Population Growth

1. Population Growth • Geometric Growth • Exponential Growth • Logistic Population Growth • Limits to Population Growth • Density Dependent • Density Independent • Intrinsic Rates of Increase • Our Future Chapter 11

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.

5. The Black Death! Exponential Growth of Human Population www.globalchange.umich.edu/.../human_pop.html

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

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?