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Population Ecology

Population Ecology. ES 100 10/23/06. Announcements:. Problem Set will be posted on course website today. Start early! Due Friday, November 3rd Midterm: 1 week from today Last year’s midterm is posted on website This year: will require a bit more thinking. Mathematical Models. Uses:

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Population Ecology

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  1. Population Ecology ES 100 10/23/06

  2. Announcements: • Problem Set will be posted on course website today. • Start early! • Due Friday, November 3rd • Midterm: 1 week from today • Last year’s midterm is posted on website • This year: will require a bit more thinking

  3. Mathematical Models Uses: • synthesize information • look at a system quantitatively • test your understanding • predict system dynamics • make management decisions

  4. dN dt Population Growth • t= time • N = population size (number of individuals) • = (instantaneous) rate of change in population size • r = maximum/intrinsic growth rate (1/time) = b-d (birth rate – death rate)

  5. dN dt Population Growth • Lets build a simple model (to start) = r * N • Constant growth rate  exponential growth • Assumptions: • Closed population (no immigration, emigration) • Unlimited resources • No genetic structure • No age/size structure • Continuous growth with no time lags

  6. Projecting Population Size • Nt = N0ert • N0 = initial population size • Nt = population size at time t • e  2.7171 • r = intrinsic growth rate • t = time

  7. Doubling Time

  8. When Is Exponential Growth a Good Model? • r-strategists • Unlimited resources • Vacant niche

  9. Let’s Try It! The brown rat (Rattus norvegicus) is known to have an intrinsic growth rate of: 0.015 individual/individual*day Suppose your house is infested with 20 rats. • How long will it be before the population doubles? • How many rats would you expect to have after 2 months? Is the model more sensitive to N0 or r?

  10. Can the population really grow forever? What should this curve look like to be more realistic? Population size (N) Time (t)

  11. Population Growth Population Density: # of individuals of a certain species in a given area • Logistic growth • Assumes that density-dependent factors affect population • Growth rate should decline when the population size gets large • Symmetrical S-shaped curve with an upper asymptote

  12. dN dt Population Growth • How do you model logistic growth? • How do you write an equation to fit that S-shaped curve? • Start with exponential growth • = r * N

  13. N K dN dt Population Growth • How do you model logistic growth? • How do you write an equation to fit that S-shaped curve? • Population growth rate (dN/dt) is limited by carrying capacity • = r * N (1 – )

  14. What does (1-N/K) mean? Unused Portion of K If green area represents carrying capacity, and yellow area represents current population size… K = 100 individuals N = 15 individuals (1-N/K) = 0.85 population is growing at 85% of the growth rate of an exponentially increasing population

  15. N K dN dt Population Growth • = r * N (1 – ) • Logistic growth • Lets look at 3 cases: • N<<K (population is small compared to carrying capacity) • Result? • N=K (population size is at carrying capacity) • Result? • N>>K (population exceeds carrying capacity) • Result?

  16. Population Size as a Function of Time

  17. At What Population Size does the Population Grow Fastest? • Population growth rate (dN/dt) is slope of the S-curve • Maximum value occurs at ½ of K • This value is often used to maximize sustainable yield (# of individuals harvested) /time Bush pg. 225

  18. Fisheries Management:MSY (maximum sustainable yield) • What is the maximum # of individuals that can be harvested, year after year, without lowering N? = rK/4 which is dN/dt at N= 1/2 K • What happens if a fisherman ‘cheats’? • What happens if environmental conditions fluctuate and it is a ‘bad year’ for the fishery?

  19. Assumptions of Logistic Growth Model: • Closed population (no immigration, emigration) • No genetic structure • No age/size structure • Continuous growth with no time lags • Constant carrying capacity • Population growth governed by intraspecific competition

  20. Lets Try It! Formulas: A fisheries biologist is maximizing her fishing yield by maintaining a population of lake trout at exactly 500 fish. Predict the initial population growth rate if the population is stocked with an additional 600 fish. Assume that the intrinsic growth rate for trout is 0.005 individuals/individual*day . How many fish will there be after 2 months?

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