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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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Species habitat associations

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

Species-Habitat Associations

Objective: To incorporate habitat suitability predictions

into a stand-level forest ecosystem model

+

=


Species habitat associations

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


Species habitat associations

Logistic regression model output

Predicted

Predicted

0

1

0

1

ü

û

123

16

0

Observed

û

ü

9

74

1


Species habitat associations

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


    Species habitat associations

    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.


    Species habitat associations

    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


    Species habitat associations

    Sample Simulation > Sample Sim’on


    Species habitat associations

    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)


    Species habitat associations

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


    Species habitat associations

    High Landscape Spatial Periodicity (SP)


    Species habitat associations

    Medium Landscape Spatial Periodicity (SP)


    Species habitat associations

    Low Landscape Spatial Periodicity (SP)


    Species habitat associations

    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)


    Species habitat associations

    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)


    Species habitat associations

    Territory establishment can be…

    Species centred

    Resource centred

    …but in either case sufficient resources must be accumulated for an individual to establish a territory


    Species habitat associations

    If territory establishment is…

    Species centred

    …then the ‘Position function” sets the parameters for territory establishment


    Species habitat associations

    Territory establishment

    Saturation

    Half-saturation


    Species habitat associations

    Territory densities may be…

    High

    Low

    …so realistic simulations must be calibrated to the real world


    Species habitat associations

    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)


    Species habitat associations

    Detection Function

    Point-count radius

    Vegetation plot radius


    Species habitat associations

    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)


    Species habitat associations

    The statistical model

    • Deterministic model structure

      • Multiple regression, Logistic

    • Model error

      • Normal, Poisson, Binomial

    • Model selection

      • Parsimony (AIC), Bonferroni’s alpha, Statistical significance


    Species habitat associations

    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


    Species habitat associations

    The deterministic model

    • Logarithmic:

      • Yi= e f(X) + εi

    • Yi = detection (0,1,2,...)

    • X•i = resource value


    Species habitat associations

    The deterministic model

    • Logistic:

    • Yi= Ae f(X) /(1+ e f(X)) + εi

    • Yi = detection (0,1,2,…)

    • X•i = resource value


    Species habitat associations

    Choosing the correct model form


    Species habitat associations

    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


    Species habitat associations

    The statistical model

    • Deterministic model structure

      • Multiple regression, Logistic

    • Model error

      • Normal, Poisson, Binomial

    • Model selection

      • Parsimony (AIC), Bonferroni’s alpha, Statistical significance


    Species habitat associations

    Poisson error

    Repeated samples of individuals randomly dispersed are Poisson-distributed


    Species habitat associations

    Poisson error


    Species habitat associations

    Negative-binomial error


    Species habitat associations

    Normal error


    Species habitat associations

    Binomial error


    Species habitat associations

    The statistical model

    • Deterministic model structure

      • Multiple regression, Logistic

    • Model error

      • Normal, Poisson, Binomial

    • Model selection

      • Parsimony (AIC), Bonferroni’s alpha, Statistical significance


    Species habitat associations

    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


    Species habitat associations

    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


    Species habitat associations

    1 Resource Required - 1 Resource Queried

    Success identifying ‘True’ Model

    Logistic-Poisson

    Multiple Regression - Normal


    Species habitat associations

    1 Resource Required - 1 Resource Queried

    Success identifying ‘True’ Model

    Logistic-Poisson

    Logistic-Binomial


    Species habitat associations

    4 Resources Required - 4 Resources Queried

    Medium SP - Resources uncorrelated – 100% detection - Full

    True

    Valid

    Misleading


    Species habitat associations

    4 Resources Required - 4 Resources Queried

    High SP - Resources uncorrelated – 100% detection - Full

    True

    Valid

    Misleading


    Species habitat associations

    4 Resources Required - 4 Resources Queried

    Low SP - Resources uncorrelated – 100% detection - Full

    True

    Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

    Medium SP - Resources uncorrelated – 100% detection - Full

    True / Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

    High SP - Resources uncorrelated – 100% detection - Full

    True / Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

    Low SP - Resources uncorrelated – 100% detection - Full

    True / Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

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

    True / Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

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

    True / Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

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

    True / Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

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

    True / Valid

    Misleading


    Species habitat associations

    1 Resources Required - 4 Resources Queried

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

    True / Valid

    Misleading


    Species habitat associations

    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


    Species habitat associations

    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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