Species-Habitat Associations

1. 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

2. Species-Habitat Associations Objective: To incorporate habitat suitability predictions into a stand-level forest ecosystem model + =

3. Can we show statistically that the relative quantity of a resource on the landscape predicts the presence of a species such as Northern Flicker?

4. Logistic regression model output Predicted Predicted 0 1 0 1 ü û 123 16 0 Observed û ü 9 74 1

5. 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

6. 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.

7. 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

8. Sample Simulation > Sample Sim’on

9. 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)

10. Spatial contrast is essential for, but doesn’t guarantee, success

11. High Landscape Spatial Periodicity (SP)

12. Medium Landscape Spatial Periodicity (SP)

13. Low Landscape Spatial Periodicity (SP)

14. 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)

15. 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)

16. Territory establishment can be… Species centred Resource centred …but in either case sufficient resources must be accumulated for an individual to establish a territory

17. If territory establishment is… Species centred …then the ‘Position function” sets the parameters for territory establishment

18. Territory establishment Saturation Half-saturation

19. Territory densities may be… High Low …so realistic simulations must be calibrated to the real world

20. 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)

22. Detection Function Point-count radius Vegetation plot radius

23. 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)

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

25. 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

26. The deterministic model • Logarithmic: • Yi= e f(X) + εi • Yi = detection (0,1,2,...) • X•i = resource value

27. The deterministic model • Logistic: • Yi= Ae f(X) /(1+ e f(X)) + εi • Yi = detection (0,1,2,…) • X•i = resource value

28. Choosing the correct model form

29. 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

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

31. Poisson error Repeated samples of individuals randomly dispersed are Poisson-distributed

32. Poisson error

33. Negative-binomial error

34. Normal error

35. Binomial error

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

37. 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

38. 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

39. 1 Resource Required - 1 Resource Queried Success identifying ‘True’ Model Logistic-Poisson Multiple Regression - Normal

40. 1 Resource Required - 1 Resource Queried Success identifying ‘True’ Model Logistic-Poisson Logistic-Binomial

41. 4 Resources Required - 4 Resources Queried Medium SP - Resources uncorrelated – 100% detection - Full True Valid Misleading

42. 4 Resources Required - 4 Resources Queried High SP - Resources uncorrelated – 100% detection - Full True Valid Misleading

43. 4 Resources Required - 4 Resources Queried Low SP - Resources uncorrelated – 100% detection - Full True Valid Misleading

44. 1 Resources Required - 4 Resources Queried Medium SP - Resources uncorrelated – 100% detection - Full True / Valid Misleading

45. 1 Resources Required - 4 Resources Queried High SP - Resources uncorrelated – 100% detection - Full True / Valid Misleading

46. 1 Resources Required - 4 Resources Queried Low SP - Resources uncorrelated – 100% detection - Full True / Valid Misleading

47. 1 Resources Required - 4 Resources Queried Medium SP - Resources 50% correlated – 100% detection - Full True / Valid Misleading

48. 1 Resources Required - 4 Resources Queried Medium SP - Resources 50% correlated – 25% detection - Full True / Valid Misleading

49. 1 Resources Required - 4 Resources Queried Medium SP - Resources 50% correlated - 25% detection - 50% Full True / Valid Misleading

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