species-habitat associations

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




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

Detection FunctionDetection Function

Point-count radius

Vegetation plot radius

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


•Logarithmic:Logarithmic:

YYii= e = e f(X) f(X) + +

εεii

YYii = detection (0,1,2,...) = detection (0,1,2,...)



•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,…)


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



4 Resource = 164 Resource = 16

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

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


TrueTrue ValidValid

High SP - Resources uncorrelated – 100% detection - FullHigh SP - Resources uncorrelated – 100% detection - Full



TrueTrue ValidValid MisleadingMisleading

Low SP - Resources uncorrelated – 100% detection - FullLow SP - Resources uncorrelated – 100% detection - Full


True / ValidTrue / Valid MisleadingMisleading

Medium SP - Resources uncorrelated – 100% detection - FullMedium SP - Resources uncorrelated – 100% detection - Full



High SP - Resources uncorrelated – 100% detection - FullHigh SP - Resources uncorrelated – 100% detection - Full

True / ValidTrue / Valid



Low SP - Resources uncorrelated – 100% detection - FullLow SP - Resources uncorrelated – 100% detection - Full




Medium SP - Resources 50% correlated – 100% detection - FullMedium SP - Resources 50% correlated – 100% detection - Full




Medium SP - Resources 50% correlated - 25% detection - 50% FullMedium SP - Resources 50% correlated - 25% detection - 50% Full




High SP - Resources 50% correlated – 25% detection – 50% FullHigh SP - Resources 50% correlated – 25% detection – 50% Full


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!

species-habitat associations

Documents

beta bb

bb theta

bb variance

areas of good habitat

areas of poor habitat

alpha bb

territorial species

beta variance