BIOLOGY 304
      POPULATION GROWTH

 


 

  • overview
  • Links
    •

  • textbook model http://www.blackwellpublishing.com/townsend/model/Index.html

     

  • Assignment for Monday pp. 154-172
    • life histories
    • age structures
    • mortality/survivorship curves
    • life tables
    • Also lab
  • Assignment for Wednesday  pp. 172-188
    • rates
    • exponential pop growth
    • intraspecific reg à logistic growth
  • Friday demos  and begin next lab 
    • stochastic effects
    • critter applications:  Is yours r or K?  and why?
    • lab 1 report due
  • the next week:
    • applications for human populations and their food populations (Chapter 12)
      • Monday 3 Feb : Read lab instructions, especially the human population parts, and prepare for vocabulary test on pp. 402-411.  How would you explain the wild differences in fig. 12.3?  Be prepared to discuss questions #2 & 3 on p. p. 438.
      • Wednesday 5 Feb.: Vocabulary test on pp. 411-417.  Compare fig. 12.5 to 5.18  Then try to understand fig. 12.6 and 12.8 and answer question 4 on p. 438.
    • Friday 7 Feb, turn in your next critter file
      • lab for population worksheets   
      • Make corrections and additions to File 1.  Wherever you make corrections and additions, include a note on your email to make sure the grader notices.
      • Four additional questions are found in the instructions for Critter File 2

 

 

Assignment for Monday pp. 154-172; questions #1,2,3,5 on p. 189;

life histories 5.4   
life histories 5.5
age structures 5.8   http://www.census.gov/ipc/www/idbpyr.html
 
mortality/survivorship curves5.7,5.9,5.10
life tables (table  5.1, 5.2, snail example, squirrel example, hand-outs) Also lab
also see uses (check search engines for demographic, vital statistics, life-table, "life history," actuarial) like these:

Assignment for Wednesday  pp. 172-188; questions #7, 8, 9, 10.  MORE equations and math stuff are on the lab worksheet instructions.  This assignment goes with steps 1-4 in the interactive model  http://www.blackwellpublishing.com/townsend/model/Index.html.  Try it! 

  Ch05f16.gif (18009 bytes)       dN/dt :  Growth Curves show the population growth rate (dN/dt), just like what you might already have learned about slopes (dy/dx) in math or physics classes. 

Both curves show that the rate of growth changes with the population size (N).   The other factors, r and K, are assumed to be constants.  (K= carrying capacity, from the original German "Kapazität.")
other rates:
(not dN/dt), like the birth and death and migration rates, and r, the intrinsic rate, are all "specific" = "per capita" rates, like the age-specific rates you understood on the life tables.

 

In the equations above,

r = exponential & fixed = 
ln (1+"APR"), like compounding interest

assuming that the "r" never changes; it's the genetically determined physiological max of birth and net migration rates, and minimum possible mortality rates.

Even though "r" doesn't change in the logistic equation above, the biological thing that is happening is that the other biological rates (birth, death, etc.) are not operating at the population's genetic potential max and mins. 

Notice that variable rates or birth and death are shown on almost all the textbook figures.  Would you want to take out a loan with a variable interest rate?  

exponential pop growth 

. Nt = N0ert
or Nfuture = Nnowert
     or  $future = $nowert

This equation is used to predict the future population size when the present size and "r" are known. This equation can be derived from the equation on the exponential curve on fig 5.16.

Nt is the size of the population after time t. N0 is the size of the population at the beginning of time t. "e" is the base of the natural logarithms, approximately equal to 2.718...(Euler constant). To determine the value of Nt, you multiply r and t, raise e to the power of that product [key in "ex" or "INV ln x" on some calculators], and then multiply that by N0.

intraspecific reg à
logistic growth

 

 
r and K species

be prepared to make a chart of comparing and contrasting

 

HUMAN POPULATIONS:

  

  1. sample values for r
    adapted from Gotelli, N.J .1995.  A Primer of Ecology.  Sinaur.
    virus 300 day-1
    E. coli 60 day-1
    protozoan 1.5 day-1
    flatworms 0.5 day-1
    flour beetles 0.1 day-1
    rats .015 day-1
    cows .001 day-1
    beech trees .0001 day-1
       
    US human 1978 -.005 year-1
    grizzly -.003 year-1
    turtle .003 year-1
    lizard .02 year-1
    squirrel .1 year-1
    cows .3 year-1
    snail .7 year-1
    weed .9  year-1
    pheasant (alien) 1.3 year-1

The point is to try to harvest at the peak of the n-curve

look for "Deep Crisis" at http://www.sciam.com/sciam_frontiers.cfm

 

                                    


 

Links

POPULATION GROWTH

Global Human Population Growth:

SOFTWARE and Professional Stuff

  • Lab http://fisher.forestry.uga.edu/popdyn/
  • Software for Population Analysis  (reviews, links)
  • popgrowth with stocasticity
            http://www.esajournals.org/archive/0012-9623/080/04/
             pdf/i0012-9623-080-04-0235.pdf
  • mark-recap
  • mark-recap-Manitoba
    catch.exe in lab folder
  • commercial software
  • ESA labs (classics)
  • CAPTURE (as well as other population estimation programs
    such as RELEASE and SURGE) have been superceded by
    a comprehnsive package that handles virtually all types of
    models based on data from marked animals. MARK is
    windows-based and throroughly documented online.
    You can download it from:
    http://www.cnr.colostate.edu/~gwhite/mark/mark.htm   or http://canuck.dnr.cornell.edu/mark/
  • Also note the repository of ecological software at
    http://nhsbig.inhs.uiuc.edu
  • NIH Image is a public domain image processing and analysis program for the Macintosh. It was developed at the Research Services Branch (RSB) of the National Institute
    of Mental Health (NIMH), part of the National Institutes of Health (NIH).
    A free PC version of Image, called Scion Image for Windows,
    is available from Scion Corporation. http://www.scioncorp.com/frames/fr_scion_products.htm
    There is also Image/J, a Java program inspired by Image that "runs anywhere".
    Image can acquire, display, edit, enhance, analyze and animate
    images. It reads and writes TIFF, PICT, PICS and MacPaint files, providing compatibility with many other
    applications, including programs for scanning, processing, editing, publishing and analyzing images. It supports many standard image processing functions, including contrast enhancement, density profiling, smoothing, sharpening, edge detection, median filtering, and spatial convolution with user defined kernels.
    Image can be used to measure area, mean, centroid, perimeter, etc. of user defined regions of interest. It also performs automated particle analysis and provides tools for measuring     path lengths and angles. Spatial calibration is supported to provide real world area and length measurements. Density calibration can be done against radiation or optical density standards using user specified units. Results can be printed,
    exported to text files, or copied to the Clipboard.
  • free copies of CAPTURE (as well as other population software):
    http://www.mbr.nbs.gov/software.html
    & http://www.cnr.colostate.edu/~gwhite/software.html
  • we marked 5 male crickets with small dots of different colored "liquid paper"
    for identification, put them together in an aquarium, and watched their
    interactions. The students observed the establishment of a dominance
    heirarchy. Then a female cricket was put into the aquarium and the students
    observed which male or males attempted mating, how the female reacted,
    and the outcomes of those interactions.  
    Vicky Hollenbeck <hollenbv@UCS.ORST.EDU>

  • When explaining the magnitudes attainable with exponential functions I often use this example. Although it is not biological it is intuitive, and can be demonstrated on a blackboard. With x and y in cm, y = e^x. Draw the x,y axes, and label them as you go. After x = 6 cm you will have to point to y.

    • x e^x

    • 0 1

    • 1 2.7

    • 2 7.4

    • 3 20

    • 4 55

    • 5 148

    • 6 403 (above the ceiling of most rooms)

    • 10 22026 (above a 70 story skyscraper)

    • 11 59874 (above Empire State Building)

    • 25 7x10^10 (beyond the moon)

    • 31 2.9x10^13 (beyond the sun)

    • 43 4.7x10^18 (beyond Alpha Centauri, x-axis still shorter than width of large, opened textbook)

    Tom Mosca III <tcm@VIMS.EDU>

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