1 1 Population Growth Chapter 11. 2 2 Outline Geometric Growth Exponential Growth Logistic Population Growth Limits to Population Growth Density Dependent.

11Population GrowthChapter 11

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Outline

Geometric Growth Exponential Growth Logistic Population Growth Limits to Population Growth

Density Dependent Density Independent

Intrinsic Rates of Increase

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Geometric Growth- pulsed reproduction annual plant or insect When generations do not overlap, growth can be

modeled geometrically.

Nt = Noλt

Nt = Number of individuals at time t.

No = Initial number of individuals. λ = Geometric rate of increase (Constant ratio) t = Number of time intervals or generations.

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Fig. 11.2

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Fig. 11.3

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Exponential Growth Continuous population growth in an unlimited

environment can be modeled exponentially.

dN / dt = rmax N

Appropriate for populations with overlapping generations. As population size (N) increases, rate of population

increase (dN/dt) gets larger.

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Assumes a population is growing without limits at its maximal rate Rate is symbolized r and called the biotic potential

The Exponential Growth Model

Growth rate = dN/dt = riNNo. of individuals

in a population

Intrinsic rate of increase

Change over time

The actual rate of population increase is

r = (b – d) + (i – e)

Birthrate Deathrate Net immigration

Net emigration

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Exponential Growth

For an exponentially growing population, size at any time can be calculated as:

Nt = Noermaxt

Nt = Number individuals at time t. N0 = Initial number of individuals. e = Base of natural logarithms. rmax = Per capita rate of increase (constant) t = Number of time intervals.

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Exponential Population Growth

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Logistic Population Growth As resources are depleted, population growth

rate slows and eventually stops: logistic population growth. Sigmoid (S-shaped) population growth curve. Carrying capacity (K) is the number of individuals of a

population the environment can support. Finite amount of resources can only support a finite number

of individuals.

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Logistic Population Growth

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Fig. 11.9

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Fig. 11.10

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Fig. 11.11

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Fig. 11.12

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dN/dt=rmax N

Add element that slows growth as pop size approaches K

dN/dt=rmax N(K-N) K

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Logistic Population GrowthdN/dt = rmaxN(1-N/K)

rmax = Maximum per capita rate of increase under ideal conditions.

When N nears K, the right side of the equation nears zero. As population size increases, logistic growth rate

becomes a small fraction of growth rate. Highest when N=K/2. N/K = Environmental resistance.

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Limits to Population Growth

Environment limits population growth by altering birth and death rates. Density-dependent factors

Disease, Resource competition Density-independent factors

Natural disasters

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Galapagos Finch Population Growth Boag and Grant - Geospiza fortis was

numerically dominant finch (1,200). After drought of 1977, population fell to (180).

Food plants failed to produce seed crop. 1983 - 10x normal rainfall caused population to grow

(1,100) due to abundance of seeds and caterpillars.

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Galapagos Finch Population Growth

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Fig. 11.19

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Fig. 11.18

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Cactus Finches and Cactus Reproduction Grant and Grant documented several ways

finches utilized cacti: Open flower buds in dry season to eat pollen Consume nectar and pollen from mature flowers Eat seed coating (aril) Eat seeds Eat insects from rotting cactus pads

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Cactus Finches and Cactus Reproduction Finches tend to destroy stigmas, thus flowers

cannot be fertilized. Wet season activity may reduce seeds available

to finches during the dry season. Opuntia helleri main source for cactus finches.

Negatively impacted by El Nino (1983). Stigma snapping delayed recovery.

Interplay of biotic and abiotic factors.

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