I. Spatial Distributions

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I. Spatial Distributions II. Demography A.
Life Tables B. Age Class Distributions C.
Survivorship Curves D. Growth Potential 1.
Components
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I. Spatial Distributions II. Demography A.
Life Tables B. Age Class Distributions C.
Survivorship Curves D. Growth Potential 1.
Components Age classes (x) x 0, x 1,
etc. Initial size of the population nx, at
x 0. Survivorship (lx) proportion of
population surviving to age x.
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I. Spatial Distributions II. Demography A.
Life Tables B. Age Class Distributions C.
Survivorship Curves D. Growth Potential 1.
Components Age classes (x) x 0, x 1,
etc. Initial size of the population nx, at
x 0. Survivorship (lx) proportion of
population surviving to age x. Fecundity
rate mx female offspring/female/from time x
to x1
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I. Spatial Distributions II. Demography A.
Life Tables B. Age Class Distributions C.
Survivorship Curves D. Growth Potential 1.
Components Age classes (x) x 0, x 1,
etc. Initial size of the population nx, at
x 0. Survivorship (lx) proportion of
population surviving to age x. Fecundity
rate mx female offspring/female/from time x
to x1 Aside Birth Rate (Natality)
fertility capacity to breed fecundity
offspring/unit time - potential
physiological maximum - realized number
actually produced birth rate
offspring/female/unit time
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I. Spatial Distributions II. Demography A.
Life Tables B. Age Class Distributions C.
Survivorship Curves D. Growth Potential 1.
Components 2. R Net Reproductive Rate
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D. Growth Potential 1. Components 2. R Net
Reproductive Rate Survivorship (lx)
proportion of population surviving to age x.
Fecundity rate mx female offspring/female/fro
m time x to x1
R SUM(lxmx)
R 3.0
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D. Growth Potential 1. Components 2. R Net
Reproductive Rate Survivorship (lx)
proportion of population surviving to age x.
Fecundity rate mx female offspring/female/fro
m time x to x1
R SUM(lxmx) G (generation time) SUM(xlxmx)/R
G 4/3 1.33
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D. Growth Potential 1. Components 2. R Net
Reproductive Rate 3. Per Capita Rate of Increase
(r)
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D. Growth Potential 1. Components 2. R Net
Reproductive Rate 3. Per Capita Rate of Increase
(r) a. Annual/Biennial Species
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D. Growth Potential 1. Components 2. R Net
Reproductive Rate 3. Per Capita Rate of Increase
(r) a. Annual Species The 'geometric
rate of increase' N(t1)/Nt R. Organisms
reproduce once in their lifetime, and generations
don't overlap. In other words, suppose these were
3 years in the life of a given biennial species.
If we had 1000 organisms at the beginning (Nt),
we'd have 3000 livings seeds and no adults at the
end of the third year (Nt1)... R 3000/1000
3
Basically, the fecundity table reduces to
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D. Growth Potential 1. Components 2. R Net
Reproductive Rate 3. Per Capita Rate of Increase
(r) a. Annual Species The 'geometric
rate of increase' N(t1)/Nt R. Organisms
reproduce once in their lifetime, and generations
don't overlap. In other words, suppose these were
summer months an the life of a given species. If
we had 1000 organisms at the beginning of
summer(Nt), we'd have 3000 livings seeds and no
adults at the end of summer (Nt1)... R
3000/1000 3 b. Perennial Species With
overlapping generations, things are a little more
complex. r intrinsic rate of increase ln(R)/G
ln(3)/1.33 0.824.

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b. Perennial Species With overlapping
generations, things are a little more complex. r
intrinsic rate of increase ln(R)/G
ln(3)/1.33 0.824.
Suppose they reproduce earlier??

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b. Perennial Species With overlapping
generations, things are a little more complex. r
intrinsic rate of increase ln(R)/G
ln(3)/1.33 0.824.
Suppose they reproduce earlier??
How long is a generation? G SUM(xlxmx)/R 3/3
1.00 (equals mean time interval between birth
of parent and birth of offspring) r ln(R)/1.
For example above, r 1.10. So, breeding early
increases the rate of population growth.

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I. Spatial Distributions II. Demography III. Life
History Adaptations
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I. Spatial Distributions II. Demography III. Life
History Adaptations - Obviously, because
selection maximizes the reproductive success
within a population, factors that directly
influence the reproductive potential of a
population are under direct selective
control.
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I. Spatial Distributions II. Demography III. Life
History Adaptations - Obviously, because
selection maximizes the reproductive success
within a population, factors that directly
influence the reproductive potential of a
population are under direct selective control.
A. Evolution of Demographic Strategies
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I. Spatial Distributions II. Demography III. Life
History Adaptations - Obviously, because
selection maximizes the reproductive success
within a population, factors that directly
influence the reproductive potential of a
population are under direct selective control.
A. Evolution of Demographic Strategies 1.
Only populations with positive r values will
perpetuate themselves
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I. Spatial Distributions II. Demography III. Life
History Adaptations - Obviously, because
selection maximizes the reproductive success
within a population, factors that directly
influence the reproductive potential of a
population are under direct selective control.
A. Evolution of Demographic Strategies 1.
Only populations with positive r values will
perpetuate themselves 2. r is a function of x,
lx, and mx
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I. Spatial Distributions II. Demography III. Life
History Adaptations - Obviously, because
selection maximizes the reproductive success
within a population, factors that directly
influence the reproductive potential of a
population are under direct selective control.
A. Evolution of Demographic Strategies 1.
Only populations with positive r values will
perpetuate themselves 2. r is a function of x,
lx, and mx 3. so r can be increased by
increasing - first age of reproduction (x) -
survivorship (lx) - fecundity (mx)
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population
R SUM(lxmx) 10 G SUM (xlxmx)/R 10/10 1
r ln(R)/G 2.303
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population - increase fecundity and increase
growth potential (obviously)
R SUM(lxmx) 10 G SUM (xlxmx)/R 10/10 1
r ln(R)/G 2.303
R SUM(lxmx) 11 G SUM (xlxmx)/R 11/11 1
r ln(R)/G 2.398
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population - increase fecundity, increase
growth potential (rather obvious) - early
reproduction has HUGE effect
R SUM(lxmx) 11 G SUM (xlxmx)/R 11/11 1
r ln(R)/G 2.398
R SUM(lxmx) 12 G 5.5/15.5 0.833 r
ln(R)/G 2.983
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population - increase fecundity, increase
growth potential (rather obvious) - early
reproduction has HUGE effect - increased
survivorship doesn't do as much (r even
declines!!)
R SUM(lxmx) 11 G SUM (xlxmx)/R 11/11 1
r ln(R)/G 2.398
R SUM(lxmx) 20 G 30/20 1.5 r ln(R)/G
2.00
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population - increase fecundity, increase
growth potential (rather obvious) - early
reproduction has HUGE effect - increased
survivorship doesn't do as much (r even
declines!!) So think about this... investing in
survivorship is NOT ADAPTIVE....
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population - increase fecundity, increase
growth potential (rather obvious) - early
reproduction has HUGE effect - increased
survivorship doesn't do as much (r even
declines!!) So think about this... investing in
survivorship is NOT ADAPTIVE.... UNLESS, if by
deferring reproduction until later in life,
FECUNDITY can be DISPROPOTIONATELY LARGE.
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population 2. The advantage of a perennial
lifestyle
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population 2. The advantage of a perennial
lifestyle - early reproduction reduces
survival. By delaying reproduction, the organism
can grow larger and eventually invest MORE
energy, in an absolute sense, in
reproduction.
GROWTH
GROWTH
METABOLISM
METABOLISM
REPRODUCTION
REPRODUCTION
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population 2. The advantage of a perennial
lifestyle - early reproduction reduces
survival. By delaying reproduction, the organism
can grow larger and eventually invest MORE
energy, in an absolute sense, in
reproduction.
R SUM(lxmx) 230 G 530/230 2.30 r
ln(R)/G 2.36 Original r 2.303
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies 1. Start with this
population 2. The advantage of a perennial
lifestyle - early reproduction reduces
survival. By delaying reproduction, the organism
can grow larger and eventually invest MORE
energy, in an absolute sense, in
reproduction.
R SUM(lxmx) 230 G 530/230 2.30 r
ln(R)/G 2.36 Original r 2.303
But surprisingly, it doesn't crank it up MUCH...
earlier reproduction has a greater effect. Late
reproduction imposes a heavy fitness COST.
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists Annuals - low
survivorship, small energy budget
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists Annuals - low
survivorship, small energy budget Invest in
reproduction early
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists Annuals - low
survivorship, small energy budget Invest in
reproduction early small budget, can only make
small offspring... maximize number
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists Annuals - low
survivorship, small energy budget Invest in
reproduction early small budget, can only make
small offspring... maximize number Lots of small
offspring, each with low prob of survival
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists Annuals - low
survivorship, small energy budget Invest in
reproduction early small budget, can only make
small offspring... maximize number Lots of small
offspring, each with low prob of
survival Dominate in early successional stages
with lots of resources and no competition -
they can reproduce rapidly and usurp the
resources.
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists Annuals - low
survivorship, small energy budget Invest in
reproduction early small budget, can only make
small offspring... maximize number Lots of small
offspring, each with low prob of
survival Dominate in early successional stages
with lots of resources and no competition -
they can reproduce rapidly and usurp the
resources. High priority on long distance
dispersal to find next 'open' habitat
37
I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists Annuals - low
survivorship, small energy budget Invest in
reproduction early small budget, can only make
small offspring... maximize number Lots of small
offspring, each with low prob of
survival Dominate in early successional stages
with lots of resources and no competition -
they can reproduce rapidly and usurp the
resources. High priority on long distance
dispersal to find next 'open' habitat Can
recover quickly after a disturbance
38
I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists 2. K -
strategists
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists 2. K -
strategists Perennials - high survivorship,
large energy budget when mature
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists 2. K -
strategists Perennials - high survivorship,
large energy budget when mature Invest in growth
early and reproduction late
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists 2. K -
strategists Perennials - high survivorship,
large energy budget when mature Invest in growth
early and reproduction late large budget, can
make many small or a few large offspring
42
I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists 2. K -
strategists Perennials - high survivorship,
large energy budget when mature Invest in growth
early and reproduction late large budget, can
make many small or a few large offspring Dominate
in late successional stages where selection
favors strong competitors. Their large size
give them a competitive edge
43
I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists 2. K -
strategists Perennials - high survivorship,
large energy budget when mature Invest in growth
early and reproduction late large budget, can
make many small or a few large offspring Dominate
in late successional stages where selection
favors strong competitors. Their large size
give them a competitive edge Dispersal not
quite as important
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I. Spatial Distributions II. Demography III. Life
History Adaptations A. Evolution of
Demographic Strategies B. Life History
Strategies 1. r - strategists 2. K -
strategists Perennials - high survivorship,
large energy budget when mature Invest in growth
early and reproduction late large budget, can
make many small or a few large offspring Dominate
in late successional stages where selection
favors strong competitors. Their large size
give them a competitive edge Dispersal not
quite as important populations slow to recover
after a disturbance
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have dN/dt rN
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have dN/dt rN r (b-d) per capita
growth rate with unlimited resources
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have dN/dt rN r (b-d) per capita
growth rate with unlimited resources 2.
Doubling Time
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have dN/dt rN r (b-d) per capita
growth rate with unlimited resources 2.
Doubling Time If doubling, then Nt/No 2
ert
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have dN/dt rN r (b-d) per capita
growth rate with unlimited resources 2.
Doubling Time If doubling, then Nt/No 2
ert ln(2) rt
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have dN/dt rN r (b-d) per capita
growth rate with unlimited resources 2.
Doubling Time If doubling, then Nt/No 2
ert ln(2) rt 0.69315/r t
(time to double)
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I. Spatial Distributions II. Demography III. Life
History Adaptations IV. Population Growth A.
Exponential Growth 1. Rate Nt Noert If
we take the derivative with respect to time, we
have dN/dt rN r (b-d) per capita
growth rate with unlimited resources 2.
Doubling Time If doubling, then Nt/No 2
ert ln(2) rt 0.69315/r t
(time to double) humans - r
0.03 t 23 years.