Population Estimation

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Population Estimation

• BIOL 500
• 30 November 2009

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Population Estimation

• Goal Estimate N, to.
• test population-growth models.
• compare relative abundance.
• track game species.
• track endangered species.

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Total Count

• Rarely possible, except with small populations of
  large, conspicuous animals or plants
• Exs Whooping cranes (188 in recent aerial
• count of nesting grounds)
• Large mammals
• Trees

4
Sampling and Extrapolation

• Ex Zebra mussels discovered in Edinboro Lake in
  Oct. 2000 (data from Jim Grazio, DEP)
• 45 randomly-chosen sampling stations
• Attention to depth and littoral zone distribution
  by depth
• Peaks
• 271 mussels/m2 at 0.76 m in Nov. 2000
• 76 mussels/m2 at 1.3 m in May 2001
• Total estimate of 37,273,524 in Nov. 2000, prior
  to lake draw-down
• Population down to just 21,991,379 in May 2001

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Line Transect Estimates

• Observer moves in straight line through habitat
• Records for each specimen seen its perpendicular
  distance to the transect
• Equations give density by assuming declining
  observability with distance from transect

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HANDOUTLacki et al. 1994
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Index of Relative Abundance

• Quantifications that do not yield estimates of N
  and thus are only useful on a comparative basis
• Catch per trap-night or per unit effort
• Counting feces, burrows, mud chimneys of
  crayfish, gorilla nests, etc.
• Listening for calls

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HANDOUTNelson and Graves 2004
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Mark-Release-Recapture Methods

• Rely on the ratio of markedunmarked animals in
  subsequent samples
• Model assumptions are vitally important
• Lincoln-Peterson method
• Schnabel method (aka Schumacher-Eschmayer method)
• Jolly-Seber method (aka Jolly-Seber-Cormack
  method)

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Lincoln-Peterson Estimator

• Two samples
• N total population (unknown)
• n total captured in second sample
• m marked animals captured in second sample
• M total marked and released during first sample
  (assumed to be present when second sample is
  taken)

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Lincoln-Peterson Estimator

• n/N ? m/M
• Proportion of total population
• caught in the second sample left
• approximately equal to
• proportion of the marked population
• caught in the second sample right
• N (nM)/m

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Fig. 8.4 p. 119

N (2016)/5 64
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Critical Assumptions of the Lincoln-Peterson
Estimator

• n/N ? m/M if and only if
• a) No marks are lost.
• b) The population is closed.
• c) Marked and unmarked animals are equally
  catchable.
• Trap-happy or trap-shy behavior would
  introduce bias into estimate of N

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Schnabel Estimator

• Multiple recapture censusing periods
• Yields weighted average of L-P estimates
• N ?niMi / ?mi 1

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Critical Assumptions of theSchnabel Estimator

• Same three as for L-P

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Jolly-Seber Estimator

• Published simultaneously in Biometrika in 1965
• Allows for an open population
• Series of estimates of Ni (allowed to vary)
• Also, estimates of rate of loss and number of
  additions between sampling periods
• Key estimate Mi, rather than simply keeping a
  running log of how many animals have been marked
  and released

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Fig. 8.2 p. 116
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New Variables for the J-S Estimator

• Zi animals caught prior to i, not at i, and
  after i
• Assumed present at i, but not caught at that time
• Ri animals caught at i and at least once again
  thereafter

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HANDOUTKrebs 5th edition
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J-S Equation

• Zi /Mi mi ? Ri /ni
• The proportion of marked animals present at i
  which
• we do not account for then, but do later left
• approximately equal to
• proportion of the total catch at i that we catch
  later right
• Mi Zi ni /Ri mi
• Thus Ni niMi /mi

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Critical Assumptions of the J-S Estimator

• 1) No loss of marks
• 2) No individual variation in capture probability
• 3) No animals leave, then re-enter the population
• Doing so would invalidate Zi

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Sample Calculations

• Z3 5221884 39
• R3 33138 54
• M3 (39?164)/54 37 155
• N3 (169?155)/37 708

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Calculating Survivorship Rates

• pi survivorship rate, i to i1
• Mi1/Mi ni mi
• ni mi represents new marked animals
• Ex p3-4 205/155 164 37 0.727
• Estimates that 72.7 remain in the
  populationalive and not emigratedbetween Sample
  3 and Sample 4

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Calculating Numbers of Additions

• Bi number of births, i to i1
• Ni1 Nipi
• Ex B3-4 765 (708?0.727) 250
• Estimates 250 new animals (births immigrants)
  between Sample 3 and Sample 4

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HANDOUTRegehr et al. 2006