DOC PREVIEW
Alpha Diversity Indices

This preview shows page 1-2-3-4-27-28-29-30-56-57-58-59 out of 59 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 59 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

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 IndicesQ-StatisticIntro to Alpha Diversity IndicesSimpsonMcIntoshBerger-ParkerShannon-WienerBrillouinJack-Knifing Diversity IndicesPielou’s Hierarchical Diversity IndexWeek 1Week 2Lecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] of DiversitiesDiversity of DiversitiesDifference between the diversities is usually one of relative emphasis of two main envir. aspectsTwo key featuresRichnessAbundance – our emphasis todayEach index differs in the mathematical method of relating these featuresOne is often given greater prominence than the otherFormulae significantly differ between indicesLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] LevelsDiversity LevelsProgress from local to regional levelsPoint: diversity at a single point or microenvironment•Our emphasis thus farAlpha: within habitat diversity•Usually consists of several subsamples in a habitatBeta: species diversity along transects & gradients•High Beta indicates number of spp increases rapidly with additional sampling sites along the gradientGamma: diversity of a larger geographical unit (island)Epsilon: regional diversityLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Statistic IntroductionA bridge between the abundance models & diversity indicesDoes not involve fitting a model •as in the abundance modelsProvides an indication of community diversityNo 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 speciesProposed by Kempton & Taylor (1976)Lecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Statistic VisuallyMeasures “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 StatisticRelationship to other indicesSimilar to the  value in the log series modelQ = (0.371)(S*) / Biases in QMay 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 #6Assemble table with 3 columns# Individuals, # Species, Summed # speciesDetermine R1 and R2R1 should be > or = 0.25 * SR2 should be > or = 0.75 * SCalculate QQ = [((nR1)/2) + nr + ((nR2)/2)] / [ln(R2/R1)]•nR1 and nR2 = # species in each quartile classnr = 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 IndicesQ-StatisticIntro to Alpha Diversity IndicesSimpsonMcIntoshBerger-ParkerShannon-WienerBrillouinJack-Knifing Diversity IndicesPielou’s Hierarchical Diversity IndexWeek 1Week 2Lecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Diversity IndicesAlpha Diversity IndicesAll based on proportional species abundancesSpecies 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 modelsAllows 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 richnessSpecies abundance models only consider evennessNo assumptions made about species abundance distributionsCause of distributionShape of curve“Non-parametric” Free of assumptions of normalityLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] General CategoriesTwo General CategoriesInformation Theory (complicated computation)Diversity (or information) of a natural system is similar to info in a code or messageExamples: Shannon-Wiener and Brillouin IndicesSpecies Dominance Measures (simple comput.)Weighted towards abundance of the commonest speciesTotal species richness is downweighted relative to evennessExamples: Simpson, McIntosh, and Berger-ParkerLecture 4 – Alpha Diversity Indices © 2003 Dr. James A. Danoff-Burg, [email protected] Diversity IndicesAlpha Diversity IndicesQ-StatisticIntro to Alpha Diversity IndicesSimpsonMcIntoshBerger-ParkerShannon-WienerBrillouinJack-Knifing Diversity IndicesPielou’s Hierarchical Diversity IndexWeek


Alpha Diversity Indices

Download Alpha Diversity Indices
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Alpha Diversity Indices and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Alpha Diversity Indices 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?