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
Species-Habitat Associations
Objective:
To incorporate habitat suitability predictions
into a stand-level forest ecosystem model
+
=
Can we show statistically that the relative quantity
of a resource on the landscape predicts the
presence of a species such as Northern Flicker?
Logistic regression model output
Predicted
0
1
Predicted
0
1
0
 
123
16
1
 
9
74
Observed
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
000000000000000000000000001000000000011011 11 1 I
Predicted --------------+--------------+--------------+--------------Prob:
0
.25
.5
.75
1
Group: 000000000000000000000000000000111111111111111111111111111111
0 = Absent
1 = Present
Predicted
0
Observed
1
0
 
1
 
Habitat is over 100%
saturated; birds occur in
areas of poor habitat.
Sampling intensity is too low; birds
occur within good habitat but sampling
does not capture all occurrences.
Habitat is not 100% saturated;
there are areas of good habitat
which are unoccupied.
Spatial variability is too low or spatial
periodicity of key habitat attributes is
too high, given sampling intensity.
The playback tape pulls in individuals
from outside the point-count radius.
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
Sample Simulation > Sample Sim’on
To be as realistic as possible we need to make
decisions concerning…
•The characteristics of the landscape (resources)
•The species’ distribution on thelandscape
• The sampling method
• The statistical model(s)
Spatial
contrast is
essential
for, but
doesn’t
guarantee,
success
High Landscape Spatial Periodicity (SP)
Medium Landscape Spatial Periodicity (SP)
Low Landscape Spatial Periodicity (SP)
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)
To be as realistic as possible we had to make
decisions concerning:
•The characteristics of the landscape
•The species’ distribution on thelandscape
• The sampling method
• The statistical model(s)
Territory establishment can be…
Species centred
Resource centred
…but in either case sufficient resources must be accumulated for
an individual to establish a territory
If territory establishment is…
Species centred
…then the ‘Position function” sets the parameters for territory
establishment
Territory establishment
Saturation
Half-saturation
Territory densities may be…
Low
High
…so realistic simulations must be calibrated to the real world
To be as realistic as possible we had to make
decisions concerning:
•The characteristics of the landscape
•The species’ distribution on thelandscape
• The sampling method
• The statistical model(s)
Detection Function
Point-count radius
Vegetation plot radius
To be as realistic as possible we had to make
decisions concerning:
•The characteristics of the landscape
•The species’ distribution on thelandscape
• The sampling method
• The statistical model(s)
The statistical model
•Deterministic model structure
Multiple regression, Logistic
•Model error
Normal, Poisson, Binomial
•Model selection
Parsimony (AIC), Bonferroni’s alpha, Statistical significance
The deterministic model
•Multiple regression (with 2 resources)
Yi= B0 + B1X1i + B2X2i + B12X1iX2i + εi
or
Yi= f(X) + εi
Yi = detection (0,1,2,…)
X•i = resource value
The deterministic model
•Logarithmic:
Yi= e f(X) + εi
Yi = detection (0,1,2,...)
X•i = resource value
The deterministic model
•Logistic:
Yi= Ae f(X) /(1+ e f(X)) + εi
Yi = detection (0,1,2,…)
X•i = resource value
Choosing the correct model form
Linear model: 1 to 4 resources
1 Resource:
Yi = B0 + B1X1i + εi
4 Resources:
Yi =
B0 + B1X1i + B2X2i + B3X3i + B4X4i
Number of
parameters
required
for…
+ B12X1iX2i + B13X1iX3i + B14X1iX4i
1 Resource = 2
+ B23X2iX3i + B24X2iX4i + B34X3iX4i
2 Resource = 4
+ B123X1iX2i X3i + B124X1iX2i X4i
+ B134X1iX3i X4i + B234X2iX3i X4i
+ B1234X1iX2i X3i X4i + εi
3 Resource = 8
4 Resource = 16
The statistical model
•Deterministic model structure
Multiple regression, Logistic
•Model error
Normal, Poisson, Binomial
•Model selection
Parsimony (AIC), Bonferroni’s alpha, Statistical significance
Poisson error
Repeated
samples of
individuals
randomly
dispersed are
Poissondistributed
Poisson error
Negative-binomial error
Normal error
Binomial error
The statistical model
•Deterministic model structure
Multiple regression, Logistic
•Model error
Normal, Poisson, Binomial
•Model selection
Parsimony (AIC), Bonferroni’s alpha, Statistical significance
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 Bonferroni’s adjusted  is:
1 Resource = 0.0500
2 Resource = .0169
3 Resource = 0.0073
4 Resource = 0.0034
True, Valid and Misleading Models
•If the ‘True’ model is: Yi =
B0 + B123X1iX2i X3i
•Then:
is a ‘Valid’ model
•Yi =
B0 + B3X3i
•Yi =
B0 + B12X1i X2i is a ‘Valid’ model
•Yi =
B0 + B4X4i
•Yi =
B0 + B14X1i X4i is a ‘Misleading’ model
is a ‘Misleading’ model
1 Resource Required - 1 Resource Queried
Success identifying ‘True’ Model
Logistic-Poisson
Multiple Regression - Normal
1 Resource Required - 1 Resource Queried
Success identifying ‘True’ Model
Logistic-Poisson
Logistic-Binomial
4 Resources Required - 4 Resources Queried
Medium SP - Resources uncorrelated – 100% detection - Full
True
Valid
Misleading
4 Resources Required - 4 Resources Queried
High SP - Resources uncorrelated – 100% detection - Full
True
Valid
Misleading
4 Resources Required - 4 Resources Queried
Low SP - Resources uncorrelated – 100% detection - Full
True
Valid
Misleading
1 Resources Required - 4 Resources Queried
Medium SP - Resources uncorrelated – 100% detection - Full
True / Valid
Misleading
1 Resources Required - 4 Resources Queried
High SP - Resources uncorrelated – 100% detection - Full
True / Valid
Misleading
1 Resources Required - 4 Resources Queried
Low SP - Resources uncorrelated – 100% detection - Full
True / Valid
Misleading
1 Resources Required - 4 Resources Queried
Medium SP - Resources 50% correlated – 100% detection - Full
True / Valid
Misleading
1 Resources Required - 4 Resources Queried
Medium SP - Resources 50% correlated – 25% detection - Full
True / Valid
Misleading
1 Resources Required - 4 Resources Queried
Medium SP - Resources 50% correlated - 25% detection - 50% Full
True / Valid
Misleading
1 Resources Required - 4 Resources Queried
High SP - Resources 50% correlated – 25% detection – 50% Full
True / Valid
Misleading
1 Resources Required - 4 Resources Queried
Medium SP - Resources 95% correlated – 25% detection - Full
True / Valid
Misleading
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-point:within-point’ variability must
be increased for both resources and species-of-interest
•Point-count method must be designed with spatial
period considerations in mind
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!