PopulationDiversityEstimation - To what extent can we...

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To what extent can we idealize the properties of the system and still obtain satisfactory results? The answer to this question can only be given in the end by experiment. Only the comparison of the answers provided by analysis of our model with the results of the experiment will enable us to judge whether the idealization is legitimate. Andronov, Theory of Oscillators, 1937. 1
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opulation diversity estimation: Population diversity estimation: The state of the art, and the new software CatchAll Marine Biological Laboratory November 24, 2009 John Bunge epartment of Statistical Science Department of Statistical Science Cornell University 2
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Thanks to: Linda Amaral Zettler Mitchell Sogin BL MBL Linda Woodard, Center for Advanced Computing, Cornell Sean Connolly, Statistics, Cornell Kathryn Barger, AstraZeneca ankmar Böhning, U. of Reading Dankmar Böhning, U. of Reading Slava Epstein, Biology, Northeastern University horsten Stoeck Biology University of Kaiserslautern Thorsten Stoeck, Biology, University of Kaiserslautern Collaborators and co authors too numerous to mention! National Science Foundation (#0816638) 3
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Biodiversity “indices” Species richness C = total number of species Simpson’s index C i i p 1 2 C Shannon’s index p i = proportion of population in i th species i i i p p 1 log etc. h ll bt i fl tt it i l ti t f di it ii l Challenge : obtain formal statistical estimate of diversity, from empirical data , with associated quantitative statistics and qualitative assessments. Focus on species richness C . 4
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What kind of data? General abundance array Incidence array list total list total s p e c i e s 1 234… k species 1 2 3 4 k 1 1 030…15 1 10 10…13 2 0 1 0 0 0 1 2 0 1 0 0 0 1 3 3 202…3 1 0 3 11 01…14 4 0 000…11 4 00 00…11 ……………… …… …………… c 1 022…27 c 11…14 freq. count freq. count 12 2 2 33 1 44 2 51 5 66 71 7 88 99 10 1 10 5 Not often encountered Typical capture-recapture experiment
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We will take frequency count data as given freq count freq count freq count 1 513 11 8 49 2 00 2 149 12 4 100 1 3 65 13 5 108 1 4 34 14 3 120 1 4 5 32 Moorea LTER Microbial 454 data 5 24 15 2 232 1 6 16 16 1 289 1 7 17 17 1 430 1 8 12 18 1 91 3 1 10 5 20 1 c = 912 total species n = 4646 total individuals (sequences) 6
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Plot frequency count data ( i , f i ) 00 500 600 400 500 600 200 300 400 count 200 300 0 100 0 100 200 300 400 500 0 100 1 10 100 1000 frequency frequency 7
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Frequency count data 2000 with estimated zero count 1400 1600 1800 Estimated zero count = 1768 Est. total # of species = 912 + 1768 = 2680 SE 202 00 1000 1200 count 00 400 600 800 0 200 0 50 100 150 200 250 300 350 400 450 500 frequency 8
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How to estimate zero count, or total? Need model . 1993 JASA review: > 200 papers Standard model has emerged: C classes or species (individuals in capture recapture) in population Species i contributes members to sample according to Poisson process with mean p p g p λ i , i = 1, …, C (say w.l.o.g. until time t = 1) λ i are realizations of i.i.d. random variables Λ i , i = 1, …, C ht ibd di t ib ti ith df from stochastic abundance distribution with c.d.f. F , p.d.f. f Then sample counts are unconditionally mixed Poisson j ,... 2 , 1 , 0 , ) ( !
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This note was uploaded on 01/28/2012 for the course STATISTICS 3010 taught by Professor Ooz during the Spring '11 term at Cornell University (Engineering School).

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PopulationDiversityEstimation - To what extent can we...

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