CAPTURE

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The Lincoln Index

• CAPTURE MARK RECAPTURE METHOD

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The Lincoln Index

• Used to estimate the size of an animal
  population.
• Capture animals
• Mark them with a tag
• Release them and wait a period of time
• Capture animals again

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(No Transcript)
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Pitfall Trap
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Tiger census..
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Assumptions

• The population of organisms are closed, no
  immigration or emigration.
• The marked organisms mix completely with the
  rest of the population during the time between
  samples.

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Assumption

• The proportion of animals caught to the whole
  population is the same as the marked animals in
  the second sample.
• First Capture Marked animals, second
  capture
• Whole population second capture

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Equation

• n1 m2
• N n2
• n1 number of animals first marked and released.
• n2 number of animals captured in the second
  sample
• m2 number of marked animals in the second
  sample
• Solve for N n1 . n2 to find the total
  population
• m2

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Limitations

• Marking or capturing the animal might change its
  behavior to avoid recapture
• The mark might be toxic or cause predators to see
  it
• Marks might cause the animal to be rejected by
  its own population
• Trapping might cause the animal to avoid the
  traps in the future or to choose to be trapped to
  get food!

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The marks must not harm the animal
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Assumptions

• No animals are born or die during the period
  tested
• No animals immigrate or emigrate in the period
  tested.
• Animals do not die because of the markings.
• The tags do not fall off.

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What is the estimated snail population in a
woodland?

• In a woodland, the undergrowth was sampled for
  snails and 430 were found and marked. They were
  then released and the population similarly
  sampled after a two-week period. This second
  sampling produced 410 snails, 100 of which were
  marked.

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Answer

• n1 430
• n2 410
• m2 100
• N 430 x 410 1763 snails
• 100

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Woodlice

• Woodlice are terrestrial crustaceans that live
  under logs and stones in damp soil. To assess the
  population of woodlice in an area, students
  collected as many of the animals as they could
  find, and marked each with a drop of fluorescent
  paint. A total of 303 were marked. 24 hours
  later, woodlice were collected again in the same
  place. This time 297 were found, of which 99 were
  marked from the first time. What is the estimated
  population of woodlice in this area?

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Population estimate

• N 303 x 297 909
• 99

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Voles

• While studying field voles, an ecologist caught
  500 and ringed a foot of each before releasing
  them. Every day for the next two weeks he
  examined the waste material found in the nests of
  their predators. He collected a total of 300
  field vole skulls and 15 rings.
• How many field voles were
• probably in the area examined?

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Population estimate

• N 300 x 500 10 000
• 15

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A harder problem from the 2009 IB exam

• A population of meadow voles in an area of
  woodland was sampled using small mammal traps
• over a period of four days. On each occasion any
  unmarked individuals were marked and all
• the voles from the capture were then released.
  The following table represents the data obtained
• on each of the four days.

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Estimate the population size
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Vole population calculation

• n1 number in the first sample and marked.
• 81910-2 35
• You need to know how many animals were marked!
• n2 number in the second sample 23
• m2 number in the second sample with a mark 8
• N 35x23 100.6 The size of the population is
  101 as 8 100.6 voles is impossible!

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Estimate the size of a turtle population

• year Captured Marked
• pond turtles 1992 18
• 1993 34 12
• 1994 30 18

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Results1992 18 1993 34 (12) 1994
30 (18)

• The total number marked is 18 34 12 40
• The population estimate
• 1992-94 N 40(30) 67 turtles
• 18
• This assumes that none of the paint came off of
  the turtles over the course of two years.

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Mini experiment

• Does the size of the first capture, n1, while the
  size of the second capture is held constant,
  affect the accuracy of the population estimate,
  N?
• Does the size of the second capture, n2, while
  the size of the first capture is held constant,
  affect the accuracy of the population estimate,
  N?

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Hypothesis?

• Do you think that the Lincoln Index is more
  reliable if many animals are captured and marked
  in the first capture?
• Do you think that the Lincoln Index is more
  reliable if many animals are captured in the
  second capture?

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Mini experiment with beans

• You will use beans instead of animals to study
  the accuracy of the Lincoln index.
• Independent variable
• Vary either the size of the first capture OR the
  second capture while holding the other variable
  constant
• Dependent variable
• The value for m2 will change, so the value for
  the population estimate, N, will change. maybe

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Minilab Investigation with beans

• Count 150 beans into a cup
• Capture as many beans as you choose, n1
• Mark the captured beans.
• Release the marked beans into the cup and mix.
• Capture a second sample, n2
• Count the number of marked beans in the second
  sample, m2
• Repeat for four more trials, using the same size
  captures. ( Five trials of the same experiment
  should improve your accuracy and allows you to
  calculate the standard deviation.)
• Change the size of the first OR second capture
  while keeping the same value for the other
  capture. Repeat
• Change the number of beans captured again so that
  you the independent variable changes five times.

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Data processing show a sample calculation

• Calculate the population estimates, N
• N n1 x n2
• m2
• Calculate the mean values of N for each
  independent variable.
• Calculate the standard deviation. (excel use
  stdev)
• Calculate the percent error between the
  population estimates and true value for each of
  the independent variables.

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Data table Numbers of beans captured, marked,
recaptured and that had marks 1
n1 n2 Trial 1 m2 Trial 2 m2 Trial 3 m2 Trial 4 m2 Trial 5 m2




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Data Processing Calculate the population
estimate, N, for each trial
For each independent variable The population estimate, N
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Mean value

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The mean value of N for each independent
variable, the standard deviation and the percent
error
Independent variable Mean population estimate, N Standard deviation Percent Error





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Graph the results using an x, y scatterplot

• Do the population estimates improve with
  increasing first or second captures?
• The independent variable is on the x axis
• The dependent variable is on the y axis

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Rubric for grading