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## Species-Habitat Associations

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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**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 Predicted 0 1 0 1 ü û 123 16 0 Observed û ü 9 74 1**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 11011110111111111 1 I • C I 0111100110011101011111 1 I • Y I 011100001001110001111111 I • 5 + 00 00110000000011000000111111111 + • I 001000100000000000000001111101 1 11 I • I 0 00000000000000000000000010001000110 11 I • I 0 1 00000000000000000000000000100000000001101111 1 I • Predicted --------------+--------------+--------------+--------------- • Prob: 0 .25 .5 .75 1 • Group: 000000000000000000000000000000111111111111111111111111111111 0 = Absent 1 = Present**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.**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**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)**Spatial contrast is essential for, but doesn’t guarantee,**success**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 the landscape • 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…**High Low …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 the landscape • 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 the landscape • 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**Linear model: 1 to 4 resources**• 1 Resource: • Yi = B0 + B1X1i + εi • 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 + εi Number of parameters required for… 1 Resource = 2 2 Resource = 4 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 Poisson-distributed**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: • 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**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