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If resources are unlimited, populations can grow exponentially…

If resources are unlimited, populations can grow exponentially…. Population growth rates depend on population size. dN/dt = r max N dN/dt = change in population size over time r max = maximum per capita growth rate N = current population size

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If resources are unlimited, populations can grow exponentially…

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  1. If resources are unlimited, populations can grow exponentially… Population growth rates depend on population size. dN/dt = rmax N dN/dt = change in population size over time rmax = maximum per capita growth rate N = current population size As population size (N) increases, so does rate of population increase (dN/dt).

  2. 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. Is this realistic? Could such an increase go on forever? Why not?

  3. Logistic Population Growth As resources depleted, growth rate slows, eventually stops: logistic population growth. Sigmoid (S-shaped) population growth curve. Carrying capacity (K) = population size environment can sustain. Finite resources support finite population.

  4. Logistic Population Growth dN/dt = rmaxN(1-N/K) When N nears K, 1-N/K nears zero. As population size increases, logistic growth becomes small fraction of exponential growth rate. Highest when N=K/2. N/K = Environmental resistance.

  5. Can also be written as: dN/dt = rmaxN(K-N)/K

  6. Limits to Population Growth Environment limits population growth by altering birth and death rates. Density-dependent factors (determines K) Disease, Resource competition (typically biotic) Density-independent factors (random fluctuations) Natural disasters, Weather (typically abiotic) Interactions Abound! – not always easy to tease apart density independence/dependece

  7. 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; abundant seeds + caterpillars; finch population = 1100. Abiotic and biotic factors both contribute to growth rate

  8. Review Exponential Growth Logistic Population Growth Limits to Population Growth Density Dependent Density Independent

  9. What is K for humans? That is a very good question…no body really knows – depends on a lot of things Some scientists think 2 billion = ‘reasonably good quality of life for everyone’

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