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Lecture 9: Population Growth

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Estimating Rates for an Annual Plant (P. drummondii)

Overlapping or non-overlapping generations?

Ro = Net reproductive rate

  • Average number of offspring produced by an individual in a population during its lifetime.


  • lx = % pop. surviving to each age (x)
  • mx= Average number seeds produced by each individual in each age category
  • X = Age interval in days

Ro = Net reproductive rate

Ro < 1

Ro > 1

Ro = 1


  • Because P. drummondii has non-overlapping generations and pulsed reproduction, estimate growth rate as geometric rate of increase (λ)

Geometric Rate of Increase (λ):

  • λ = N t+1 / Nt
  • N t+1 = Size of population at future time
  • Nt = Size of population at some earlier time


  • λ = 2,408/996
  • λ = 2.41

Estimating Rates when Generations Overlap

Common Mud Turtle ( K. subrubrum


  • Ro = 0.601
  • Can also calculate:
  • Generation Time (T) = Ave. time from egg to egg

T = Σ xlxmx / Ro

x = Age in years

T = 10.6 years


Per Capita Rate of Increase (r) = birthrate – death rate    <---- Exponential growth - continuous reproduction

r = ln Ro / T

r = ln (0.601)/10.6 = - 0.05


Fecundity schedule more complicated

  • Number of females that nest each year
  • Clutch size
  • Number of female vs. male offspring

Generation time versus body size

What other factors influence population dynamics?


Exploring population dynamics

  • Births, deaths, survivorship
  • Age distribution
  • Rates of population change
  • Dispersal


  • Dispersal into populations (immigration)
  • Dispersal out of populations (emigration)

Snail kites in Florida

What else regulates population growth?

Density dependent factors


The Malthusian Doctrine (1798)

  1. Food is necessary for existence (of humans)
  2. The “passion between the sexes is necessary and will remain nearly in its present state.”

---> Populations will be checked by death from starvation when food resources are exhausted.


Pearl and Reed’s U.S. Population projection


Rather than assume exponential growth, they assumed that r

Decreases as N increases

r = r0(1-N/K)


Copyright 2008, by the Contributing Authors. Cite/attribute Resource . Baker, M. A., factpetersen. (2008, March 14). Lecture 9: Population Growth. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: This work is licensed under a Creative Commons License Creative Commons License