Lecture 16-Populations 2

# Lecture 16-Populations 2 - Populations Populations can grow...

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Populations Populations can grow in several ways: Linear growth—the population increases steadily over time Exponential growth—the population grows at an exponential rate Logistic (sigmoidal) growth—population experiences exponential growth, then levels off

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Sigmoidal growth Exponential growth
Populations Calculating how a population will grow in the future: N t+1 = λ (N t) Future population size = (Net repro. rate) (Original pop. size)

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Populations 2200 λ = net reproductive rate 2200 λ = (# kids produced) x (probability that kids survive to adulthood) Total # of kids produced = fertility
Describing Exponential Growth The exponential growth equation: N t = N 0 e rt • N 0 = initial population size • N t = number of individuals after “t” time e = ~2.72 (natural logarithm base) r = exponential growth rate

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In an exponential growth situation, the rate at which individuals are added to the population is: dN = rN dt This is the derivative of the exponential equation, N t = N 0 e rt
Geometric Growth The equation for geometric growth, N t = N 0 λ t is the same equation as the one for exponential growth. ... N t = N 0 e rt ....except that λ replaces e r

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Intrinsic Rate of Increase • r m = intrinsic rate of increase (Malthusian parameter) Maximum possible growth rate under ideal conditions the exponential rate of increase of a population with a stable age distribution
Intrinsic Rate of Increase Most populations don’t have a stable age distribution! • r m is more useful for identifying environmental conditions affecting population growth than as an accurate predictor of population growth

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Intrinsic Rate of Increase r m = intrinsic rate of increase = exponential rate of increase of a population with a stable age distribution Most populations don’t have a stable age distribution! R 0 = net reproductive rate (fecundity x survival of newborns)
Survival and Fertility Decline in Crowded Populations Survival is reduced by: Limited food Increased waste Increased vulnerability to predators Increased stress Disease Infanticide Cannibalism

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Survival and Fertility Decline in Crowded Populations Fertility is reduced by: Limited food for adults Increased behavioral interactions (fights, stress) Smaller adults due to competition during adolescence
Perfect Conditions Rarely Exist Forever! Limiting factor = any environmental factor that limits the abundance or distribution of an organism

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## This note was uploaded on 08/30/2008 for the course BIOS 230 taught by Professor Gibbons during the Spring '08 term at Ill. Chicago.

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Lecture 16-Populations 2 - Populations Populations can grow...

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