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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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slide1
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

slide2
Species-Habitat Associations

Objective: To incorporate habitat suitability predictions

into a stand-level forest ecosystem model

+

=

slide3
Can we show statistically that the relative quantity of a resource on the landscape predicts the presence of a species such as Northern Flicker?
slide4
Logistic regression model output

Predicted

Predicted

0

1

0

1

ü

û

123

16

0

Observed

û

ü

9

74

1

slide5
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

slide6
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.

slide7
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
slide9
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)
slide14
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)
slide15
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)
slide16
Territory establishment can be…

Species centred

Resource centred

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

slide17
If territory establishment is…

Species centred

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

slide18
Territory establishment

Saturation

Half-saturation

slide19
Territory densities may be…

High

Low

…so realistic simulations must be calibrated to the real world

slide20
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)
slide22
Detection Function

Point-count radius

Vegetation plot radius

slide23
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)
slide24
The statistical model
  • Deterministic model structure
    • Multiple regression, Logistic
  • Model error
    • Normal, Poisson, Binomial
  • Model selection
    • Parsimony (AIC), Bonferroni’s alpha, Statistical significance
slide25
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
slide26
The deterministic model
  • Logarithmic:
    • Yi= e f(X) + εi
  • Yi = detection (0,1,2,...)
  • X•i = resource value
slide27
The deterministic model
  • Logistic:
  • Yi= Ae f(X) /(1+ e f(X)) + εi
  • Yi = detection (0,1,2,…)
  • X•i = resource value
slide29
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

slide30
The statistical model
  • Deterministic model structure
    • Multiple regression, Logistic
  • Model error
    • Normal, Poisson, Binomial
  • Model selection
    • Parsimony (AIC), Bonferroni’s alpha, Statistical significance
slide31
Poisson error

Repeated samples of individuals randomly dispersed are Poisson-distributed

slide36
The statistical model
  • Deterministic model structure
    • Multiple regression, Logistic
  • Model error
    • Normal, Poisson, Binomial
  • Model selection
    • Parsimony (AIC), Bonferroni’s alpha, Statistical significance
slide37
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

slide38
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
slide39
1 Resource Required - 1 Resource Queried

Success identifying ‘True’ Model

Logistic-Poisson

Multiple Regression - Normal

slide40
1 Resource Required - 1 Resource Queried

Success identifying ‘True’ Model

Logistic-Poisson

Logistic-Binomial

slide41
4 Resources Required - 4 Resources Queried

Medium SP - Resources uncorrelated – 100% detection - Full

True

Valid

Misleading

slide42
4 Resources Required - 4 Resources Queried

High SP - Resources uncorrelated – 100% detection - Full

True

Valid

Misleading

slide43
4 Resources Required - 4 Resources Queried

Low SP - Resources uncorrelated – 100% detection - Full

True

Valid

Misleading

slide44
1 Resources Required - 4 Resources Queried

Medium SP - Resources uncorrelated – 100% detection - Full

True / Valid

Misleading

slide45
1 Resources Required - 4 Resources Queried

High SP - Resources uncorrelated – 100% detection - Full

True / Valid

Misleading

slide46
1 Resources Required - 4 Resources Queried

Low SP - Resources uncorrelated – 100% detection - Full

True / Valid

Misleading

slide47
1 Resources Required - 4 Resources Queried

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

True / Valid

Misleading

slide48
1 Resources Required - 4 Resources Queried

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

True / Valid

Misleading

slide49
1 Resources Required - 4 Resources Queried

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

True / Valid

Misleading

slide50
1 Resources Required - 4 Resources Queried

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

True / Valid

Misleading

slide51
1 Resources Required - 4 Resources Queried

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

True / Valid

Misleading

slide52
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
slide53
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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