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NRS 402, Wildlife Biometrics

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NRS 402, Wildlife Biometrics

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    1. NRS 402, Wildlife Biometrics Mark-Recapture Techniques Lectures 2 & 3

    2. What Kind of Data Do I Collect? Crude Density Relative Abundance

    3. Petersen-Lincoln Method John Graunt - used this method to estimate the London human population in 1662. C.G.J. Petersen - Danish fisheries biologist used the method to estimate fish populations in 1896. F.C. Lincoln - In 1930, Lincoln used the method to estimate ducks from band returns.

    4. Frederick C. Lincoln In 1920, Lincoln formed the continental bird banding program that remains the cornerstone of avian research in the U.S. Calculating Waterfowl Abundance on the Basis of Banding Returns. Published in1930, this brief circular presented the famous "Lincoln Index" method for estimating abundance from recaptures of marked animals.

    5. Petersen-Lincoln Index Strength - It provides information on birth, death, and movement rates. Weakness - It takes much time to get required data and must meet a very restrictive set of assumptions.

    6. Population “Types” Closed Population - does not change in size during the study period; effects of birth, death, and movements are negligible. Open Population - population that changes in size and composition from births, deaths, and movements.

    7. Petersen-Lincoln Index Use with closed population, single marking. It is the simplest mark-recapture method. Assumes that the second sample must be a random sample. M = no. of individuals marked at t1 C = total no. captured at t2 R = no. individuals marked in capture at t2 N-hat = size of population at time of marking, t1

    8. Petersen-Lincoln Index N-hat/M = C/R or N-hat = CM/R This formula gives a biased estimate, that is, it tends to overestimate the population. The bias is quite large for small populations.

    9. Seber (1982) Unbiased estimator! Used in samples taken without replacement. N-hat = [(M+1)(C+1)/(R+1)] - 1 Unbiased estimate if (M+C) ? N and nearly unbiased if R > 7. Used without replacement in second sample. Any one individual can only be counted once.

    10. Bailey (1952) Unbiased estimator! Used with replacement N-hat = M(C+1)/(R+1) Nearly unbiased for R > 7 Bailey, N. T. J. 1951. On estimating the size of mobile populations from recapture data. Biometrika 38: 293-306.

    11. Confidence Intervals Range of values which is expected to include the true population a given percentage of the time. Want CI to be as small as possible. On average, 95% (or whatever) of confidence intervals will include the true mean. But, we usually have only one estimate!

    12. When to Use What CI!? If R/C < 0.10, and R < 50, use Poisson Confidence Interval R > 50, use Normal Approximation CI If R/C > 0.10, use Binomial CI

    13. Poisson Confidence Intervals Use Table 2.1 M = 600 C = 200 R = 13; this is ? in the table. 95% CI Values for Lower = 6.686 95% CI Values for Upper = 21.364

    14. Poisson CI Calculation Lower 95% CI or CL N-hat = (601)(201)/(21.364 + 1) = 5,402 Upper 95% CI or CL N-hat = (601)(201)/(6.686 + 1) = 15,716 No sweat, right!?

    15. Normal Approximation CI “Large Sample” method R/C +/- {Z? ([(1-f)(R/C)(1-R/C)/(C-1)]^^2)+(1/2C)} f = Fraction of total population sampled at t2 which approximates R/M 1/2C = correction for continuity Z? = standard normal deviate for (1 - ?) level of confidence. A constant that defines 100(1 - ?) % CLs. Z? = 1.96 for 95% CLs and 2.576 for 99% CLs.

    16. Simplified Normal Approximation For large samples and a large population size, both (1-f) and 1/2C are negligible, therefore the formula can be simplified to: R/C +/- Z? {[(R/C)(1-R/C)/(C-1)]^^2} Mathematical Example: M = 1800 C = 800 R = 73

    17. Binomial CI Graphic determination - use Fig. 2.2 Example: M = 50; C = 22; R = 14 R/C = 14/22 = 0.64 = p = sample proportion ? 95 % CIs for R/C = 0.83 and 0.40

    18. Binomial CI How do you use these numbers to calculate CIs? R/C = 0.83 or 0.40 NL = (1)(50)/0.83 = 60 NU = (1)(50)/0.40 = 125 It is a simple N-hat = MC/R!

    19. Large Sample Size CIs Use Normal Approximation or Use Binomial if: R/C is: 0.5 0.4 0.3 0.2 0.1 And C is = 30 50 80 200 600 Example: if R/C = 0.35, we must capture 60 to 70 animals at t2 to use Binomial Cis When in doubt, use binomial - conservative and always correct. But follow the rules!

    20. Assumptions Population is closed, so that N is constant. All have the same chance of being caught. Marking does not affect their catchability. Animals do not lose marks between the 2 sampling periods. All marks are reported in the second sample.

    21. Go Forth and Sample with Confidence (Intervals, that is!)

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