Table 1.

Notation used throughout the main text

Inoculum size	$\mathbf{n}=(n_1,n_2,\dots ,n_i,\cdots )$
Total inoculum size	$n=n_1+n_2+\cdots +n_i+\cdots$
Composition of inoculum	$x_i=n_i/n$
	$\mathbf{x}=(x_1,x_2,\dots ,x_i,\dots )$
Seeding probabilities	$\mathbb{P}[\mathbf{n}|\overline{n},\overline{\mathbf{x}}]={\prod }_i\frac{{(\overline{n}{\overline{x}}_i)}^{n_i}}{n_i!}{e}^{-\overline{n}{\overline{x}}_i}$
Averages over seeding	$\langle F(n,\mathbf{x})\rangle ={\sum }_{\mathbf{n}}\mathbb{P}[\mathbf{n}|\overline{n},\overline{\mathbf{x}}]F(n,\mathbf{x})$
Cycle index	$(\tau )$
Mixing time	$T_{\text{mix}}$
Depletion time	$T_{\text{depl}}(\mathbf{n},\text{environment})$
Within-deme observables
Population sizes	$\mathbf{N}=(N_1(t),N_2(t),\dots )$
Population composition	$\mathbf{X}=(X_1(t),X_2(t),\dots )$
	$X_i=N_i/N$
Growth rate	${\alpha }_i(t)=\alpha (1+\delta {\alpha }_i)A(t)$
Yield	${\phi }_i(t)=\phi (1+\delta {\phi }_i)Y(t)$
Resources	$S(t)$, $S(0)=S_0$
	$\phi \sim 1\Rightarrow N(T_{\text{depl}})\approx \mathcal{O}(S_0)$
Depletion	$\alpha (t>T_{\text{depl}})=0$
Public good dynamics
Production rates	$\mathit{\rho }=({\rho }_1,{\rho }_2,\dots ,{\rho }_i,\cdots )$
	usually ${\rho }_1>0,{\rho }_i\approx 0,i\ge 2$
Antibiotics parameters	B(t); $\kappa$, $\gamma$, $\mu$$\Rightarrow$$\alpha (t)$
see “Collective reduction of antibiotics” section
Pyoverdine parameters	P(t); $\sigma$$\Rightarrow$$\phi (t)$
see “Iron extraction via siderophores” section