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04-For-A4 Forest Management · May 2014

Question 3 of 7: Age-Class Structure — Harvest Rotation versus Fire Cycle

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

EGBC National Exam — Forest Engineering, 04-For-A4 Forest Management, May 2014. Closed book; approved Casio/Sharp calculator only. 3 hours. Seven questions; the instructions call for Questions 1, 2, 3, 6 and 7 plus EITHER Question 4 or Question 5.

Reference texts: Davis, Johnson, Bettinger & Howard, Forest Management: To Sustain Ecological, Economic, and Social Values (age-class regulation, area/volume control, biodiversity planning); Klemperer, Forest Resource Economics and Finance (discounted cash flow, break-even stumpage/rate analysis); Smith et al., The Practice of Silviculture: Applied Forest Ecology (silvicultural systems, natural disturbance regimes); Van Wagner (1978), “Age-class distribution and the forest fire cycle,” Can. J. For. Res. 8 (negative-exponential fire-origin age structure); BC Forest and Range Practices Act and BC Ministry of Forests guidance (Canadian regulatory context).

Check: the paper prints two different mark totals for the same questions — the page-1 scoring table lists [1]=16, [2]=16, [3]=16, [4]=16, [5]=16, [6]=20, [7]=16 (a 116-mark table), while the mark shown directly beside each question is [1]=14, [2]=14, [3]=12, [4]=12, [5]=12, [6]=20, [7]=16. The per-question values sum to a clean 100-mark paper once one of Q4/Q5 is chosen (14+14+12+12+20+16=88, +12=100), matching the stated 5-of-7-plus-either format exactly, so the headings below use the per-question values and treat the page-1 table as a template artifact.

Question 3: Age-Class Structure — Harvest Rotation versus Fire Cycle (12 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Two initially-similar forests, both even-aged and clearcut oldest-first: Forest A on a 50-year harvest rotation, Forest B on a 100-year harvest rotation. Compared against stand-replacing fire with a constant per-year burn probability equal to 1⁄fire cycle (50 years for A's comparison, 100 years for B's), independent of stand age.

Find. The forest age-class structure 100 years hence under (i) oldest-first harvest rotation and (ii) the equivalent-length stand-replacing fire cycle, for each forest, and the key structural difference between the two disturbance regimes.

Approach. A constant-rotation, oldest-first harvest regime converges — once it has run for at least one full rotation, which 100 years satisfies for both R=50 and R=100 — onto the regulated (normal) forest: an equal area in every one-year age class from 0 up to the rotation age, and zero area older than the rotation age, because no stand is ever allowed to age past R before being cut. A stand-replacing fire regime with a constant, age-independent annual burn probability p=1/F instead produces the classic negative-exponential age-class distribution (Van Wagner, 1978): the probability a given stand has survived to age a without burning is (1−p)a≈e−a/F, so the proportion of the forest in each age class declines exponentially with age and — critically — never reaches zero. Both processes are applied to each forest at its own characteristic length (50 years for A, 100 years for B) to draw the four curves.

50100150200Stand age (yrs)% Forest AreaForest A (50-yr)50100150200Stand age (yrs)% Forest AreaForest B (100-yr)Harvest rotation (uniform, cutoff at R)Fire cycle (negative-exponential, long tail)
Fig. 1 — Age-class structure 100 years hence. Solid line: oldest-first harvest rotation (uniform/rectangular, hard cutoff at the rotation age R). Dashed line: equivalent-length stand-replacing fire cycle (negative-exponential, long tail of old stands beyond R). Left panel Forest A (R=50); right panel Forest B (R=100). Curves are schematic (relative area by age), not to a numeric area scale.

The rotation-managed curve is rectangular: flat at a constant proportion 100/R per one-year age class, then a vertical drop to zero exactly at age R — there are literally no stands older than the rotation because the harvest rule forbids it. The fire-origin curve is monotonically declining with a long right tail: it is highest at age zero (freshly burned/regenerating area) and falls off smoothly, but because burn probability does not depend on age, a small but non-zero fraction of the forest always survives well past the nominal cycle length — stands two, three or more cycles old are rare but real, something a hard-cutoff rotation forest can never produce. Doubling the characteristic length (Forest B vs Forest A) stretches both curves horizontally: the rotation forest's flat plateau widens and its cutoff moves out to age 100, and the fire-origin forest's exponential decay simply slows (a longer mean residence time), but the qualitative contrast — rectangular-with-hard-cutoff versus exponential-with-long-tail — holds at both lengths. That qualitative difference, not the exact curve values, is the key feature the question asks to be “clearly revealed”: even-aged, fixed-rotation management structurally excludes old forest, while a natural fire regime of the same average return interval always retains some.