Francesco Dell'isola

Henri Gouin

Pierre Seppecher

Radius and surface tension of microscopic bubbles by second gradient theory

Keywords: Continuum mechanics, Gas liquid interface, Particle size, Bubbles, Surface tension, Equilibrium, Theoretical study, PACS: 47.55.db, 64.70.Fx, 68.03.Cd, 68.03.-g

 and Tolman (1948).

Introduction

The microscopic bubbles we consider in this paper contain enough molecules to be modelled as a continuous strongly non-homogeneous system. To the clas-Email addresses: isola@scilla.ing.uniroma1.it (Francesco dell'Isola), henri.gouin@univ-cezanne.fr (Henri Gouin), seppecher@imath.fr (Pierre Seppecher).

Preprint submitted to : Comptes Rendus Acad. Sci. Paris II b, t. 320, n o 5, p. 211-216 (1995).

sical expression for the free energy valid for homogeneous continua has to be added a term depending on the variation of mass density. Usually the additional term is assumed to depend on the gradient of density only [START_REF] Cahn | Free energy of a non uniform system III[END_REF][START_REF] Serrin | New perspectives in thermodynamics[END_REF]. Hence the expression for stress tensor differs from that valid for elastic fluids as even in equilibrium conditions shear components also appear. The form of the balance equation of force valid for second gradient fluids is found in [START_REF] Germain | La méthode des puissances virtuelles en mécanique des milieux continus[END_REF], Casal (1962). In 1948, Tolman established, by using a Gibbs-like approach to Laplace theory, some relationships between the radius and the surface tension of bubbles in equilibrium with their liquid phase. This work produced many theoritical and experimental investigations concerning bubbles of quasi-molecular dimensions [START_REF] Fisher | Determination of the capillary pressure in menisci of molecular dimensions[END_REF]Kumar,1991). In this case the theory of Laplace is not suitable as the vapour bubble consists mainly or exclusively of the interfacial phase. However, to interpret the experimental evidence it is still important to attribute a radius and an energy to microscopic germs: we do this by means of an equivalent model of Laplace type. We note that Cahn and Hilliard did not consider the mechanical aspect of the nucleation phenomenon. They only considered the thermodynamic pressure (i.e. the spherical part of stress tensor deriving from the classical expression for free energy) while in [START_REF] Casal | Connection between the energy equation and the motion equation in Korteweg's theory of capillarity[END_REF] is shown, for second gradient fluids, the existence of a capillary non-spherical stress tensor whose trace includes -but does not reduce to -quoted thermodynamic pressure. The analysis of some preliminary numerical calculations allows us to conclude that the theory of second gradient fluids, reinterpreted through a comparison with Laplace theory, leads to predictions closer to the experimental evidence than those available in the literature for radii close to the critical one. A further improvement is conceivable by considering non-constant capillarity coefficient as suggested by De Gennes (1981).

Equilibrium of bubbles and Gibbs rule by the second gradient theory

The balance equations of force for capillary fluids are available in the literature (see e.g. [START_REF] Serrin | New perspectives in thermodynamics[END_REF]. The most simple model taking into account the nonhomogeneity effects introduces a unique additional physical constant C [START_REF] Casal | Connection between the energy equation and the motion equation in Korteweg's theory of capillarity[END_REF]. Its value in mks units is very small: its effects are notable only inside interfaces. Balance of forces, in equilibrium conditions, reads (τ , ρ, Ω denoting stress tensor of non-dissipative capillary fluids, mass density and potential of body forces):

div τ -ρ grad Ω = 0, (1)
with τ = -p Id + C grad ρ ⊗ grad ρ, where p = P -C (grad ρ) 2 2 + Cρ ∆ρ, with denoting by P and ∆ the thermodynamic pressure and the Laplace operator respectively. Equation (1) implies:

grad P + ρ grad(Ω -C ∆ρ) = 0. ( 2
)
With assuming isothermal equilibrium conditions, relation (2) becomes:

µ(ρ) -C ∆ρ + Ω = C ste , ( 3
)
where µ is the specific free enthalpy (i.e. the chemical Gibbs potential) relative to the fluid in a homogeneous state with mass density ρ and temperature T .

If Ω is negligible, the equilibrium of a bubble surrounded by its liquid phase with density ρ l is represented by a spherically symmetric profile of density satisfying (Rocard, 1952;Cahn & Hilliard,1959):

C d 2 ρ dr 2 + 2 C r dρ dr = µ(ρ) -µ(ρ l ). (4)
Equation( 4) has to be supplemented with appropriate boundary conditions:

-(a) because of spherical symmetry, the derivative of ρ vanishes at the origin, -(b) as we have assumed that the bubble is surrounded by a homogeneous liquid, the derivative of ρ vanishes at infinity.

If ρ P l is the density of the liquid phase in the equilibrium state with plane interface and the function µ is smooth enough, then the theory of Fuchs equations (Valiron) implies that:

(i) for every ρ l in an interval ρ m , ρ P l , Eq. ( 4) and conditions (a)-(b) uniquely determine an increasing mass density profile ρ(r) and in particular its value ρ v at the origin: we say that ρ(r) satisfies the capillary fluids version of the Gibbs Phase Rule;

(ii) the function ρ is twice differentiable at the origin;

(iii) as dµ dρ ρ l > 0, ρ converges at least exponentially to ρ l when r tends to infinity. With denoting with a prime the radial derivative and by ψ the free energy per volume, Eq. ( 4) implies:

Cρ ′′ ρ ′ + 2C r ρ ′2 = µ(ρ)ρ ′ -µ(ρ l )ρ ′ , (5)
and by integrating

C 2 ρ ′2 + r 0 2C x ρ ′2 (x) dx = ψ(ρ) -ψ(ρ v ) + µ(ρ l )(ρ v -ρ). (6)
3 Nucleation energy of bubbles

We deal here with bubbles which are small with respect to a typical size of the liquid phase. More precisely, a mass density field ρ, whose mean value is ρ 0 , in a domain D of volume v(D) represents a small bubble if ρ l and

ε ≪ 1 exist such that B = {x ∈ D ρ(x) -ρ l ρ 0 > ε} satisfies v(B) v(D) < ε. We note that, as D (ρ -ρ 0 ) dV = 0, ρ 0 -ρ l ρ 0 = O(ε)
. We now evaluate (in the absence of capillarity effects and at the first order of approximation in ε) the difference between the free energy of such a small bubble configuration and the homogeneous configuration of density ρ 0 . This difference, which is part of the nucleation energy of the bubble, is w =

D (ψ(ρ) -ψ(ρ 0 )) dV. As D ρ 0 dV = D ρ dV, the energy w = D [ψ(ρ)-aρ-ψ(ρ 0 )+aρ 0 ]
dV does not depend on the choice of the constant a. The total energy is well defined but its localization is somewhat arbitrary. This indetermination is related to the arbitrariness in the choice of chemical potentials. With the choice a = µ(ρ l ) the energy is localized inside B. Indeed, with using the previous estimation for ρ 0ρ l we obtain:

w = B [ψ(ρ) -µ(ρ l )(ρ -ρ l ) -ψ(ρ l )] dV + O(ε 2 ).
To the non-capillary part of nucleation energy of a bubble in an unbounded domain we have to add the interfacial (capillary) energy. In the Gibbs-Laplace theory we have for bubbles of radius R and surface tension σ:

W = 4πR 2 σ + 4 3 πR 3 [ψ(ρ v ) -ψ(ρ l ) + µ(ρ l )(ρ l -ρ v )]. (7)
In the theory of second gradient fluids, following Cahn and Hilliard, we have:

W = D [ψ(ρ) -ψ(ρ l ) -µ(ρ l )(ρ -ρ l ) + C 2 (grad ρ) 2 ] dV. (8)
Let P =ρµψ denote the thermodynamic pressure. The conditions

µ(ρ l ) = µ(ρ v ), (9)
P(ρ l ) -P(ρ v )= - 2σ R , (10)
valid -for isothermal equilibrium -only in Laplace theory, transform Eq.( 7) into:

W = 4 3 πR 2 σ, (11)
and imply that the nucleation energy of the bubble is the third of the creation energy of its interface. We can extend this result to the theory of second gradient fluids. Let φ(ρ) = ψ(ρ)ψ(ρ l )µ(ρ l )(ρρ l ); by multiplying Eq. ( 6) by r 2 and integrating it over [0,∞] we get:

∞ 0 r 2 C 2 ρ ′2 -φ(ρ) dr + ∞ 0 r 2 φ(ρ v ) + r 0 2C x ρ ′2 (x) dx dr = 0, ( 12
)
by integrating by parts and using Eq. ( 6) again, we obtain:

∞ 0 r 2 C 6 ρ ′2 + φ(ρ) dr + r 3 3 φ(ρ) - C 2 ρ ′2 ∞ 0 = 0. ( 13
)
Because of (i) -(iii) of Sect. 2, the last term vanishes so that we obtain

W = 4π ∞ 0 r 2 C 2 ρ ′2 + φ(ρ) dr = 4 3 π ∞ 0 Cr 2 ρ ′2 dr. (14)
With denoting by R 2 m the mean value of r 2 with respect to the measure ρ ′2 dr, Eq.( 14) reads

W = 4 3 πR 2 m ∞ 0 Cρ ′2 dr. ( 15
)
For a large enough bubble (i.e. when ρ l tends to ρ P l ):

(i) R m is the radius, (ii) Equation ( 15) reduces to Equation (11), as surface tension for plane interface is

∞ 0 Cρ ′2 dr.
4 Comparison between Laplace and second gradient theories. Equivalent bubbles

In second gradient theory the stress tensor in the center of a spherical bubble takes the value τ = -p v Id where p v = P(ρ v ). As Equation (4) implies

Cρ v ∆ρ v = ρ v (µ(ρ v ) -µ(ρ l )), we have p v -p l = ψ(ρ l ) -ψ(ρ v ) + µ(ρ l )(ρ v -ρ l ). ( 16
)
Let us note that this difference is not equal to the corresponding difference of thermodynamic pressures as, for microscopic bubbles, µ(ρ l ) differs from µ(ρ v ). As experimental results [START_REF] Fisher | Determination of the capillary pressure in menisci of molecular dimensions[END_REF] deal with measures of stresses, then we have to use p v -p l instead of P(ρ v )-P(ρ l ) in the comparison between Laplace and second gradient theories. We can now define the surface tension and the radius of a bubble by identifying the nucleation energies and the pressure differences computed in both theories. Indeed

p v -p l = 2σ R and 4 3 π ∞ 0 Cr 2 ρ ′2 dr = 4 3 πR 2 σ imply R = 2C ∞ 0 r 2 ρ ′2 dr 1 3 [ψ(ρ l ) -ψ(ρ v ) + µ(ρ l )(ρ v -ρ l )] -1 3 , (17)
and

σ = C 4 ∞ 0 r 2 ρ ′2 dr 1 3 [ψ(ρ l ) -ψ(ρ v ) + µ(ρ l )(ρ v -ρ l )] 2 3 . ( 18
)

Conclusion

Let us notice that our treatment is based on Eq. ( 1) obtained by a continuum model. However, van Kampen (1964) obtained the same differential equation by using ideas and methods of statistical mechanics. Eq. ( 14) has allowed us to evaluate the nucleation free energy of a bubble, once the mass density profile is known, i.e. once the liquid phase density ρ l has been assigned. Equation ( 16) allows us to understand the difference between thermodynamic and stress pressure. These two equations do not depend on a particular constitutive law and determine the radius and surface tension for a microscopic bubble. This is done by identifying the pressure jump and nucleation energy of Laplace theory with the corresponding quantities in the second gradient theory. This method has never been used in literature: for example, [START_REF] Cahn | Free energy of a non uniform system III[END_REF] and [START_REF] Evans | The nature of the liquid-vapor interface and other topics in the statistical mechanics of non-uniform, classical fluids[END_REF] used for surface tension the expression valid for plane interfaces, and did not investigate the relationship between surface tension and radius. Our Eqs. ( 17)-( 18) give such a relationship in an implicit form: in fact, both surface tension and radius depend on the density profile, which, in turn, depends on ρ l . When the radius tends to infinity, our expression for surface tension reduces to that for plane interfaces. We observe that the relationship between σ and R depends on thermodynamic potential. Numerical calculations were performed by Dell'Isola, [START_REF] Dell'isola | Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations[END_REF] using equations ( 17)-( 18) and van der Waals-type potential proposed by van Kampen (1964), Rocard (1967) and [START_REF] Peng | A new two-constant equation of state[END_REF]. It was able to observe that, for bubbles whose radius is close to the critical one, the predicted variations of the surface tension (for water and cyclohexane at 20 • C) are in good agreement with the experimental observations [START_REF] Katz | Condensation of a supersatured vapor III. The homogeneous nucleation of CCl 4 ,CHCl 3 , CCl 3 F and C 2 H 2 Cl 4[END_REF]Fisher & Israelachvili, 1980). This is not the case for the theoretical treatment proposed by Tolman (1947) and [START_REF] Kumar | Curvature dependence of surface free energy and nucleation kinetics of CCl 4 and C 2 H 2 Cl 4 vapours[END_REF].

Tolman R.C., Consideration of the Gibbs theory of surface tension, J. Chem. Phys., 16, pp. 758-774 (1948).

Valiron G., Equations fonctionnelles, applications, Masson, Paris, 1950.

Van Kampen N.G., Condensation of a classical gas with long range attraction, Phys. Rev., 135, A362-A369 (1964).

-----------------------------

Abridged French version

Rayon et tension superficielle des bulles microscopiques en théorie du second gradient

Résumé

La théorie de Laplace est inadaptée pour étudier les bulles de dimensions moléculaires. La théorie des fluides doués de capillarité interne nous permet de proposer une expression de la tension superficielle et du rayon des bulles comme fonctionelles du potentiel chimique. Cette expression, en accord avec l'expérience, améliore les résultas obtenus par Cahn-Hilliard et Tolman.

Version française abrégée

Pour étudier le comportement d'un fluide fortement hétérogène on ajoute à l'expression de la densité d'énergie libre d'un fluide homogène un terme limité, le plus souvent, à un développement au second ordre en gradients [START_REF] Cahn | Free energy of a non uniform system III[END_REF][START_REF] Serrin | New perspectives in thermodynamics[END_REF].

Les équations du mouvement de ces fluides sont obtenues par la théorie du second gradient [START_REF] Casal | La capillarité interne[END_REF][START_REF] Germain | La méthode des puissances virtuelles en mécanique des milieux continus[END_REF]. Tolman (1948) a étudié la tension superficielle des bulles en fonction de leur rayon. Des mesures expérimentales ont été faites pour des bulles de dimensions quasi moléculaires (Fisher, 1950;[START_REF] Kumar | Curvature dependence of surface free energy and nucleation kinetics of CCl 4 and C 2 H 2 Cl 4 vapours[END_REF]. Pour de telles dimensions la théorie de Laplace est disqualifiée car la bulle de vapeur devient l'interface elle-même. Il est néanmoins important de donner une dimension et une énergie pour les germes microscopiques puis de les comparer à un modèle équivalent de type Laplace. On peut ainsi interpréter les résultats des expériences. Le modèle le plus simple de fluide du second gradient ne fait intervenir qu'une seule constante physique supplémentaire C. L'équation de l'équilibre est alors l'équation (1) [START_REF] Serrin | New perspectives in thermodynamics[END_REF] où τ s' interprète comme le tenseur des containtes, Ω, ρ et P désignent respectivement le potentiel des forces de masse, la densité de masse et la pression hydrodynamique. Si les forces de masse sont négligeables, l'équilibre isotherme d'une bulle supposée sphérique dans une phase liquide de densité ρ l est représenté par une solution de l'équation (4). Pour chaque valeur ρ l dans une plage convenable on obtient un profil croissant unique et une valeur de la densité ρ v au centre de la bulle. Le règle de Gibbs est donc bien vérifiée. Nous comparons l'énergie libre d'un fluide homogène de densité ρ o contenu dans un domaine D et l'énergie libre de la même masse de fluide dans D formée par un liquide homogène contenant une petite bulle V . Cela nous conduit aux expressions ( 7) et (8) pour l'énergie de nucléation W d'une bulle dans un domaine infini, respectivement en théorie de Laplace et en théorie du second gradient. Les conditions d'équilibre liquide-vapeur en théorie de Laplace permettent d'écrire W sous la forme de l'équation (11). La série d'égalités ( 5), ( 6), ( 12), ( 13), ( 14) montre que ce résultat se généralise sous la forme de l'équation (15) où R 2 m désigne la valeur moyenne de r 2 relativement à la mesure ρ ′2 . En théorie du second gradient, le tenseur des contraintes est sphérique à l'origine ainsi qu'à l'infini mais, alors qu'à l'infini la pression se confond avec la pression thermodynamique p l = P (ρ l ), cela est faux à l'origine où p v = P (ρ v ) -Cρ v ∆ρ v . En identifiant la différence de pression entre l'origine et l'infini ainsi que l'énergie de nucléation dans les deux théories, on obtient les définitions ( 17) et (18) pour le rayon R et la tension superficielle σ de la bulle. Notre raisonnement est basé sur l'équation (1) obtenue par un modèle de mécanique des milieux continus. Il faut noter que van Kampen (1964) a obtenu la même équation par des considérations de mécanique statistique. L'équation ( 14) nous permet d'évaluer l'énergie de nucléation à partir du profil de densité donc de ρ l . La détermination du rayon et de la tension de surface d'une bulle microscopique par identification de l'énergie de nucléation et du saut de pression donné par la théorie de Laplace avec les quantités correspondantes en théorie du second gradient n'a jamais été utilisée dans la littérature: par exemple [START_REF] Cahn | Free energy of a non uniform system III[END_REF] et [START_REF] Evans | The nature of the liquid-vapor interface and other topics in the statistical mechanics of non-uniform, classical fluids[END_REF] ont utilisé une expression de la tension superficielle valable pour une interface plane uniquement et n'ont pas étudié la relation liant le rayon et la tension superficielle. Les équations ( 17) et (18) permettent d'obtenir une telle relation sous forme implicite: le rayon et la tension superficielle dépendent tous deux du profil de densité qui lui-même dépend de ρ l . Notre expression de la tension de surface se réduit, quand le rayon de la bulle R tend vers l'infini (i.e. quand ρ l tend vers la valeur ρ P l valable pour une interface plane), à l'expression usuelle [START_REF] Cahn | Free energy of a non uniform system III[END_REF]. L'étude des variations de la tension superficielle en fonction du rayon nécessite le choix d'une loi d'état. Dell 'Isola, Gouin et Rotoli (1996) ont utilisé les potentiels chimiques du type de van der Waals proposés par van Kampen (1964), Rocard (1967) ou [START_REF] Peng | A new two-constant equation of state[END_REF], pour effectuer des calculs numériques: ils montrent que, pour des bulles de rayon voisin du rayon critique, la variation prévue de la tension superficielle correspond aux mesures expérimentales de [START_REF] Katz | Condensation of a supersatured vapor III. The homogeneous nucleation of CCl 4 ,CHCl 3 , CCl 3 F and C 2 H 2 Cl 4[END_REF][START_REF] Fisher | Determination of the capillary pressure in menisci of molecular dimensions[END_REF] alors que les prévisions de Tolman (1947) et [START_REF] Kumar | Curvature dependence of surface free energy and nucleation kinetics of CCl 4 and C 2 H 2 Cl 4 vapours[END_REF] ne sont pas réalisées.


Pina Brinker
email: p.brinker@rug.nl

Michael C Fontaine

Leo W Beukeboom

Joana Falcao Salles
email: j.falcao.salles@rug.nl

Host, symbionts, and the microbiome: the missing tripartite interaction

Keywords: Insects, Phenotype, Wolbachia, Mosquitoes, Metacommunity, Drosophila

Symbiosis between microbial associates and a host is a ubiquitous feature of life on earth, modulating host phenotypes. In addition to endosymbionts, organisms harbour a collection of host-associated microbes, the microbiome that can impact important host traits. In this opinion we will argue that the mutual influences of the microbiome and endosymbionts, as well as their combined influence on the host are still understudied. Focussing on the endosymbiont Wolbachia, we will present growing evidence indicating that host phenotypic effects are exerted in interaction with the remainder microbiome and the host. We thus advocate that only through an integrated approach that considers multiple interacting partners and environmental influences, we will be able to gain a better understanding of host-microbe associations.

Interacting entities

Arthropods commonly host a wide variety of microbes (see Glossary), some of which live within a host in a close and long-term biological interaction. Such endosymbionts can exert effects on the host ranging from positive (mutualistic, i.e. providing benefits [START_REF] Brownlie | Symbiont-mediated protection in insect hosts[END_REF]) to negative (parasitic, i.e. imposing substantial costs [START_REF] Ivanov | Modulation of immune homeostasis by commensal bacteria[END_REF]) interactions. Thus, endosymbionts are important modulators of host phenotypes, providing heritable variation upon which natural selection can act [START_REF] Moran | Genomics and evolution of heritable bacterial symbionts[END_REF][START_REF] Corbin | Heritable symbionts in a world of varying temperature[END_REF].

Historically, symbiosis research has focused on binary interactions between hosts and individual endosymbionts. In recent years this view was broadened to include all microbes that copiously colonize animals, the so-called microbiome, as they are additional important modulators of host traits (Box 1). Due to the historical focus on binary interactions comparatively little is known about interactions between microbes within the microbiome and how these interactions impact the host [START_REF] Deines | Transitioning from microbiome composition to microbial community interactions: The potential of the metaorganism Hydra as an experimental model[END_REF]. A more holistic approach towards the multitude of interactions is however needed for a better understanding of the varied mechanisms by which microbes drive animal health, development, and evolution [START_REF] Petersen | Microbiomes in natura: Importance of invertebrates in understanding the natural variety of animal-microbe Interactions[END_REF]. This is especially true as symbionts are part of a complex ecosystem including host, symbiont, microbiome and their environment.

Here symbionts, host and the remainder microbiome interact with each other, but are also influenced by free-living microbial communities and environmental conditions, e.g. temperature, diet, as well as other organisms (Box 2). Focusing only on one type of interaction, i.e. between host and symbiont or between host and the microbiome, under artificial conditions that do not reflect the potential influence of the environment (Box 3) will provide only an incomplete picture of host-microbe interactions.

In this opinion article, we argue that an important area for future research relies on disentangling how endosymbionts, the remainder microbiome and the host interact with each other and how their environment is shaping these interactions (Figure 1). Note that we consider symbionts here as a separate microbial entity due to historical focus on binary interactions of symbiont and host. With this separation we can highlight the differences between both, but in fact the microbial symbionts are part of the microbiome and as such, should be studied together. We postulate that phenotypic effects of symbionts are modulated by other microbes, the host and the tripartite interaction between them. Drawing on the wealth of information on the endosymbiont Wolbachia, we will discuss studies that embraced this holistic view. We will argue for re-investigating well-known symbioses with respect to the interactions with other microbes, reviewing studies that indicate that symbioses are more influenced by other partners than the host itself. Throughout this opinion we will advocate the importance of this broader approach to gain a better understanding of symbionts and the role of the microbiome and the host in shaping host fitness.

Symbionts, the sole manipulator?

In the last years researchers started to investigate microbe-symbiont interactions in model organisms such as the fruit fly Drosophila melanogaster [START_REF] Simhadri | The gut commensal microbiome of Drosophila melanogaster is modified by the endosymbiont Wolbachia[END_REF], the parasitoid wasps Nasonia [START_REF] Dittmer | Disentangling a holobiont -Recent advances and perspectives in Nasonia wasps[END_REF], and in mosquitoes as vectors of important human diseases [START_REF] Novakova | Mosquito microbiome dynamics, a background for prevalence and seasonality of West Nile virus[END_REF].

Additionally, projects like the parasite-microbiome-project [START_REF] Dheilly | Parasite Microbiome Project: Systematic investigation of microbiome dynamics within and across parasite-host interactions[END_REF] started investigating microbiome dynamics within and across parasite-host interactions. Nevertheless, microbe-microbe interactions within a host, their influence on the host and how these interactions are influenced by the environment are still understudied [START_REF] Deines | Transitioning from microbiome composition to microbial community interactions: The potential of the metaorganism Hydra as an experimental model[END_REF].

Symbionts and the remainder microbiome can influence each other and by doing so potentially shape their effects on host phenotype. For example the microbiome can be a potential barrier to transmission of heritable symbionts through competitive exclusion of maternally inherited bacteria, as shown for the American dog tick Dermacentor variabilis [11] and the fruit fly D. melanogaster [START_REF] Goto | Asymmetrical interactions between Wolbachia and Spiroplasma endosymbionts coexisting in the same insect host[END_REF]. On the other hand, symbionts and host can together control and shape the microbiome as shown in Lepidoptera [START_REF] Johnston | Host and symbiont jointly control gut microbiota during complete metamorphosis[END_REF], D. melanogaster [START_REF] Simhadri | The gut commensal microbiome of Drosophila melanogaster is modified by the endosymbiont Wolbachia[END_REF]14] and the mosquito Aedes aegypti [15]. These interactions between the different members of the microbial community within a host can either be direct via competition for resources and space [START_REF] Goto | Asymmetrical interactions between Wolbachia and Spiroplasma endosymbionts coexisting in the same insect host[END_REF], or indirect via the induction of a general immune response [START_REF] Abraham | Pathogen-mediated manipulation of arthropod microbiota to promote infection[END_REF]17]. A direct competition has been hypothesized for the protective phenotypes induced by the endosymbiont Wolbachia against pathogens in Drosophila and Aedes, resulting in abundance-dependent protection [START_REF] Lu | Wolbachia induces density-dependent inhibition to dengue virus in mosquito cells[END_REF]19]. Competition for resources or space between Wolbachia and other bacteria is also likely for the terrestrial isopod Armadillidium vulgare. In this pill bug, total bacterial loads increase in some, but not all tissues of Wolbachia-infected individuals [START_REF] Dittmer | Host tissues as microhabitats for Wolbachia and quantitative insights into the bacterial community in terrestrial isopods[END_REF] and Wolbachia presence decreases the abundance of bacterial phylotypes [START_REF] Dittmer | Feminizing Wolbachia influence microbiota composition in the terrestrial isopod Armadillidium vulgare[END_REF]. Indirect interaction between the different members of the microbial community of a host has also been found. In bumble bees (Bombus terrestris), variation in gut microbiome seems to drive the general defence against parasites and the evolution of gut parasites by interactions with the remainder microbiome as well as with host genotypes [17]. Similarly, in ticks (Ixodes scapularis), parasites induce the expression of specific glycoproteins, which alter the host microbiome to their advantage, i.e. to promote infection [START_REF] Abraham | Pathogen-mediated manipulation of arthropod microbiota to promote infection[END_REF]. For the nutritional mutualisms between Wolbachia and the bedbug Cimex lectularius the exchange of genetic material between Wolbachia and other symbionts (likely Cardinium or Rickettsia) coinfecting the same insect host, have likely enabled Wolbachia to become an obligate, needed, symbiont providing B vitamins for the nutrition of Cimex lectularius [START_REF] Hosokawa | Wolbachia as a bacteriocyte-associated nutritional mutualist[END_REF][START_REF] Nikoh | Evolutionary origin of insect-Wolbachia nutritional mutualism[END_REF]. These studies highlight the complexity of the tripartite interaction between host species, microbiome and symbionts, across different hosts and foster the development of a framework in which interactions, host phenotype and environment are jointly explored.

The environmental component

The environment influences microbes within a host and thus potentially their interactions as well as their effect on host phenotype. It is for example known that the abiotic environment, i.e. temperature, affects symbiont density [START_REF] Corbin | Heritable symbionts in a world of varying temperature[END_REF][START_REF] Hurst | Male-killing Wolbachia in Drosophila: A temperature-sensitive trait with a threshold bacterial density[END_REF]. As example a reduction, or elimination of Wolbachia due to high temperature was found for D. melanogaster, mites, and other species [START_REF] Corbin | Heritable symbionts in a world of varying temperature[END_REF][START_REF] Hurst | Male-killing Wolbachia in Drosophila: A temperature-sensitive trait with a threshold bacterial density[END_REF][START_REF] Van Opijnen | High temperatures eliminate Wolbachia, a cytoplasmic incompatibility inducing endosymbiont, from the two-spotted spider mite[END_REF][START_REF] Sumi | Wolbachia density changes seasonally amongst populations of the pale grass blue butterfly, Zizeeria maha (Lepidoptera: Lycaenidae)[END_REF]. In line with this, seasonal changes of Wolbachia density were observed in Lepidoptera [START_REF] Sumi | Wolbachia density changes seasonally amongst populations of the pale grass blue butterfly, Zizeeria maha (Lepidoptera: Lycaenidae)[END_REF], mosquitoes [START_REF] Novakova | Mosquito microbiome dynamics, a background for prevalence and seasonality of West Nile virus[END_REF] and other blood sucking arthropods [START_REF] Cohen | Similarities and seasonal variations in bacterial communities from the blood of rodents and from their flea vectors[END_REF]. In mosquitoes, high temperature caused a reduction of Wolbachia density and a concomitant greater host susceptibility to viruses [START_REF] Novakova | Mosquito microbiome dynamics, a background for prevalence and seasonality of West Nile virus[END_REF]. Also the biotic environment could potentially influence within-host microbe-microbe interactions through horizontal exchange of microbes from free-living microbial populations [START_REF] Adair | Making a microbiome: The many determinants of host-associated microbial community composition[END_REF] (Box 2). This could lead to microbial community shifts and therefore changes in microbe-microbe interactions potentially influencing host fitness. These interactions are defined by metacommunities, local communities linked by dispersal, but also extinction and recolonization of potentially interacting species [29]. Thus, local communities are influenced by processes operating at the level of the entire metacommunity [START_REF] Sumi | Wolbachia density changes seasonally amongst populations of the pale grass blue butterfly, Zizeeria maha (Lepidoptera: Lycaenidae)[END_REF]. The few studies that investigated the influence of metacommunities discovered that the microbial communities associated with different interaction partners, e.g. plants and insects, shared microbes [START_REF] Bili | Bacterial community diversity harboured by interacting species[END_REF]31], such as vertically transmitted symbionts from the genus Wolbachia, Rickettsia, and Spiroplasma [START_REF] Bili | Bacterial community diversity harboured by interacting species[END_REF].

As phenotypic host effects of a symbiosis are closely tied to interactions with the remainder microbiome and environmental factors, biotic and abiotic, the absence of an integrative approach might mask the mechanistic interpretation of the data, leading to inconclusive results. Taking Wolbachia as model, in the next section we will provide a brief introduction of what is known for Wolbachia-microbe interactions and two examples in which a deeper understanding of the complex interactions between hosts, symbionts and the microbiome could explain discrepancies. The first one is of great relevance for human health and refers to investigations on the vectorcompetence of Wolbachia infected mosquitoes and their role in the transmission of human pathogens. The second example refers the reproductive manipulation by Wolbachia in several arthropod species and takes a more evolutionary perspective.

Interactions between the endosymbiont Wolbachia and other microbes

Wolbachia in interaction: known facts

The endosymbiont Wolbachiaone of the most widely distributed symbionts worldwide, infecting an estimated 40% of terrestrial arthropods [START_REF] Zug | Still a host of hosts for Wolbachia: Analysis of recent data suggests that 40% of terrestrial arthropod species are infected[END_REF] -is a strong manipulator of a wide range of host traits [33]. It gained specific interest due to its protection against various viruses in naturally infected fruit flies [START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF] and its capacity to reduce the density and transmission of pathogens in mosquito species [35,[START_REF] Pereira | Wolbachia significantly impacts the vector competence of Aedes aegypti for Mayaro virus[END_REF].

In contrast to long-held beliefs, Wolbachia is not restricted to host germ line cells and reproductive organs, but is present in cells throughout somatic tissues and even in the gut lumen of some insects and their faeces [START_REF] Sicard | A host as an ecosystem: Wolbachia coping with environmental constraints[END_REF][START_REF] Pietri | The rich somatic life of Wolbachia[END_REF]. Thus, direct interactions with other microbes of the host or indirect interactions via the hosts' immune system are likely. Direct interactions between Wolbachia and other microbes have been observed in fruit flies. A co-infection with the endobacterium Spiroplasma reduced Wolbachia density while Spiroplasma numbers remained unaffected by the presence of Wolbachia [START_REF] Goto | Asymmetrical interactions between Wolbachia and Spiroplasma endosymbionts coexisting in the same insect host[END_REF]. The investigation of the effect of Wolbachia infection on the composition of the gut microbiome in D. melanogaster showed an even more complex picture. Here the presence of Wolbachia is a significant determinant of the overall composition of the gut microbiome. Interestingly this was neither caused by a direct interaction between Wolbachia and the gut microbiome, as Wolbachia is absent from the gut lumen in the fly, nor was it indirectly modulated through the activation of the fly's immune system through Wolbachia [START_REF] Simhadri | The gut commensal microbiome of Drosophila melanogaster is modified by the endosymbiont Wolbachia[END_REF]. This highlights the importance of considering a multitude of possible interactions between microbes and between microbes and the host in studies of the dynamics and effects of Wolbachia-infections.

The quest for disease eradication

An integrated approach, considering multiple interactions between microbes and between microbes and hosts, is especially important when developing microbe-based disease vector control strategies. Wolbachia is currently being developed as a novel arthropod-borne disease control agent (http:// www.eliminatedengue.com); hereby the mode of a successful transmission is an important factor. Under laboratory conditions the native microbiome of Anopheles mosquitoes was found to impede vertical transmission of Wolbachia through antagonistic microbe-microbe interactions between the bacterium Asaia and Wolbachia [39]. Similar antagonistic microbe interactions were found in a survey of various mosquito species in Canada, with the presence and abundance of Wolbachia fluctuating over season, as well as with the presence of the bacteria Asaia and Pseudomonas [START_REF] Novakova | Mosquito microbiome dynamics, a background for prevalence and seasonality of West Nile virus[END_REF]. This suggests that, in addition to environmental effects, interaction of Wolbachia with other microbes may explain some of the variation in vector competence of mosquitoes. In contrast to these results, a stable infection with Wolbachia in lab-reared mosquitoes A. aegypti had only few effects on the microbiome. Moreover, significant changes in the microbiome composition did not affect the dengue virus blocking phenotype caused by Wolbachia infection in this mosquito [START_REF] Audsley | The microbiome composition of Aedes aegypti is not critical for Wolbachia-mediated inhibition of dengue virus[END_REF]. However, analyses of A. aegypti transinfected with Wolbachia, released in the field in Brazil and Vietnam to inhibit the dengue virus, revealed that Wolbachia increases susceptibility of mosquitoes to dengue infection. This contradicting result was due to the wide variability in exposure doses of Wolbachia naturally experienced by mosquitoes [41]. The authors concluded that reliable predictions of vectorial capacity of transinfected mosquitoes require an informed account of mosquito pathogens and their interplay with Wolbachia.

Additionally recent interaction networks, looking at co-occurrence and co-exclusion of microbes, established for several mosquito species (laboratory vs. field) revealed that Wolbachia is a highly interconnected taxon, mostly co-exclusionary with other bacteria [START_REF] Hegde | Microbiome interaction networks and community structure from lab reared and field-collected Aedes aegypti, Aedes albopictus, and Culex quinquefasciatus mosquito vectors[END_REF].

The mosquito studies indeed show that the abundance and effect of Wolbachia is closely tied to the remaining microbiome. This highlights the importance of considering the composition of the microbiome and host genetic background in studies investigating phenotypes induced by Wolbachia and when formulating microbe-based disease vector control strategies. In line with that, assessing the involvement of microbe-microbe interactions within a host and how they are influenced in the field, due to biotic or abiotic factors, is critical as it may affect the efficiency of Wolbachia-mediated manipulations (Box 2, Box 3).

The joint reproductive manipulation of Wolbachia and other microbes

The endosymbiont Wolbachia is especially well known for its four distinct reproductive phenotypes, that promote its own vertical transmission from mother to offspring [START_REF] Hurst | Reproductive parasitism: Maternally inherited symbionts in a biparental world[END_REF]. There is growing evidence that the reproductive manipulation by Wolbachia is not only exerted by the endosymbiont alone but in interaction with other microbes, i.e. the microbiome of the host, other symbionts, or the host itself.

Wolbachia has repeatedly been reported to cause different phenotypes, either in experimental settings when transferred between hosts, for example in Lepidoptera [44] or Drosophila sibling species [START_REF] Jaenike | Coupled population dynamics of endosymbionts within and between hosts[END_REF], or naturally over evolutionary timescales, e.g. in moths and fruit flies [START_REF] Ma | Manipulation of arthropod sex determination by endosymbionts: Diversity and molecular mechanisms[END_REF]. Additionally, many species show geographical variation in symbiont prevalence, including Wolbachia with a lower presence in warmer regions [START_REF] Corbin | Heritable symbionts in a world of varying temperature[END_REF], as for example reported for many species infected with parthenogenesis-inducing Wolbachia [47]. The causes for this distributional pattern in prevalence remain speculative, but a possible explanation is that it is driven by variation in microbial communities of host populations in interaction with their abiotic environment (Box 2).

Another line of evidence indicating a modulating role of the microbiome in reproductive manipulation by Wolbachia comes from studies investigating Wolbachia abundance (titre) in a host. The efficiency and phenotype of reproductive manipulation can depend on a threshold of Wolbachia titre, i.e. a minimum number of bacteria are required for exerting the manipulative action. A low titre can lead to a switch of the Wolbachia-induced phenotype in Drosophila bifasciata [START_REF] Hurst | Male-killing Wolbachia in Drosophila: A temperature-sensitive trait with a threshold bacterial density[END_REF], or to changes in the efficiency of parthenogenesis induction in the parasitic wasp Asobara japonica [START_REF] Ma | Diploid males support a two-step mechanism of endosymbiont-induced thelytoky in a parasitoid wasp[END_REF]. In both studies, variation in the Wolbachia titre were manifested under identical rearing conditions, for the latter even in a clonal host reproduction system, suggesting a strong influence on Wolbachia titre by other partners, such as the microbiome.

Together, these examples illustrate that Wolbachia may be a potent manipulator of host reproduction, but not in isolation but rather in interaction with the host genome and the remainder of the microbiome and in addition influenced by interaction with the environment. By shifting the focus away from Wolbachia as the only manipulator it becomes clear that manipulation of a host phenotype is likely not only caused by a single microbe (Wolbachia), but also strongly influenced by interaction with other microbes, and by the host genotype itself.

Concluding remarks

Throughout this manuscript we have pointed out growing evidence that host phenotypic effects such as reproductive manipulation by the endosymbiont Wolbachia are not only exerted by an endosymbiont alone but in interaction with others microbes. This and other examples, call for an integrative approach in studying host-microbe associations including host gene expression and interactions between microbes and environmental factors, on these interacting partners (see Outstanding Questions). The latter is especially important in the light of the upcoming challenges of our world, e.g. global warming and disease control. For instance, the protective effect of Wolbachia against important human diseases in insect vectors [49] is highly dependent upon temperature. Therefore global warming might cause a decrease in protective Wolbachia, undermining on-going long-term biological control programmes of mosquitoes. In this respect, a broader and more natural approach in studing host associated microbes is needed, as laboratory studies might often not be directly translatable to the field [41] (Box 3). Although in this manuscript our focus is on the traits vector-competence and reproductive manipulation conferred by Wolbachia in arthropod associations, we would like to point out that an involvement of other host associated microbes is also likely for other traits conferred by Wolbachia.

As an example, the nutritional symbiosis between Wolbachia and bedbugs showed that Wolbachia-microbe interactions, i.e. the complementation of functions by gene exchange between different components of the microbiome, can strongly influence the host phenotype through genetic changes in the symbiont [START_REF] Hosokawa | Wolbachia as a bacteriocyte-associated nutritional mutualist[END_REF][START_REF] Nikoh | Evolutionary origin of insect-Wolbachia nutritional mutualism[END_REF]. As similar microbe-microbe interactions are not restricted to Wolbachia but also other symbionts, a holistic approach should be extended to all symbioses [START_REF] Santos-Garcia | To B or not to B : Comparative genomics suggests Arsenophonus as a source of B vitamins in whiteflies[END_REF].

Finally, the interpretation of data on host-microbe associations has to be done carefully, keeping in mind that small changes in composition and/or abundance of the microbial community might have great phenotypic consequences for the host, as low-abundance or rare microbial taxa can represent hub species [START_REF] Agler | Microbial hub taxa link host and abiotic factors to plant microbiome variation[END_REF] that are crucial for the host functioning, as shown for plants and soil ecosystems [52]. Network analyses of the host-associated microbial communities might represent an important tool [START_REF] Layeghifard | Disentangling interactions in the microbiome: A network perspective[END_REF] for basic insights into interaction dynamics within microbial communities. For instance, this approach has recently revealed that for several mosquito species (in the laboratory and field), Wolbachia is a highly interconnected taxon, being mostly negatively correlated with other bacteria (i.e. its abundance leads to a reduction in the abundance of other species) [START_REF] Hegde | Microbiome interaction networks and community structure from lab reared and field-collected Aedes aegypti, Aedes albopictus, and Culex quinquefasciatus mosquito vectors[END_REF]. The integration of microbial network analyses with host gene expression networks could provide valuable insights into the complexity of the tripartite interactions.

Box 1: The host as an Ecosystem

Historically, symbiosis research in insects has focused primarily on binary interactions between hosts and individual endosymbionts [START_REF] Moran | Genomics and evolution of heritable bacterial symbionts[END_REF]33] and therefore observed phenotypic effects were attributed to the single symbiont. This binary point of view was challenged in recent years. The 'microbiome revolution' [START_REF] Blaser | The microbiome revolution[END_REF] of the past 10 years revealed that all animals are copiously colonized by microorganisms, collectively called the microbiome, of which the symbionts are part. During this revolution it was realized that similar to single symbionts, the microbiome can also impact important host traits [17, [START_REF] Wong | Gut microbiota dictates the metabolic response of Drosophila to diet[END_REF][START_REF] Shropshire | Speciation by symbiosis: The microbiome and behavior[END_REF] and thus influence the ecology and evolution of their hosts [57],

acting as an extended genome of the host, the hologenome [START_REF] Zilber-Rosenberg | Role of microorganisms in the evolution of animals and plants: The hologenome theory of evolution[END_REF]. Therefore, it has been proposed that the host itself should be viewed as a complex ecosystem, in which not only single symbionts interact with the host, but also the microbiome interacts with symbionts and hosts [START_REF] Sicard | A host as an ecosystem: Wolbachia coping with environmental constraints[END_REF]57]. An additional scale of complexity has recently gained attention, namely that host-microbe associations are also part of a wider microbial community maintained by transmission between individual hosts and dispersal between host-associated and free-living microbial communities [START_REF] Dittmer | Disentangling a holobiont -Recent advances and perspectives in Nasonia wasps[END_REF][START_REF] Adair | Making a microbiome: The many determinants of host-associated microbial community composition[END_REF]. In 2017, Carrier & Reitzel [START_REF] Carrier | The hologenome across environments and the implications of a host-associated microbial repertoire[END_REF] introduced the idea of a "host-associated microbial repertoire," which is the sum of microbial species a host may associate with over the course of its life under all encountered environmental circumstances. Due to this plasticity in the microbiome, the microbiome genome could allow hosts to adapt and survive under changing environmental conditions thus providing the time necessary for the host genome to adapt and evolve [START_REF] Rosenberg | The hologenome concept of evolution after 10 years[END_REF]. From this it becomes clear that one host can harbour a diverse microbial community, the entities of which interact with each other, potentially competing for space, energy, and resources, and ultimately influencing the condition of the host by conferring multiple detrimental, neutral, or beneficial effects [START_REF] Bonnet | The tick microbiome: Why non-pathogenic microorganisms matter in tick biology and pathogen transmission[END_REF]. Therefore, a more holistic approach in studying the interaction between the different partners is needed.

Box 2: Factors influencing host microbiome specificity

Host-microbe interactions are shaped by a multitude of factors, i.e. factors associated with the host such as immunity [START_REF] Chandler | Bacterial communities of diverse Drosophila species: Ecological context of a host-microbe model system[END_REF], phylogeny [63], host population background [64], physicochemical conditions in the insect habitat (e.g., gut pH, oxygen tensions), and structural filters in the gut [65] but also environmental factors such as diet [START_REF] Colman | Do diet and taxonomy influence insect gut bacterial communities?[END_REF] and temperature [START_REF] Russell | Costs and benefits of symbiont infection in aphids: Variation among symbionts and across temperatures[END_REF]. Abiotic factors do have a crucial effect on microbes and the host, and therefore on their interactions. External environmental conditions significantly affect the infective states of hosts including the density of the endosymbionts inhabiting the host body, e.g. high temperature [START_REF] Corbin | Heritable symbionts in a world of varying temperature[END_REF][START_REF] Van Opijnen | High temperatures eliminate Wolbachia, a cytoplasmic incompatibility inducing endosymbiont, from the two-spotted spider mite[END_REF][START_REF] Sumi | Wolbachia density changes seasonally amongst populations of the pale grass blue butterfly, Zizeeria maha (Lepidoptera: Lycaenidae)[END_REF] with occurring seasonal changes of symbiont density such as Wolbachia [START_REF] Novakova | Mosquito microbiome dynamics, a background for prevalence and seasonality of West Nile virus[END_REF][START_REF] Sumi | Wolbachia density changes seasonally amongst populations of the pale grass blue butterfly, Zizeeria maha (Lepidoptera: Lycaenidae)[END_REF][START_REF] Cohen | Similarities and seasonal variations in bacterial communities from the blood of rodents and from their flea vectors[END_REF].

In addition, these associations are also part of a wider microbial community maintained by transmission between individual hosts and dispersal between hostassociated and free-living microbial communities [START_REF] Dittmer | Disentangling a holobiont -Recent advances and perspectives in Nasonia wasps[END_REF][START_REF] Adair | Making a microbiome: The many determinants of host-associated microbial community composition[END_REF][START_REF] Carrier | The hologenome across environments and the implications of a host-associated microbial repertoire[END_REF]. While our understanding of the factors that affect the composition and abundance of the microbiome is expanding, there are still many unanswered questions regarding microbiome assembly and maintenance. Exposure to environmental microbes has undoubtedly a major influence on the microbial communities of an organism [START_REF] Hegde | Microbiome interaction networks and community structure from lab reared and field-collected Aedes aegypti, Aedes albopictus, and Culex quinquefasciatus mosquito vectors[END_REF], as metacommunity studies revealed that microbial communities associated with different interaction partners (species) differ in terms of composition and abundance, but shared microbes among the macro-partners [START_REF] Bili | Bacterial community diversity harboured by interacting species[END_REF]31]. Unravelling the role of environment in shaping the host-associated microbiome (including symbionts) is crucial to place the specificity of interactions in an evolutionary context, for instance, by understanding whether deterministic processes lead to the selection of the horizontally transmitted microbes.

Box 3: Importance of laboratory versus field studies

Given the strong influence of environmental factors (Box1, Box2) on host-microbe interactions, the transitions from laboratory studies to the field might bear some difficulty [START_REF] Carrier | The hologenome across environments and the implications of a host-associated microbial repertoire[END_REF]. Laboratory settings potentially restrict the full spectrum of hostmicrobe-associations compared to the natural setting where these associations have evolved [START_REF] Chandler | Bacterial communities of diverse Drosophila species: Ecological context of a host-microbe model system[END_REF]. Thus, it may limit the interpretation of the functional roles microbes play in host biology ([59]; Box2).

A good example for this is the Wolbachia-mediated inhibition of dengue virus. Under laboratory condition it was indicated that the microbiome composition of the mosquito Aedes aegypti is not critical for inhibition [START_REF] Audsley | The microbiome composition of Aedes aegypti is not critical for Wolbachia-mediated inhibition of dengue virus[END_REF]. However, when released into the wild the picture became more complex. Wolbachia, when introgressed into different genetic backgrounds increased the mean and the variance in mosquito susceptibility to dengue infection [41]. While the respective impacts of these factors are not easily disentangled, similarly complex multifactorial patterns likely underlie many host-microbe associations under ecologically realistic conditions. Given that Wolbachia appears to modify host susceptibility to a broad spectrum of pathogens [START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: A comparative analysis of Wolbachia strains[END_REF], reliable predictions of invasiveness and vectorial capacity of transinfected mosquitoes require an informed account of natural mosquito pathogens and their interplay with Wolbachia [41]. A first step to get a more complete picture of the symbiotic effects of Wolbachia is to investigate these complex interactions simultaneously in the lab and field. In addition, a beneficial approach would be the mimicry of environmental factors, biotic and abiotic, in the lab. Microbiome and symbiont manipulation is often achieved through the use of antibiotics. However such approaches may have several overlooked side-effects. First, antibiotics may affect different components of the microbiome differently and hence alter the interaction networks. Second, results obtained in the absence of (parts of) the microbiome tell only one side of the story, as microbe-microbe interactions might modulate host response. Hence, in order to unravel the interactions and impact of host phenotype, host recolonization by a variety of well characterized microbes, or whole microbial communities, is required. Also the enrichment of the microbial diversity, mimicking possible biotic environmental influences such as transmission of free-living microbial communities, might be worthwile. Although these manipulations can only provide a mechanistic understanding of the tripartide interaction and may not be translatable to field settings, they nevertheless are an important first step in gaining a better understanding of host-microbe interactions. microbial associates and a host is a ubiquitous feature of life on earth, modulating host phenotypes (host-symbiont interactions). In addition to endosymbionts, organisms harbour a collection of host-associated microbes, the microbiome that can impact important host traits (host-microbe interactions). These microbes interact with each other either direct via competition for resources and space, or indirect via the induction of a general immune response, potentially leading in changes of microbial community diversity, or abundance (microbe-microbe interactions). Therefore, a symbiont induced host phenotype, such as reproductive manipulation, parasite protection, or nutrition, is not only modulated by binary interactions, but also by a multitude of interaction between host, symbiont and the remainder microbiome, continuously influencing each other. Additionally, these interactions are influenced by their environment (grey circle), such as temperature, or diet, but by direct interaction with free living microbial communities. We thus advocate that only through an integrated approach that considers multiple interacting partners and environmental influences will we be able to gain a better understanding of host-microbe associations.

Figure 1 .

 1 Figure 1. Multipartite interactions affect the host phenotype. Symbiosis between

Acknowledgments

We thank two anonymous reviewers for their helpful comments on a previous version of the manuscript and Martijn Schenkel and Sylvia Gerritsma for their preliminary work, which inspired the development of this opinion article. P.B. was supported by a scholarship of the Adaptive Life program from the University of Groningen, The Netherlands.

Glossary:

Ecosystem: the complex network of living organisms, their physical environment, and their interactions in a particular unit of space. In our context a host, its associated microbiome and all potential interactions among living organisms and with environmental conditions.

Endosymbionts: microbial associates living within the body or cells of another organism (host).

Hologenome: the sum of the genetic information of the host and its microbiome.

Horizontal transmission: transmission of microbes between individuals, species or

with free-living microbes.

Host: organism in which an endosymbiont or microbiome live.

Host-microbe interactions: interactions between any microbial species or microbial communities (either a symbiont or part of the remainder microbial community) and a host.

Hub species: microbial species that are strongly interconnected by several links within a network and play an important role in community functioning and/or stability.

Abiotic factors and host genotype can directly act on hub species, thus spreading the effects to the whole microbial community.

Metacommunity: a set of interacting communities that are regulated by processes such as dispersal, extinction and recolonization.

Microbes: microscopic organisms, including bacteria, fungi, protozoa, and viruses.

Microbiome: a community of microbes that inhabit a particular environment.

Parthenogenesis: clonal reproduction, in which an unfertilized egg develops into a new individual.

Phenotype: the set of observable characteristics of an individual resulting from the interaction of its genotype with the environment.

Phenotypic effects: changes in a phenotype caused by an external influencing factor, here symbionts.

Remainder microbiome: the microbiome excluding the symbiont under investigation.

Note that we consider symbionts here as a separate microbial entity due to historical reasons and to highlight the differences between both, but in fact they are a part of the microbiome and as such, should be studied together.

Symbiont: here microbial associate of any type in a close and long-term biological interaction (mutualism, commensalism or parasitism) with biological organisms, of the same or of different species.

Traits: characteristics or attributes of an organism that are expressed by genes and/or influenced by the environment.

Vectorial capacity: the capability for disease transmission by a vector to a host, as influenced by behavioral, ecological and environmental factors, such as population density, host preference, feeding habits or frequency, duration of latent period, or longevity.

Vertical transmission: maternal transmission of microbes to offspring.