Exam 3 #6

UIC BioS 101 Nyberg

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DEMOGRAPHY

The number of individuals in each age or stage group leads to improved population projection (compared to just knowing N).

Speaker Notes:

1

Individuals in a population are not equal. One of the most important variable for mammals is age.

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UIC BioS 101 Nyberg

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Reading

• Read section 52.1 Demography.

• Box 52.1 on life tables & growth

• Read p. 1186-88 on age structure.

• Study Figures 52.14 & 52.15.

• Life Tables Lab in labbook.

Speaker Notes:

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UIC BioS 101 Nyberg

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Catastrophes

• Extreme conditions which kill many individuals in a population is an event known as a catastrophe.

• Typically a catastrophe results in differential (unequal) mortality among age groups (classes).

• Some populations have not able to recover after dramatic reductions.

Speaker Notes:

3

Fish populations do not always recover after overfishing. This seems to imply that the ‘resources environment’ has changed.

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Age of Individuals

• Previous models have treated all individuals in the population as equivalent or equal.

• The probability of reproductive success in real populations is dependent on the age, genotype, geographic location and other characteristics.

Speaker Notes:

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Age of individuals effects survivorship and fecundity

• Individuals progress through stages of life (immature to mature) as they age.

• Knowing the age of an individual is probably the most useful character to predict survival or reproductive status in humans and other mammals.

• Age is irreversible, that is, one always gets older.

Speaker Notes:

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Cohort

• To study change with age we can follow a ‘cohort’ of individuals born at same time from birth to death (longitudinal study).

• More commonly we study individuals of different ages at one time (crosssectional study)

Speaker Notes:

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UIC BioS 101 Nyberg

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Age

• These models divide age into intervals given integer values, 0, 1, 2, ….

• The length of the interval might be 1 year for dogs. For humans it is usually 5 years.

• The symbol x is used for AGE.

Speaker Notes:

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S(x) & D(x)

• S(0) is the number of new borns in the cohort.

• S(1) is the number of individuals in the cohort that survive to age 1.

• The difference S(0) –S(1) = number that died between birth and age 1 = D(0)

• S(x+1) = S(x) – D(x)

• S(some large age) = 0, all die

Speaker Notes:

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UIC BioS 101 Nyberg

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Proportionate survival =Survivorship

• Survivorship is the probability of a new born surviving to age X.

• The symbol for survivorship is l(x).

• l(x) = S(x)/S(0) where S(0) is the number of new borns in the cohort and S(x) is number of new borns in cohort that survive to age X.

Speaker Notes:

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UIC BioS 101 Nyberg

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Survivorship values

• l(0) =1 as S(0)/S(0) = 1

• l(>>x) =0 as S(>>x)/S(0) = 0 as eventually all individuals die.

• Mammals have high survivorship at young ages and then steep declines at old age. This is known as a type I curve.

Speaker Notes:

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Type II survivorship

• If survivorship declines exponentially with age then survivorship curve is described as type II.

• Type II survivorship implies that the probability of dying does NOT change with age, i.e., is constant.

Speaker Notes:

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Survivorship Curves

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UIC BioS 101 Nyberg

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Speaker Notes:

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Fecundity, age specific

• The number of female offspring produced by a female of age X in next year is called m(x) = fecundity at age X.

• m(x) starts out at zero and then increases. In mammals it declines with advanced age.

• Maturnity is origin of variable name, m.

Speaker Notes:

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UIC BioS 101 Nyberg

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Net Reproductive Rate

• R0 is the symbol for net reproductive rate = average number of female offspring produced by average new born female.

• R0 = Σl(x)m(x) from x=0 until age all newborns are dead.

Speaker Notes:

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UIC BioS 101 Nyberg

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R0 and population growth

• If R0 is > 1 then population is increasing in size.

• If R0 is less than 1 then the population will decrease in toal number of individuals.

• The model assumes survivorship and fecundity don’t change with time.

Speaker Notes:

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A life table

AGE, x

Proportion

Surviving

to age x

Daughters born per female of age x

l(x)

m(x)

l(x)•m(x)

Speaker Notes:

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Population projection 1

Projection of population assumes l(x) and m(x) are parameters, i.e., constants for particular species.

Speaker Notes:

Figure 52.18 a

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Population projection 2

Speaker Notes:

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Population projection 3

Speaker Notes:

Figurec52.18c

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Population growth is more dependent on numbers in certain age classes than total number

Declining or stable population

Growing population

Speaker Notes:

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Projections normally assume that things stay the same, but frequently that is not true.

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UIC BioS 101 Nyberg

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Per Capita Growth Rate

• The per capita growth rate of a population is the increase in number (ΔN) per individual (N) per time period (t), but if only some age classes reproduce, then the per capita growth rate is lowered by individuals in post-reproductive ages.

Speaker Notes:

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UIC BioS 101 Nyberg

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Number of Humans

The doubling time of the human population has been decreasing, that is our rate of growth is faster, not slower as expected in logistic model.

Speaker Notes:

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The shortening doubling time can be called supra exponential growth.

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Exam 3 #6

UIC BioS 101 Nyberg

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Life tables can be applied to stages

Two important differences from human life tables are illustrated:

1. Life tables can be used with stages (not just age),

2. Survivorship and fecundity are sensitive to environmental conditions –in this case the amount of light available near the ground.

Speaker Notes:

23

Why do you think there are more seedlings when there is more light?

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UIC BioS 101 Nyberg

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Problem

• Calculate R0 for this life table.

• Is this population increasing or decreasing?

Speaker Notes:

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UIC BioS 101 Nyberg

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Vocabulary

• Population projection

• Catastrophe

• Population recovery

• Census

• Age

• Net Reproductive Rate

• Attribute

• l(x), m(x), l(x)•m(x), R0

• Survivorship

• Fecundity

• Stage vs age

Speaker Notes:

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