Modelling fungal competition for space:Towards prediction of community dynamics

Figure 1.  Examples from the empirical system of fungal mycelia. (a) One-species setting of an extending mycelium inoculated at the centre of the 22.4 $ \times $ 22.4 cm dish. (b) Transparency of drawn boundaries of three-species mycelia inoculated randomly at 49 sites indicated by the letters H (for Hf), T (Tv) and V (Vc). (c) The transparency of the mycelial boundaries of (b), processed in ImageJ for obtaining species relative occupancy at time $ t = 0 $ d

Figure 2.  One-species empirical dynamics compared to the model dynamics from the ODE (17). Circles are for the Tv empirical relative cover of the dish, and curves are for the relative abundance of Tv in a well-mixed culture with the ODE model. (a) A single Tv mycelium inoculated at the centre of a dish in the empirical system, extending before reaching the edges of the dish. (b) Three Tv mycelia closely inoculated at the dish centre, fusing to form one mycelium which extended and covered the dish. The initial conditions were equal to the relative cover of Tv on the empirical dishes at time $ t = 0 $ d. The extension rate parameter $ e_A \approx 0.35 $ d$ ^{-1} $

Figure 3.  One-species empirical dynamics compared to the model dynamics with the one-species PDE (34). Circles are for the Tv empirical relative cover of the dish, and curves are for Tv from the PDE model. (a) A single Tv mycelium inoculated at the centre of a dish in the empirical system (inset is the PDE model's solution at $ t = 12 $ d), extending before reaching the edges of the dish (as in Fig. 2a). (b) Three Tv mycelia closely inoculated at the dish centre (inset is a numerical solution of the PDE model at $ t = 12 $ d), fusing to form one mycelium which extended and covered the dish (as in Fig. 2b). The PDE model for Tv had initial conditions similar to the empirical setting, with growth rate $ \epsilon_A = 2.16 $ d$ ^{-1} $, and diffusion coefficient $ \delta_A = 0.017 $ cm$ ^2 $ d$ ^{-1} $. It was assumed that a mycelium is present when its density $ A > 0.01 $. The relative cover in the PDE solution was estimated by Monte Carlo integration of the mycelium present (the curve in each panel is 95% confidence region of the mean relative cover in the PDE solution from 100 Monte Carlo integrations)

Figure 4.  Prediction of the three-species empirical community dynamics with the PDE (35–37). The data points are for the empirical relative cover of the species in time, and the curves are for the PDE model. The inset shows the PDE numerical solution at time $ t = 40 $ d. Colour–point (of each species): red–circle (Hf), cyan–square (Tv), and blue–$ \times $ (Vc). The PDE model had initial conditions similar to the empirical setting, with the following parameter values (species A was Hf, B was Tv, and C was Vc): $ \epsilon_A = 0.78 $ d$ ^{-1} $, $ \epsilon_B = 2.16 $ d$ ^{-1} $, $ \epsilon_C = 1.14 $ d$ ^{-1} $, $ \delta_A = 0.0062 $ cm$ ^2 $ d$ ^{-1} $, $ \delta_B = 0.017 $ cm$ ^2 $ d$ ^{-1} $, $ \delta_C = 0.0091 $ cm$ ^2 $ d$ ^{-1} $, $ \rho_A = 0.22 $ d$ ^{-1} $, and $ \rho_B = 0 $ d$ ^{-1} $. Local extension and replacement rates were taken from the mean boundary extension and replacement rates in the empirical dishes, as for the extension in the one-species PDE. It was assumed that a mycelium is present when its density is greater than 0.5. The relative cover in the PDE solution was estimated by Monte Carlo integration of the mycelium present (the curves are 95% confidence regions of the mean relative cover in the PDE solution from 100 Monte Carlo integrations)