multi-scale analysis: options for modeling presence/absence of bird species kathryn m. georgitis 1,...

Multi-scale Analysis: Options for Modeling

Presence/Absence of Bird Species

Kathryn M. Georgitis1, Alix I. Gitelman1, and Nick Danz2

1 Statistics Department, Oregon State University2 Natural Resources Research Institute University of Minnesota-Duluth

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

R82-9096-01

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

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?

Concentric Circle Sampling Design

1000m

500m

100 m

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

Interesting Features of the Data

Correlation between Explanatory Variables

Spatial Extent

pine and oak-pine/spruce-fir

lowland non-forest/n. hardwoods

n. hardwoods /aspen-birch

100m -0.31 (0.08) -0.08 (0.08) -0.07 (0.08)

500m 0.03 (0.08) -0.17 (0.08) -0.14 (0.08)

1000m 0.11 (0.08) -0.24 (0.08) -0.26 (0.08)

5000m 0.21 (0.08) -0.58 (0.06) -0.63 (0.06)

Correlation Between Pine and Oak-Pine Measured at Different Scales

Spatial Extent

100m 500m 1000m 5000m

100m 1 0.81(0.05)

0.70(0.06)

0.45(0.07)

500m 1 0.95(0.03)

0.70(0.06)

1000m 1 0.79(0.05)

Relationship between Land Cover

Variables and Spatial Extent

010002000300040005000

Spatial Extent (m)

01

02

03

04

05

06

0

Pe

rce

nta

ge

o

f P

in

e a

nd

O

ak-P

in

e

Chequamegon ForestChippew a ForestSt. Croix ForestSuperior Forest

0 1000 2000 3000 4000 5000

Spatial Extent (m)

010

2030

4050

60

Per

cent

age

of P

ine

and

Oak

-Pin

e

Chequamegon ForestChippewa ForestSt. Croix ForestSuperior Forest

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

Option 1: Separate Models Approach

(100m) M1 : log(

(500m) M5 : log(

(1000m)M10 : log(

(5000m)M50 : log(

where Y denotes n-length vector of binary response with Pr(Yi=1) = i,

denotes matrix of explanatory variables at the 100m scale

Model Significant explanatory variables selected using BIC criteria

M1 lowland conifer, pine and oak-pine

M5 lowland conifer, pine and oak-pine, spruce-fir, spruce-fir:pine and oak-pine

M10 pine and oak-pine, spruce-fir, spruce-fir:pine and oak-pine

M50 pine and oak-pine, foresta, foresta:spruce-fir, spruce-fir

a: The forest variable is an indicator for stands located in the Chequamegon national forest in Wisconsin.



• Disadvantages:– does not account for possible

relationships between spatial extents

– multi-collinearity of explanatory variable

– 210 possible models for each spatial extent

Option 2: One Model for all Spatial Extents

Mall : log ( (1-)-1) = all

all

where

Y denotes n-length vector of binary response with Pr(Yi=1) = i,

all = [

Spatial extent

Explanatory variables selected using BIC for Mall

100m aspen-birch, northern hardwoods, pine and oak-pine, spruce-fir

500m

none

1000m

spruce-fir

100m:1000m

pine and oak-pine:spruce-fir


Advantages:– allows for interactions between

scales

Disadvantages:– serious multi-collinearity problems

– 230 possible models


Option 3: Model using Functionals of Explanatory Variables

• Difference Model Mdiff : log ( (1-)-1) = diff

diffwhere diff = (element-

wise)

• Proportional Model Mprop : log ( (1-)-1) = prop prop

where prop = (element-wise)

Option 3: Model using Functionals of Explanatory

Variables

Model

Explanatory variables selected using BIC

Mdiff

pine and oak-pinediff

Mprop

aspen-birchprop , pine and oak-pineprop

Option 3: Model using Functionals of Explanatory

Variables• Advantages:

– incorporates two spatial extents

• Disadvantages:– biologically meaningful?– multi-collinearity– model selection

Option 4: Graphical Model - think of explanatory variables and response

holistically (i.e., as a single multivariate observation)

Logistic Regression Model

X1

Y

X2 X3 X4 X1

Y

X2 X3 X4

Bayesian Network (Graphical) Model

Option 4: Graphical Model

For comparison with MALL, we use the same “explanatory” variables

aspen-birch 100m

pine & oak-pine 100m

spruce-fir 1000m

PineWarbler

spruce-fir 100m

n. hardwoods 100m


spruce-fir 100m


spruce-fir 1000m

Pine Warbler

aspen-birch 100m

N. hardwoods 100m

Diagram of MALL

spruce-fir 100m


spruce-fir 1000m

Pine Warbler

aspen-birch 100m

N. hardwoods 100m

Diagram of Bayesian MALL

log ( (1-)-1) = all ; fixed ~ Multinomial(P,100)

log(spruce-fir1000)~ N

log ( (1-)-1) = + log(spruce-fir1000)

Where= variables in MALL


Comparison of MALL and Bayesian MALL

Land cover type variable MALL Bayesian MALL

intercept -3.87 (1.27) -4.20 (1.18)

aspen-birch100 0.02 (0.01)

0.03 (0.01)

northern hardwoods100 0.03 (0.01)

0.03 (0.01)

pine and oak-pine100 0.06 (0.01)

0.10 (0.02)

spruce-fir100 0.02 (0.01)

0.02 (0.01)

log(spruce-fir1000) 0.3 (0.44) 0.34 (0.41)

pine and oak-pine100: log(spruce-fir1000)

-0.02 (0.008) -0.02 (0.008)


spruce-fir 100m


spruce-fir 1000m

Pine Warbler

aspen-birch 100m

N. hardwoods 100m

spruce-fir 100m


spruce-fir 1000m

Pine Warbler

aspen-birch 100m

N. hardwoods 100m

Where Z= variables in MALL

~ Multinomial(P,100)


log ( (1-)-1) = + log(spruce-fir1000)

i ~ Multinomial(Pi,100)

Pi=(Pi,1, Pi,2, Pi,3, Pi,4, Pi,5)

log(Pi,1/(1- Pi,1))=log(spruce-fir1000)


log( (1-)-1) = + pine & oak-pine100

Bayesian MALL Bayesian Network Model


Comparison of two Bayesian Network Models

Component -2log likelihood for

Bayesian MALL

-2 log likelihood for Bayes Network

Model PIWA 160.9 179.4

100m Scale 25699.5 24478

1000m Scale 379.4 379.4

Total 26239.8 25036.8

BIC total 26354 (13) 25062 (11)


• Advantages:– considers ecological system holistically– can eliminate multi-collinearity– biologically meaningful

• Disadvantages:– model selection– implementation issues

Acknowledgements

Don Stevens, OSU

Jerry Niemi, N.R.R.I Univ. of Minn., Duluth

JoAnn Hanowski, N.R.R.I Univ. of Minn., Duluth

multi-scale analysis: options for modeling presence/absence of bird species kathryn m. georgitis 1,...

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