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Lecture 10 Population Age and Size Structure

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Title: Lecture 10 Population Age and Size Structure


1
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • A. Age
  • B. Size
  • C. Stage of development
  • D. Gender

2
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • A. Age a young rattlesnake or elephant or
    human or giant sequoia has a birth rate of zero.
    Very old individuals often have a high death
    rate.
  • B. Size
  • C. Stage of development
  • D. Gender

3
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • A. Age a young rattlesnake or elephant or
    human or giant sequoia has a birth rate of zero.
    Very old individuals often have a high death
    rate.
  • B. Size small plants produce fewer offspring
    and have higher death rates than larger
    plants of the same age.
  • C. Stage of development
  • D. Gender

4
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • A. Age a young rattlesnake or elephant or
    human or giant sequoia has a birth rate of zero.
    Very old individuals often have a high death
    rate.
  • B. Size small plants produce fewer offspring
    and have higher death rates than larger
    plants of the same age. Small animals of many
    species may also not produce as many offspring
    or live as long as larger individuals of the
    same age.
  • C. Stage of development
  • D. Gender

5
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • A. Age a young rattlesnake or elephant or
    human or giant sequoia has a birth rate of zero.
    Very old individuals often have a high death
    rate.
  • B. Size small plants produce fewer offspring
    and have higher death rates than larger
    plants of the same age. Small animals of many
    species may also not produce as many offspring
    or live as long as larger individuals of the
    same age.
  • C. Stage of development most insects go
    through dramatically different stages of
    development, but many other organisms also have
    distinct juvenile and adult stages.
  • D. Gender

6
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • A. Age a young rattlesnake or elephant or
    human or giant sequoia has a birth rate of zero.
    Very old individuals often have a high death
    rate.
  • B. Size small plants produce fewer offspring
    and have higher death rates than larger
    plants of the same age. Small animals of many
    species may also not produce as many offspring
    or live as long as larger individuals of the
    same age.
  • C. Stage of development most insects go
    through dramatically different stages of
    development, but many other organisms also have
    distinct juvenile and adult stages. Juveniles of
    many bird species may be as large as adults but
    have very different coloration (so stage isnt
    the same as size).
  • D. Gender

7
Juvenile mallard (Anas platyrhyncos)
Male and female mallards
prairiefrontier.com
8
Bald eagle juvenile (Haliaeetus leucocephalus)
Bald eagle adult (Haliaeetus leucocephalus)
Photo by Tim Knight (homepage.mac.com)
9
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • C. Stage of development most insects go
    through dramatically different stages of
    development, but many other organisms also have
    distinct juvenile and adult stages. Juveniles of
    many bird species may be as large as adults but
    have very different coloration (so stage isnt
    the same as size). Seeds of many plants can
    live for hundreds of years without germinating
    (so stage isnt the same as age).
  • D. Gender

10
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • C. Stage of development most insects go
    through dramatically different stages of
    development, but many other organisms also have
    distinct juvenile and adult stages. Juveniles of
    many bird species may be as large as adults but
    have very different coloration (so stage isnt
    the same as size). Seeds of many plants can
    live for hundreds of years without germinating
    (so stage isnt the same as age).
  • D. Gender only females give birth in animals
    so most analyses of animal populations are of
    females.

11
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • C. Stage of development most insects go
    through dramatically different stages of
    development, but many other organisms also have
    distinct juvenile and adult stages. Juveniles of
    many bird species may be as large as adults but
    have very different coloration (so stage isnt
    the same as size). Seeds of many plants can
    live for hundreds of years without germinating
    (so stage isnt the same as age).
  • D. Gender only females give birth in animals
    so most analyses of animal populations are of
    females. Females and males often have different
    death rates also. For example, human mortality
    rates are higher in men than in women in many
    countries

12
Lecture 10 Population Age and Size Structure
  • I. Factors Affecting Birth and Death Rates in
    Populations
  • C. Stage of development most insects go
    through dramatically different stages of
    development, but many other organisms also have
    distinct juvenile and adult stages. Juveniles of
    many bird species may be as large as adults but
    have very different coloration (so stage isnt
    the same as size). Seeds of many plants can
    live for hundreds of years without germinating
    (so stage isnt the same as age).
  • D. Gender only females give birth in animals
    so most analyses of animal populations are of
    females. Females and males often have different
    death rates also. For example, human mortality
    rates are higher in men than in women in many
    countries but it hasnt always been that way.

13
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table?
  • B. Life table parameters
  • C. Classification methods for life tables
  • D. Cohort vs static life tables

14
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table? Table showing the
    number of individuals alive over time in a
    population and the mortality rates at different
    times.
  • B. Life table parameters
  • C. Classification methods for life tables
  • D. Cohort vs static life tables

15
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table? Table showing the
    number of individuals alive over time in a
    population and the mortality rates at different
    times.
  • B. Life table parameters (FIGS. 1,2)
  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • C. Classification methods for life tables
  • D. Cohort vs static life tables

16
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table? Table showing the
    number of individuals alive over time in a
    population and the mortality rates at different
    times.
  • B. Life table parameters (FIGS. 1,2)
  • 1. Time interval corresponding to age, age
    class, size class, or stage of development
    x
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • C. Classification methods for life tables
  • D. Cohort vs static life tables

17
Phlox drummondii
Larry Allain_at_ USGS NWRC Plants Database
18
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table? Table showing the
    number of individuals alive over time in a
    population and the mortality rates at different
    times.
  • B. Life table parameters (FIGS. 1,2)
  • 1. Time interval corresponding to age, age
    class, size class, or stage of development
    x
  • 2. Number of individuals surviving to time x
    ax or nx or Nx.
  • 3.
  • 4.
  • 5.
  • 6.
  • C. Classification methods for life tables
  • D. Cohort vs static life tables

19
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20
Western spruce budworm (Choristoneura
occidentalis)
Damage by spruce budworm
Spruce budworm adult
Entomology.umn.edu
Adult spruce budworm Climatology.umn.edu
21
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table? Table showing the
    number of individuals alive over time in a
    population and the mortality rates at different
    times.
  • B. Life table parameters (FIGS. 1,2)
  • 1. Time interval corresponding to age, age
    class, size class, or stage of development
    x
  • 2. Number of individuals surviving to time x
    ax or nx or Nx.
  • 3. Survivorship, the proportion or
    standardized number of individuals surviving
    to time x lx.
  • 4.
  • 5.
  • 6.

22
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23
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24
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table? Table showing the
    number of individuals alive over time in a
    population and the mortality rates at different
    times.
  • B. Life table parameters (FIGS. 1,2)
  • 1. Time interval corresponding to age, age
    class, size class, or stage of development
    x
  • 2. Number of individuals surviving to time x
    ax or nx or Nx.
  • 3. Survivorship, the proportion or
    standardized number of individuals
    surviving to time x lx.
  • 4. Number of individuals dying between times
    x and x1 dx
  • 5.
  • 6.

25
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26
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27
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • A. What is a life table? Table showing the
    number of individuals alive over time in a
    population and the mortality rates at different
    times.
  • B. Life table parameters (FIGS. 1,2)
  • 1. Time interval corresponding to age, age
    class, size class, or stage of development
    x
  • 2. Number of individuals surviving to time x
    ax or nx or Nx.
  • 3. Survivorship, the proportion or
    standardized number of individuals
    surviving to time x lx.
  • 4. Number of individuals dying between times
    x and x1 dx
  • 5. Mortality rate (proportion of individuals
    dying) between times x and x1 qx.
  • 6.

28
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29
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30
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • B. Life table parameters (FIGS. 1,2)
  • 1. Time interval corresponding to age, age
    class, size class, or stage of
    development x
  • 2. Number of individuals surviving to time x
    ax or nx or Nx.
  • 3. Survivorship, the proportion or
    standardized number of individuals
    surviving to time x lx.
  • 4. Number of individuals dying between times
    x and x1 dx
  • 5. Mortality rate (proportion of individuals
    dying) between times x and x1 qx.
  • 6. Mean life expectation (expectancy) for
    individuals reaching time x ex.

31
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1.
  • 2.
  • 3.

32
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1. Age classes or intervals (FIGS. 1,3,4)
  • 2.
  • 3.

33
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34
Red deer hind (Cervus elaphus)
Paul Hobson photo
Red deer stag
Falconergame.co.uk
35
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36
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1. Age classes or intervals (FIGS. 1,3,4)
  • 2. Stage of development (FIG. 2)
  • 3.

37
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38
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1. Age classes or intervals (FIGS. 1,3,4)
  • 2. Stage of development (FIG. 2)
  • 3. Size classes or intervals. This is often
    used for plants.

39
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1. Age classes or intervals (FIGS. 1,3,4)
  • 2. Stage of development (FIG. 2)
  • 3. Size classes or intervals. This is often
    used for plants.
  • Forest tree example 10-20 cm, 20-40 cm

40
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1. Age classes or intervals (FIGS. 1,3,4)
  • 2. Stage of development (FIG. 2)
  • 3. Size classes or intervals. This is often
    used for plants.
  • Forest tree example 10-20 cm, 20-40 cm
  • D. Cohort vs static life tables
  • 1. Cohort (dynamic, age-specific) life tables
    (FIGS. 1,2,3)
  • 2. Static (time-specific) life tables (FIG.
    4)

41
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1. Age classes or intervals (FIGS. 1,3,4)
  • 2. Stage of development (FIG. 2)
  • 3. Size classes or intervals. This is often
    used for plants.
  • Forest tree example 10-20 cm, 20-40 cm
  • D. Cohort vs static life tables
  • 1. Cohort (dynamic, age-specific) life tables
    (FIGS. 1,2,3)
  • A cohort is a group of individuals of the
    same age (age-mates).
  • 2. Static (time-specific) life tables (FIG.
    4)

42
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • C. Classification methods for life tables (FIGS.
    1,2,3,4)
  • 1. Age classes or intervals (FIGS. 1,3,4)
  • 2. Stage of development (FIG. 2)
  • 3. Size classes or intervals. This is often
    used for plants.
  • Forest tree example 10-20 cm, 20-40 cm
  • D. Cohort vs static life tables
  • 1. Cohort (dynamic, age-specific) life tables
    (FIGS. 1,2,3)
  • A cohort is a group of individuals of the
    same age (age-mates). To develop a
    cohort life table, you follow all individuals of
    a cohort from birth until every individual
    has died.
  • 2. Static (time-specific) life tables (FIG.
    4)

43
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • D. Cohort vs static life tables
  • 1. Cohort (dynamic, age-specific) life tables
    (FIGS. 1,2,3)
  • A cohort is a group of individuals of the
    same age (age-mates). To develop a
    cohort life table, you follow all individuals of
    a cohort from birth until every individual
    has died. The most useful and most accurate
    life table but . . .
  • 2. Static (time-specific) life tables (FIG.
    4)

44
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • D. Cohort vs static life tables
  • 1. Cohort (dynamic, age-specific) life tables
    (FIGS. 1,2,3)
  • A cohort is a group of individuals of the
    same age (age-mates). To develop a
    cohort life table, you follow all individuals of
    a cohort from birth until every individual
    has died. The most useful and most accurate
    life table but it may be difficult to locate
    all individuals at birth and follow them until
    the last one has died.
  • 2. Static (time-specific) life tables (FIG.
    4)

45
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • D. Cohort vs static life tables
  • 1. Cohort (dynamic, age-specific) life tables
    (FIGS. 1,2,3)
  • A cohort is a group of individuals of the
    same age (age-mates). To develop a
    cohort life table, you follow all individuals of
    a cohort from birth until every individual
    has died. The most useful and most accurate
    life table but it may be difficult to locate
    all individuals at birth and follow them until
    the last one has died. Its not good for
    long-lived species!
  • 2. Static (time-specific) life tables (FIG.
    4)

46
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47
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48
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49
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • D. Cohort vs static life tables
  • 1. Cohort (dynamic, age-specific) life tables
    (FIGS. 1,2,3)
  • A cohort is a group of individuals of the
    same age (age-mates). To develop a
    cohort life table, you follow all individuals of
    a cohort from birth until every individual
    has died. The most useful and most accurate
    life table but it may be difficult to locate
    all individuals at birth and follow them until
    the last one has died. Its not good for
    long-lived species!
  • 2. Static (time-specific) life tables (FIG.
    4)
  • To develop a static life table, you first
    estimate the age of each individual in a
    population at a particular time.

50
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • D. Cohort vs static life tables
  • 2. Static (time-specific) life tables
    (FIG. 4)
  • To develop a static life table, you first
    estimate the age of each individual in a
    population at a particular time. Assuming that b
    and d have remained constant since the
    oldest individual was born, you work back
    from the oldest individuals to the youngest
    to estimate how many were born in each year.

51
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52
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • D. Cohort vs static life tables
  • 2. Static (time-specific) life tables (FIG.
    4)
  • To develop a static life table, you first
    estimate the age of each individual in a
    population at a particular time. Assuming that b
    and d have remained constant since the
    oldest individual was born, you work back
    from the oldest individuals to the youngest
    to estimate how many were born in each year.
    Sometimes these data are smoothed to
    eliminate oddities as we see for ages 6
    and 7 in FIG. 4.

53
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54
Lecture 10 Population Age and Size Structure
  • II. Life Tables
  • D. Cohort vs static life tables
  • 2. Static (time-specific) life tables (FIG.
    4)
  • To develop a static life table, you first
    estimate the age of each individual in a
    population at a particular time. Assuming that b
    and d have remained constant since the
    oldest individual was born, you work back
    from the oldest individuals to the youngest
    to estimate how many were born in each year.
    Sometimes these data are smoothed to
    eliminate oddities as we see for ages 6
    and 7 in FIG. 4. Static life tables are used for
    long-lived organisms like trees,
    humans, and other large mammals.

55
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • A. How to develop survivorship curves
  • B. Three standard survivorship curves (FIG. 5)
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

56
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • A. How to develop survivorship curves
  • Plot the logarithm of survivorship (log lx) on
    Y-axis and age, size, or stage on
    X-axis. Usually use natural logs but can use any
    base.
  • B. Three standard survivorship curves (FIG. 5)
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

57
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • A. How to develop survivorship curves
  • Plot the logarithm of survivorship (log lx) on
    Y-axis and age, size, or stage on X-axis.
    Usually use natural logs but can use any base.
    These curves show the proportion of individuals
    dying (i.e. the mortality rate) at each age,
    size, or stage.
  • B. Three standard survivorship curves (FIG. 5)
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

58
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59
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • A. How to develop survivorship curves
  • Plot the logarithm of survivorship (log lx) on
    Y-axis and age, size, or stage on X-axis.
    Usually use natural logs but can use any base.
    These curves show the proportion of individuals
    dying (i.e. the mortality rate) at each age,
    size, or stage.
  • B. Three standard survivorship curves (FIG. 5)
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

60
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • A. How to develop survivorship curves
  • Plot the logarithm of survivorship (log lx) on
    Y-axis and age, size, or stage on X-axis.
    Usually use natural logs but can use any base.
    These curves show the proportion of individuals
    dying (i.e. the mortality rate) at each age,
    size, or stage.
  • B. Three standard survivorship curves (FIG. 5)
  • Developed by Pearl--often called Deevey
    curves. These show general patterns of
    mortality in natural populations.
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

61
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62
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • B. Three standard survivorship curves (FIG. 5)
  • Developed by Pearl--often called Deevey
    curves. These show general patterns of
    mortality in natural populations. In Type I
    curves, most mortality occurs late in life.
    Typical of humans and other large organisms that
    have few offspring and give much parental care.
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

63
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64
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • B. Three standard survivorship curves (FIG. 5)
  • Developed by Pearl--often called Deevey
    curves. These show general patterns of
    mortality in natural populations. In Type I
    curves, most mortality occurs late in life.
    Typical of humans and other large organisms that
    have few offspring and give much parental care.
    Type II curves have fairly constant mortality
    rate throughout life. Typical of many bird
    species and other organisms with intermediate
    number of offspring and parental care.
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

65
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66
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • B. Three standard survivorship curves (FIG. 5)
  • Developed by Pearl--often called Deevey
    curves. These show general patterns of
    mortality in natural populations. In Type I
    curves, most mortality occurs late in life.
    Typical of humans and other large organisms that
    have few offspring and give much parental care.
    Type II curves have fairly constant mortality
    rate throughout life. Typical of many bird
    species and other organisms with intermediate
    number of offspring and parental care. In Type
    III curves, most mortality occurs early in life.
    Typical of insects, marine invertebrates,
    plants, and other organisms that produce many
    offspring but few survive because there is
    little parental care for individual offspring.
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

67
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68
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)

69
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70
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)
  • Dall sheep in FIG. 6 have Type I survivorship.

71
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72
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)
  • Dall sheep in FIG. 6 have Type I survivorship.
  • Various birds in FIG. 7 have Type II
    survivorship.

73
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74
Lecture 10 Population Age and Size Structure
  • III. Survivorship Curves
  • C. Examples of survivorship curves in nature
    (FIGS. 6,7,8)
  • Dall sheep in FIG. 6 have Type I survivorship.
  • Various birds in FIG. 7 have Type II
    survivorship.
  • The tropical palms in FIG. 8 have Type III
    survivorship.

75
Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • A. What is a fecundity schedule?
  • B. Fecundity schedule parameters
  • C. What does net reproductive rate represent?
  • D. Examples

76
Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • A. What is a fecundity schedule? A table
    showing the number of offspring produced at each
    age (or size or stage) and also showing the
    survival of the parent.
  • B. Fecundity schedule parameters
  • C. What does net reproductive rate represent?
  • D. Examples

77
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78
Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • A. What is a fecundity schedule? A table
    showing the number of offspring produced at each
    age (or size or stage) and also showing the
    survival of the parent.
  • B. Fecundity schedule parameters
  • 1. Number of offspring produced per
    individual from age (or time) x to x1
    mx or bx.

79
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80
Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • A. What is a fecundity schedule? A table
    showing the number of offspring produced at each
    age (or size or stage) and also showing the
    survival of the parent.
  • B. Fecundity schedule parameters
  • 1. Number of offspring produced per
    individual from age (or time) x to x1
    mx or bx.
  • 2. Number of offspring produced by all
    individuals from age (or time) x to x1
    Fx.

81
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82
Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • A. What is a fecundity schedule? A table
    showing the number of offspring produced at each
    age (or size or stage) and also showing the
    survival of the parent.
  • B. Fecundity schedule parameters
  • 1. Number of offspring produced per
    individual from age (or time) x to x1
    mx or bx.
  • 2. Number of offspring produced by all
    individuals from age (or time) x to x1
    Fx.
  • 3. Net reproductive rate R0 sum of
    products of lx and mx values.

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Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • B. Fecundity schedule parameters
  • 1. Number of offspring produced per
    individual from age (or time) x to x1
    mx or bx.
  • 2. Number of offspring produced by all
    individuals from age (or time) x to x1
    Fx.
  • 3. Net reproductive rate R0 sum of
    products of lx and mx values.
  • C. What does the net reproductive rate represent?

85
Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • B. Fecundity schedule parameters
  • 1. Number of offspring produced per
    individual from age (or time) x to x1
    mx or bx.
  • 2. Number of offspring produced by all
    individuals from age (or time) x to x1
    Fx.
  • 3. Net reproductive rate R0 sum of
    products of lx and mx values.
  • C. What does the net reproductive rate
    represent? R0 measures the growth (or
    decline) in a population from one generation to
    the next. Its similar to ? but ? measures
    growth in the population from one year to the
    next.

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Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • C. What does the net reproductive rate
    represent? R0 measures the growth (or
    decline) in a population from one generation to
    the next. Its similar to ? but ? measures
    growth in the population from one year to
    the next.
  • D. Examples
  • 1. Phlox (FIG. 9)
  • 2. Red deer (hinds)(FIG. 10)
  • 3. Field grasshopper (FIG. 11)
  • 4. Human females (FIG. 12)

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Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • C. What does the net reproductive rate
    represent? R0 measures the growth (or
    decline) in a population from one generation to
    the next. Its similar to ? but ? measures
    growth in the population from one year to
    the next.
  • D. Examples
  • 1. Phlox (FIG. 9). R0 2.4177 so each
    individual in the previous generation
    replaces itself with more than 2 individuals in
    the next generation. The population will
    increase.
  • 2. Red deer (hinds)(FIG. 10)
  • 3. Field grasshopper (FIG. 11)
  • 4. Human females (FIG. 12)

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Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • D. Examples
  • 1. Phlox (FIG. 9). R0 2.4177 so each
    individual in the previous generation
    replaces itself with more than 2 individuals in
    the next generation. The population will
    increase.
  • 2. Red deer (hinds)(FIG. 10). R0 1.316 so
    the population should increase.
  • 3. Field grasshopper (FIG. 11)
  • 4. Human females (FIG. 12)

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Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • D. Examples
  • 1. Phlox (FIG. 9). R0 2.4177 so each
    individual in the previous generation
    replaces itself with more than 2 individuals in
    the next generation. The population will
    increase.
  • 2. Red deer (hinds)(FIG. 10). R0 1.316 so
    the population should increase.
  • 3. Field grasshopper (FIG. 11). R0 0.51 so
    the population will decline.
  • 4. Human females (FIG. 12)

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Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • D. Examples
  • 1. Phlox (FIG. 9). R0 2.4177 so each
    individual in the previous generation
    replaces itself with about 2.4 individuals in the
    next generation. The population will
    increase.
  • 2. Red deer (hinds)(FIG. 10). R0 1.316 so
    the population should increase.
  • 3. Field grasshopper (FIG. 11). R0 0.51 so
    the population will decline.
  • 4. Human females (FIG. 12). R0 1.0061 so
    the population of women in the U.S. is
    increasing at a rate of 0.61.

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Lecture 10 Population Age and Size Structure
  • IV. Fecundity Schedules
  • D. Examples
  • 1. Phlox (FIG. 9). R0 2.4177 so each
    individual in the previous generation
    replaces itself with about 2.4 individuals in the
    next generation. The population will
    increase.
  • 2. Red deer (hinds)(FIG. 10). R0 1.316 so
    the population should increase.
  • 3. Field grasshopper (FIG. 11). R0 0.51 so
    the population will decline.
  • 4. Human females (FIG. 12). R0 1.0061 so
    the population of women in the U.S. is
    increasing at a rate of 0.61. That is
    currently the approximate growth rate in the
    U.S.

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • A. Age-classified populations (Leslie matrix
    models)(FIG. 13A)
  • B. Size-classified populations (FIG. 13B)
  • C. Stage-classified populations (FIG. 14)
  • D. Assumptions of matrix models
  • E. Projecting population growth using matrix
    models (FIGS. 15,16,17)
  • F. Including density-dependence to make matrix
    models more realistic.

97
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • A. Age-classified populations (Leslie matrix
    models)(FIG. 13A)
  • 1. Life-cycle graphs
  • 2. Transition matrix models

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • A. Age-classified populations (Leslie matrix
    models)(FIG. 13A)
  • 1. Life-cycle graphs - show all age classes,
    the probability of surviving from one age
    to the next (P), and the fecundity at each
    age (F).
  • 2. Transition matrix models

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • A. Age-classified populations (Leslie matrix
    models)(FIG. 13A)
  • 1. Life-cycle graphs - show all age classes,
    the probability of surviving from one
    age to the next (P), and the fecundity at
    each age (F).
  • 2. Transition matrix models

101
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • A. Age-classified populations (Leslie matrix
    models)(FIG. 13A)
  • 1. Life-cycle graphs - show all age classes,
    the probability of surviving from one age
    to the next (P), and the fecundity at each
    age (F).
  • 2. Transition matrix models. Matrix Aa
    contains the same information as the
    life-cycle graph. Columns indicate age
    classes at the present (time t) and rows indicate
    the same age classes at time t 1.

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • A. Age-classified populations (Leslie matrix
    models)(FIG. 13A)
  • 1. Life-cycle graphs - show all age classes,
    the probability of surviving from one age
    to the next (P), and the fecundity at each
    age (F).
  • 2. Transition matrix models. Matrix Aa
    contains the same information as the
    life-cycle graph. Columns indicate age
    classes at the present (time t) and rows indicate
    the same age classes at time t 1.
  • B. Size-classified populations (FIG. 13B)
  • 1. Life-cycle graphs
  • 2. Transition matrix models

104
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • A. Age-classified populations (Leslie matrix
    models)(FIG. 13A)
  • 1. Life-cycle graphs - show all age classes,
    the probability of surviving from one age
    to the next (P), and the fecundity at each
    age (F).
  • 2. Transition matrix models. Matrix Aa
    contains the same information as
    the life-cycle graph. Columns indicate age
    classes at the present (time t) and rows
    indicate the same age classes at time t
    1.
  • B. Size-classified populations (FIG. 13B)
  • 1. Life-cycle graphs - show all size classes,
    the probability of surviving but remaining
    in the same size class (P), the
    probability of growing into the next size class
    (G), and fecundity of each size class
    (F).
  • 2. Transition matrix models

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • B. Size-classified populations (FIG. 13B)
  • 1. Life-cycle graphs - show all size classes,
    the probability of surviving but remaining
    in the same size class (P), the
    probability of growing into the next size class
    (G), and fecundity of each size class
    (F).
  • 2. Transition matrix models. Contain the
    same P, G, and F values as the life-cycle
    graphs.

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • B. Size-classified populations (FIG. 13B)
  • 1. Life-cycle graphs - show all size classes,
    the probability of surviving but remaining
    in the same size class (P), the
    probability of growing into the next size class
    (G), and fecundity of each size class
    (F).
  • 2. Transition matrix models. Contain the
    same P, G, and F values as the life-cycle
    graphs. Notice that the age-classified matrix
    has all zeroes on the diagonal, whereas the
    size-classified matrix may have values
    greater than zero.

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • B. Size-classified populations (FIG. 13B)
  • 2. Transition matrix models. Contain the
    same P, G, and F values as the life-cycle
    graphs, with arrows indicating probability of
    staying in the same size class (P) or of
    growing (G) and the fecundity (F). Notice
    that the age-classified matrix has all zeroes
    on the diagonal, whereas the size-classified
    matrix may have values greater than zero.
  • C. Stage-classified populations (FIG. 14)
  • 1. Insect stages of development (FIG. 14a)
  • 2. Stages of development in a tree population
    (FIG. 14b)
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • C. Stage-classified populations (FIG. 14)
  • 1. Insect stages of development (FIG. 14a)
  • 2. Stages of development in a tree population
    (FIG. 14b)
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • C. Stage-classified populations (FIG. 14)
  • 1. Insect stages of development (FIG. 14a)
  • Each circle now represents a different
    stage of development. Notice the different
    notation for P and F.
  • 2. Stages of development in a tree population
    (FIG. 14b)
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • C. Stage-classified populations (FIG. 14)
  • 1. Insect stages of development (FIG. 14a)
  • Each circle now represents a different
    stage of development. Notice the different
    notation for P and F.
  • 2. Stages of development in a tree population
    (FIG. 14b)
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • C. Stage-classified populations (FIG. 14)
  • 1. Insect stages of development (FIG. 14a)
  • Each circle now represents a different
    stage of development. Notice the different
    notation for P and F.
  • 2. Stages of development in a tree population
    (FIG. 14b)
  • Numbered stages could be seed, seedling,
    sapling, mature tree, and senescent tree
    (past its prime).
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • C. Stage-classified populations (FIG. 14)
  • 1. Insect stages of development (FIG. 14a)
  • Each circle now represents a different
    stage of development. Notice the different
    notation for P and F.
  • 2. Stages of development in a tree population
    (FIG. 14b)
  • Numbered stages could be seed, seedling,
    sapling, mature tree, and senescent tree
    (past its prime).
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • C. Stage-classified populations (FIG. 14)
  • 1. Insect stages of development (FIG. 14a)
  • Each circle now represents a different
    stage of development. Notice the
    different notation for P and F.
  • 2. Stages of development in a tree population
    (FIG. 14b)
  • Numbered stages could be seed, seedling,
    sapling, mature tree, and senescent tree
    (past its prime).
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)
  • The coral life cycle is more complicated.
    It can grow slowly or quickly and it can
    reproduce sexually (F) or asexually (P) by
    fragmenting into smaller pieces.

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • C. Stage-classified populations (FIG. 14)
  • 3. Coral life stages with sexual and asexual
    reproduction (FIG. 14c)
  • The coral life cycle is more complicated.
    It can grow slowly or quickly and it can
    reproduce sexually (F) or asexually (P) by
    fragmenting into smaller pieces.
  • Remember that stage-classified and
    size-classified matrices can both have positive
    values along the diagonal. Age-classified
    matrices can only have zeroes on the diagonal
    (because you cant stay the same age from one
    year to the next). Age-classified matrices are
    often called Leslie matrices in honor of Patrick
    Leslie. Also remember that fecundity (number of
    offspring) is shown on the first row of the
    matrix.

124
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • Remember that stage-classified and
    size-classified matrices can both have positive
    values along the diagonal. Age-classified
    matrices can only have zeroes on the diagonal
    (because you cant stay the same age from one
    year to the next). Age-classified matrices are
    often called Leslie matrices in honor of Patrick
    Leslie. Also remember that fecundity (number of
    offspring) is shown on the first row of the
    matrix.
  • D. Assumptions of transition matrix models
  • 1. Stationarity
  • 2. Markov property

125
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • D. Assumptions of transition matrix models
  • 1. Stationarity - P, G, and F values dont
    change over time. No stochastic effects of
    weather or disturbance and no resource
    limitation.
  • 2. Markov property

126
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • D. Assumptions of transition matrix models
  • 1. Stationarity - P, G, and F values dont
    change over time. No stochastic effects of
    weather or disturbance and no resource
    limitation.
  • 2. Markov property - P, G, and F values only
    depend on the current age, size, or stage of
    development and not on the past history of
    the individual. In the coral example, the
    probability of a medium-sized individual
    becoming a large individual doesnt depend
    on how long it has been in the medium-sized
    stage or how it got to that stage.

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • D. Assumptions of transition matrix models
  • 2. Markov property - P, G, and F values only
    depend on the current age, size, or stage of
    development and not on the past history of
    the individual. In the coral example, the
    probability of a medium-sized individual
    becoming a large individual dont depend on
    how long it has been in the medium-sized stage or
    how it got to that stage.
  • E. Projecting population growth using matrix
    models (FIGS. 15,16,17)

129
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • D. Assumptions of transition matrix models
  • 2. Markov property - P, G, and F values only
    depend on the current age, size, or stage of
    development and not on the past history of the
    individual. In the coral example, the
    probability of a medium-sized individual
    becoming a large individual dont depend on
    how long it has been in the medium-sized stage or
    how it got to that stage.
  • E. Projecting population growth using matrix
    models (FIGS. 15,16,17)
  • We use matrix multiplication to project
    population growth into the future. We
    multiply the matrix by an initial population
    vector that shows how many individuals are in
    each age or size class or stage of
    development.

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • E. Projecting population growth using matrix
    models (FIGS. 15,16,17)
  • We use matrix multiplication to project
    population growth into the future. We multiply
    the matrix by an initial population vector that
    shows how many individuals are in each age or
    size class or stage of development. By repeated
    multiplication, we can predict the growth rate
    (?), future N, and the expected proportion of
    individuals in each age or size class or stage
    of development (see handout).

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • E. Projecting population growth using matrix
    models (FIGS. 15,16,17)
  • We use matrix multiplication to project
    population growth into the future. We multiply
    the matrix by an initial population vector that
    shows how many individuals are in each age or
    size class or stage of development. By repeated
    multiplication, we can predict the growth rate
    (?), future N, and the expected proportion of
    individuals in each age or size class or stage
    of development (see handout). We can also
    determine what part of the life cycle is most
    important for maintaining the population at a
    reasonable size and what type of conservation
    efforts might be most effective.

134
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • E. Projecting population growth using matrix
    models (FIGS. 15,16,17)
  • Properties of matrix models
  • 1. The proportion of individuals in each age or
    size class or stage of development eventually
    stabilizes (FIG. 15).

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • E. Projecting population growth using matrix
    models (FIGS. 15,16,17)
  • Properties of matrix models
  • 1. The proportion of individuals in each age or
    size class or stage of development eventually
    stabilizes (FIG. 15).
  • 2. The stable population growth rate, ?,
    depends only on the matrix, not on the
    starting population (FIG. 16).

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • E. Projecting population growth using matrix
    models (FIGS. 15, 16, 17)
  • Properties of matrix models
  • 1. The proportion of individuals in each age or
    size class or stage of development eventually
    stabilizes (FIG. 15).
  • 2. The stable population growth rate, ?,
    depends only on the matrix, not on the
    starting population (FIG. 16).
  • 3. If a model has only one positive fecundity
    value, the population will cycle (FIG. 17).

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Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • F. Including density-dependence to make matrix
    models more realistic (FIGS. 18, 19, 20).

141
Lecture 10 Population Age and Size Structure
  • V. Life Cycle Graphs and Transition Matrix
    Models
  • F. Including density-dependence to make matrix
    models more realistic (FIGS. 18, 19, 20).
    Instead of having constant probabilities and
    fecundities in the matrix, you can use functions
    that depend on population density to account for
    resource limitations. This makes the
    models similar to logistic models and much more
    realistic.

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Lecture 10 Population Age and Size Structure
  • VI. Application of Matrix Population Models in
    Conservation and Management
  • A. Three important applications
  • B. Procedure
  • C. Exam
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