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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 Delta, B.C., Canada Clive Goodinson Vancouver, B.C., Canada 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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Predicted Observed Logistic regression model output Predicted

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Observed Groups and Predicted Probabilities I 1 I F I 1 1 I R E I I Q I I U I I E N I I C I I Y I I I I I I I I Predicted Prob: Group: Logistic regression model 0 = Absent1 = Present

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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 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.

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

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Sample Simulation > Sample Sim’on

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To be as realistic as possible we need to make decisions concerning… The characteristics of the landscape (resources)The characteristics of the landscape (resources) The species’ distribution on thelandscapeThe species’ distribution on thelandscape The sampling method The sampling method The statistical model(s) The statistical model(s)

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Spatial contrast is essential for, but doesn’t 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) 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)

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To be as realistic as possible we had to make decisions concerning: The characteristics of the landscapeThe characteristics of the landscape The species’ distribution on thelandscapeThe species’ distribution on thelandscape The sampling method The sampling method The statistical model(s) 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… Low …so realistic simulations must be calibrated to the real world High

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To be as realistic as possible we had to make decisions concerning: The characteristics of the landscapeThe characteristics of the landscape The species’ distribution on thelandscapeThe species’ distribution on thelandscape The sampling method The sampling method The statistical model(s) The statistical model(s)

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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 landscapeThe characteristics of the landscape The species’ distribution on thelandscapeThe species’ distribution on thelandscape The sampling method The sampling method The statistical model(s) The statistical model(s)

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The statistical model Deterministic model structureDeterministic model structure Multiple regression, Logistic Model errorModel error Normal, Poisson, Binomial Model selectionModel selection Parsimony (AIC), Bonferroni’s alpha, Statistical significance

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The deterministic model Multiple regression (with 2 resources)Multiple regression (with 2 resources) Y i = B 0 + B 1 X 1i + B 2 X 2i + B 12 X 1i X 2i + ε i or Y i = f(X) + ε i Y i = detection (0,1,2,…) Xi = resource value

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The deterministic model Logarithmic:Logarithmic: Y i = e f(X) + ε i Y i = detection (0,1,2,...) Xi = resource value

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The deterministic model Logistic:Logistic: Y i = Ae f(X) /(1+ e f(X) ) + ε i Y i = 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: Y i = B 0 + B 1 X 1i + ε i 4 Resources: Y i = B 0 + B 1 X 1i + B 2 X 2i + B 3 X 3i + B 4 X 4i + B 12 X 1i X 2i + B 13 X 1i X 3i + B 14 X 1i X 4i + B 23 X 2i X 3i + B 24 X 2i X 4i + B 34 X 3i X 4i + B 23 X 2i X 3i + B 24 X 2i X 4i + B 34 X 3i X 4i + B 123 X 1i X 2i X 3i + B 124 X 1i X 2i X 4i + B 134 X 1i X 3i X 4i + B 234 X 2i X 3i X 4i + B 1234 X 1i X 2i X 3i X 4i + ε i Number of parameters requiredfor… 1 Resource = 2 2 Resource = 4 3 Resource = 8 4 Resource = 16

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The statistical model Deterministic model structureDeterministic model structure Multiple regression, Logistic Model errorModel error Normal, Poisson, Binomial Model selectionModel selection Parsimony (AIC), Bonferroni’s 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 structureDeterministic model structure Multiple regression, Logistic Model errorModel error Normal, Poisson, Binomial Model selectionModel selection Parsimony (AIC), Bonferroni’s alpha, Statistical significance

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Model 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 from the ‘null’ model to be acceptedThe ‘best’ model must be statistically significant from the ‘null’ model to be accepted If =0.05, then Bonferroni’s adjusted is: 1 Resource = Resource = Resource = Resource =

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True, Valid and Misleading Models If the ‘True’ model is: Y i = B 0 + B 123 X 1i X 2i X 3iIf the ‘True’ model is: Y i = B 0 + B 123 X 1i X 2i X 3i Then:Then: Y i = B 0 + B 3 X 3i is a ‘Valid’ modelY i = B 0 + B 3 X 3i is a ‘Valid’ model Y i = B 0 + B 12 X 1i X 2i is a ‘Valid’ modelY i = B 0 + B 12 X 1i X 2i is a ‘Valid’ model Y i = B 0 + B 4 X 4i is a ‘Misleading’ modelY i = B 0 + B 4 X 4i is a ‘Misleading’ model Y i = B 0 + B 14 X 1i X 4i is a ‘Misleading’ modelY i = B 0 + B 14 X 1i X 4i is a ‘Misleading’ model

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1 Resource Required - 1 Resource Queried Logistic-Poisson Multiple Regression - Normal Success identifying ‘True’ Model

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1 Resource Required - 1 Resource Queried Logistic-PoissonLogistic-Binomial Success identifying ‘True’ Model

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4 Resources Required - 4 Resources Queried TrueValid Medium SP - Resources uncorrelated – 100% detection - Full Misleading

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4 Resources Required - 4 Resources Queried TrueValid High SP - Resources uncorrelated – 100% detection - Full Misleading

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4 Resources Required - 4 Resources Queried TrueValidMisleading Low SP - Resources uncorrelated – 100% detection - Full

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1 Resources Required - 4 Resources Queried True / Valid Misleading Medium SP - Resources uncorrelated – 100% detection - Full

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1 Resources Required - 4 Resources Queried Misleading High SP - Resources uncorrelated – 100% detection - Full True / Valid

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1 Resources Required - 4 Resources Queried Misleading Low SP - Resources uncorrelated – 100% detection - Full True / Valid

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1 Resources Required - 4 Resources Queried Misleading Medium SP - Resources 50% correlated – 100% detection - Full True / Valid

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1 Resources Required - 4 Resources Queried Misleading Medium SP - Resources 50% correlated – 25% detection - Full True / Valid

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1 Resources Required - 4 Resources Queried Misleading Medium SP - Resources 50% correlated - 25% detection - 50% Full True / Valid

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1 Resources Required - 4 Resources Queried Misleading High SP - Resources 50% correlated – 25% detection – 50% Full True / Valid

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1 Resources Required - 4 Resources Queried Misleading Medium SP - Resources 95% correlated – 25% detection - Full 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-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

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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!

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