{"id":"barbosa-2019-michaelis-menten","source":{"id":"barbosa-2019","citation":"Barbosa, R.I., Ramírez-Narváez, P.N., Fearnside, P.M., Villacorta, C.D.A., Carvalho, L.C. da S. (2019). Allometric models to estimate tree height in northern Amazonian ecotone forests. Acta Amazonica, 49(2), 81-90.","title":"Allometric models to estimate tree height in northern Amazonian ecotone forests","authors":["Barbosa, R.I.","Ramírez-Narváez, P.N.","Fearnside, P.M."],"year":2019,"venue":"Acta Amazonica","doi":"10.1590/1809-4392201801642","url":"https://doi.org/10.1590/1809-4392201801642","read_url":"https://www.scielo.br/j/aa/a/Csx7XwJFd3whWsjNzDSSQpw/?lang=en","access":"open","license":"Creative Commons Attribution License (as stated in the article)","checked_at":"2026-11-02","status":"current"},"name":"Height from DBH, Michaelis-Menten (Table 3, best fit)","output":{"quantity":"height"},"expression":"45.8528 * D / (32.833 + D)","published":{"expression":"45.8528 * X / (32.833 + X)","units":{"X":"cm"},"variables":{"X":"D"},"output_unit":"m"},"taxon":{"level":"mixed","name":"Mixed tree species of ombrophilous/seasonal forest ecotone (65 fallen trees)","group":"mixed"},"region":{"scope":"site","countries":["BR"],"place":"Maracá Ecological Station (PPBio grid), Roraima, northern Brazilian Amazonia","biomes":["tropical"]},"stand":"natural","fit":{"n_trees":65,"dbh_min_cm":10,"h_min_m":11.7,"h_max_m":37.7,"r2":0.7149,"method":"Nonlinear/linear regression (CurveExpert/R) on 65 directly measured fallen trees; r2 is the adjusted R² printed in Table 3; Syx = 3.347 m"},"evidence":[{"field":"expression","quote":"Michaelis-Menten Y = β0 × X / β1 + X 45.8528 32.8330 - 3.347 0.7149 157.09","locator":"Table 3"},{"field":"fit.n_trees","quote":"A total of 65 individual trees were sampled","locator":"Material and Methods, Sampling design"},{"field":"fit.dbh_min_cm","quote":"with stem diameter ≥10 cm","locator":"Material and Methods, Sampling design"},{"field":"fit.h_min_m","quote":"(mean ± CI 0.05 = 24.1 ± 1.5 m; range = 11.7 - 37.7 m)","locator":"Results, paragraph on Figure 3"},{"field":"fit.r2","quote":"R² adj","locator":"Table 3 column header"}],"check":[{"inputs":{"D":20},"expected":17.358,"origin":"computed","note":"hand-computed from the published coefficients in Table 3"},{"inputs":{"D":40},"expected":25.182,"origin":"computed","note":"hand-computed from the published coefficients in Table 3"},{"inputs":{"D":70},"expected":31.213,"origin":"computed","note":"hand-computed from the published coefficients in Table 3"}],"verification":"original_read","checked_at":"2026-11-02","notes":"Best model by the authors' ranking (lowest Syx, highest adjusted R²). Y = β0·X/(β1+X), with the printed layout a fraction. Stem diameter was measured at 1.30 m, or 0.5 m above buttresses, on recently fallen trees (live or dead). The paper reports no maximum DBH in the text (see Table S1), so dbh_max is left out. Table 3 ranks five models; this is one of the four with fully legible coefficients (the Modified Hoerl row, with b1 = 0.000035, was not used)."}