Heron Talk

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The challenge of statistically identifying
species-resource relationships on an
uncooperative landscape Or Facts, true facts,
and statistics a lesson in numeracy Barry D.
Smith Kathy Martin Canadian Wildlife Service,
Pacific Wildlife Research Centre Delta, B.C.,
Canada Clive Goodinson Free Agent,Vancouver,
B.C., Canada
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Species-Habitat Associations
Objective To incorporate habitat suitability
predictions into a stand-level forest ecosystem
model


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Can we show statistically that the relative
quantity of a resource on the landscape predicts
the presence of a species such as Northern
Flicker?
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Logistic regression model output
Predicted
Predicted
0
1
0
1
ü
û
123
16
0
Observed
û
ü
9
74
1
5
Logistic regression model
Observed Groups and Predicted Probabilities
20 1
I
1 I
I 1
I F I
1 1 I R 15
1 1
E I 1 1 1
1 I Q I
1 1 1 111 1 1
I U I 11 11 11 111 1
11 I E 10
1 11111 11 11111 11 1 N
I 1 1 10111101 11111111 1
I C I
011110011001110101111 1 1 I Y
I 01110000100111000111111 1
I 5 00
001100000000110000001111111 11
I 001000100000000000000001111101
1 11 I I 0
00000000000000000000000010001000110 11 I
I 0 1 000000000000000000000000001000
000000011011 11 1 I Predicted ------------------
--------------------------------------- Prob
0 .25 .5 .75
1 Group 000000000000000000000000000
000111111111111111111111111111111
0 Absent
1 Present
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Predicted
Sampling intensity is too low birds occur within
good habitat but sampling does not capture all
occurrences.
0
1
ü
û
0
Observed
Habitat is not 100 saturated there are areas of
good habitat which are unoccupied.
û
ü
1
Spatial variability is too low or spatial
periodicity of key habitat attributes is too
high, given sampling intensity.
Habitat is over 100 saturated birds occur in
areas of poor habitat.
The playback tape pulls in individuals from
outside the point-count radius.
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So, can we expect be successful in detecting
species-habitat associations when they exist?

• We use simulations where
• we generated a landscape, then
• populated that landscape with a (territorial)
  species, then
• sampled the species and landscape repeatedly
  to assess our ability to detect a known
  association

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Sample Simulation gt Sample Simon
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To be as realistic as possible we need to make
decisions concerning

• The characteristics of the landscape (resources)
• The species distribution on the landscape
• The sampling method
• The statistical model(s)

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Spatial contrast is essential for, but doesnt
guarantee, success
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High Landscape Spatial Periodicity (SP)
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Medium Landscape Spatial Periodicity (SP)
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Low Landscape Spatial Periodicity (SP)
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It might help to conceptualize required resources
by consolidating them into four fundamental
suites

• Shelter (e.g., sleeping, breeding)
• Food (self, provisioning)
• Comfort (e.g. weather, temperature)
• Safety (predation risk)

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To be as realistic as possible we had to make
decisions concerning

• The characteristics of the landscape
• The species distribution on the landscape
• The sampling method
• The statistical model(s)

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Territory establishment can be
Resource centred
Species centred
but in either case sufficient resources must be
accumulated for an individual to establish a
territory
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If territory establishment is
Species centred
then the Position function sets the parameters
for territory establishment
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Territory establishment
Saturation
Half-saturation
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Territory densities may be
High
Low
so realistic simulations must be calibrated to
the real world
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To be as realistic as possible we had to make
decisions concerning

• The characteristics of the landscape
• The species distribution on the landscape
• The sampling method
• The statistical model(s)

21
(No Transcript)
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Detection Function
Point-count radius
Vegetation plot radius
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To be as realistic as possible we had to make
decisions concerning

• The characteristics of the landscape
• The species distribution on the landscape
• The sampling method
• The statistical model(s)

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The statistical model

• Deterministic model structure
• Multiple regression, Logistic
• Model error
• Normal, Poisson, Binomial
• Model selection
• Parsimony (AIC), Bonferronis alpha, Statistical
  significance

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The deterministic model

• Multiple regression (with 2 resources)
• Yi B0 B1X1i B2X2i B12X1iX2i ei
• or Yi f(X) ei

Yi detection (0,1,2,) Xi resource value
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The deterministic model

• Logarithmic
• Yi e f(X) ei

Yi detection (0,1,2,...) Xi resource value
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The deterministic model

• Logistic
• Yi Ae f(X) /(1 e f(X)) ei

Yi detection (0,1,2,) Xi resource value
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Choosing the correct model form
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Linear model 1 to 4 resources
1 Resource Yi B0 B1X1i ei 4
Resources Yi B0 B1X1i B2X2i B3X3i
B4X4i B12X1iX2i B13X1iX3i B14X1iX4i
B23X2iX3i B24X2iX4i B34X3iX4i
B123X1iX2i X3i B124X1iX2i X4i
B134X1iX3i X4i B234X2iX3i X4i
B1234X1iX2i X3i X4i ei
Number of parameters required for 1 Resource
2 2 Resource 4 3 Resource 8 4 Resource 16
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The statistical model

• Deterministic model structure
• Multiple regression, Logistic
• Model error
• Normal, Poisson, Binomial
• Model selection
• Parsimony (AIC), Bonferronis alpha, Statistical
  significance

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Poisson error
Repeated samples of individuals randomly
dispersed are Poisson-distributed
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Poisson error
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Negative-binomial error
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Normal error
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Binomial error
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The statistical model

• Deterministic model structure
• Multiple regression, Logistic
• Model error
• Normal, Poisson, Binomial
• Model selection
• Parsimony (AIC), Bonferronis alpha, Statistical
  significance

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Model Selection

• Use AIC to judge the best of several trial models
• The best model must be statistically
  significant from the null model to be
  accepted

If ?0.05, then Bonferronis adjusted ? is 1
Resource 0.0500 2 Resource .0169
3 Resource 0.0073 4 Resource 0.0034
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True, Valid and Misleading Models

• If the True model is Yi B0
  B123X1iX2i X3i
• Then
• Yi B0 B3X3i is a Valid model
• Yi B0 B12X1i X2i is a Valid model
• Yi B0 B4X4i is a
  Misleading model
• Yi B0 B14X1i X4i is a Misleading
  model

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1 Resource Required - 1 Resource Queried
Success identifying True Model
Logistic-Poisson
Multiple Regression - Normal
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1 Resource Required - 1 Resource Queried
Success identifying True Model
Logistic-Poisson
Logistic-Binomial
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4 Resources Required - 4 Resources Queried
Medium SP - Resources uncorrelated 100
detection - Full
True
Valid
Misleading
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4 Resources Required - 4 Resources Queried
High SP - Resources uncorrelated 100
detection - Full
True
Valid
Misleading
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4 Resources Required - 4 Resources Queried
Low SP - Resources uncorrelated 100 detection
- Full
True
Valid
Misleading
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1 Resources Required - 4 Resources Queried
Medium SP - Resources uncorrelated 100
detection - Full
True / Valid
Misleading
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1 Resources Required - 4 Resources Queried
High SP - Resources uncorrelated 100
detection - Full
Misleading
True / Valid
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1 Resources Required - 4 Resources Queried
Low SP - Resources uncorrelated 100 detection
- Full
Misleading
True / Valid
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1 Resources Required - 4 Resources Queried
Medium SP - Resources 50 correlated 100
detection - Full
Misleading
True / Valid
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1 Resources Required - 4 Resources Queried
Medium SP - Resources 50 correlated 25
detection - Full
Misleading
True / Valid
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1 Resources Required - 4 Resources Queried
Medium SP - Resources 50 correlated - 25
detection - 50 Full
Misleading
True / Valid
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1 Resources Required - 4 Resources Queried
High SP - Resources 50 correlated 25
detection 50 Full
Misleading
True / Valid
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1 Resources Required - 4 Resources Queried
Medium SP - Resources 95 correlated 25
detection - Full
Misleading
True / Valid
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Technical Conclusions

• A-priori hypotheses concerning species-habitat
  associations are essential
• Required resources should be amalgamated by suite
• Resource contrast is essential and should be
  planned
• Ratio of between-pointwithin-point variability
  must be increased for both resources
  and species-of-interest
• Point-count method must be designed with spatial
  period considerations in mind

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Key Conservation Conclusion
At best Affirmative conclusions about the
importance of critical resources based on
statistical correlations alone are not justified!
At worst Affirmative conclusions about the
importance of critical resources based on
statistical correlations alone, and without
documenting the spatial characteristics of the
landscape etc., are completely indefensible!