Readings

1
Readings

• Table 10.1, p. 246
• Table 10.2, p. 248
• Life Histories, pp. 284-291

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Population Dynamics
Fundamental Equation N(t1) N(t) B D I
E N(t1) - N(t) B D I E ?N B
D I E
B
E
D
I
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Estimating Patterns of Survival

• Three main methods of estimation
• Cohort life table
• Identify individuals born at same time and keep
  records from birth.

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Estimating Patterns of Survival

• Three main methods of estimation
• Static life table
• Record age at death of individuals.

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Estimating Patterns of Survival

• Three main methods of estimation
• Age distribution
• Calculate difference in proportion of individuals
  in each age class.
• Assumes differences from mortality.

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Cohort vs Static Life Tables
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High Survival Among the Young

• Murie collected Dall Sheep skulls, Ovis dalli
• Major Assumption Proportion of skulls in each
  age class represented typical proportion of
  individuals dying at that age
• Reasonable given sample size of 608

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High Survival Among the Young

• Constructed survivorship curve
• Discovered
• bi-modal mortality
• lt1 yr
• 9-13 yrs

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Survivorship Curves

• Type I Majority of mortality occurs among older
  individuals.
• Dall Sheep
• Type II Constant rate of survival throughout
  lifetime.
• American Robins
• Type III High mortality among young, followed by
  high survivorship.
• Sea Turtles

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Survivorship Curves

• Plot
• Log10lx vs. X

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Dall sheep (Ovis dalli)
Life Table
12
Static life table for Dall Sheep
x age class nx number alive dx
number dead lx proportion
surviving S1000 per 1000 alive
Ovis dalli dalli
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Static life table for Dall Sheep
Age class x 0 newborns 100 survive Age
class x 1 only 623 in this age class
752-129 prop surviving (l1) 623/752
0.828 Age class x 2 only 509 survive
623-114 prop surviving (l2) 509/752 0.677
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Age Distribution

• Age distribution of a population reflects its
  history of survival, reproduction, and growth
  potential
• Miller published data on age distribution of
  white oak (Quercus alba)
• Determined relationship between age and trunk
  diameter
• Age distribution biased towards young trees.
• Sufficient reproduction for replacement
• Stable population

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Age Distribution
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Age Distribution

• Rio Grande Cottonwood populations (Populus
  deltoides wislizenii) are declining
• Old trees not being replaced
• Reproduction depends on seasonal floods
• Prepare seed bed
• Keep nursery areas moist
• Because floods are absent, there are now fewer
  germination areas

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Dynamic Population in a Variable Climate

• Grant and Grant studied Galapagos Finches.
• Drought in 1977 resulted in no recruitment
• Gap in age distribution
• Additional droughts in 1984 and 1985
• Reproductive output driven by exceptional year in
  1983
• Responsiveness of population age structure to
  environmental variation

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Age Structure
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Creation of Stable Age Distribution
1st Gen.
2nd Gen.
3rd Gen.
3 2 1 Age
Not Stable
Not Stable
Stable
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Rates of Population Change

• Birth Rate Number of young born per female
• Fecundity Schedule Tabulation of birth rates for
  females of different ages

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Frequency of Reproduction in Populations
generation
Discrete, non-overlapping
Number of offspring
Discrete, overlapping
Continuous
Time
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Estimating Rates for an Annual Plant

• P. drummondii
• Ro Net reproductive rate Average number of
  seeds produced by an individual in a population
  during its lifetime
• RoSlxmx
• X Age interval in days
• lx pop. surviving to each age (x)
• mx Average number seeds produced by each
  individual in each age category

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Estimating Rates for an Annual Plant

• Because P. drummondii has non-overlapping
  generations, can estimate growth rate
• Geometric Rate of Increase (?)
• ? N t1 / Nt
• N t1 Size of population at future time
• Nt Size of population at some earlier time

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Estimating Rates when Generations Overlap

• Common Mud Turtle
• (K. subrubrum)
• About half turtles nest each yr
• Average generation time
• T S xlxmx / Ro
• X Age in years
• Per Capita Rate of Increase
• r ln Ro / T
• ln Base natural logarithms

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Fecundity (Fertility) Schedule
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Life Table Calculations
7.70
Sum
14.67
02.953.061.520.26 7.70