The evolutionary and coevolutionary consequences of defensive microbes for host-parasite interactions

Background Animal and plant species can harbour microbes that provide them with protection against enemies. These beneficial microbes can be a significant component of host defence that complement or replaces a repertoire of immunity, but they can also be costly. Given their impact on host and parasite fitness, defensive microbes have the potential to influence host-parasite interactions on an evolutionary timescale. Results Using a phenotypic framework, we explore the evolutionary and coevolutionary dynamics of a host-parasite interaction in the presence of defensive microbes. We show that costs of host-defensive microbe systems are critical in determining whether a defensive microbe based system or an immune system provides better host protection investment. Partitioning the coevolutionary dynamics yields testable predictions. The density of defensive microbes influences the strength of selection resulting from host - defensive microbe - parasite coevolutionary interactions. We find that they lessen the negative effects of infection on hosts and reduce infectivity by directly competing with parasites. Conclusions Defensive microbes might thus play a central role in host-parasite interactions, by outright replacing host-based defences, engaging in within-host competition with parasites, and ultimately driving tripartite coevolutionary dynamics. Electronic supplementary material The online version of this article (doi:10.1186/s12862-017-1030-z) contains supplementary material, which is available to authorized users.

where the host dynamics (H I ) are governed by costs and benefits of investment in immunity 9 (to level I). f (r, I) and g(µ, I) are the birth rate and death rate of hosts, respectively, under 10 costly investment in immunity. λ(I) is the clearance of parasites P I by immune cells. More 11 explicitly, costly investment in immunity by hosts can be described by: where λ I is the parasite clearance rate by immune cells. Taking net growth rate ( 1 H I dH I dt ) as a 13 measure of (Fisherian) fitness, hosts acquiring protection through immunity have fitness: Host dynamics where defensive microbes provide protection from parasites (eqn 7) is defined 15 as: where f (r, D m ) and g(µ, D m ) are birth rate and death rate of hosts, respectively, under costly 17 investment in defensive microbes (D m ), and λ(D m ) is the clearance of parasites P Dm by 18 defensive microbes. More explicitly: Host fitness in the presence of the defensive microbes is then: For a defensive microbe system to evolve then host fitness in the presence of defensive microbe 21 must be greater than the fitness in the presence of immune system protection: Under no costs ( r−µ 1+Dm ≡ r−µ 1+I , 1 1+Dm → 1) and equivalent clearance rates λ max ≡ λ I then this 24 inequality simplifies to: Defensive microbe protection is expected to evolve when it leads to lower parasite densities 26 than occurs when host immunity provides protection. To illustrate that the inequality condition (P * Dm < P * I ) holds we simulate the parasite (P ) 30 dynamics in the presence of defensive microbes ((D m ) or host immunity (I). Under defensive 31 microbe protection, the within-host dynamics are governed by: where γ is the parasite replication rate, µ P is the background pathogen death rate and α Dm is 33 the increased rate at which parasites die due to the effects of the defensive microbes.

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Under host immunity, the within-host dynamics are governed by: where α I is the increased rate at which parasites die due to the effects of the immune system, 37 λ 0 is the rate at which the immune system is stimulated and µ I is the loss of immune cells.

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Other parameters are as defined above. 39 40 Figure 1 shows the outcome of a numerical simulation of these dynamics. In the presence of 41 defensive microbes, parasites are eliminated (P * Dm = 0) whereas in the presence of host 42 immunity, parasite steady state density is greater (P * I ≈ 11.75). Host fitness in the presence of 43 defensive microbes is then expected to be higher than that achieved under immunity. Variation 44 in the costs of immunity or protection through defensive microbes will influence whether a 45 defensive microbe strategy will spread and persist. Costly host investment in immunity and/or 46 defensive microbes will modify the inequality and depending on the relative magnitude of these 47 costs determine when a defensive microbe protection will evolve. Individual-based approach to the evolution of defensive microbe system 50 To compliment the population-level approaches (invasion analysis, numerical simulations), in 51 this section we outline an individual-based approach to understand when a defensive microbe 52 system strategy would be evolutionarily more likely than an immunity-based strategy.

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Assumptions 54 In this individual-based approach for the evolution of defensive microbe protection we make 55 two main assumptions:

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• A host chooses to invest in protection from either defensive microbes or innate 57 immunity.

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• A host gives birth with probability Pr(birth), becomes infected with probability 59 Pr(infected) or dies with probability Pr(death). These probabilities are dependent on 60 whether a host has innate immunity or defensive microbe protection. The infected host (P ) and empty (0) Using methods from linear algebra, we can determine the long-term outcome of the Then for the long-term outcome, the state S in the next time point is: So 80 S n = NΛ n N −1 .
We can use this spectral (eigen)decomposition of a Markov matrix to investigate the long-term 81 probability of investing in a defensive microbe system over innate immunity. The probabilities 82 of host birth, death or infection establish parameter space to explore different probabilistic 83 outcomes for a defensive microbe system as parameter values change. As such, the host birth rate is r 1+α , the host death rate is µ 1+α and the host infection rate is The resulting Markov transition matrix is then: gives an empty state in the next time step, the probability of infected host mortality is 1.
101 102 the deterministic model approaches (invasion analysis; numerical simulations). Figure A2 104 shows the probability of investing in the defensive microbe system as a function of the costs of 105 immunity (α I ) and the benefits of defensive microbes (β D ) As costs of immunity and benefits 106 of defensive microbes increase, defensive microbe systems are favoured over immunity-based 107 strategies. However, this defensive microbe system can be expected at intermediate levels of