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Population Growth Chapter 11

Geometric Growth

Exponential Growth

Logistic Population Growth

Limits to Population Growth

Density Dependent

Density Independent

Intrinsic Rates of Increase

Our Future

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Geometric Growth

• 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. t = Number of time intervals or generations.

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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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Exponential Growth

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

Nt = Noert

• Nt = Number individuals at time t.

• N0 = Initial number of individuals.

• e = Base of natural logarithms.• rmax = Per capita rate of increase.

• t = Number of time intervals.

5www.globalchange.umich.edu/.../human_pop.html

Exponential Growth of Human Population

The Black Death!

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Logistic Population Growth

• As resources are depleted, population growth rate slows and eventually stops, this is called logistic population growth. Sigmoid (S-shaped) pop. growth curve. Carrying capacity (K) is the number of

individuals of a population the environment can support.

A finite amount of resources can only support a finite number of individuals.

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Logistic Population Growth

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Logistic Population Growth

dN/dt = rmaxN(1-N/K)

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

• rmax occurs at extremely low population size.

• Growth rate (dN/dt) is greatest when N=K/2.• When N nears K, the both (1-N/K) and r approach

zero.• N/K = Environmental resistance; defines when

resources limit further growth.• If N>K, then dN/dt is negative; population declines.

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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 for adults and caterpillars nestlings.

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Galapagos Finch Population Growth

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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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Population Growth by SmallMarine Invertebrates

• Populations of marine pelagic tunicate (Thalia democratica) grow at exponential rates in response to phytoplankton blooms. Numerical response can increase

population size dramatically due to extremely high reproductive rates.

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Intrinsic Rates of Increase (r)

• On average, small organisms have higher rates of per capita increase and more variable populations than large organisms.

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Our Future?

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