Introduc)on to Hierarchical Models 8/25/14. Hierarchical Models in Population Ecology. What are they and why should we use them? Topics of Discussion

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1 ,,,, 8/5/14 Herarchcal Models n Populaton Ecology What are they and why should we use them? y z, θ,1 1,, 3,,3 Jared S. Laufenberg PhD Canddate Unversty of Tennessee Dept of Forestry, Wldlfe and Fsheres May, :15 AM Room 160 PBB Topcs of Dscusson Ø Introducton to herarchcal models What s a herarchy? What s a statstcal model? What s a herarchcal model? What s NOT a herarchcal model? Ø Herarchcal models n populaton ecology Bref prmer to populaton ecology Process-only models Process + observaton model Hyper-parameter models Ø Why should we use herarchcal models? Scope and scale of nference Correct accountng of varance Borrowng strength Ø Areas of actve development Integrated populaton models Spatal capture-recapture models Ø Herarchcal modelng resources Introduc)on to Herarchcal Models y z, θ,1 1,, 3,,3 1

2 8/5/14 Introducton to Herarchcal Models What s a herarchy? Defnton: herarchy (noun) A seres of ordered groupngs of people or thngs wthn a system Royle et al. 013 Defnton: classfcaton (noun) the arrangement of enttes n a herarchcal seres of nested classes, n whch smlar or related classes at one herarchcal level are combned comprehensvely nto more nclusve classes at the next hgher level Mayr and Bock 00 Introducton to Herarchcal Models What s a herarchy? Ø Herarches n populaton ecology: ECOLOGICAL SCALES OF ORGANIZATION Metacommunty: dstrbuton of communtes Communty: dstrbuton of metapopulatons Metapopulaton: dstrbuton of populatons Populaton: dstrbuton of ndvduals How dfferent factors affect dfferent herarchcal levels Introducton to Herarchcal Models What s a herarchy? Dstrbuton and abundance of ovenbrds:

3 8/5/14 Introducton to Herarchcal Models What s a herarchy? Dstrbuton and abundance of ovenbrds: Occurrence dependent on patch sze Condtonal on occurrence 0.5 x 0.5 Hgh - - Medum Low x x Introducton to Herarchcal Models What s a herarchy? Dstrbuton and abundance of ovenbrds: Occurrence dependent on patch sze Condtonal on occurrence Local densty dependent on habtat qualty Hgh Medum 0.5 x Low x x Introducton to Herarchcal Models What s a herarchy? Ø Herarches n populaton ecology: NUMBER OF RECRUITS AS OUTCOME OF A SERIES OF PROCESSES Survvng adults Eggs produced Fertlzed eggs Hatched eggs Survvng tadpoles 3

4 8/5/14 Introducton to Herarchcal Models What s a statstcal model? Defnton: statstcal model (noun) A formal descrpton of a number generatng process comprsed of a determnstc and a stochastc component, expressed algebracally, and based on probablty dstrbutons (.e., parametrc) Parametrc statstcal modelng means descrbng a carcature of the machne that plausbly could have produced the numbers we observe Kery 010 Determnstc Stochastc Introducton to Herarchcal Models The Herarchcal Model Defnton: herarchcal model (noun) A seres of [parametrc] models, ordered by ther condtonal probablty structure aka: state-space, mult-level, random-effects, GLMM, nested Example: SPECIES OCCURRENCE MODEL State process Royle et al. 013 Observaton process Observaton s CONDITIONAL on true state Introducton to Herarchcal Models NOT Herarchcal Models Ø Step-down or Stepwse model selecton The ad hoc process of holdng model structure constant for some parameters, whle nvestgatng structures for others Example: Cormack-Jolly-Seber model Model parameters: ϕ (apparent survval) and p (detecton probablty) 1) Hold ϕ constant, test alternatve structures for p ) Hold best structure for p constant, test ϕ NOT RECOMMENDED Doherty et al. 01 4

5 8/5/14 Introducton to Herarchcal Models NOT Herarchcal Models Ø Mult-stage analyses (.e., statstcs on statstcs) The process of usng estmates from an ntal analyss as nput data for a secondary analyss Example: Evaluate habtat effects on local abundance (N) Obtan estmate N-hat Introducton to Herarchcal Models NOT Herarchcal Models Ø Mult-stage analyses (.e., statstcs on statstcs) The process of usng estmates from an ntal analyss as nput data for a secondary analyss Example: Evaluate habtat effects on abundance (N) 1) Estmate abundances from encounter data N-hat 1 N-hat N-hat 6 ) Test for relatonshp between N estmates and habtat varables A WELL KNOWN NO NO n STATISTICS N-hat 4 N-hat 3 N-hat 7 N-hat 5 N-hat 8 N-hat 9 Introducton to Herarchcal Models NOT Herarchcal Models Ø Bayesan nference A statstcal nference paradgm based on Bayes theorem that uses probablty to descrbe all unknown quanttes Bayesan herarchcal modelng: The fttng of herarchcal models usng Bayesan methods Herarchcal models can also be ft usng frequentst methods 5

6 ,, 8/5/14 Herarchcal Models n Populaton Ecology y z, θ,1 1,, 3,,3 Herarchcal Models n Populaton Ecology Populaton ecology Ø Abundance and dstrbuton of ndvduals and speces Ø Dynamcs of populatons, metapopulatons, communtes, etc. Ø Factors affectng abundance, dstrbuton, and dynamcs Herarchcal Models n Populaton Ecology How do we use herarchcal models n the study of populaton ecology? Ø Match structure of the statstcal model to the structure of our conceptual model of ecologcal processes Frog recruts revsted: # of recruts (R) nto adult class 6

7 8/5/14 Herarchcal Models n Populaton Ecology How do we use herarchcal models n the study of populaton ecology? Ø Match structure of the statstcal model to the structure of our conceptual model of ecologcal processes Frog recruts revsted: # of recruts (R) nto adult class e.g., female body mass, pathologes, etc e.g., male body mass, pathologes, etc e.g., predator densty, temp, etc e.g., predator densty, temp, etc Herarchcal Models n Populaton Ecology How do we use herarchcal models n the study of populaton ecology? Ø Incorporate condtonal observaton process nto model structure to account for mperfect detecton Example: CORMACK-JOLLY-SEBER MODEL State process A A A A A D D Observaton process Observaton s CONDITIONAL on true state Herarchcal Models n Populaton Ecology How do we use herarchcal models n the study of populaton ecology? Ø Impose addtonal structure va hyper-parameters Example: CORMACK-JOLLY-SEBER MODEL Indvdual covarates Temporal covarate and random effects and random effects Evolutonary processes on ftness Envronmental processes on ftness 7

8 ,, 8/5/14 Why Should We Use Herarchcal Models? y z, θ,1 1,, 3,,3 Why Use Herarchcal Models? Scope and Scale of Inference Ø Extend nference beyond levels under study Generalze to populaton from whch sample unts were drawn ü Need to known means and varances of global processes Ø Scale-dependent nference Evaluate factors affectng dfferent levels of ecologcal processes ü Dstrbuton and abundance of ovenbrds Why Use Herarchcal Models? Correct accountng of varance Ø Random effects allow parttonng of process and samplng varances Crtcal for populaton proecton models used n populaton vablty analyses Ø Avods varance-accountng problems wth mult-stage analyses Volaton of constant samplng varance assumpton Ø Allows modelng covarances among dfferent parameters Temporal covarance between survval and recrutment 8

9 ,, 8/5/14 Why Use Herarchcal Models? Borrowng strength Ø Fxed effects can result n mprecse or extreme groupspecfc estmates for small samples Ø By constranng parameters by a common dstrbuton (random effects), ndvdual estmates are pulled toward the global mean (e.g., shrnkage) Ø Indvdual estmates borrow strength from the ensemble Ø Assumpton of exchangeablty must hold Areas of Actve Development y z, θ,1 1,, 3,,3 Areas of Actve Development Integrated Populaton Models Ø Integrate data from multple sources to model ndvdual demographc processes Capture-recapture and known-fate data for survval Ø Integrate data from multple demographc processes to model populaton dynamcs Capture-recapture, reproducton, known-fate, and band-return data Ø Extend populaton models to metapopulaton and communty models Shared nformaton among multple populatons or smlar speces 9

10 ,, 8/5/14 Areas of Actve Development Spatal Capture-Recapture Models Ø Explct modelng of terrtoralty Spatal nteractons among ndvduals Ø Extendng models to accommodate gregarous speces Non-ndependence of ndvdual actvty centers Ø Development of explct movement models Dspersal, transence, and mgraton Herarchcal Modelng Resources y z, θ,1 1,, 3,,3 Herarchcal Modelng Resources Royle, J. A., and R. M. Dorazo Herarchcal modelng and nference n ecology. The analyss of data from populatons, metapopulatons and communtes. Academc Press, London, UK. Kery, M., and M. Schaub. 01. Bayesan populaton analyss usng WnBUGS. A herarchcal perspectve. Academc Press, Waltham, Massachusetts, USA. 10

11 8/5/14 Herarchcal Modelng Resources Kery, M Introducton to WnBUGS for ecologsts. A Bayesan approach to regreeson, ANOVA, mxed models and related analyss. Academc Press, Burlngton, Massachusetts, USA. Lnk, W. A., and R. J. Barker Bayesan nference wth ecologcal applcatons. Academc Press, London, UK. Royle, J. A., R. B. Chandler, R. Sollmann, and B. Gardner Spatal capture-recapture. Academc Press, Waltham, Massachusetts, USA LITERATURE CITED Ø Doherty, P. F., G. C. Whte, and K. P. Burnham. 01. Comparson of model buldng selecton strateges. Journal of Ornthology 15:S317 S33. Ø Kery, M Introducton to WnBUGS for ecologsts. A Bayesan approach to regreeson, ANOVA, mxed models and related analyss. Academc Press, Burlngton, Massachusetts, USA. Ø Mayr, E., and W. J. Bock. 00. Classfcatons and other orderng systems. Journal of Zoologcal Systematcs and Evolutonary Research 40: Ø Royle, J. A., R. B. Chandler, R. Sollmann, and B. Gardner Spatal capturerecapture. Academc Press, Waltham, Massachusetts, USA PHOTO CREDITS Ø Chautauqua/Sectons/Seasons_Of_Wldlfe/Waterfowl%051x19.pg Ø Ø 11