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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

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

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

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

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

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

Juvenile mallard (Anas platyrhyncos)

Male and female mallards

prairiefrontier.com

Bald eagle juvenile (Haliaeetus leucocephalus)

Bald eagle adult (Haliaeetus leucocephalus)

Photo by Tim Knight (homepage.mac.com)

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

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.

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

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.

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

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

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

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

Phlox drummondii

Larry Allain_at_ USGS NWRC Plants Database

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

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Western spruce budworm (Choristoneura

occidentalis)

Damage by spruce budworm

Spruce budworm adult

Entomology.umn.edu

Adult spruce budworm Climatology.umn.edu

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.

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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.

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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.

(No Transcript)

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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.

Lecture 10 Population Age and Size Structure

- II. Life Tables
- C. Classification methods for life tables (FIGS.

1,2,3,4) - 1.
- 2.
- 3.

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.

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Red deer hind (Cervus elaphus)

Paul Hobson photo

Red deer stag

Falconergame.co.uk

(No Transcript)

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.

(No Transcript)

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.

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

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)

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)

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)

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)

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)

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)

(No Transcript)

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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.

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.

(No Transcript)

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.

(No Transcript)

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.

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)

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)

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)

(No Transcript)

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)

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)

(No Transcript)

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)

(No Transcript)

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)

(No Transcript)

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)

(No Transcript)

Lecture 10 Population Age and Size Structure

- III. Survivorship Curves
- C. Examples of survivorship curves in nature

(FIGS. 6,7,8)

(No Transcript)

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.

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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.

(No Transcript)

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.

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

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

(No Transcript)

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.

(No Transcript)

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.

(No Transcript)

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.

(No Transcript)

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?

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.

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)

(No Transcript)

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)

(No Transcript)

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)

(No Transcript)

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)

(No Transcript)

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.

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.

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.

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

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

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

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)

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.

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

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

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)

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.

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).

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