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Population Growth

Population Growth. Chapter 11. Outline. Geometric Growth Exponential Growth Logistic Population Growth Limits to Population Growth Density Dependent Density Independent Intrinsic Rates of Increase. Geometric Growth. When generations do not overlap, growth can be modeled geometrically.

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Population Growth

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  1. Population Growth Chapter 11

  2. Outline • Geometric Growth • Exponential Growth • Logistic Population Growth • Limits to Population Growth • Density Dependent • Density Independent • Intrinsic Rates of Increase

  3. Geometric Growth • When generations do not overlap, growth can be modeled geometrically. Nt = Not • Nt = Number of individuals at time t. • No = Initial number of individuals. •  = Geometric rate of increase. • t = Number of time intervals or generations.

  4. 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.

  5. 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. • t = Number of time intervals.

  6. Exponential Population Growth

  7. 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.

  8. Logistic Population Growth

  9. Logistic Population Growth dN/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.

  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 and caterpillars.

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

  16. Population Growth by SmallMarine Invertebrates • Populations of marine pelagic tunicate (Thalia democratica) grow at exponential rates in response to phytoplankton plumes. • Numerical response can increase population size dramatically due to extremely high reproductive rates.

  17. Growth of a Whale Population • Pacific gray whale (Eschrichtius robustus) divided into Western and Eastern Pacific subpopulations. • Rice and Wolman estimated average annual mortality rate of 0.089 and calculated annual birth rate of 0.13. 0.13 - 0.089 = 0.041 • Gray Whale population growing at 4.1% per yr.

  18. Growth of a Whale Population • Reilly et.al. used annual migration counts from 1967-1980 to obtain 2.5% growth rate. • Thus from 1967-1980, pattern of growth in California gray whale population fit the exponential model: Nt = Noe0.025t

  19. Review • Geometric Growth • Exponential Growth • Logistic Population Growth • Limits to Population Growth • Density Dependent • Density Independent • Intrinsic Rates of Increase

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