1
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
2
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.
3
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.
4
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!
6
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.
7
Logistic Population Growth
8
9
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.
10
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
11
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.
12
Galapagos Finch Population Growth
13
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
14
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.
15
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.
16
Intrinsic Rates of Increase (r)
• On average, small organisms have higher rates of per capita increase and more variable populations than large organisms.
17
Our Future?
18