Lecture 25: Population Growth

1. Levels in Ecology: Individuals, Populations, Communities, Ecosystems

2. Reasons to understand population growth

3. Malthusian growth

4. Properties of populations
    1. Birth rate b
    2. Death rate d
    3. Sex ratio

5. N, t, D N, D t D N / D t = (b — d) N

r = b — d = per capita population growth rate

D N / D t = dN / dt = r N If b>d, then r>0, population is _____________

If b<d, then r<0, population is _____________

If b=d, then r=0, population is _____________

  1. Exponential Growth
    1. rmax = intrinsic rate of increase = a constant = when conditions are optimal for a population, average b — average d = rmax

      2. Under optimal conditions, dN / dt = rmax N = rate of population change under Exponential Growth

    2. Assumptions of Exponential Growth
    3. Example: In a rapidly breeding, continuously expanding cockroach population, rmax = 0.09 per day. What is the rate of increase of a population of 1000 cockroaches?

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    4. Population size at time t: Nt = N0 e rmax t
    5. Continue cockroach example… What is the size of that same cockroach population after 10 generations (t = 10)?

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    6. When does exponential growth occur?

 

7. Logistic Growth Fig. 52.14

K = carrying capacity of environment

_ K = point of maximum sustainable yield

dN / dt = rmax N (K — N) Density-dependent term

K

What happens to dN / dt if N(t) is near 0? If N(t) = K? If N(t) >K? (Table 52.2)