the challenge of statistically identifying species-resource relationships on an uncooperative...
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The challenge of statistically identifying The challenge of statistically identifying species-resource relationships on an species-resource relationships on an
uncooperative landscapeuncooperative landscapeOr…Or…
Facts, true facts, and statistics: a lesson in numeracyFacts, true facts, and statistics: a lesson in numeracy
Barry D. Smith & Kathy MartinBarry D. Smith & Kathy MartinCanadian Wildlife Service, Pacific Wildlife Research CentreCanadian Wildlife Service, Pacific Wildlife Research Centre
Delta, B.C., CanadaDelta, B.C., Canada
Clive GoodinsonClive Goodinson
Free Agent,Vancouver, B.C., CanadaVancouver, B.C., Canada
Species-Habitat AssociationsSpecies-Habitat Associations
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Objective: To incorporate habitat suitability predictionsinto 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?
0
1
0 1Predicted
Observed
Logistic regression model output
123 16
9 74
0 1Predicted
Observed Groups and Predicted Probabilities
20 + 1 + I 1 I I 1 IF I 1 1 IR 15 + 1 1 +E I 1 1 1 1 IQ I 1 1 1 111 1 1 IU I 11 11 11 111 1 11 IE 10 + 1 11111 11 11111 11 1 +N I 1 1 10111101 11111111 1 IC I 011110011001110101111 1 1 IY I 01110000100111000111111 1 I 5 + 00 001100000000110000001111111 11 + I 001000100000000000000001111101 1 11 I I 0 00000000000000000000000010001000110 11 I I 0 1 000000000000000000000000001000000000011011 11 1 IPredicted --------------+--------------+--------------+--------------- Prob: 0 .25 .5 .75 1 Group: 000000000000000000000000000000111111111111111111111111111111
Logistic regression model
0 = Absent 1 = Present
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.
Habitat is over 100% saturated; birds occur in areas of poor habitat.
0
1
0 1
Predicted
Observed
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 So, can we expect be successful in detecting species-habitat associations when they exist?species-habitat associations when they exist?
We use simulations where:We use simulations where:
we generated a landscape, thenwe generated a landscape, then
• populated that landscape with a populated that landscape with a (territorial) species, then(territorial) species, then
• sampled the species and landscape sampled the species and landscape repeatedly to assess our ability to repeatedly to assess our ability to
detect a known associationdetect a known association
Sample Simulation > Sample Sim’onSample Simulation > Sample Sim’on
To be as realistic as possible we need to make To be as realistic as possible we need to make decisions concerning…decisions concerning…
•The characteristics of the landscape (resources)The characteristics of the landscape (resources)
•The species’ distribution on theThe species’ distribution on the landscapelandscape
• The sampling methodThe sampling method
• The statistical model(s)The statistical model(s)
Spatial Spatial contrast is contrast is essential essential for, but for, but doesn’t doesn’t guarantee, guarantee, successsuccess
HighHigh Landscape Spatial Periodicity (SP) Landscape Spatial Periodicity (SP)
MediumMedium Landscape Spatial Periodicity (SP) Landscape Spatial Periodicity (SP)
LowLow Landscape Spatial Periodicity (SP) Landscape Spatial Periodicity (SP)
It might help to conceptualize required It might help to conceptualize required resources by consolidating them into four resources by consolidating them into four fundamental suites:fundamental suites:
• Shelter (e.g., sleeping, breeding)Shelter (e.g., sleeping, breeding)
• Food (self, provisioning)Food (self, provisioning)
• Comfort (e.g. weather, temperature)Comfort (e.g. weather, temperature)
• Safety (predation risk)Safety (predation risk)
To be as realistic as possible we had to make To be as realistic as possible we had to make decisions concerning:decisions concerning:
•The characteristics of the landscapeThe characteristics of the landscape
•The species’ distribution on theThe species’ distribution on the landscapelandscape
• The sampling methodThe sampling method
• The statistical model(s)The statistical model(s)
Territory establishment can be…Territory establishment can be…
Resource centredResource centredSpecies centredSpecies centred
……but in either case sufficient resources must be accumulated for but in either case sufficient resources must be accumulated for an individual to establish a territoryan individual to establish a territory
If territory establishment is…If territory establishment is…
Species centredSpecies centred
……then the ‘Position function” sets the parameters for territory then the ‘Position function” sets the parameters for territory establishmentestablishment
Territory establishmentTerritory establishment
Saturation
Half-saturation
Territory densities may be…Territory densities may be…
LowLow
……so realistic simulations must be calibrated to the real worldso realistic simulations must be calibrated to the real world
HighHigh
To be as realistic as possible we had to make To be as realistic as possible we had to make decisions concerning:decisions concerning:
•The characteristics of the landscapeThe characteristics of the landscape
•The species’ distribution on theThe species’ distribution on the landscapelandscape
• The sampling methodThe sampling method
• The statistical model(s)The statistical model(s)
Detection FunctionDetection Function
Point-count radius
Vegetation plot radius
To be as realistic as possible we had to make To be as realistic as possible we had to make decisions concerning:decisions concerning:
•The characteristics of the landscapeThe characteristics of the landscape
•The species’ distribution on theThe species’ distribution on the landscapelandscape
• The sampling methodThe sampling method
• The statistical model(s)The statistical model(s)
The statistical modelThe statistical model
•Deterministic model structureDeterministic model structure
Multiple regression, LogisticMultiple regression, Logistic
•Model errorModel error
Normal, Poisson, BinomialNormal, Poisson, Binomial
•Model selectionModel selection
Parsimony (AIC), Bonferroni’s alpha, Statistical significanceParsimony (AIC), Bonferroni’s alpha, Statistical significance
The deterministic modelThe deterministic model
•Multiple regression (with 2 resources)Multiple regression (with 2 resources)
YYii= B= B00 + B + B11XX1i 1i + B+ B22XX2i 2i + B+ B1212XX1i1iXX2i 2i + + εεii
or or YYii= f(X) + = f(X) + εεii
YYii = detection (0,1,2,…) = detection (0,1,2,…)
XX••i i = resource value= resource value
The deterministic modelThe deterministic model
•Logarithmic:Logarithmic:
YYii= e = e f(X) f(X) + +
εεii
YYii = detection (0,1,2,...) = detection (0,1,2,...)
XX••i i = resource value= resource value
The deterministic modelThe deterministic model
•Logistic:Logistic:
YYii= Ae = Ae f(X)f(X) /(1+ e /(1+ e f(X)f(X)) + ) + εεii
YYii = detection (0,1,2,…) = detection (0,1,2,…)
XX••i i = resource value= resource value
Choosing the correct model formChoosing the correct model form
Linear model: 1 to 4 resourcesLinear model: 1 to 4 resources1 Resource: 1 Resource:
YYi i = B= B00 + B + B11XX1i 1i + + εεii
4 Resources:4 Resources:
YYi i == B B00 + B + B11XX1i 1i + B+ B22XX2i 2i + B+ B33XX3i 3i + B+ B44XX4i4i
+ B+ B1212XX1i1iXX2i 2i + B+ B1313XX1i1iXX3i 3i + B+ B1414XX1i1iXX4i 4i
+ B+ B2323XX2i2iXX3i 3i + B+ B2424XX2i2iXX4i 4i + +
BB3434XX3i3iXX4i4i
+ B+ B123123XX1i1iXX2i 2i XX3i 3i + B + B124124XX1i1iXX2i 2i XX4i4i
+ B+ B134134XX1i1iXX3i 3i XX4i 4i + B + B234234XX2i2iXX3i 3i XX4i4i
+ B+ B12341234XX1i1iXX2i 2i XX3i 3i XX4i4i + + εεii
Number of Number of parametersparametersrequiredrequiredfor…for…
1 Resource = 2 1 Resource = 2
2 Resource = 4 2 Resource = 4
3 Resource = 8 3 Resource = 8
4 Resource = 164 Resource = 16
The statistical modelThe statistical model
•Deterministic model structureDeterministic model structure
Multiple regression, LogisticMultiple regression, Logistic
•Model errorModel error
Normal, Poisson, BinomialNormal, Poisson, Binomial
•Model selectionModel selection
Parsimony (AIC), Bonferroni’s alpha, Statistical significanceParsimony (AIC), Bonferroni’s alpha, Statistical significance
Poisson errorPoisson error
Repeated Repeated samples of samples of individuals individuals randomly randomly dispersed are dispersed are Poisson-Poisson-distributeddistributed
Poisson errorPoisson error
Negative-binomial errorNegative-binomial error
Normal errorNormal error
Binomial errorBinomial error
The statistical modelThe statistical model
•Deterministic model structureDeterministic model structure
Multiple regression, LogisticMultiple regression, Logistic
•Model errorModel error
Normal, Poisson, BinomialNormal, Poisson, Binomial
•Model selectionModel selection
Parsimony (AIC), Bonferroni’s alpha, Statistical significanceParsimony (AIC), Bonferroni’s alpha, Statistical significance
Model SelectionModel Selection
•Use AIC to judge the best of several trial modelsUse AIC to judge the best of several trial models
•The ‘best’ model must be statistically significant The ‘best’ model must be statistically significant from the ‘null’from the ‘null’ model to be accepted model to be accepted
If If =0.05, then Bonferroni’s adjusted =0.05, then Bonferroni’s adjusted is: is:
1 Resource = 0.0500 1 Resource = 0.0500 2 Resource = .0169 2 Resource = .0169
3 Resource = 0.0073 3 Resource = 0.0073 4 Resource = 0.00344 Resource = 0.0034
True, Valid and Misleading ModelsTrue, Valid and Misleading Models
•If the ‘True’ model is: If the ‘True’ model is: YYi i == B B00 + B + B123123XX1i1iXX2i 2i XX3i 3i
•Then:Then:
•YYi i == B B00 + B + B33XX3i 3i is a ‘Valid’ model is a ‘Valid’ model
•YYi i == B B00 + B + B1212XX1i 1i XX2i2i is a ‘Valid’ model is a ‘Valid’ model
•YYi i == B B00 + B + B44XX4i 4i is a ‘Misleading’ modelis a ‘Misleading’ model
•YYi i == B B00 + B + B1414XX1i 1i XX4i4i is a ‘Misleading’ model is a ‘Misleading’ model
1 Resource Required - 1 Resource Queried1 Resource Required - 1 Resource Queried
Logistic-PoissonLogistic-Poisson Multiple Regression - NormalMultiple Regression - Normal
Success identifying ‘True’ ModelSuccess identifying ‘True’ Model
1 Resource Required - 1 Resource Queried1 Resource Required - 1 Resource Queried
Logistic-PoissonLogistic-Poisson Logistic-BinomialLogistic-Binomial
Success identifying ‘True’ ModelSuccess identifying ‘True’ Model
4 Resources Required - 4 Resources Queried4 Resources Required - 4 Resources Queried
TrueTrue ValidValid
Medium SP - Resources uncorrelated – 100% detection - FullMedium SP - Resources uncorrelated – 100% detection - Full
MisleadingMisleading
4 Resources Required - 4 Resources Queried4 Resources Required - 4 Resources Queried
TrueTrue ValidValid
High SP - Resources uncorrelated – 100% detection - FullHigh SP - Resources uncorrelated – 100% detection - Full
MisleadingMisleading
4 Resources Required - 4 Resources Queried4 Resources Required - 4 Resources Queried
TrueTrue ValidValid MisleadingMisleading
Low SP - Resources uncorrelated – 100% detection - FullLow SP - Resources uncorrelated – 100% detection - Full
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
True / ValidTrue / Valid MisleadingMisleading
Medium SP - Resources uncorrelated – 100% detection - FullMedium SP - Resources uncorrelated – 100% detection - Full
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
MisleadingMisleading
High SP - Resources uncorrelated – 100% detection - FullHigh SP - Resources uncorrelated – 100% detection - Full
True / ValidTrue / Valid
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
MisleadingMisleading
Low SP - Resources uncorrelated – 100% detection - FullLow SP - Resources uncorrelated – 100% detection - Full
True / ValidTrue / Valid
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
MisleadingMisleading
Medium SP - Resources 50% correlated – 100% detection - FullMedium SP - Resources 50% correlated – 100% detection - Full
True / ValidTrue / Valid
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
MisleadingMisleading
Medium SP - Resources 50% correlated – 25% detection - FullMedium SP - Resources 50% correlated – 25% detection - Full
True / ValidTrue / Valid
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
MisleadingMisleading
Medium SP - Resources 50% correlated - 25% detection - 50% FullMedium SP - Resources 50% correlated - 25% detection - 50% Full
True / ValidTrue / Valid
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
MisleadingMisleading
High SP - Resources 50% correlated – 25% detection – 50% FullHigh SP - Resources 50% correlated – 25% detection – 50% Full
True / ValidTrue / Valid
1 Resources Required - 4 Resources Queried1 Resources Required - 4 Resources Queried
MisleadingMisleading
Medium SP - Resources 95% correlated – 25% detection - FullMedium SP - Resources 95% correlated – 25% detection - Full
True / ValidTrue / Valid
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
At best:
Affirmative conclusions about the importance of ‘critical resources’ based on statistical correlations alone are not justified!
Key Conservation Conclusion
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!