Seminar at Auburn University, 2014

1. The role of spatial models in applied
ecological research
Richard Chandler
Warnell School of Forestry and Natural Resources
University of Georgia

2. Tobler's first law of geography
Everything is related
to everything else, but
near things are more
related than distant
things.
Waldo Tobler
Introduction Metapopulations Scale of habitat selection 2 / 35

3. Implications of Tobler's Law
Stuart Hurlbert
Pseudoreplication
Introduction Metapopulations Scale of habitat selection 3 / 35

4. Fisher's solution
Randomized Complete
Block Design
R. A. Fisher
Introduction Metapopulations Scale of habitat selection 4 / 35

5. Thoughts on Fisher and Hurlbert
Blocking is very important in manipulative
experiments, but. . .
Introduction Metapopulations Scale of habitat selection 5 / 35

6. Thoughts on Fisher and Hurlbert
Blocking is very important in manipulative
experiments, but. . .
How far away should our blocks be?
How large should our blocks be?
What do we do if spatial correlation is
continuous?
What caused the spatial correlation in the

7. rst place?
Introduction Metapopulations Scale of habitat selection 5 / 35

8. Recent Innovations
Soaking up variation with (spatial)
random eects
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9. Recent Innovations
Soaking up variation with (spatial)
random eects
We need a new approach to understand
the mechanisms that underlie spatial
dependence
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10. Mechanistic models of spatial dependence
Why are nearer things more similar?
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11. Mechanistic models of spatial dependence
Why are nearer things more similar?
Ecological theory tells us. . .
Introduction Metapopulations Scale of habitat selection 7 / 35

12. Mechanistic models of spatial dependence
Why are nearer things more similar?
Ecological theory tells us. . .
Dispersal
Connectivity
Conspeci

13. c attraction
Resource selection in patchy environments
Introduction Metapopulations Scale of habitat selection 7 / 35

14. Mechanistic models of spatial dependence
Why are nearer things more similar?
Ecological theory tells us. . .
Dispersal
Connectivity
Conspeci

15. c attraction
Resource selection in patchy environments
Spatial correlation provides information
about these processes
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16. Mechanistic models of spatial dependence
Tools for inference { hierarchical models
Introduction Metapopulations Scale of habitat selection 8 / 35

17. Mechanistic models of spatial dependence
Tools for inference { hierarchical models
Other uses of these tools
Modeling the detection process
Designing cost-ecient studies
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18. Mechanistic models of spatial dependence
Case studies
(1) Metapopulation dynamics and
the viability of desert-breeding
amphibians
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19. Mechanistic models of spatial dependence
Case studies
(1) Metapopulation dynamics and
the viability of desert-breeding
amphibians
(2) Understanding the spatial scale
of habitat selection
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20. Metapopulations
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21. Motivating questions
(1) What is extinction risk over the next 100
years?
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22. Motivating questions
(1) What is extinction risk over the next 100
years?
(2) How do hydrology and connectivity aect
extinction risk?
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23. Motivating questions
(1) What is extinction risk over the next 100
years?
(2) How do hydrology and connectivity aect
extinction risk?
(3) What are the best management options for
maintaining metapopulation viability?
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24. Leopard frog data
Year
2007 2008 . . . 2013
Site 1 2 3 1 2 3 . . . 1 2 3
1 0 1 1 0 0 0 . . . 1 0 1
2 0 0 0 0 0 0 . . . 0 0 0
3 { { { 1 1 0 . . . 0 0 1
...
...
...
...
...
...
...
...
...
...
...
41 0 1 1 0 1 0 . . . 0 0 0
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25. Leopard frog data
Year
2007 2008 . . . 2013
Site 1 2 3 1 2 3 . . . 1 2 3
1 0 1 1 0 0 0 . . . 1 0 1
2 0 0 0 0 0 0 . . . 0 0 0
3 { { { 1 1 0 . . . 0 0 1
...
...
...
...
...
...
...
...
...
...
...
41 0 1 1 0 1 0 . . . 0 0 0
42 { { { { { { . . . { { {
...
... ...
...
...
...
...
...
...
...
...
273 { { { { { { . . . { { {
Introduction Metapopulations Scale of habitat selection 12 / 35

26. Leopard frog data
Year
2007 2008 . . . 2013
Site 1 2 3 1 2 3 . . . 1 2 3
1 0 1 1 0 0 0 . . . 1 0 1
2 0 0 0 0 0 0 . . . 0 0 0
3 { { { 1 1 0 . . . 0 0 1
...
...
...
...
...
...
...
...
...
...
...
41 0 1 1 0 1 0 . . . 0 0 0
42 { { { { { { . . . { { {
...
... ...
...
...
...
...
...
...
...
...
273 { { { { { { . . . { { {
Plus, coordinates and covariates for each site
Introduction Metapopulations Scale of habitat selection 12 / 35

27. Metapopulation theory
Basic elements
Dispersal-based colonization
function
Rescue eect
Correlated extinction
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28. Metapopulation theory
Basic elements
Dispersal-based colonization
function
Rescue eect
Correlated extinction
Missing elements
Observation model
Introduction Metapopulations Scale of habitat selection 13 / 35

29. Metapopulation theory
Basic elements
Dispersal-based colonization
function
Rescue eect
Correlated extinction
Missing elements
Observation model
MacKenzie et al. (2003) occupancy models
provided the latter, but not the former
Introduction Metapopulations Scale of habitat selection 13 / 35

30. Standard dynamic occupancy model
Initial occupancy
zi;1 Bern( )
Colonization and extinction
zi;k Bern(i;k)
i;k = (1 zi;k)
+ zi;k(1 )
Detection
yi;j;k Bern(zi;k p)
Introduction Metapopulations Scale of habitat selection 14 / 35

31. Standard dynamic occupancy model
Initial occupancy
zi;1 Bern( )
Colonization and extinction
zi;k Bern(i;k)
i;k = (1 zi;k)
+ zi;k(1 )
Detection
yi;j;k Bern(zi;k p)
Useful, but doesn't allow for
metapopulation extinction
Introduction Metapopulations Scale of habitat selection 14 / 35

32. A spatial occupancy model
Probability that site i is colonized by 1 individual from site m
(xi; xm)k =
0 exp(kxi xmk2=(22))zm;k1
Introduction Metapopulations Scale of habitat selection 15 / 35

33. A spatial occupancy model
Probability that site i is colonized by 1 individual from site m
(xi; xm)k =
0 exp(kxi xmk2=(22))zm;k1
Probability that site i is colonized by 1 individual from any site
i;k = 1
(
MY
m=1
1
(xi; xm)k
)
Introduction Metapopulations Scale of habitat selection 15 / 35

34. A spatial occupancy model
Probability that site i is colonized by 1 individual from site m
(xi; xm)k =
0 exp(kxi xmk2=(22))zm;k1
Probability that site i is colonized by 1 individual from any site
i;k = 1
(
MY
m=1
1
(xi; xm)k
)
Hence:
Metapopulation extinction is possible
Useful for PVA, connectivity planning
Introduction Metapopulations Scale of habitat selection 15 / 35

35. Results { Local extinction and hydroperiod
l
l
l
0.0 0.2 0.4 0.6 0.8 1.0
Local extinction probability (e)
Intermittent Semi−permanent Permanent
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36. Results { Colonization
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37. Results { Colonization and connectivity
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38. Results { Proportion of sites occupied
2000 2020 2040 2060 2080 2100
0.0 0.2 0.4 0.6 0.8 1.0
Year
Proportion of sites occupied
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39. Results { Extinction risk
2000 2020 2040 2060 2080 2100
0.00 0.02 0.04 0.06 0.08 0.10
Year
Metapopulation extinction probability
Status quo
How important are sites with permanent water?
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40. Results { Extinction risk
2000 2020 2040 2060 2080 2100
0.00 0.02 0.04 0.06 0.08 0.10
Year
Metapopulation extinction probability
1 failed site
Status quo
How important are sites with permanent water?
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41. Results { Extinction risk
2000 2020 2040 2060 2080 2100
0.00 0.02 0.04 0.06 0.08 0.10
Year
Metapopulation extinction probability
2 failed sites
1 failed site
Status quo
How important are sites with permanent water?
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42. Future directions
Landscape resistance to
movement
Abundance-based
formulation
Decision analysis
Introduction Metapopulations Scale of habitat selection 21 / 35

43. Trailing-edge populations
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44. Trailing-edge populations
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45. Trailing-edge populations
Introduction Metapopulations Scale of habitat selection 22 / 35

46. Trailing-edge populations
Introduction Metapopulations Scale of habitat selection 22 / 35

47. Trailing-edge populations
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48. Trailing-edge populations
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49. Trailing-edge populations
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50. Trailing-edge populations
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51. Hypotheses
Populations at southern range limits are:
Genetically unique
Declining due to rapid environmental change
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52. Hypotheses
Populations at southern range limits are:
Genetically unique
Declining due to rapid environmental change
Questions
Will they be able to adapt or move?
How can forest managment and landscape
planning increase viability?
Introduction Metapopulations Scale of habitat selection 23 / 35

53. First steps
Habitat selection and habitat-speci

54. c demographics
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55. The scale problem
How does an individual select a site?
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56. What is the scale of habitat selection?
The standard approach
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57. What is the scale of habitat selection?
The standard approach
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58. What is the scale of habitat selection?
A new approach
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59. What is the scale of habitat selection?
A new approach
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60. What is the scale of habitat selection?
A new approach
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61. What is the scale of habitat selection?
A new approach
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62. Outcome { spatial variation in abundance
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63. Outcome { spatial variation in abundance
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64. Canada Warbler example
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65. Canada Warbler results
Model Parameters AIC
NDVI + s(Elevation) + s(Elevation)2 5 77.4
NDVI + s(Elevation) 4 79.5
NDVI + Elevation + Elevation2 3 80.0
NDVI + Elevation 3 80.8
s(NDVI) + Elevation 4 83.0
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66. Canada Warbler results
0 200 400 600 800 1000
0.0 0.2 0.4 0.6 0.8 1.0
Distance (meters)
Smoothing weight
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67. Canada Warbler results
0 200 400 600 800 1000
0.0 0.2 0.4 0.6 0.8 1.0
Distance (meters)
Smoothing weight
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68. Canada Warbler results
Introduction Metapopulations Scale of habitat selection 32 / 35

69. Conclusions
(1) Spatial correlation results from ecological
processes
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70. Conclusions
(1) Spatial correlation results from ecological
processes
(2) Spatial models use the correlation as
information about these processes
Introduction Metapopulations Scale of habitat selection 33 / 35

71. Thanks
Leopard frog research team
I Erin Muths
I Blake Hossack
I Brent Sigafus
I Cecil Schwalbe
I Chris Jarchow
I Paige Howell
Canada Warbler research team
I Sam Merker
I Anna Joy Lehmicke
I Carly Chandler
I Jared Feura (photographs)
Funding
I USGS Amphibian Research and Monitoring Initiative
I Warnell School of Forestry and Natural Resources

72. Questions?