============================================================================== PART 0 - MODEL PARAMETERS (club's own choices; see docstring) ============================================================================== trunk: H=40 m, path L=42 m, DBH=100 cm conducting area A = 0.4712 m^2 (60% of basal area) rho_e = 120 ohm.m, rho_d = 900 kg/m^3, c = 2000 J/kg/K liana: d=4 cm, path L=45 m conducting area A = 1.257e-03 m^2 rho_e = 180 ohm.m, rho_d = 700 kg/m^3, c = 3000 J/kg/K flash: continuing current 200 A for 115 ms; return stroke peak 30 kA area ratio A_trunk / A_liana = 375 ============================================================================== PART A - THE CIRCUIT: TWO RESISTORS, TWO DIFFERENT STORIES ============================================================================== -- resistance and mass of each path ------------------------------------------ R_trunk = rho L / A = 120 x 42 / 0.4712 = 10.7 kohm R_liana = rho L / A = 180 x 45 / 1.257e-03 = 6.446 Mohm R_liana / R_trunk = 603 m_trunk = 17,813 kg (17.8 tonnes of wood in the path) m_liana = 39.6 kg m_trunk / m_liana = 450 -- LIMIT A1 - shared voltage: the two paths span the same crown-to-ground gap conductances: G_trunk = 93.5 uS, G_liana = 155.1 nS current fraction taken by the liana = 0.001657 (0.1657 %) I_trunk = 199.669 A I_liana = 0.3313 A P_trunk = I^2 R = 426.4 MW P_liana = 707.5 kW power per kg: trunk 23,937 W/kg liana 17,873 W/kg >>> liana / trunk heating rate per kg = 0.747 temperature rise over the 115 ms continuing current: trunk dT = 1.38 K -> 26.4 degC liana dT = 0.69 K -> 25.7 degC VERDICT: in this limit NOTHING is damaged. The model fails to reproduce the paper's observation. That failure is diagnostic. -- LIMIT A2 - shared current: the liana carries the full continuing current -- same I = 200 A through each path, separately: P_trunk = 427.8 MW -> 24,017 W/kg P_liana = 257.8 GW -> 6.514 GW/kg >>> liana / trunk heating rate per kg = 271,205 closed form (rho_l/rho_t)(A_t/A_l)^2(rho_dt/rho_dl) = 271,205 [check] bracket spanned by the two limits: 0.75x ... 271,205x that is a factor of 363,221 of pure modelling ignorance. ============================================================================== PART B - WHY LIMIT A1 IS BLIND TO THICKNESS (exact cancellation) ============================================================================== For a path of length L, area A, resistivity rho_e, density rho_d holding a voltage V across its ends: R = rho_e L / A P = V^2 / R = V^2 A / (rho_e L) m = rho_d L A P/m = V^2 / (rho_e rho_d L^2) <-- A has cancelled exactly Heating per kilogram in a shared-voltage divider depends ONLY on material and path length. Making a stem thinner gives it less current AND less mass to spread that current over, in precisely equal measure. The 4 cm vine and the 1 m trunk are, to this model, the same object. numerical check at V = 2.135 MV: identity trunk 23,937.4 W/kg liana 17,873.2 W/kg simulation trunk 23,937.4 W/kg liana 17,873.2 W/kg predicted ratio = (rho_t rho_dt L_t^2)/(rho_l rho_dl L_l^2) = 0.7467 simulated ratio = 0.7467 [agrees] A doubling of liana diameter changes this ratio by exactly 0.000. liana d = 1.0 cm -> I = 0.0207 A, m = 2.47 kg, P/m = 17,928.9 W/kg liana d = 2.0 cm -> I = 0.0829 A, m = 9.90 kg, P/m = 17,917.7 W/kg liana d = 4.0 cm -> I = 0.3313 A, m = 39.58 kg, P/m = 17,873.2 W/kg liana d = 8.0 cm -> I = 1.3187 A, m = 158.34 kg, P/m = 17,696.9 W/kg liana d = 16.0 cm -> I = 5.1723 A, m = 633.35 kg, P/m = 17,017.1 W/kg ============================================================================== PART C - HEATING: ENERGY IN, TEMPERATURE OUT, TIME TO FAILURE ============================================================================== -- per-kilogram energy budgets of the two tissues ---------------------------- to kill cambium (reach 60 degC): trunk 70,000 J/kg liana 105,000 J/kg to reach 100 degC AND flash all tissue water to steam: trunk 1,167,000 J/kg liana 1,581,000 J/kg -- time to cross each threshold, at the heating rates computed above --------- case t to 60 degC t to steam-out trunk, shared-voltage limit 2.924 s 48.75 s liana, shared-voltage limit 5.875 s 88.46 s trunk, full 200 A 2.915 s 48.59 s liana, full 200 A 16.12 us 242.7 us the continuing current lasts 115 ms = 0.115 s. >>> at full current the liana reaches total steam-out in 242.7 us, i.e. in the first 0.2111% of the flash. >>> the trunk at the SAME current would need 48.6 s, which is 423x longer than the flash lasts. -- how much current does each actually need, to be destroyed? ---------------- liana, full steam-out : I_crit = 9.19 A (4.6% of the continuing current) liana, cambium death : I_crit = 2.37 A (1.2% of it) trunk, full steam-out : I_crit = 4111 A (21x the continuing current) >>> safety ratio in current, trunk vs liana = 447x >>> safety ratio in energy , trunk vs liana = 200,188x -- the return stroke, for scale ---------------------------------------------- action integral of a median first return stroke S = 55,000 A^2.s if the trunk conducted ALL of it: E = S x R = 588.2 MJ -> dT = 16.5 K spread over 17.8 tonnes (In reality most of the return stroke flashes over the wet bark surface. Our model has no flashover in it; this is its largest single omission.) ============================================================================== PART D - FITNESS: 300-YEAR MONTE CARLO, TOLERATE vs AVOID ============================================================================== strike hazard, prone = 0.017857 /yr (1 per 56 yr) strike hazard, avoiding = 0.011286 /yr (1 per 89 yr) the prone morphology is struck 58% more often (paper reports 49-68% more often for D. oleifera proportions) crown area ratio = 1.282 -- D1 - TOLERANCE ALONE (identical trees, 20,000 each) ----------------------- tolerant intolerant mean lifetime seed output (a.u.) 45.12 6.24 median age at death (yr) 89 39 fraction alive at 300 yr 0.071 0.002 mean strikes received 2.01 0.95 mean liana load, live trees 0.405 0.747 >>> LIFETIME SEED OUTPUT RATIO (tolerant / intolerant) = 7.23x paper's reported figure: ~14x discrepancy factor: 1.94 (below) -- D2 - THE TRADE-OFF (tall+tolerant vs shorter+intolerant) ------------------ mean lifetime seed output: prone 45.12 avoiding 6.79 >>> RATIO = 6.64x Smaller, as it should be: the avoider genuinely buys lower strike risk with its shorter stature. Growing tall is not free. -- where the D1 advantage comes from (one factor off at a time) -------------- full model (8,000 trees) 6.82x no liana effect on seed output (fec=0) 5.12x no canopy-gap bonus (gap=0) 6.42x no liana effect on mortality (mort=0) 6.59x none of the three 4.58x (what survives the last line is pure survival.) -- sensitivity of D1: is 14x inside our plausible range? --------------------- p(die | struck) liana fec. gap bonus ratio 0.56 0.40 0.25 4.58x 0.56 0.40 0.50 4.70x 0.56 0.40 0.80 4.83x 0.56 0.70 0.25 5.20x 0.56 0.70 0.50 5.32x 0.56 0.70 0.80 5.45x 0.56 0.85 0.25 5.68x 0.56 0.85 0.50 5.80x 0.56 0.85 0.80 5.92x 0.64 0.40 0.25 5.67x 0.64 0.40 0.50 5.85x 0.64 0.40 0.80 6.04x 0.64 0.70 0.25 6.63x 0.64 0.70 0.50 6.82x 0.64 0.70 0.80 7.03x 0.64 0.85 0.25 7.41x 0.64 0.85 0.50 7.60x 0.64 0.85 0.80 7.81x 0.78 0.40 0.25 8.43x 0.78 0.40 0.50 8.81x 0.78 0.40 0.80 9.23x 0.78 0.70 0.25 10.52x 0.78 0.70 0.50 10.97x 0.78 0.70 0.80 11.48x 0.78 0.85 0.25 12.45x 0.78 0.85 0.50 12.94x 0.78 0.85 0.80 13.49x range across that grid: 4.58x to 13.49x (median 6.82x) the paper's 14x IS NOT inside it. ============================================================================== FIGURE DATA (copied by hand into the article's inline SVGs) ============================================================================== [FIG2] heating rate per kilogram, W/kg, log scale trunk, shared-voltage 23,937.4 log10 = 4.38 liana, shared-voltage 17,873.2 log10 = 4.25 liana at 5% of current 16,283,761.7 log10 = 7.21 liana at 25% of current 407,094,041.4 log10 = 8.61 liana, full 200 A 6,513,504,662.7 log10 = 9.81 destruction threshold (liana) 13,747,826 W/kg log10 = 7.14 destruction threshold (trunk) 10,147,826 W/kg log10 = 7.01 [FIG3] temperature vs time at full 200 A (deg C), log-time t = 1 us liana 27.2 C trunk 25.0 C t = 10 us liana 46.7 C trunk 25.0 C t = 100 us liana 100.0 C trunk 25.0 C t = 1 ms liana 100.0 C trunk 25.0 C t = 10 ms liana 100.0 C trunk 25.1 C t = 115 ms liana 100.0 C trunk 26.4 C t = 1 s liana 100.0 C trunk 37.0 C t = 10 s liana 100.0 C trunk 100.0 C t = 100 s liana 100.0 C trunk 100.0 C [FIG4] survivorship and mean liana load, D1 (every 20 yr) yr S_tol S_intol L_tol L_intol 0 1.000 1.000 0.000 0.000 20 0.863 0.699 0.094 0.111 40 0.739 0.483 0.161 0.224 60 0.631 0.330 0.241 0.378 80 0.535 0.221 0.302 0.527 100 0.453 0.143 0.342 0.629 120 0.381 0.092 0.371 0.684 140 0.320 0.060 0.390 0.724 160 0.268 0.039 0.402 0.742 180 0.223 0.025 0.407 0.749 200 0.188 0.016 0.422 0.773 220 0.156 0.011 0.426 0.773 240 0.126 0.006 0.424 0.765 260 0.104 0.004 0.414 0.787 280 0.087 0.003 0.411 0.788 300 0.071 0.002 0.423 0.764 [FIG4b] cumulative mean seed output, D1 (every 20 yr) 60 tolerant 0.00 intolerant 0.00 ratio 0.00 80 tolerant 2.76 intolerant 0.96 ratio 2.89 100 tolerant 9.45 intolerant 2.65 ratio 3.56 120 tolerant 16.72 intolerant 4.01 ratio 4.17 140 tolerant 22.70 intolerant 4.85 ratio 4.68 160 tolerant 27.65 intolerant 5.37 ratio 5.15 180 tolerant 31.75 intolerant 5.70 ratio 5.57 200 tolerant 35.17 intolerant 5.91 ratio 5.95 220 tolerant 37.99 intolerant 6.04 ratio 6.29 240 tolerant 40.31 intolerant 6.13 ratio 6.58 260 tolerant 42.21 intolerant 6.18 ratio 6.83 280 tolerant 43.81 intolerant 6.22 ratio 7.05 300 tolerant 45.12 intolerant 6.24 ratio 7.23 ============================================================================== PART E - HOW MUCH DO OUR RESISTIVITY GUESSES MATTER? ============================================================================== rho_liana/rho_trunk A1 ratio A2 ratio 0.25 4.407 45,201 0.50 2.225 90,402 1.00 1.118 180,804 1.50 0.747 271,205 2.00 0.560 361,607 4.00 0.281 723,214 The A2 column moves by a factor of 16 across the whole sweep; the A1 column never leaves the neighbourhood of 1. The qualitative conclusion - that thickness only matters in the shared-current limit - is robust to everything we do not know about resistivity. ============================================================================== KEY NUMBERS USED IN THE ARTICLE ============================================================================== trunk conducting cross-section 0.4712 m^2 liana conducting cross-section 1.257e-03 m^2 area ratio 375x R_trunk 10.7 kohm R_liana 6.446 Mohm mass in trunk path 17.8 t mass in liana path 39.6 kg liana share of current (shared-V) 0.1657 % heating ratio, shared-voltage limit 0.75x heating ratio, shared-current limit 271,205x trunk dT over 115 ms (shared-V) 1.38 K liana dT over 115 ms (shared-V) 0.69 K liana time to steam-out at 200 A 242.7 us trunk time to steam-out at 200 A 49 s current that destroys the liana 9.2 A current that destroys the trunk 4,111 A trunk safety margin in energy 200,188x fitness ratio D1, our Monte Carlo 7.23x fitness ratio D2 (trade-off) 6.64x fitness ratio, the paper ~14x Reminder: every number above is the club's own model output, not a result from Gora et al. (2025). The paper measured outcomes in a forest; we only checked that the physics does not forbid them.