How to assemble a beneficial microbiome in three easy steps

There is great interest in explaining how beneficial microbiomes are assembled. Antibiotic-producing microbiomes are arguably the most abundant class of beneficial microbiome in nature, having been found on corals, arthropods, molluscs, vertebrates and plant rhizospheres. An exemplar is the attine ants, which cultivate a fungus for food and host a cuticular microbiome that releases antibiotics to defend the fungus from parasites. One explanation posits long-term vertical transmission of P seudonocardia bacteria, which (somehow) evolve new compounds in arms-race fashion against parasites. Alternatively, attines (somehow) selectively recruit multiple, non-coevolved actinobacterial genera from the soil, enabling a ‘multi-drug’ strategy against parasites. We reconcile the models by showing that when hosts fuel interference competition by providing abundant resources, the interference competition favours the recruitment of antibiotic-producing (and -resistant) bacteria. This partner-choice mechanism is more effective when at least one actinobacterial symbiont is vertically transmitted or has a high immigration rate, as in disease-suppressive soils.

that the host can evolve mechanisms to detect overall pathogen level, is a reactive strategy maintained or not?
We assume that individuals start with a high I S at the beginning of their life, then I S decreases to a lower level after the beneficial goes to fixation (e.g. P close to zero). Then if pathogen concentration increases (because of immigration for example), a reactive strategy increases 10 I S . The conjecture is that this reactive strategy has a higher fitness than a nonreactive one, which is defined as producing a high level of I S regardless of parasite concentration.
How do we implement this scenario in a simple model?
Let us start with the same model as above. The dynamics lead pathogen's density to be close to zero after a while. Within this initial time interval, I S takes a high fixed value. We assume that after a time T, I S becomes I S (P/B), such that I S (P/B) increases with p in a saturating manner. That is, the reactive individual uses the following substrate-producing algorithm: Parameter Θ is the half-saturation constant, which gives the relative concentration of P, where the concentration-dependent part of substrate production is half of the maximum (I S -20 I 0 )/2. By using this type of function, I S (P/B) increases with P/B in a Michaelis-Menten-like manner and varies between I 0 and I S according to the concentration of P.
We compare the above strategy with a nonreactive host producing the same level of I S (P/B)=I S for its entire lifetime (e.g. I S =I 0 ). Thus we study system (1) with the additional assumption of reactive substrate production: 25 To compare the relative successes of reactive and nonreactive hosts, we measure their fitnesses as the weighted average of I S (t) and P(t) so that where W 0 is a constant independent of the strategy we study here, a is the relative cost of 30 substrate production compared to parasite load, and . is the time average for the lifetime of the individual. (By using this fitness function, it is assumed that fitness decreases because of increased substrate production or increased parasite infection, and a measures the cost of substrate production in units of cost of parasite infection.) Numerical studies. -We analyzed system (S2) numerically. We used the same parameter a broader range of parameters. We have two general conclusions according to the simulations: a) A reactive host is fitter than a nonreactive one, unless substrate production is very cheap (Fig S1, S2). 40 Fig. S1. The time evolution of beneficial (dashed red) and pathogen (green) strains and substrate production rate (black). In the nonreactive model (left hand side), production rate is constant (I s =10), while in the reactive model, substrate production follows function (S1) with parameters T=5, I S =15, b) A reactive host defends against pathogen invasion almost as effectively as a nonreactive host Here we study the effect of parasite invasion. We assume that after the beneficial goes to fixation, the parasite (after a time interval t P ) continuously invades the host with rate I P ( Fig   S3, S4). Again we can compute the fitness of the two host models and compare them as a function of relative cost of substrate production (Fig S4). Fig. S4. Fitness difference as a function of the relative cost of substrate production. We use the same dynamical parameters as above. It is clear that constant invasion of parasite causes a significant load to the reactive host, since the critical value of a is higher compared to the previous model. In other words, compared to the non-immigration scenario, the substrate has to be more expensive in order to make the reactive strategy fitter. Nonetheless, the trend is the same. It is worth evolving a strategy that reacts to parasite load by increasing substrate production, if substrate is not too cheap compared to the parasite load.
One risk to a reactive host is that Pathogen invasion might occasionally be very intense, leading to successful Pathogen spread within the host. Naturally, such invasions are more likely to be successful in reactive hosts than in nonreactive hosts. This difference simply causes W 0 to be smaller for reactive hosts than for nonreactive ones, and thus, ΔW will be positive for a larger relative cost a.

Host evolves an optimal I S
We consider a simple non-reacting host (that is, it produces a constant level of I S ), and we are interested in whether selection among hosts can result in an optimal level of I S . We define 80 average host fitness based on the assumptions in the Reactive hosts section above: It generally depends on concentrations of P and B and their invasion rates, etc., but we do not have independent estimates of these quantities. Thus, we consider many hosts with evenly distributed initial conditions of P and B. According to this assumption and our estimated 90 basin of attraction (Fig. 2) We are interested in the optimal I s level, so the question is whether s dI dW has local maxima.
The other solution of (S6) is a local minimum. Note that this analysis conservatively assumes that P and B concentrations are exogenously determined. A more realistic but more complicated model would allow the concentrations of P and B to change in the next generation after I S changes. That is, if I S increases, then P decreases and B increases in the next generation, which makes the above dynamic more efficient. Thus, this negative feedback 105 loop between I S and P intuitively does not change the general conclusion that there exists an optimal I S ; I S will merely be optimal at a lower level than in our conservative model.

Beneficials evolve an optimal α
Considering the problem as a coevolutionary process, we study not only the evolution of I s in the host but also the evolution of allocation of resources to antibiotics by the bacteria. 110 Antibiotic resistance is a character of Beneficial bacteria, and thus their average fitness can be estimated as a quantity proportional to the approximated basin of attraction for the Bdominated state, assuming that initial conditions are evenly distributed in [0, 1]. Thus is too complex, and there is no way to compute α when W B is maximal in a closed form, but Fig. 2B (main text) shows that is flat as a function of α, while for every I s , 120 there is a maximum point to which α evolves. Thus, if I s evolves in the host to a level such that the P-B system is bistable, then the Beneficial bacteria evolve to an optimal, positive α * .
Note again that we have assumed conservatively that P and B concentrations are determined entirely exogenously.