Lec8_08BIEB102

Lec8_08BIEB102 - BIEB Lecture 8: Population growth &...

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I. Exponential growth III. Logistic growth IV. Density dependence V. Fluctuations & cycles
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Population growth can be broken down into four processes: Births & deaths Both depend on current population size Immigration & emigration Individuals moving among populations N t+1 = N t + B - D + I - E N = B - D + I - E N = B - D today’s lecture will focus on local populations Population Density Births Deaths Emigration Immigration
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I. Exponential growth In exponential growth new individuals are added continuously to the population. For continuous growth, the population growth rate = dN / dt dN/dt = B - D = bN - dN = (b-d)N b = instantaneous birth rate (births / [(individuals)(time)] d = instantaneous death rate (deaths / [(individuals)(time)] * dN/dt =(b-d)N = rN r = exponential growth rate = instantaneous rate of increase r has the units ( individuals / [(individuals)(time)] ) * note abstraction
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I. Exponential growth Exponential growth: a continuously accelerating curve of increase To predict the number of individuals at a particular point in time, the equation dN/dt = rN can be integrated to obtain N(t) = N(0) e rt Ricklefs Figure 14.3 ln N time ln N(t) = ln N(0) + rt
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I. Exponential growth Other views of exponential growth N N dN/dt (1/N) (dN / dt)
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I. Exponential growth How long before an exponentially growing population doubles in size? Derive from: N(t) = N(0) e rt
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I. Exponential growth Some actual doubling times (after Gotelli (1998)) Species r doubling time T phage 300 3.3 minutes E.coli 58.7 17 minutes Paramecium 1.6 10.5 hours Flour beetle 0.1 7 days Brown rat 0.015 47 days Cow 0.001 1.9 years
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Exponential growth sneaks up on you! But populations never grow exponentially for long. Ricklefs Figure 14.1 I. Exponential growth
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II. Logistic growth Biologists beginning with understood that populations cannot grow exponentially for long. Increasing population size gives rise to … … shortages in food and other limiting resources. … greater intraspecific aggression. … increased attention from predators. … greater risk of disease outbreaks. These factors can act to lower birth rates and elevate death rates.
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II. Logistic growth Ricklefs Figure 15.3 An empirical example of logistic growth: Domestic sheep introduced onto the island of Tasmania fluctuated around a mean of c. 1.75 million for 75 y.
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II. Logistic growth Additional empirical examples of logistic growth: a) bacteria, b) wildebeest, and c) annual plant (sedge) Begon, Harper & Townsend (2006)
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II. Logistic growth Population growth rates decrease with increasing N Raymond Pearl and LJ Reed collated over 100 years of US census data Instead of r being a constant as in exponential growth, r = r 0 (1 - (N/K)) where K = carrying capacity , or the number of individuals environment can support Ricklefs Figure 14.14
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II. Logistic growth Properties of continuous logistic growth
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Lec8_08BIEB102 - BIEB Lecture 8: Population growth &...

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