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Calculations / Statistics

Calculations / Statistics. Laboratory 1: Nearest Neighbor and Population Dispersion. Hole NND 1 4.3 cm 2 2.6 cm 3 7.9 cm. Just because Point 2 is the Nearest Neighbor of Point 1 does not mean that

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Calculations / Statistics

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  1. Calculations / Statistics

  2. Laboratory 1: Nearest Neighbor and Population Dispersion

  3. HoleNND 1 4.3 cm 2 2.6 cm 3 7.9 cm Just because Point 2 is the Nearest Neighbor of Point 1 does not mean that Point 1 is the Nearest Neighbor of Point 2

  4. Calculations • Density (mA) = number of individuals / area • Mnemonic – DNA • Using NND • Density (mE) = 1 / [ 4 (r-bar1)2] • r1 = distance to 1st Nearest Neighbor for 1 ind. • r-bar1 = mean of r1 for all ind.’s in a plot • Calculate mE for each plot and compare to direct mA • Calculate mEI = 1.43 mE and determine if closer to mA

  5. Calculations • Is Ucapugilatordistribution random? • Substitution of mA = 1 / [ 4 (r-bar1)2] • Rearrange to (r-bar1)2 = 1 / (4 mA) • Also expressed as (r-bar1)2 = 0.25 /mA • So, if overdispersed(r-bar1)2 = 1.154 /mA • if random (r-bar1)2 = 0.25 /mA • if least dispersed (r-bar1)2 = 0 /mA • Ranges from 0 < x < 1.154 and eqn is • (r-bar1)2 = x /mA

  6. Calculations HoleNND 1 4.3 cm 2 2.6 cm 3 7.9 cm Calculate r-bar1 Calculate mA Calculate mE Is dispersion random?

  7. Laboratory 2:Mark and Recapture

  8. Exercise • Calculate N using Equations 3 and 4 • Calculate 95% confidence interval using Equation 6 • SE = sqrt [M2(n+1)(n-R)] / [(R+1)2 (R+2)] • Express as N + (t)*(SE) and N – (t)*(SE) • For t-value use 1.96 as expressed in Table 1 • Do this for all three recapture periods

  9. Laboratory 3: Age Structure and Survivorship

  10. Age Pyramids • Can be used to compare population structure among many different sites or the same population at different times of the year or from year to year Tuscaloosa County, AL 2000 Census

  11. Life Tables • Compile stats for each age class or cohort • Must first identify the number and type of age interval for the analysis • Assign collected individuals to the appropriate age class • lx = 1000/93; qx = dx/lx; Lx = 0.5*(lx1+lx2); • Tx = sum of Lx for all rows of interest; ex = Tx/lx

  12. Survivorship Curves • Type 1 = High survival rate for young, low survivor rate after a particular old age • Type 2 = A constant rate of mortality occurs at all ages • Type 3 = High juvenile mortality rate with low mortality thereafter • Expressed as log (freq of survivors)

  13. Panama City Trip

  14. Plot and Transect Density Calculations • Di = ni/A • Calculate average density of urchins (#/m2 ) by quadrat sampling and by belt transect methods • Are they in close agreement? • If not, why do you think they are different?

  15. Look at Trawling Data

  16. Look at Trawling Data • Seven replicate trawl samples in turtle grass (Thalassiatestudinum) and Six on sand bottom

  17. Community Structure: Trawling • Graphical Examination • Species-Sample or Collectors Curve • Relative Abundance Curve • Lognormal Curve • Species Diversity Indices • Shannon-Weiner Index (H’) • Simpson Index (C)

  18. Graphs: Collectors Curve • Cumulative number of species (Number of new species) is plotted against the number of samples taken Curve has not become asymptotic. What does this suggest we need to do?

  19. Graphs: Species Abundance (Dominance Density) Curve • Rank the species based on number collected (1 = most abundant, 2 = next most abundant, etc.) • Plot abundance on logarithmic scale against the corresponding rank A B

  20. Graphs: Lognormal Curve • X-axis is divided into geometric abundance intervals (each interval width is a multiple of 2, so that the scale is the logarithm of the abundance to the base 2) • Plot number of species having certain abundances against the logarithmic abundance intervals

  21. Species Diversity Indices • Shannon-Weiner Diversity Index (H’) • Combines two components of diversity: • Species Richness - Number of species (higher number increases diversity) • Species evenness (relative abundance/dominance; evenness increases diversity) • The greater the value of H’, the greater the diversity

  22. Species Diversity Indices • Simpson Index (C) • Probability of picking two organisms at random that are different species • Gives less weight to more rare species and more weight to common species • Values range from 0 (low diversity) to [1 – (1/S)] • Where S = number of species

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