Practice Population Problems

Closed population - define: a population with no immigration or emigration (or we ignore the fact that there is)

1. A bacterial culture has an intrinsic rate of growth (r_c) of 12%/hour.  A  microbiologist has estimated the population to be 1,957,039 in a petri dish. How many bacteria will there be in the next hour?  How long will it take for the culture to double in size?

Answer:    N = 1,957,039      r_c= 12%/100% = .12    

    ΔN = rN = 0.12(1,957,039) = 234,844.68  + 1,957,039 = 2,191,884 (rounded up)

    Doubling time = 70/r_c% = 70/12% = 5.83 hours

2. A forest ecologist is monitoring the tree population in a small woodlot.  He has determined that the current population of trees is 1285.  He also know that for every 100 trees, an average of twenty-six seeds survive to becoming a tree in ten years.  He also knows that for every 100 trees, 5 will die in ten years.  What would be the projection for the number of trees in the woodlot in 10 years?  in 20 years?

Answer: N = 1285, b = 26/100 = 0.26    d = 5/100 = 0.05

            r = b-d = 0.26-0.05 = 0.21

            ΔN = rN = 0.21 x 1285 = 269.85 or 270

   Population in 10 years = N + ΔN = 1285 + 270 = 1555

   Population in 20 years: 1555 x 0.21 = 326.55 or 327 ® 1555 + 327 = 1882

Open population - define: a population that includes migration

3. The resource biologist at Chincoteague National Wildlife Refuge wants to calculate how many horses from the Virginia side of Assateague Island should be rounded up  at the Volunteer Fire Department Horse Auction in July.  The current population is 112.  On average, each year 25 horses are born into the population and 8 die.  An average of 2 horses break through the fence and immigrate from the Maryland  side.  How many horses should be removed from the population (emigration) to keep it stable?

Answer = We want to make r = 0 to keep population stable and we also need to use an open r, therefore r_o = (b-d) + (i-e) = 0.  Isolate e to get e = (b-d)+i

          e = 25-8+2 = 19 horses have to be removed to keep population at 112.

4. The population of mice in a prairie is estimated to be 476 in 2002.  In an average year, 46 mice are born per 100 mice, 53 die per 100, 17 per 100 move into the the prairie from the adjacent habitat and 12 per 100 move out.  What is the intrinsic rate of growth (r_c), what is the annual population growth (r_o), and what is the net migration rate? 

Answer:  r_c = b-d = 0.46-0.53 = -0.07

               r_o = (b-d)+(i-e) = (0.46-0.53)+(0.17-0.12) = -0.07+0.05 = -0.02

            NMR = i-e =  (0.17-0.12) = 0.05

Because the annual rate of growth is negative, this population is declining.

Also, look at the population pyramids for these countries at:

http://www.census.gov/ipc/www/idbsum.html

and describe them as expanding, stable, diminishing, or transitional or maybe they just defy description.  

Albania: 2000 - expanding       2025 - stable

Eritrea:  2000 - expanding       2025 - expanding

Iraq:     2000 - expanding       2025 - expanding

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© Joan McKearnan 2007

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Last revised: Wednesday, 11 April 2007