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1 “Futures in Biology” Healthcare Jobs/Alternatives to Medical School Tuesday, November 14, :30 p.m. JH 009 A 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 Hospital Lisa Garcia, Medical Technologist, Bloomington Hospital Melissa Randolph, Cyto-technologist, Clarian Health Partners An 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

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2 N 0 = 1 N 1 = 2 N 2 = 4 N 3 = 8 N 4 = 16 N 5 = 32 Live Population at a given generation

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3 N 0 = 1 N 1 = 2 N 2 = 4 N 3 = 8 N 4 = 16 N 5 = 32 Live Population at a given generation

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4 Geometric Population Growth in Discrete Time N = N t+1 - N t = R R = Total Population Growth Rate

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5 N 0 = 1 N 1 = 2 Live Population R 1 = N 1 – N 0 = 2 -1 = 1

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6 N 0 = 1 N 1 = 2 N 2 = 4 Live Population R 2 = N 2 – N 1 = 4 -2 = 2

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7 N 0 = 1 N 1 = 2 N 2 = 4 N 3 = 8 Live Population R 3 = N 3 – N 2 = = 4

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8 N 0 = 1 N 1 = 2 N 2 = 4 N 3 = 8 N 4 = 16 Live Population R 4 = N 4 – N 3 = = 8

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9 N 0 = 1 N 1 = 2 N 2 = 4 N 3 = 8 N 4 = 16 N 5 = 32 Live Population R 5 = ???

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10 N 0 = 1 N 1 = 2 N 2 = 4 N 3 = 8 N 4 = 16 N 5 = 32 Live Population R 5 = N 5 – N 4 = = 16

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11 Geometric Population Growth : NtNt RtRt Plot R t = (N t+1 – N t ) against N t. Population Growth Rate, R, is proportional to Population size or Density, N t.

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12 Basic Equation for Exponential Growth Chapter 11 at end of your Custom Text N: Number of individuals t: time interval N t = Number of individuals in the current time interval N t+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) N t+1 = N t + bN t - dN t = N t + (b - d) N t N t = (1 + b - d) t N 0 Population size at time t+1 = Population size at time t + # of births - # of deaths

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13 Basic Equation for Geometric Population Growth = R = Geometric Rate of Population Increase = 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. N t = bN t-1 + (1 – d)N t-1 N t = t N 0

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

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15 Geometric Population Growth: Line of Log(N t ) versus Time (t) N t = t N 0 Log(N t ) = {Log( )}t + Log(N 0 ) This graph is a straight line!

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16 Geometric Population Growth: Line of Log(N t ) versus Time (t) Time, t Log(N t ) Log(N t ) = {Log( )}t + Log(N 0 ) This graph is a straight line!

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17 Geometric Population Growth: Line of Log(N t ) versus Time (t) Time, t Log(N t ) Log(N t ) = {Log( )}t + Log(N 0 ) This graph is a straight line! Slope of the Line = Log

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18 Geometric Population Growth in Discrete Time = Exponential Population Growth in Continuous Time N = N t+1 - N t = r N t dN/dt = r N t r = “maximum intrinsic rate of increase” r = Log A Constant Value

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19 Geometric Population Growth: Line of Log(N t ) versus Time (t) Time, t Log(N t ) Log(N t ) = {Log( )}t + Log(N 0 ) This graph is a straight line! Slope of the Line = r

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20 Geometric Population Growth in Discrete Time = Exponential Population Growth in Continuous Time If dN/dt = r N t, Then N t = N 0 e rt r = “maximum intrinsic rate of increase”

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21 Geometric or Exponential Growth : NtNt Plot of ‘r’ against N t. Population Growth Rate per capita, r, is constant as population size or density, N t, changes. r

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

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

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