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Multi-scale Analysis: Options for Modeling Presence/Absence of Bird Species

Multi-scale Analysis: Options for Modeling Presence/Absence of Bird Species. Kathryn M. Georgitis 1 , Alix I. Gitelman 1 , and Nick Danz 2 1 Statistics Department, Oregon State University 2 Natural Resources Research Institute University of Minnesota-Duluth. Designs and Models for.

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Multi-scale Analysis: Options for Modeling Presence/Absence of Bird Species

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  1. Multi-scale Analysis: Options for ModelingPresence/Absence of Bird Species Kathryn M. Georgitis1, Alix I. Gitelman1, and Nick Danz2 1 Statistics Department, Oregon State University 2 Natural Resources Research Institute University of Minnesota-Duluth

  2. Designs and Models for Aquatic Resource Surveys R82-9096-01 DAMARS The research described in this presentation has been funded by the U.S. Environmental Protection Agency through the STAR Cooperative Agreement CR82-9096-01 Program on Designs and Models for Aquatic Resource Surveys at Oregon State University. It has not been subjected to the Agency's review and therefore does not necessarily reflect the views of the Agency, and no official endorsement should be inferred

  3. Talk Overview • Ecological Question of Interest • Western Great Lakes Breeding Bird Study • Interesting Features of our Example • Options for Modeling Species Presence/Absence (1) Separate Models for Each Spatial Extent (2) One Model for all Spatial Extents (3) Model using Functionals of Explanatory Variables (4) Graphical Model

  4. Ecological Question of Interest • How does the relationship between landscape characteristics and presence of a bird species change with scale? • What scale is the most useful in terms of understanding bird presence/absence?

  5. Concentric Circle Sampling Design 1000m 500m 100 m

  6. Western Great Lakes Breeding Bird Study • Response Variable: • Presence/Absence of Pine Warbler • Explanatory Variables: • % land cover within 4 different spatial extents • Ten land cover types

  7. Interesting Features of the Data Correlation between Explanatory Variables

  8. Correlation Between Pine and Oak-Pine Measured at Different Scales

  9. Relationship between Land Cover Variables and Spatial Extent

  10. Options for Modeling Presence/Absence of Pine Warbler (1) Separate Models for Each Spatial Extent (2) One Model for all Spatial Extents (3) Model using Functionals of Explanatory Variables (4) Bayesian Network (Graphical) Model

  11. Option 1: Separate Models Approach (100m)M1 : log(p(1-p)-1) = C1b1 (500m)M5 : log(p(1-p)-1) = C5b5 (1000m)M10 : log(p(1-p)-1) = C10b10 (5000m)M50 : log(p(1-p)-1) = C50b50 where Y denotes n-length vector of binary response with Pr(Yi=1) = pi, C1 denotes matrix of explanatory variables at the 100m scale

  12. Option 1: Separate Models Approach

  13. Option 1: Separate Models Approach • Disadvantages: • does not account for possible relationships between spatial extents • multi-collinearity of explanatory variable • 210 possible models for each spatial extent

  14. Options for Modeling Presence/Absence of Pine Warbler (1) Separate Models for Each Spatial Extent (2) One Model for all Spatial Extents (3) Model using Functionals of Explanatory Variables (4) Bayesian Network (Graphical) Model

  15. Option 2: One Model for all Spatial Extents Mall: log(p(1-p)-1) = Zall ball where Y denotes n-length vector of binary response with Pr(Yi=1) = pi, Zall = [C1, C5, C10]

  16. Option 2: One Model for all Spatial Extents

  17. Option 2: One Model for all Spatial Extents Advantages: • allows for interactions between scales Disadvantages: • serious multi-collinearity problems • 230 possible models

  18. Options for Modeling Presence/Absence of Pine Warbler (1) Separate Models for Each Spatial Extent (2) One Model for all Spatial Extents (3) Model using Functionals of Explanatory Variables (4) Bayesian Network (Graphical) Model

  19. Option 3: Model using Functionals of Explanatory Variables • Difference Model Mdiff: log (p(1-p)-1) = Zdiff bdiffwhereZdiff = C5 - C1 (element-wise) • Proportional Model Mprop: log(p(1-p)-1) = Zprop bprop whereZprop = C5 /C1(element-wise)

  20. Option 3: Model using Functionals of Explanatory Variables

  21. Option 3: Model using Functionals of Explanatory Variables • Advantages: • incorporates two spatial extents • Disadvantages: • biologically meaningful? • multi-collinearity • model selection

  22. Options for Modeling Presence/Absence of Pine Warbler (1) Separate Models for Each Spatial Extent (2) One Model for all Spatial Extents (3) Model using Functionals of Explanatory Variables (4) Bayesian Network (Graphical) Model

  23. X1 X2 X3 X4 X1 X2 X3 X4 Y Y Option 4: Graphical Model - think of explanatory variables and response holistically (i.e., as a single multivariate observation) Logistic Regression Model Bayesian Network (Graphical) Model

  24. spruce-fir 1000m aspen-birch 100m n. hardwoods 100m spruce-fir 100m pine & oak-pine 100m Pine Warbler Option 4: Graphical Model For comparison with MALL, we use the same “explanatory” variables

  25. spruce-fir 100m spruce-fir 1000m spruce-fir 100m N. hardwoods 100m aspen-birch 100m pine & oak-pine 100m Option 4: Graphical Model Diagram of MALL Diagram of Bayesian MALL spruce-fir 1000m N. hardwoods 100m aspen-birch 100m pine & oak-pine 100m Pine Warbler Pine Warbler • Where Z= variables in MALL log(p (1-p)-1) = Zball ; fixed Z • Z~ Multinomial(P,100) • log(spruce-fir1000)~ N(m,s2) • log (p (1-p)-1) = Zb+ b5log(spruce-fir1000)

  26. Option 4: Graphical ModelComparison of MALL and Bayesian MALL

  27. Pine Warbler spruce-fir 1000m spruce-fir 1000m spruce-fir 100m N. hardwoods 100m spruce-fir 100m N. hardwoods 100m aspen-birch 100m aspen-birch 100m pine & oak-pine 100m pine & oak-pine 100m Option 4: Graphical Model Bayesian MALL Bayesian Network Model Pine Warbler • Where Z= variables in MALL • Z~ Multinomial(P,100) • log(spruce-fir1000)~ N(m,s2) • log (p (1-p)-1) = Zb+ b5 log(spruce-fir1000) • Zi~ Multinomial(Pi,100) • Pi=(Pi,1,Pi,2, Pi,3,Pi,4,Pi,5) • log(Pi,1/(1- Pi,1))=f0 + f1 log(spruce-fir1000) • log(spruce-fir1000)~ N(m,s2) • log(p (1-p)-1) = b0 + b1 pine & oak-pine100

  28. Option 4: Graphical ModelComparison of two Bayesian Network Models

  29. Option 4: Graphical Model • Advantages: • considers ecological system holistically • can eliminate multi-collinearity • biologically meaningful • Disadvantages: • model selection • implementation issues

  30. Acknowledgements Don Stevens, OSU Jerry Niemi, N.R.R.I Univ. of Minn., Duluth JoAnn Hanowski, N.R.R.I Univ. of Minn., Duluth

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