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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

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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


    Sample Simulation > Sample Sim’on


    To be as realistic as possible we need to make decisions concerning…

    • The characteristics of the landscape (resources)

    • The species’ distribution on thelandscape

    • The sampling method

    • The statistical model(s)


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


    High Landscape Spatial Periodicity (SP)


    Medium Landscape Spatial Periodicity (SP)


    Low Landscape Spatial Periodicity (SP)


    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 thelandscape

    • 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 thelandscape

    • 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 thelandscape

    • 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


    Choosing the correct model form


    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


    Poisson error


    Negative-binomial error


    Normal error


    Binomial error


    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


    1 Resources Required - 4 Resources Queried

    Medium SP - Resources 95% correlated – 25% detection - Full

    True / Valid

    Misleading


    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


    Key Conservation Conclusion

    At best:

    Affirmative conclusions about the importance of ‘critical resources’ based on statistical correlations alone are not justified!

    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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