Extended Data Fig. 5: Pattern of spatial phosphorus (P) absorption aligns with regulated fungal wave growth.

(a) P concentration of agar in fungal compartment of root organ cultures measured at 4 times points starting after fungal network crosses into fungal-only compartment (red = 0 days, dark orange = 3 days, light orange = 6 days, yellow = 9 days). \(r=0\) mm corresponds to cross-over point where fungal colony enters fungal-only compartment and \(r=40\) mm corresponds to the opposite end, where P depletion will take the longest to form. By 9 days (yellow line), P is almost completely depleted from the agar in the fungal-only compartment. Error bars correspond to mean ± 2 s.e.m. (b-c) The data of (a) were used to parameterize the model of P depletion by the fungal travelling wave defined in Supplementary Discussion 4.2.5. (b) Total phosphorous captured by the colony per unit length of root over 600 h of colony propagation (see Fig. 3e for spatial profiles) as a function of wave speed \({v}_{\text{wave}}\). At a fixed saturation density, the more the fungal colony invests in spatial exploration (i.e. the higher the wave speed), the more phosphorous it can absorb from its environment. This is because it can better escape its self-generated P depletion zone. (c) Carbon cost for the phosphorous captured by the colony over the same 600 h interval. The cost is defined as the total carbon cost of growth divided by the total amount of P acquired over the duration of travelling-wave growth. Carbon cost is calculated in the same manner as was done for experimental data, as explained in Supplementary Discussion 4.3.4.