1. (Understanding How Populations Work)
Chapter 10
Population Dynamics
(Understanding How Populations Work)

2. Homework
Chapter 9

3. 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.

4. 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)

5. 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.

6. 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.

7. 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).

8. 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

9. Question D Total of 30 whales photo “marked”.
50 whales observed later, of which 10 were photo “marked”.
M =
n =
m = 30 50 10
Population = 30 (50 + 1) = 139
Size (N) (10 + 1)

10. 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 = white oak / m2
Which density value is better?
Density per hectare is in whole numbers, rather than a small fraction of a tree.

11. 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.

12. Question G Average 12 velagers / 0.1 ml water.
Density = Avg Velagers / Volume (liter)
= 12 / liter
= 120,000 velagers / liter

13. (Understanding How Populations Work)
Chapter 10
Population Dynamics
(Understanding How Populations Work)

14. 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)

15. Dynamics of Death
Survivorship

16. 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)

17. 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

18. Example Calculations for Cohort Survivorship
Age
Class
Number of
Survivors ( nx )
Survivorship ( Lx )
653
1.000 1
325
= 325 / 653 2
163
= 163 / 653 3 81
= 81 / 653 4 35
= 35 / 653

19. 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

20. Computing Survivorship From Age-at-Death
Class
How Many Died at That Age
Number of Survivors (nx)
Survivor-ship (Lx)
223
530
1.000 1
145
307 =
0.579 2 89
162 =
0.306 3 58 =
0.138 4 15
= 73-58
0.028
Total

21. Computing Survivorship From Age-at-Death
Class
How Many Died at That Age
Number of Survivors (nx)
Survivor-ship (Lx)
223
530
1.000 1
145
307 =
0.579 2 89
162 =
0.306 3 58 =
0.138 4 15
= 73-58
0.028
Total

22. Three Types of Survivorship Curves
Logarithmic
Scale

23. Mortality due to predation affects old more than young)

24. Type 2 Survivorship Curve: Constant Mortality Rate
Winter mortality due to freezing affects all ages equally)
Mortality due to floods affects all ages equally)

25. Type 3 Survivorship Curve: Perennial Plant Species
Mortality due to predation affects seeds and seedlings more than mature plants

26. Dynamics of Birth

27. 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.

28. Interactions Between Survivorship and Birth Rates

29. 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.

30. Computing Net Reproductive Rate (R0)
Age
Class
Survivorship Lx
Birth Rate mx
Lx mx
1.000 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

31. 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

32. Computing Generation Time (T)
Age
(X)
Survivorship Lx
Birth Rate mx
Lx mx
X Lx mx
1.000 1
0.579 5
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
Total
R0 =
7.79
14.67
T = / = 1.88

33. 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.

34. Estimating r From the Life Table
r = Ln (R0) / T
“Ln” indicates the natural logarithm function.
Generation Time
Net Reproductive Rate

35. End of Part 1: Population Dynamics

36. Homework
Chapter 10 (Part 1)

37. 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 survivor-ship curve they would be extinct.

38. 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.

39. Question B Age dx nx Lx mx Lx mx X Lx mx 180 660 1.000 1 240 480 0.727
180
660
1.000 1
240
480
0.727 2
120
0.364
0.728
1.456 3 60
0.182
1.092 4
0.091
Total
R0 =
1.819
3.275

40. Problem B (continued) Generation Time ( T )
T = Sum (X Lx mx) / R0
T = / 1.819
T = 1.80
Per Capita Rate of Increase ( r )
r = Ln (R0) / T
r = Ln (1.819) / 1.80
r =

41. Homework Question C Age nx Lx mx Lx mx X Lx mx 660 1.000 1 480 0.727 2
660
1.000 1
480
0.727 2
240
0.364 3
120
0.182 4 60
0.091
Total
R0 =

42. Homework Question C Age nx Lx mx Lx mx X Lx mx 660 1.000 1 480 0.727 2
660
1.000 1
480
0.727 2
1.454
240
0.364
0.728
1.456 3
120
0.182
0.546 4 60
0.091
Total
R0 =
2.364
3.456

43. Problem C (continued) Generation Time ( T )
T = Sum (X Lx mx) / R0
T = / 2.364
T = 1.46
Per Capita Rate of Increase ( r )
r = Ln (R0) / T
r = Ln (2.364) / 1.46
r =

44. Homework Question D
Effect of shifting reproduction to younger age classes?
Increased R vs (30% increase)
Decreased T vs (19% decrease)
Increased r vs (77% increase)
Should natural selection favor early reproduction ?
If r = “fitness”, this analysis suggests YES.

45. 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.

46. Population Dynamics Part 2

47. Understanding Population Growth Rate
Ln (R0)
r = _____ T
High net reproductive rate results in high r
(rapid population growth)
Small generation time results in high r .
WHY ?

48. Effect of Generation Time
20 yrs
20 yrs
20 yrs
60 yrs

49. Effect of Generation Time
30 yrs
30 yrs
60 yrs

50. Effect of Net Reproductive Rate

51. 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 ???

52. 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 ?

53. 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

54. Trade – Offs (Assuming Limited Resources)
Allocating resources to reproduction reduces resources available for adult survivorship (immune system, fat reserve).
mx Lx

55. 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)

56. 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

57. 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

58. Importance of Dispersal
Gene flow among separate populations
Re-colonization of empty habitats
Enhances utilization of shifting or ephemeral resources
PROBLEM: Exotic species

59. Dispersing/sedentary stages of organisms

60. Northward Expansion of Tree Species After Continental Glaciers Receded 12,000 yrs BP

61. Invasion of Africanized Honeybees
Exotic Species:
Invasion of Africanized Honeybees

62. 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 ???

63. The End

64. Reflect the Past Predict the Future
Age Distributions
Reflect the Past
Predict the Future

65. Age Distribution of a White Oak Population

66. Age Distribution of a Cottonwood Population

67. Age Distribution of a Cactus Finch Population
(Variation of Lx and mx Over Time)

68. Age Distributions for Human Populations:
Predictors of Future Population Growth
Population Size
Will be Stable
Population Size
Will Decline
Population Size
Will Increase
Rapidly

69. Geometric rate of increase
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Geometric rate of increase
Figure 10.10
10-9    

70. Dispersal distances by collared dove fledglings
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

71. Rates of expansion by animal populations
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

72. Dispersal/numerical response by predators
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

73. Colonization cycle of stream invertebrates
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Colonization cycle of stream invertebrates
Figure 10.19
10-18    

74. Variation in per capita rate of increase
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

75. Effect of dichloroaniline concentration
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

76. Survivorship: Cohort Lifetable

77. Survivorship of plant and rotifer populations