National Academies Press: OpenBook

Evaluation of the Use and Effectiveness of Wildlife Crossings (2008)

Chapter: Appendix F - Distance Sampling

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Page 157
Suggested Citation:"Appendix F - Distance Sampling." National Academies of Sciences, Engineering, and Medicine. 2008. Evaluation of the Use and Effectiveness of Wildlife Crossings. Washington, DC: The National Academies Press. doi: 10.17226/14166.
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Page 157
Page 158
Suggested Citation:"Appendix F - Distance Sampling." National Academies of Sciences, Engineering, and Medicine. 2008. Evaluation of the Use and Effectiveness of Wildlife Crossings. Washington, DC: The National Academies Press. doi: 10.17226/14166.
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Page 158

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157 Buckland et al.40 suggest that the modeling process for the analysis of line or point transect data can be visualized as hav- ing two steps. The first involves selecting a key function as the starting point (Figure 51), starting with the uniform or half- normal. The uniform model has no parameters,40 while the half-normal has one unknown parameter that has to be esti- mated from the data. The second step is to adjust the key function with a series expansion. Buckland et al.40 suggest using (1) the cosine series, (2) simple polynomials, or (3) the Hermite polynomials. All three are linear in their parame- ters.40 Given in Figure 52 are the key function and the series expansion. A P P E N D I X F Distance Sampling

Figure 51. Functions useful in modeling distance data: (1) uniform, half-normal, and negative exponential, and (2) hazard-rate model for four different values of the shape parameter b. Figure 52. Series expansions for adjusting key functions. Key functions Series expansion wUniform, 1/ Cosine, cos Uniform, 1/ Simpl a j y w w j j m = ∑ ⎛⎝⎜ ⎞⎠⎟1 π e polynomial, cos Half-nor a y w j j m j = ∑ ⎛⎝⎜ ⎞⎠⎟1 2 mal, exp Cosine, cos( / )− ⎛⎝⎜ = ∑y a j y w j j m 2 2 2 2σ π ⎞⎠⎟ −Half-normal, exp Hermite polyn( / )y2 22σ omial, where Hazard-ra a H y y y j j j m s s 2 2= ∑ ( ) = / σ te, 1 exp Cosine, cos− − ⎛ − = ∑( ( / ) )y a j y w b j j m σ π 2 ⎝⎜ ⎞⎠⎟ − − −Hazard-rate, 1 exp Simple p( ( / ) )y bσ loynomial, a y w j j m j = ∑ ⎛⎝⎜ ⎞⎠⎟2 2

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 615: Evaluation of the Use and Effectiveness of Wildlife Crossings explores the development of an interactive, web-based decision guide protocol for the selection, configuration, and location of wildlife crossings. The decision tool as outlined in the report is available online.

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