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BiodiversityAverage SizeQuadrat SamplingTransect SampleMeasuring BiodiversityDiversity IndicesShannon-Wiener Diversity Index (H)Slide 8Simpson’s IndexSlide 10BiodiversityAverage Size•Measure all trees in a transect or quadrat.•Produce a size-frequency histogram to show the size distribution.•Can also calculate the average size tree.Quadrat Sampling•Randomly select plots and count all individuals in that plot.•Each quadrat = 200m2.•Can calculate density as #/m2 then multiply by total area to estimate the total # of trees.•60,703 m2 = 15 acresQuadrat Species No.1 BoxElder 01 Button Bush 21 Chinese Tallow 11 Cottonwood 91 Maple 01 Willow 622 BoxElder 42 Button Bush 02 Chinese Tallow 02 Cottonwood 12 Maple 22 Willow 60Transect Sample•Randomly select a transect of known area and count every tree in that transect.•Each transect = 90m2.•Can calculate density for each tree species.•60,703 m2 = 15 acresTransect Species No.1 BoxElder 11 Cottonwood 11 Maple 21 Willow 272 BoxElder 22 Cottonwood 12 Maple 02 Willow 373 BoxElder 23 Cottonwood 43 Maple 03 Willow 44Measuring Biodiversity•The simplest measure of biodiversity is the number of species – called species richness.–Usually only count resident species, and not accidental or temporary immigrants•Another concept of species diversity is heterogeneity:Community 1 Community 2Species A 99 50Species B 1 50Heterogeneity is higher in a community where there are more species and when the species are more equally abundant.Diversity Indices•A mathematical measure of species diversity in a community.•Reveals important information regarding rarity and commonness of species in a community.Shannon-Wiener Diversity Index (H)•Variables associated with the Shannon-Weiner Diversity index:S – total number of species in the community (richness)pi – proportion of S made up of the ith speciesHmax = ln(S) EH – equitability (evenness; b/t 0 and 1) = H / HmaxH = - pi(lnpi)  Larger H = more diversitySpecies # piln(pi) (pi)(lnpi)1 12 0.020583 -3.88328 -0.079932 562 0.963979 -0.03669 -0.035363 8 0.013722 -4.28875 -0.058854 1 0.001715 -6.36819 -0.010921.386294 583 -0.18507H= 0.18507E = 0.18507/1.386297 = 0.1335#piln(pi2)12 0.25 -1.38629 -0.34657 Species Richness = 412 0.25 -1.38629 -0.34657ln (species richness) = Hmax = 1.38629412 0.25 -1.38629 -0.34657 H = - (sum of (pi)(lnpi)) = 1.3862912 0.25 -1.38629 -0.34657E = H/Hmax0.99999748 -1.38629Species #piln(pi2)1 12 0.05 -2.99573 -0.149792 12 0.05 -2.99573 -0.149793 12 0.05 -2.99573 -0.149794 12 0.05 -2.99573 -0.149795 12 0.05 -2.99573 -0.149796 12 0.05 -2.99573 -0.149797 12 0.05 -2.99573 -0.149798 12 0.05 -2.99573 -0.149799 12 0.05 -2.99573 -0.1497910 12 0.05 -2.99573 -0.1497911 12 0.05 -2.99573 -0.1497912 12 0.05 -2.99573 -0.1497913 12 0.05 -2.99573 -0.1497914 12 0.05 -2.99573 -0.1497915 12 0.05 -2.99573 -0.1497916 12 0.05 -2.99573 -0.1497917 12 0.05 -2.99573 -0.1497918 12 0.05 -2.99573 -0.1497919 12 0.05 -2.99573 -0.1497920 12 0.05 -2.99573 -0.14979240 -2.99573Species Richness = 20ln (species richness) = Hmax = 2.995732H = - (sum of (pi)(lnpi)) = 2.99573E = H/Hmax0.999999#piln(pi2)3 0.0625 -2.77259 -0.17329 Species Richness = 438 0.791667 -0.23361 -0.18495ln (species richness) = Hmax = 1.3862941 0.020833 -3.8712 -0.08065 H = - (sum of (pi)(lnpi)) = 0.698816 0.125 -2.07944 -0.25993E = H/Hmax0.50408548 -0.69881Species richness and equitability affect the Shannon Wiener index.Simpson’s Index•N = total number of individuals•pi = proportion of each species•Simpson’s Index of Diversity = 1 – D–Ranges from 0 to 1  Low to high diversityD = 1 - pi2 ranges from 0 to 1Species #pipi21 12 0.25 0.0625 D = 0.252 12 0.25 0.0625 1-D = 0.753 12 0.25 0.06254 12 0.25 0.062548 0.25Species #pipi21 12 0.25 0.0625 D = 0.252 12 0.25 0.0625 1-D = 0.753 12 0.25 0.06254 12 0.25 0.062548 0.25Species #pipi21 12 0.05 0.00252 12 0.05 0.00253 12 0.05 0.00254 12 0.05 0.00255 12 0.05 0.00256 12 0.05 0.00257 12 0.05 0.00258 12 0.05 0.00259 12 0.05 0.002510 12 0.05 0.002511 12 0.05 0.002512 12 0.05 0.002513 12 0.05 0.002514 12 0.05 0.002515 12 0.05 0.002516 12 0.05 0.002517 12 0.05 0.002518 12 0.05 0.002519 12 0.05 0.002520 12 0.05 0.0025240 0.05D = 0.051-D = 0.95Species #pipi21 3 0.0625 0.003906 D = 0.6467012 38 0.791667 0.626736 1-D = 0.3532993 1 0.020833 0.0004344 6 0.125 0.01562548 0.646701Species richness and equitability affect Simpson’s


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NICHOLLS BIOL 404 - Biodiversity

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