter of the correct answer for each of the multiple choice questions. (1 mark each)
15. Which is calculated by dividing the total number
of individuals of some specific age in a population in
year t+1 by the total number of individuals of that age
in the previous year?
a. px, the proportional survivorship for age x
b. bx, the age-specific birth rate
c. , the finite rate of increase
d. lx, the age-specific survival rate
16. Which is calculated by dividing the total number
of individuals in a population of age x+1 by the total
number of individuals of age x?
a. px, the proportional survivorship for age x
20. When resources limit population growth, growth is
expected to be:
a. exponential
b. logistic
c. linear
d. logarithmic
21. The reproductive value of different ages in a
population usually reach a peak at approximately
what age?
a. at birth
b. at reproductive maturity, age 
b. bx, the age-specific birth rate
c. at the age when fertility (clutch size) is maximum
c. , the finite rate of increase
d. lx, the age-specific survival rate
d. at the age when reproduction ceases, age 
17.When populations fluctuate above and below the
carrying capacity, and those fluctuations do not damp
out, we can determine that the value of r is:
22. A stochastic logistic model can be constructed by
introducing random variation in which of the
following variables?
a. the intrinsic rate of increase, r
a. < /2
b. the carrying capacity, K
b. /2 < r < 2
c. >2
c. the number in the population, Nt
d. we cannot estimate the value of r
e. all of the above answers are correct
d. both a and b are correct
23. When population growth is logistic, at what
population size is the growth rate, dN/dt, largest?
18. When a population reaches a stable age
distribution, which is true?
a. all age classes have the same mortality rate
a. when the population size is small, near 0
b. the population stops growing
b. when the population size has reached K/2
c. the population can still grow
d. the population is unstructured
c. when the population size approaches K
d. you can’t tell; it depends on the specific
characteristics of the population
19. Which of the following is a mismatch?
24. When population growth is logistic, when is the
growth rate per head, 1/N dN/dt, largest?
a. birds – type II survivorship curve
b. mammals – type I survivorship curve
a. when the population size is small, near 0
c. invertebrates – type II survivorship curve
b. when the population size has reached K/2
d. trees – type III survivorship curve
c. when the population size approaches K
d. you can’t tell; it depends on the specific
characteristics of the population
3
Name:__________________________________________
Student No.:____________________________
25. Which of the following is not an assumption made
in constructing the basic models of metapopulation
biology?
26. When is the slope of the species-area curve (in a
log – log plot) is typically larger than the 0.26
predicted by the Preston log normal distribution of
species relative abundances?
a. all patches are equidistant from each other
a. when samples from larger and larger areas that
are not really isolated are plotted
b. areas of patches are unimportant to
metapopulation persistence
b. when patches contain very high habitat diversity
c. habitat qualities of patches are identical
c. when some factor such as pollution reduces
interspecific competition among species within
sampled patches
d. population sizes on all patches are identical
e. all answers are assumptions of basic
metapopulation models
d. both a and b of the above are correct
e. both b and c of the above are correct
27. You expected a life table calculation question. Here it is. Use the information below to construct a life
table for this fictional lizard species. First calculate lx and mx values for the table (10). Use them to
calculate R0, G and r (6). Check the accuracy of r using Euler’s equation (3). If necessary, run one cycle
of correction to try to improve the estimate of r [do not expect to completely correct r; half the grade will
come from making your change in the right direction](2). Project the initial population forward through
two time steps (4). In all calculations, show your work (continuing on the next page if necessary), so that
if you make a simple mistake early in the calculations, but proceed correctly thereafter, you can be given
most of the credit even though your numeric answers are wrong. (Total 25)
Age
px
Fx
0
1
2
3
4
5
.1
.15
.15
.5
.25
0
10000
0
1000
0
100
2500 50
2500 25
0
---
e-rxlxmx
0
0
0
.7802
.3195
1.0997
---
N(0)
lx
mx
1
.1
.015
.00225
.001125
.00028
0
0
0
5000
10000
-----
try r = 1.0 e-rxlxmx
0
0
0
.5601
.2060
.7661
try .92
0
0
0
.7120
.2837
.9957
4
lxmx
xlxmx
0
0
0
0
0
0
11.25
33.75
11.25
45.0
_____
_____
R0 = 22.5
78.75
G = 3.5
r = ln 22.5/3.5 = .8895
N(1)
187500
1000
150
15
25
6
N(2)
100000
18750
150
22.5
7.5
6
Name:__________________________________________
Student No.:____________________________
28. Use the diagram below, representing a simplified life cycle for a squid, to develop a Lefkovitch (stage)
matrix for this life history. Show the matrix below. You do not need to do any actual calculations with
this matrix, just put the numbers into the proper rows and columns of the matrix. (10)
From
1
2
3
4
1
.65
100
200
400
2
.25
.7
0
0
To 3
0
.15
.7
0
4
0
0
.2
.8
5
Name:__________________________________________
Student No.:____________________________
29. The logistic is both the simplest model that incorporates effects of density and the basis of much of
ecological theory, even though we know it is inadequate and burdened with unrealistic assumptions.
There are four major assumptions. List and briefly describe the assumptions embedded in the logistic
model (12, 3 marks for each), then indicate briefly how the structure or dynamics of real populations
violates each of the assumptions you list. (8, 2 marks for each)
1. that the population is in a stable age distribution. Proportions in each age class remain constant.
2. “All individuals within the population are identical (or at least have identical life histories)". There
are no differences among individuals in the population that would affect their contributions to
population growth.
3. The relationship between the density and declining rate of increase is linear, or alternatively that r
and K are constants. If r and/or K vary, then the model prediction of growth would change.
4. There are no time lags. Responses to changes in density are instantaneous according to this
assumption. If responses to density are not instantaneous, then growth is, for the duration of the
lag, ‘chasing the wrong target’.
Possible examples for 1 are any rapidly growing population, including humans, since the usual
demographer’s curve for such a population shows an increasing proportion of younger age classes.
For 2 the physiological and size differences between males and females of any species with sexual
dimorphism, and/or differences in male and female survivorships are indications this assumption is
violated.
For 3 pointing out the Allee effect anywhere it occurs (example of cod) or environmental effects
causing K to vary (e.g. in deer) demonstrate violation.
For 4 any species that has a reasonably lengthy gestation period or an extended maturation indicates
time lag and violation.
30. You have been put in the position of a consulting conservation biologist, trying to protect an endangered
orchid species, the (fictional) pink-tufted, blue orchid. The remaining population is only 50 individuals.
After data collection it became apparent that this population was in danger, as it showed that the birth
rate in the popualtion was b=0.021 births/individual/year. The parallel death rate was d=0.020. A new
shopping mall has been planned that will reduce this population to 25 plants. What is the probability of
extinction for the current population? What is the probability of extinction for the reduced population
that would remain after construction? (10)
P0(t) = (d/b)n0
Current population: (.020/.021)50 = .952350 = .0868
Population after reduction: .952325 = .2946
6
Name:__________________________________________
Student No.:____________________________
31. From the basic equation for exponential growth, determine a formula that will calculate the time it takes
an exponentially growing population to double in size. Use the formula to determine the doubling times
for populations with r values of 0.1 and 0.05. (9)
Nt = N0ert
Nt/N0 = ert
2 = ert
ln 2 = .693 = rt
If r = .1, then t = .693/.1 = 6.93
If r = .05, then t = .693/.05 = 13.86
7