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Chapter 10
Population Dynamics
(Understanding How Populations Work)
Homework
Chapter 9
Question A
Interactions that cause clumped dispersion?
Patchy variation in habitat quality
– Physical environment
– Resource availability
Limited dispersal of young from parents
Social behavior (flock, school, herd), often as
a predation avoidance adaptation.
Question A
Interactions that cause regular dispersion?
Competition for space or resources.
Interactions that cause random dispersion?
Neutral or NO interaction
Interaction of limited dispersal of young
(causing clumped dispersion) with
competition among the young (causing
mortality and shift to regular dispersion)
Question B
How might variation in environment (soil type)
affect dispersion in plants?
Patchy variation of soil nutrients, water, or
physical environment cause plants to occur in
patches (clumped dispersion).
How might interactions among plants affect
dispersion?
Competition for space & resources causes
regular dispersion.
Question C (Part 1)
What was the main finding of studies by
Damuth (1981) & Peters & Wassenberg (1983)?
Density of animal species decreases
with increasing body size.
Question C (Part 2)
Which of the 3 types of rarity described by
(Rabinowitz 1981) is related to the findings of
Damuth (1981), Peters & Wassenberg (1983)?
Species with large body size have small local
population size (within habitats).
Question C (Part 3)
Example of endangered species affected
by pattern described by (Damuth 1981),
Peters & Wassenberg 1983)?
– Elephant
– Tiger
– Rhinoceros
– Mountain gorilla
– Panda
– Blue, Right whale
Question D
Total of 30 whales photo “marked”.
50 whales observed later, of which 10
were photo “marked”.
– M = 30
– n = 50
– m = 10
Population = 30 (50 + 1) =
Size (N)
(10 + 1)
139
Question E
Total of 30 white oak in ten 0.05 ha plots.
Density = Total oak / Total plot area
= 30 / 0.5
= 60 white oak / ha
Density = 60/10,000 = 0.006 white oak / m2
Which density value is better?
Density per hectare is in whole numbers, rather
than a small fraction of a tree.
Question F
Average 64 zebra mussels / 0.01 m2 plot.
Density = Avg Mussels / plot area
= 64 / 0.01 m2
= 6400 zebra mussels / m2
Density = 6400 x 10,000 = 64,000,000 / ha
Which density value is better?
Density per m2 is a more manageable number
than millions of mussels per ha.
Question G
Average 12 velagers / 0.1 ml water.
Density = Avg Velagers / Volume (liter)
= 12 / 0.0001 liter
= 120,000 velagers / liter
Chapter 10
Population Dynamics
(Understanding How Populations Work)
What Processes Determine
Current Population Size?
Population size in earlier time period (Nt-1)
Number of births (B)
Number of deaths (D)
Number of immigrants (I)
Number that emigrate (E)
Nt = Nt-1 + (B−D) + (I−E)
Dynamics of Death
Survivorship
Age-Specific Survivorship (Lx)
Def: The proportion of individuals born into a
population that survive to a specified age x.
Lx
=
nx / n0
x = age,
nx = number of individuals surviving to age x.
n0 = number of individuals born into
population in a single time period (Cohort)
Cohort Survivorship
Mark all individuals born in a single year
(called a cohort). n0
Each year, count the number of surviving
individuals in the cohort. nx
Lx = proportion of original cohort still alive
for each age class = x. = nx / n0
Example Calculations for Cohort
Survivorship
Age
Class
Number of
Survivors ( nx ) Survivorship ( Lx )
0
653
1.000
1
325
0.497
= 325 / 653
2
163
0.250
= 163 / 653
3
81
0.124
= 81 / 653
4
35
0.054
= 35 / 653
Survivorship From Age-at-Death
Determine age-at-death for a sample of
dead organisms.
Often based on annual growth structures.
– Annual tree rings
– Annual layers in fish scales and ear bones
– Enamel layers in bear teeth
– Ridges on horns of Dall sheep
Computing Survivorship From
Age-at-Death
Age How Many Died Number of
Survivorat That Age
Survivors (nx) ship (Lx)
Class
0
223
530
1.000
1
145
307
= 530-223
0.579
2
89
162
= 307-145
0.306
3
58
73
= 162-89
0.138
4
15
15
= 73-58
0.028
Total
530
Computing Survivorship From
Age-at-Death
Age How Many Died Number of
Survivorat That Age
Survivors (nx) ship (Lx)
Class
0
223
530
1.000
1
145
307
= 530-223
0.579
2
89
162
= 307-145
0.306
3
58
73
= 162-89
0.138
4
15
15
= 73-58
0.028
Total
530
Three Types of Survivorship Curves
Logarithmic
Scale
Mortality due to
predation affects old
more than young)
Type 2 Survivorship Curve:
Constant Mortality Rate
Winter mortality due
to freezing affects all
ages equally)
Mortality due to
floods affects all
ages equally)
Type 3 Survivorship Curve:
Perennial Plant Species
Mortality due to predation
affects seeds and
seedlings more than
mature plants
Dynamics of Birth
Age-Specific Birth Rate (mx)
Definition: The average number of young
born to female organisms of a specific age x.
Determined only by direct observation of
number of young produced by females.
Fecundity schedule: Age-specify birth rates
across an entire lifetime.
Interactions Between
Survivorship and Birth Rates
Net Reproductive Rate (R0)
Definition: The average number of
offspring produced by an individual
organism during their entire lifetime.
R0 = Sum for all age classes {Lx mx}
WHERE: x = age and Lx and mx are age-specific
survivorship and birth rates.
Computing Net Reproductive
Rate (R0)
Age Survivorship Birth Rate
Class
Lx
mx
Lx mx
0
1.000
0
0
1
0.579
5
2.95
2
0.306
10
3.06
3
0.138
11
1.52
4
0.028
9
0.26
Total
R0 =
7.79
Generation Time ( T )
Definition: The average time between
when an organism is born and when it
reproduces.
The average age of mothers
T = Sum (Age)(Lx)(mx) / R0
Computing Generation Time (T)
Age
(X)
0
Survivorship Birth Rate
Lx
mx
1.000
0
Lx mx X Lx mx
0
0
1
0.579
5
2.95
2.95
2
0.306
10
3.06
6.12
3
0.138
11
1.52
4.56
4
0.028
9
0.26
1.04
7.79
14.67
Total
R0 =
T = 14.67 / 7.79 = 1.88
Per Capita Rate of Increase (r)
The difference Birth Rate − Death Rate
+ r means births exceed deaths, so the
population size is increasing.
− r means births are less than deaths,
and the population size is decreasing.
Estimating r From the Life Table
r = Ln (R0) / T
“Ln” indicates the
natural logarithm
function.
Generation
Time
Net
Reproductive
Rate
End of Part 1:
Population Dynamics
Homework
Chapter 10 (Part 1)
Question A
Why must species very high reproductive
rates have a Type III survivorship curve ?
If these species didn’t have a Type III
survivor-ship curve the Earth would be
covered with their bodies.
Why must species low reproductive rates
have a Type I survivorship curve ?
If these species didn’t have a Type I survivorship curve they would be extinct.
Question A
What is the expected relationship b/t
reproductive rate and patterns of survival ?
The greater the number offspring produced,
the less energy / care the parent can invest in
each offspring, the lower the survivorship of
juveniles.
Question B
Age
dx
nx
Lx
mx
Lx mx
X Lx mx
0
180
660
1.000
0
0
0
1
240
480
0.727
1
0.727
0.727
2
120
240
0.364
2
0.728
1.456
3
60
120
0.182
2
0.364
1.092
4
60
60
0.091
0
0
0
Total 660
R0 = 1.819
3.275
Problem B (continued)
Generation Time ( T )
T = Sum (X Lx mx) / R0
T = 3.275 / 1.819
T = 1.80
Per Capita Rate of Increase ( r )
r = Ln (R0) / T
r = Ln (1.819) / 1.80
r = 0.332
Homework Question C
Age
nx
Lx
mx
0
660 1.000
0
1
480 0.727
2
2
240 0.364
2
3
120 0.182
1
4
60
0
Total
0.091
R0 =
Lx mx
X Lx mx
Homework Question C
Age
nx
Lx
mx
Lx mx
X Lx mx
0
660 1.000
0
0
0
1
480 0.727
2
1.454
1.454
2
240 0.364
2
0.728
1.456
3
120 0.182
1
0.182
0.546
4
60
0
0
0
Total
0.091
R0 = 2.364
3.456
Problem C (continued)
Generation Time ( T )
T = Sum (X Lx mx) / R0
T = 3.456 / 2.364
T = 1.46
Per Capita Rate of Increase ( r )
r = Ln (R0) / T
r = Ln (2.364) / 1.46
r = 0.589
Homework Question D
Effect of shifting reproduction to younger age
classes?
Increased R0 1.819 vs. 2.364 (30% increase)
Decreased T 1.800 vs. 1.46 (19% decrease)
Increased r
0.332 vs. 0.589 (77% increase)
Should natural selection favor early
reproduction ?
If r = “fitness”, this analysis suggests YES.
Question D
Any disadvantages to earlier reproduction?
Smaller mothers produce fewer, smaller,
and(or) less vigorous young.
Smaller mothers at a disadvantage in
competition for resources, less able to
provide for young.
Survivorship of small mothers and young
lower.
Population Dynamics
Part 2
Understanding Population
Growth Rate
r
=
Ln
(R
0)
_____
T
High net reproductive rate results in high r
(rapid population growth)
Small generation time results in high r .
WHY ?
Effect of Generation Time
20 yrs
20 yrs
60 yrs
20 yrs
Effect of Generation Time
30 yrs
30 yrs
60 yrs
Effect of Net Reproductive Rate
How to Increase R0 = Sum Lx mx?
Increase suvivorship: Longer-lived
individuals have more opportunities for
reproduction during their life time.
Increase birth rates: Increase the
number of offspring produced by
individuals in each age class.
Question: Can an organism do both ???
How to Decrease T ?
Rapid Growth Rate: Organisms reach
sexually mature body size sooner.
Question: What is required to do this ?
Reproduce at a smaller body size:
Less time required to reach sexual
maturity.
Any disadvantages to this ?
Body Size and
Generation Time
Larger species take
longer to grow to their
mature size.
Larger species often
reproduce throughout
their long life span.
Higher average age
of reproducing
individuals
Trade – Offs
(Assuming Limited Resources)
Allocating resources to reproduction
reduces resources available for adult
survivorship (immune system, fat
reserve).
mx
Lx
Trade - Offs
Reproducing at an earlier age (smaller
body size) means more individuals
reproduce before they die. However:
– Small adults produce small offspring that
have lower Lx than large offspring.
– Smaller parents and offspring at
disadvantage in competition for resources
with larger individuals (lower Lx and mx)
r - vs K - Selected Life History
r - selected traits
– Short generation time
– Small adult body size
– Short life span
– High birth rates
– Small offspring
– Low survivorship of
offspring
– Low Parental Care
– Type III Survivorship
K - selected traits
– Long generation time
– Large adult body size
– Long life span
– Low birth rates
– Large offspring
– High survivorship of
offspring
– High Parental Care
– Type I Survivorship
Dispersal
(Immigration and Emigration)
Causes of Dispersal
– Over-population and depletion of resources
– Environmental change alters habitat quality
– Organisms carried by wind or water currents
– Spatial/Temporal variation in resources
– Human transport
Importance of Dispersal
Gene flow among separate populations
Re-colonization of empty habitats
Enhances utilization of shifting or
ephemeral resources
PROBLEM: Exotic species
Dispersing/sedentary stages of organisms
Northward Expansion of Tree Species After
Continental Glaciers Receded 12,000 yrs BP
Exotic Species:
Invasion of Africanized
Honeybees
Expansion of Collared
Doves into Europe
Due to occasional long-distance
dispersal of young doves in
search of new territories.
Why did the collared dove not
occur in Europe before ???
The End
Age Distributions
Reflect the Past
Predict the Future
Age Distribution of a White Oak Population
Age Distribution of a Cottonwood Population
Age Distribution of a Cactus Finch Population
(Variation of Lx and mx Over Time)
Age Distributions for Human Populations:
Predictors of Future Population Growth
Population Size
Will be Stable
Population Size
Will Decline
Population Size
Will Increase
Rapidly
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Geometric rate of increase
Figure 10.10
10-9
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Dispersal distances by collared dove fledglings
Figure 10.15
10-14
Source: Hengeveld 1988
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Rates of expansion by animal populations
Figure 10.16
10-15
Source: Caughley 1977, Hengeveld 1988, Winston 1992
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Dispersal/numerical response by predators
Figure 10.18
10-17
Source: Korpimäki and Norrdahl 1991
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Colonization cycle of stream invertebrates
Figure 10.19
10-18
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Variation in per capita rate of increase
Figure 10.21
10-19
Source: Soares, Baird, and Calow 1992
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Effect of dichloroaniline concentration
Figure 10.22
10-20
Source: Baird, Barber, and Calow 1990
Survivorship: Cohort Lifetable
Survivorship of plant and rotifer populations