Lec8_08BIEB102

# Lec8_08BIEB102 - BIEB Lecture 8: Population growth &amp;...

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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
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
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
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
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.
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
II. Logistic growth Properties of continuous logistic growth

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## Lec8_08BIEB102 - BIEB Lecture 8: Population growth &amp;...

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