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Modelling combined effects of elevation, aspect and slope on species-presence and growth

Modelling combined effects of elevation, aspect and slope on species-presence and growth. Albert R. Stage and Christian Salas. Old ideas. French scientists modelled wine cork lengths on different sides of oak trees 50 years ago with: a · Cos(aspect) + b ·Sin(aspect)

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Modelling combined effects of elevation, aspect and slope on species-presence and growth

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  1. Modelling combined effects of elevation, aspect and slope on species-presence and growth Albert R. Stage and Christian Salas

  2. Old ideas • French scientists modelled wine cork lengths on different sides of oak trees 50 years ago with: a·Cos(aspect) + b·Sin(aspect) • Beers, Dress and Wensel 40 years ago (1966) recommended a·Cos(aspect + phase shift) where phase shift for the adverse aspect was assumed to be = SW • Stage 30 years ago (1976) added an interaction with slope to represent white pine site index: slope·[a·Cos(aspect) + b·Sin(aspect)+ c] and thereby allowing the data to determine the phase shift.

  3. Trig Tricks • Stage(1976) is a generalization of Beers, Dress and Wensel (1966) because: y = b0 + b1s + b2·s·cos(α) + b3·s·sin(α) is identical to: y = b0 + b1·s + cos(α - β) for β = +arctan(b3/b2) if b2 > 0 or −arctan(b2/b3) if b3 >0.

  4. Now what about Elevation? • Roise and Betters (1981) argued that optimum phase shift reverses between elevation extremes-- but omitted aspect/slope relations in their formulation. • Here we combine these concepts in terms of main effects of elevation with two elevation functions interacting with slope/aspect triplets.

  5. Introducing the two elevation/aspect interactions: • Behavior: • Sensitivity to elevation increases toward the extremes (contra Roise and Betters 1981) • Scale invariant • Linear model preferred

  6. Introducing the two elevation/aspect interactions: F1(elev)·slope·[a1·Cos(aspect) + b1Sin(aspect)+ c1] + F2(elev)·slope·[a2·Cos(aspect) + b2·Sin(aspect)+ c2] + d1·F3(elev) Some alternative pairs of functions: F1 (low) Constant = 1 elevation Log(elevation) Log (k·elevation)= Log (elev) + log(k) F2 (high) Square of elevation Square of elevation Square of elevation Square of elevation

  7. Challenging hypothesis with DATA! • Where there is agreement---

  8. Classifying forest/non-forest in UtahSlope = 20%

  9. Utah productivity

  10. Challenging hypothesis with DATA! • Where there is agreement--- • And where there is not !

  11. Douglas-fir Height GrowthF1 = ln(elev), KF2 = elev2

  12. Douglas-fir Height Growth3 elevation classes Not an artifact !

  13. So · · · ? • Proposed formulation consistent with ecological hypotheses concerning elevation-aspect-slope relations · · · • But allows data to define some surprises !

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