Fig. 1 Evolution of plant-microbe mutualism in terrestrial ecosystems. a. Land plants formed associations with early ancestors of arbuscular mycorrhizal fungi (AMF) soon after the plant’s colonization of terrestrial ecosystems (Strullu-Derrien et al, 2014). The schematic illustrates how an individual root tip (left, showing epidermal root cells in light green and cortical cells in light brown) and AMF mycelial forms intracellular structure. AMF hyphae is magnitude thinner than even the thinnest plant roots, allowing them superb ability to access soil resources from the porous soil matrix. b. The early forest emerged in the early Devonian after woody vascular plants gained dominance (Willis & McElwain, 2014). c. Land plants formed associations with ectomycorrhizal fungi (EMF) (Cairney, 2000), the descendant of wood-decaying fungi, aiding plants in accessing nutrients that otherwise would be locked into organic matter. d. Selected by the changing environmental condition, flowering plants emerged during the early Cretaceous as a milestone for plants’ adaptive innovation (Willis & McElwain, 2014). e. Another milestone for plant innovation happened belowground, shortly after the Cretaceous-Paleogene boundary Werner et al (2015), with plants forming mutualistic associations with nitrogen-fixing bacteria. These bacteria (housed in these orange cells) can breakdown the triple bond of N2 gas and supply plants with plant available forms of nitrogen. The geological timings of mutualistic relationships a, c, e are indicated by red arrows, while that of geological events b, d by blue arrows. This figure is modified based on Figure 1 in Lu & Hedin (2019). Illustration in a, c, e, from Yinan Sun, b from Andrew Lesile of Brown University, and d from the author.

Fig. 2 Phase planes of mutualistic interactions between population N1 and N2. a. The mutualistic interaction leads to stable nontrivial equilibrium when det(J) > 0 (r1 = r2 = 2, a11 = a22 = -1.5, a12 = a21 = 1). b. The mutualistic interaction leads to non-stable dynamics (infinite populations size) when det(J) < 0 (r1 = r2 = 2, a11 = a22 = -1.5, a12 = a21 = 2). The nullcline of population N1 is labeled in green and N2 in red. Black-filled circle denotes stable equilibrium while white-filled circles denote non-stable and half-stable (saddle points) equilibria. Plots are made in Julia 1.4.1.

Fig. 3 Graphical illustration of Iterated Prisoner’s Dilemma (IDP) (a) vs. Biological Market Theory (BMT) (b), and core concepts used in BMT (c). a. Two players interact in a symmetric manner repeatedly over time, with each player being able to remember interactions from the immediate last time step. The players are denoted with the same filled dots, emphasizing the symmetry inherent to this approach (for example, intraspecific cooperation between individual bats). b. Two classes of players interact through a bipartite-graph alike interaction, where each player in one class can interact with multiple players from the other class (for visual simplicity, only part of the interactions are shown here). The two classes are denoted with different symbols here to emphasize the inherent asymmetry of this approach, which makes it unique in dealing with inter-specific mutualistic interaction (for example, plants vs. microbes, bees vs. flowers). The minimal setup of a BMT model is labeled in light red, where 1 player interacts with 2 other. c. The most fundamental concepts in BMT can be divided into two broad classes based on timescale (solid time arrow): partner choice vs. partner fidelity feedback. The biological processes represented by these two classes of concepts are linked over evolutionary time (dashed line).

Fig. 4 Bistable vegetation patterns and the role of plant-microbe mutualism. a, b. An illustration of a landscape with patches of vegetation, where the abundance of mutualistic interaction A and B (in this case, Arbuscular mycorrhizal vs. ectomycorrhizal symbioses) is denoted by the darkness of the gray hue. a presents a landscape where bistable vegetation states is found where you either find a patch of vegetation extremely high or extremely low in one type of mutualism, whereas b has a mixture of both mutualistic type in each patch. c, d. The distribution of mutualist abundance can be illustrated using the frequency distribution of 5,000 random numbers (representing 5,000 landscape patches) drawn from a beta distribution: $f(y:\mu, phi)=cy^{\mu\varphi-1} (1-y)^{(1-\mu)\varphi-1}$ (y indicates percentage of A, μ as the central tendency, and ? as the dispersion coefficient). e. Patches that have different founding composition (small dots) of A and B will over time diverge into two alternative stable states (larger dot, EMF indicated in purple and AMF indicated in green). Panels c, d, e are reproduced from figures published in Lu & Hedin (2019).