Final Exam, GEOG 5930/6930

In this project, you will find four points that are being considered as entry points for a noxious weed infestation, as well as the boundary for the parcel of land that you are managing. You are asked to evaluate the potential damage for this weed if it spreads onto your property from each of the three directions indicated in the map.

From an agricultural extension agent that is familiar with this plant, you are able to determine a few rules about how this plant grows and expands:

• The plant growth rate is a function of its age and size. The growth rate, as determined from relevant literature, is determined by the equation:
  • dm/dt = am (1 - m/b)
  • where m is the mass of the plant
  • t is time
  • a is a constant (here a = .25)
  • b is a constant (b = 12)
• The plant grows twice as fast in vegetation type 6 and 14 than in other types of vegetation.
• The growth rate in all other classes (except class 8) is the same as class 2.
• The plant cannot grow in vegetation type 8.
• The plant's reproductive effort begins once it has reached a size of 1.5.
• The reprodutive rate steadily increases until the plant has a size of 5. After that it remains constant.
• At a size of 5, the plant has a 70% chance of colonizing neighboring cells.
• The plant stops reproducing after an age of 40.

• land area
• biomass

Which of the four points would result in the greatest infestation in the property? Which allotment would be the worst hit in each case?