Alpha Diversity IndicesSlide 2Diversity of DiversitiesDiversity LevelsQ Statistic IntroductionQ Statistic VisuallyQ StatisticCalculating Q - Worked Example #6Slide 9Slide 10Slide 11Two General CategoriesSlide 13Simpson Index ValuesSimpson IndexSlide 16Simpson Calculation – Worked Example 9Slide 18McIntosh IndexMcIntosh ManipulationsMcIntosh Calculation – Worked Example 10Slide 22Berger-ParkerSlide 24Berger-Parker – An ExampleBerger-Parker Calculations –Worked Example 11Slide 27Slide 28Slide 29Information TheorySlide 31Shannon-Wiener IndexShannon-WienerShannon-Wiener MathematicsSlide 35Building on H’Slide 37Comparing H’ ValuesShannon-Wiener Calculation – Worked Example 7Slide 40Brillouin IndexBrillouin MathematicsBrillouin vs. Shannon-WienerSlide 44Brillouin Calculations – Worked Example 8Slide 46Jack-Knifing Diversity IndicesJack-KnifingData for Jack-KnifingJack-Knifing ProcedureApplications of the Jack-KnifeJack-Knifing – Worked Example 12Slide 53Pielou’s Pooled Quadrat MethodPielou’s Pooled QuadratPielou’s Method UtilityPielou’s Pooled Quadrat – Worked Example 13Next week(s):Hypothetical Model CurvesAlpha Diversity IndicesAlpha Diversity IndicesJames A. Danoff-BurgDept. Ecol., Evol., & Envir. Biol.Columbia UniversityLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Diversity IndicesAlpha Diversity IndicesQ-StatisticIntro to Alpha Diversity IndicesSimpsonMcIntoshBerger-ParkerShannon-WienerBrillouinJack-Knifing Diversity IndicesPielou’s Hierarchical Diversity IndexWeek 1Week 2Lecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] of DiversitiesDiversity of DiversitiesDifference between the diversities is usually one of relative emphasis of two main envir. aspectsTwo key featuresRichnessAbundance – our emphasis todayEach index differs in the mathematical method of relating these featuresOne is often given greater prominence than the otherFormulae significantly differ between indicesLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] LevelsDiversity LevelsProgress from local to regional levelsPoint: diversity at a single point or microenvironment•Our emphasis thus farAlpha: within habitat diversity•Usually consists of several subsamples in a habitatBeta: species diversity along transects & gradients•High Beta indicates number of spp increases rapidly with additional sampling sites along the gradientGamma: diversity of a larger geographical unit (island)Epsilon: regional diversityLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Statistic IntroductionA bridge between the abundance models & diversity indicesDoes not involve fitting a model •as in the abundance modelsProvides an indication of community diversityNo weighting towards very abundant or rare species•They are excluded from the analysis•Whittaker (1972) created earlier analysis including these–Thereby more influenced by the few rare / abundant speciesProposed by Kempton & Taylor (1976)Lecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Statistic VisuallyMeasures “inter-quartile slope” on the cumulative species abundance curve25020015010050010 100 1,000 10,000Cumulative SpeciesSpecies AbundanceS = 250S/4 = 62.51st = 62.52nd = 1253rd = 187.5R1 = 62.5 = 0.25*SR2 = 187.5 = 0.75*SQ = slopeLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] StatisticQ StatisticRelationship to other indicesSimilar to the value in the log series modelQ = (0.371)(S*) / Biases in QMay be biased in small samples•Because we are including more of the rare and abundant species in the calculationLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] QCalculating Q- Worked Example #6- Worked Example #6Assemble table with 3 columns# Individuals, # Species, Summed # speciesDetermine R1 and R2R1 should be > or = 0.25 * SR2 should be > or = 0.75 * SCalculate QQ = [((nR1)/2) + nr + ((nR2)/2)] / [ln(R2/R1)]•nR1 and nR2 = # species in each quartile classnr = total number of species between the quartiles•R1 and R2 = # of individuals at each quartile break pointLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Diversity IndicesAlpha Diversity IndicesQ-StatisticIntro to Alpha Diversity IndicesSimpsonMcIntoshBerger-ParkerShannon-WienerBrillouinJack-Knifing Diversity IndicesPielou’s Hierarchical Diversity IndexWeek 1Week 2Lecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Diversity IndicesAlpha Diversity IndicesAll based on proportional species abundancesSpecies abundance models have drawbacks•Tedious and repetitive•Problems if the data do not violate more than one model–How to choose between?Building upon the species abundance modelsAllows for formal comparisons between sites / treatmentsLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Diversity IndicesAlpha Diversity Indices“Heterogeneity Indices”Consider both evenness AND richnessSpecies abundance models only consider evennessNo assumptions made about species abundance distributionsCause of distributionShape of curve“Non-parametric” Free of assumptions of normalityLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] General CategoriesTwo General CategoriesInformation Theory (complicated computation)Diversity (or information) of a natural system is similar to info in a code or messageExamples: Shannon-Wiener and Brillouin IndicesSpecies Dominance Measures (simple comput.)Weighted towards abundance of the commonest speciesTotal species richness is downweighted relative to evennessExamples: Simpson, McIntosh, and Berger-ParkerLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Diversity IndicesAlpha Diversity IndicesQ-StatisticIntro to Alpha Diversity IndicesSimpsonMcIntoshBerger-ParkerShannon-WienerBrillouinJack-Knifing Diversity IndicesPielou’s Hierarchical Diversity IndexWeek
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