1 / 9

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

thao
Download Presentation

If resources are unlimited, populations can grow exponentially…

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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’

More Related