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N 0 = 1

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N 0 = 1

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  1. “Futures in Biology”Healthcare Jobs/Alternatives to Medical SchoolTuesday, November 14, 20066:30 p.m.JH 009A reception with pizza and drinks will follow.Interested in a career in healthcare but not sure med school is right for you?  Come to this “Futures” hear how these four people found fulfilling careers in healthcare.John Couch, Cardiovascular Surgical Nurse, Bloomington HospitalLisa Garcia, Medical Technologist, Bloomington HospitalMelissa Randolph, Cyto-technologist, Clarian Health PartnersAn EMT from the IU Emergency Medical Service group will also speak with students.Sponsors: Department of Biology and Biology Club-----------------------“Futures in Biology” connects students to professionals in science-related careers.  Come to the sessions to find out how you can launch your career in biology.  We’re online at http://development.bio.indiana.edu/Futures/.

  2. Live Population at a given generation N0 = 1 N1 = 2 N2 = 4 N3 = 8 N5 = 32 N4 = 16

  3. Live Population at a given generation N0 = 1 N1 = 2 N2 = 4 N3 = 8 N5 = 32 N4 = 16

  4. Geometric Population Growth in Discrete Time DN = Nt+1 - Nt = R R = Total Population Growth Rate

  5. Live Population N0 = 1 N1 = 2 R1=N1 – N0 = 2 -1 = 1

  6. Live Population N0 = 1 N1 = 2 N2 = 4 R2 =N2 – N1 = 4 -2 = 2

  7. Live Population N0 = 1 N1 = 2 N2 = 4 N3 = 8 R3 =N3 – N2 = 8 - 4 = 4

  8. Live Population N0 = 1 N1 = 2 N2 = 4 N3 = 8 N4 = 16 R4 =N4 – N3 = 16 - 8 = 8

  9. Live Population N0 = 1 N1 = 2 N2 = 4 N3 = 8 N5 = 32 N4 = 16 R5 =???

  10. Live Population N0 = 1 N1 = 2 N2 = 4 N3 = 8 N5 = 32 N4 = 16 R5 =N5 – N4 = 32 - 16 = 16

  11. Geometric Population Growth: Plot Rt = (Nt+1 – Nt) against Nt. Population Growth Rate, R, isproportional to Population size or Density, Nt. Rt Nt

  12. Population size at time t Population size at time t+1 # of births # of deaths = + - Basic Equation for Exponential GrowthChapter 11 at end of your Custom Text N: Number of individuals t : time interval Nt = Number of individuals in the current time interval Nt+1 = Number of individuals in the next time interval b : birth rate (per capita: 1/N, per time interval 1/t) d : death rate (per capita: 1/N, per time interval 1/t) Nt+1 = Nt + bNt - dNt = Nt + (b - d) Nt Nt= (1 + b - d)tN0

  13. Basic Equation for Geometric Population Growth Nt = bNt-1 + (1 – d)Nt-1 Nt = lt N0 • =R = Geometric Rate of Population Increase l = 1 + birth rate per capita – death rate per capita • = 1 + b – d • > 1 means that births exceed deaths and N increases • < 1 means that deaths exceed births and N decreases • = 1 means that births equal deaths and N is constant.

  14. Geometric Population Growth:J-shaped Curve of Nt versus Time (t) Nt Time, t Population size, Nt , accelerates with time in a J-shaped Curve.

  15. Geometric Population Growth:Line of Log(Nt) versus Time (t) Nt = lt N0 Log(Nt) = {Log(l)}t + Log(N0) This graph is a straight line!

  16. Geometric Population Growth:Line of Log(Nt) versus Time (t) Log(Nt) Time, t Log(Nt) = {Log(l)}t + Log(N0) This graph is a straight line!

  17. Geometric Population Growth:Line of Log(Nt) versus Time (t) Slope of the Line = Log(l) Log(Nt) Time, t Log(Nt) = {Log(l)}t + Log(N0) This graph is a straight line!

  18. Geometric Population Growth in Discrete Time =Exponential Population Growth in Continuous Time DN = Nt+1 - Nt = rNt dN/dt = r Nt r = “maximumintrinsic rate of increase” r = Log(l) = A Constant Value

  19. Geometric Population Growth:Line of Log(Nt) versus Time (t) Slope of the Line = r Log(Nt) Time, t Log(Nt) = {Log(l)}t + Log(N0) This graph is a straight line!

  20. Geometric Population Growth in Discrete Time =Exponential Population Growth in Continuous Time If dN/dt = r Nt, Then Nt = N0ert r = “maximumintrinsic rate of increase”

  21. Geometric or Exponential Growth: Plot of ‘r’ against Nt. Population Growth Rate per capita, r, isconstantas population size or density, Nt, changes. r Nt

  22. Exponential Growth: 3 Equivalent Looks Population size accelerates with time: J-shaped Curve. Nt Time Populationgrow rate is proportion to population size or density. R Nt Per capita growth rate, r, is constant as population size or density increases. r Nt

  23. How do we calculate R? Option 1: Count the population twice over a specified interval of time from t to (t + 1). Nt+1 Nt R= This Method has a Weakness: Time to time variation in birth and death rates. What if this year was an odd one?

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